INTERPOLATION AND MAPPING OF THE TOTAL ELECTRON
CONTENT OVER THE MALAYSIAN REGION
LIM WEN HONG
UNIVERSITI TEKNOLOGI MALAYSIA
INTERPOLATION AND MAPPING OF THE TOTAL ELECTRON CONTENT
OVER THE MALAYSIAN REGION
LIM WEN HONG
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Master of Science (Geomatic Engineering)
Faculty of Geoinformation Science and Engineering
Universiti Teknologi Malaysia
NOVEMBER 2008
iii
To my beloved mother and father,
my lovely brothers and girl friend.
iv
ACKNOWLEDGEMENTS
Throughout the writing of this thesis, I am greatly indebted to many people who
had been guiding and encouraging me until the completion of this thesis. Thus, I
would like to thank them here for their continuous support and assistance.
Firstly, I
would like to extend my gratitude to my supervisor, Associate Professor Dr. Khairul
Anuar Abdullah who had been patiently guiding and assisting me throughout my
work.
Next, I would like to thank the lecturers in UTM, who were willing to spare
some time to enlighten and guide me through the totally new topics required to write
this thesis.
Among them were Associate Professor Dr. Hishamuddin Jamaluddin
and Dr. Hjh. Norma bt Alias who helped me through the understanding of the
formula and programming.
Last but not least, to my colleagues and friends who
had been encouraging me continuously with their feedbacks, support and prayers,
thanks you.
v
ABSTRACT
In the vast areas of satellite-related applications, the ionosphere is the main
cause of error due to the Total Electron Content (TEC), which causes the ionospheric
delay.
As a result, estimating and mapping the TEC is vital for the application of
various satellite-related fields, which are gaining momentum in Malaysia.
Thus,
this study aims to develop an efficient approach in mapping the TEC over Malaysian
region using interpolation method.
The TEC was mapped using three interpolation
methods, namely inverse distance weighting (IDW), multiquadric and sphere
multiquadric for different size of study area, different distribution and quantity of
reference points.
All the results from these three methods were compared with the
TEC derived from IRI-2001 model and calculated for the root mean square (RMS)
values.
This study found that the effects of the quantity and distribution of
reference points were conspicuous in the results obtained via both multiquadric and
sphere multiquadric methods, whereas IDW was not conspicuously affected by both
factors.
This can be seen from the RMS values obtained from the IDW for both the
well-distributed and randomly distributed two reference points were 3.1894 and
6.1681, whereas for the 18 reference points, the RMS yielded were 2.2436 and
2.5748 respectively.
Furthermore, the results, especially via the multiquadric and
IDW methods were more accurate in smaller study area’s size, where the RMS
yielded were 0.4685 and 0.0649 respectively for the 1º x 1º area size.
However,
IDW seemed to consistently generate the more accurate result for all the study area
size, where the RMS generated for all the area sizes studied ranges from 0.0649 to
1.2178.
As a conclusion, the IDW method is the most suitable interpolation for the
Malaysian region.
vi
ABSTRAK
Dalam bidang aplikasi satelit yang luas ini, lapisan ionosfera merupakan punca
utama berlakunya fenomena kelewatan ionosfera yang disebabkan oleh kandungan
elektron penuh dan menyebabkan ralat bacaan.
Oleh itu, penganggaran dan
pemetaan kandungan elektron penuh amat penting untuk kegunaan pelbagai bidang
aplikasi satelit, yang semakin mendapat peranan penting di Malaysia.
Oleh sebab
itu, tujuan kajian ini adalah untuk mengkaji kaedah paling berkesan untuk
memetakan kandungan elektron penuh di Malaysia dengan menggunakan kaedah
interpolasi.
Kandungan elektron penuh dipetakan dengan menggunakan tiga
kaedah interpolasi, iaitu kaedah inverse distance weighting (IDW), multiquadric dan
sphere multiquadric untuk pelbagai saiz kawasan kajian, dan pelbagai taburan serta
kuantiti titik rujukan.
Kesemua keputusan yang diperolehi daripada ketiga-tiga
kaedah ini akan dibandingkan dengan kandungan elektron penuh yang diperoleh
daripada model IRI 2001 untuk pengiraan nilai punca kuasa dua min (Root Mean
Square, RMS).
Kajian ini mendapati bahawa kesan kuantiti dan taburan titik-titik
rujukan terhadap keputusan yang diperoleh melalui kaedah multiquadric dan sphere
multiquadric amat jelas, manakala IDW tidak banyak dipengaruhi oleh kedua-dua
faktor ini.
Ini boleh dilihat dari nilai RMS yang diperoleh melalui kaedah IDW
untuk kedua-dua taburan serata dan berselerak bagi dua titik rujukan iaitu 3.1894 dan
6.1681, manakala bagi 18 titik rujukan, RMS yang diperolehi masing-masing adalah
2.2436 dan 2.5748.
Tambahan pula, keputusan-keputusan yang diperoleh
terutamanya melalui kaedah multiquadric dan IDW adalah lebih jitu bagi kawasan
kajian yang lebih kecil, di mana RMS yang diperolehi untuk saiz kajian 1º x 1º
adalah 0.4685 and 0.0649.
Tetapi, IDW lebih menunjukkan kejituan yang konsisten
bagi kesemua saiz kawasan kajian, di mana RMS yang diperolehi untuk semua saiz
kawasan kajian adalah dari 0.0649 ke 1.2178.
Kesimpulannya, kaedah IDW
merupakan kaedah interpolasi yang paling sesuai untuk wilayah Malaysia.
vii
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
TITLE PAGE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xi
LIST OF FIGURES
xiii
LIST OF ABBREVIATIONS
xix
LIST OF APPENDICES
xxi
INTRODUCTION
1
1.1
Overview on the Ionosphere
1
1.1.1
Definition of Ionosphere
1
1.1.2
Structure of Ionosphere
2
1.1.3
Characteristic of Ionosphere Structures
3
1.1.4
Effects of Ionosphere Delay on Satellite Application
5
1.2
Problem Statement
8
1.3
Research Objectives
8
viii
2
3
1.4
Research Scope
9
1.5
Significance of Research
9
1.6
Study Area
10
1.7
Thesis Outline
11
LITERATURE REVIEW
12
2.1
Introduction
12
2.2
Methods of Ionospheric Observation
12
2.3
Determination of Total Electron Content (TEC)
14
2.4
Ionosphere Modelling
18
2.5
Previous Studies on Mapping of the Ionosphere
20
2.6
Use of Ionospheric Data on Satellite Positioning
26
2.6.1
Effects of the Ionosphere on Position Determination
27
2.6.2
Method of Ionospheric Correction
28
REVIEWS ON INTERPOLATION TECHNIQUES
30
3.1
Introduction
30
3.2
Definition of Interpolation
31
3.3
Methods of Interpolation
32
3.3.1
The Multiquadric Technique
34
3.3.2
The Sphere Multiquadric Technique
37
3.3.3
The Inverse Distance Weighting Technique
40
3.4
4
Accuracy of Interpolation Techniques
45
INTERPOLATION OF TOTAL ELECTRON CONTENT (TEC)
46
4.1
Introduction
46
4.2
Data Collection
47
4.2.1
48
Description of Test Data
ix
5
4.2.2
Location of Test Site
48
4.2.3
Observation of Test Data
49
4.3
Flow Chart of Processing Stage
50
4.4
Interpolation using the Multiquadric Technique
52
4.5
Interpolation using the Sphere Multiquadric Technique
54
4.6
Interpolation using the Inverse Distance Weighting Technique
56
4.7
Analyses Strategy
58
RESULTS AND ANALYSIS
60
5.1
Introduction
60
5.2
Results and Analysis
62
5.2.1
Results and Analysis According to Study Area’s Size 63
5.2.1.1
Dataset 1
64
5.2.1.2
Dataset 2
68
5.2.1.3
Dataset 3
72
5.2.1.4
Dataset 4
76
5.2.1.5
Summary of Results and Analysis
According to Study Area’s Size
5.2.2
80
Results and Analysis According to Quantity and
Distribution of Reference Points
82
5.2.2.1
Dataset 1
84
5.2.2.2
Dataset 2
92
5.2.2.3
Dataset 3
101
5.2.2.4
Dataset 4
110
5.2.2.5
Dataset 5
119
5.2.2.6
Dataset 6
127
5.2.2.7
Summary of Results and Analysis
According to Quantity and Distribution
Of Reference Points
137
x
6
CONCLUSIONS AND RECOMMENDATIONS
142
6.1
Conclusions
142
6.2
Recommendations
144
REFERENCES
146
APPENDICES
160
xi
LIST OF TABLES
TABLE NO.
TITLE
5.1
Reference Points for 1º x 1º Grid Size
5.2
RMS Error for the Numerical Results of Reference Points
PAGE
64
within 1º x 1º Grid Size
67
5.3
Reference Points within 2º x 2º Grid Size
69
5.4
RMS Error for the Numerical Result of Reference Points
within 2º x 2º Grid Size
71
5.5
Reference Points within 4º x 4º Grid Size
73
5.6
RMS Error for the Numerical Results of Reference Points
within 4º x 4º g Grid Size
75
5.7
Reference Points within 8º x 8º Grid Size
77
5.8
RMS Error for the Numerical Result of Reference Points
within 8º x 8º Grid Size
79
5.9
RMS Error for the Four Sets Reference Points
81
5.10(a)
Two Well Distributed Reference Points
84
5.10(b)
Two Random Distributed Reference Points
85
5.11
RMS Error for Two Reference Points
91
xii
5.12(a)
Four Well Distributed Reference Points
93
5.12(b)
Four Random Distributed Reference Points
93
5.13
RMS Error for Four Reference Points
99
5.14(a)
Six Well Distributed Reference Points
101
5.14(b)
Six Random Distributed Reference Points
102
5.15
RMS Error for Six Reference Points
108
5.16(a)
Nine Well Distributed Reference Points
110
5.16(b)
Nine Random Distributed Reference Points
111
5.17
RMS Error for Nine Reference Points
117
5.18(a)
Thirteen Well Distributed Reference Points
119
5.18(b)
Thirteen Random Distributed Reference Points
120
5.19
RMS Error for Thirteen Reference Points
126
5.20(a)
Eighteen Well Distributed Reference Points
128
5.20(b)
Eighteen Random Distributed Reference Points
129
5.21
RMS Error for Eighteen Reference Points
135
5.22
RMS Error for All the Six Sets of Reference Points
137
xiii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Structure of Ionosphere (Komjathy, 1997)
3
1.2
Study Area
10
2.1
Single Layer Model of the Ionosphere (Schaer, 1999)
19
2.2
The Double Differencing Observation Technique
29
4.1
Study Area
47
4.2
Flow Chart of Processing Steps
51
4.3
Flow Chart of Multiquadric Processing Steps
53
4.4
Flow Chart of Sphere Multiquadric Processing Steps
55
4.5
Flow Chart of Inverse Distance Weighting Processing Steps
57
5.1
Screen Shots of Programs’ Output
61
5.2
Positions of Reference Points and Its’ Coverage Area
63
5.3(a)
Result of Reference Points within 1º x 1º Grid Size using
Multiquadric Method
5.3(b)
65
Result of Reference Points within 1º x 1º Grid Size using
Sphere Multiquadric Method
66
xiv
5.3(c)
Result of Reference Points within 1º x 1º Grid Size using
Inverse Distance Weighting Method
67
5.4
RMS Error for Reference Points within 1º x 1º Grid Size
68
5.5(a)
Result of Reference Points within 2º x 2º Grid Size using
Multiquadric Method
5.5(b)
Result of Reference Points within 2º x 2º Grid Size using
Sphere Multiquadric Method
5.5(c)
69
70
Result of Reference Points within 2º x 2º Grid Size using
Inverse Distance Weighting Method
71
5.6
RMS Error for Reference Points within 2º x 2º Grid Size
72
5.7(a)
Result of Reference Points within 4º x 4º Grid Size using
Multiquadric Method
5.7(b)
Result of Reference Points within 4º x 4º Grid Size using
Sphere Multiquadric Method
5.7(c)
73
74
Result of Reference Points within 4º x 4º Grid Size using
Inverse Distance Weighting Method
75
5.8
RMS Error for Reference Points within 4º x 4º Grid Size
76
5.9(a)
Result of Reference Points within 8º x 8º Grid Size using
Multiquadric Method
5.9(b)
Result of Reference Points within 8º x 8º Grid Size using
Sphere Multiquadric Method
5.9(c)
5.10
77
78
Result of Reference Points within 8º x 8º Grid Size using
Inverse Distance Weighting Method
79
RMS Error for 8º x 8º Grid Size Reference Points
80
xv
5.11
RMS Error for Three Different Interpolation Methods
82
5.12
RMS Error for Four Different Size of Study Area
82
5.13(a)
Positions of Two Well Distributed Reference Points
85
5.13(b)
Position of Two Random Distributed Reference Points
85
5.14(a)
Result of Two Well Distributed Reference Points using
Multiquadric Method
5.14(b)
Result of Two Well Distributed Reference Points using
Sphere Multiquadric Method
5.14(c)
89
Result of Two Random Distributed Reference Points using
Sphere Multiquadric Method
5.14(f)
88
Result of Two Random Distributed Reference Points using
Multiquadric Method
5.14(e)
87
Result of Two Well Distributed Reference Points using
Inverse Distance Weighting Method
5.14(d)
86
90
Result of Two Random Distributed Reference Points using
Inverse Distance Weighting Method
91
5.15
RMS for Two Reference Points
92
5.16(a)
Positions of Four Well Distributed Reference Points
93
5.16(b)
Position of Four Random Distributed Reference Points
94
5.17(a)
Result of Four Well Distributed Reference Points using
Multiquadric Method
5.17(b)
94
Result of Four Well Distributed Reference Points using
Sphere Multiquadric Method
95
xvi
5.17(c)
Result of Four Well Distributed Reference Points using
Inverse Distance Weighting Method
5.17(d)
Result of Four Random Distributed Reference Points using
Multiquadric Method
5.17(e)
97
Result of Four Random Distributed Reference Points using
Sphere Multiquadric Method
5.17(f)
96
98
Result of Four Random Distributed Reference Points using
Inverse Distance Weighting Method
99
5.18
RMS for the Four Reference Points
100
5.19(a)
Positions of Six Well Distributed Reference Points
101
5.19(b)
Position of Six Random Distributed Reference Points
102
5.20(a)
Result of Six Well Distributed Reference Points using
Multiquadric Method
5.20(b)
Result of Six Well Distributed Reference Points using
Sphere Multiquadric Method
5.20(c)
5.21
106
Result of Six Random Distributed Reference Points using
Sphere Multiquadric Method
5.20(f)
105
Result of Six Random Distributed Reference Points using
Multiquadric Method
5.20(e)
104
Result of Six Well Distributed Reference Points using
Inverse Distance Weighting Method
5.20(d)
103
107
Result of Six Random Distributed Reference Points using
Inverse Distance Weighting Method
108
RMS for the Six Reference Points
109
xvii
5.22(a)
Positions of Nine Well Distributed Reference Points
110
5.22(b)
Positions of Nine Random Distributed Reference Points
111
5.23(a)
Result of Nine Well Distributed Reference Points using
Multiquadric Method
5.23(b)
Result of Nine Well Distributed Reference Points using
Sphere Multiquadric Method
5.23(c)
115
Result of Nine Random Distributed Reference Points using
Sphere Multiquadric Method
5.23(f)
114
Result of Nine Random Distributed Reference Points using
Multiquadric Method
5.23(e)
113
Result of Nine Well Distributed Reference Points using
Inverse Distance Weighting Method
5.23(d)
112
116
Result of Nine Random Distributed Reference Points using
Inverse Distance Weighting Method
117
5.24
RMS for the Nine Reference Points
118
5.25(a)
Positions of Thirteen Well Distributed Reference Points
120
5.25(b)
Positions of Thirteen Random Distributed Reference Points
121
5.26(a)
Result of Thirteen Well Distributed Reference Points using
Multiquadric Method
5.26(b)
Result of Thirteen Well Distributed Reference Points using
Sphere Multiquadric Method
5.26(c)
121
122
Result of Thirteen Well Distributed Reference Points using
Inverse Distance Weighting Method
123
xviii
5.26(d)
Result of Thirteen Random Distributed Reference Points
using Multiquadric Method
5.26(e)
Result of Thirteen Random Distributed Reference Points
using Sphere Multiquadric Method
5.26(f)
124
125
Result of Thirteen Random Distributed Reference Points
using Inverse Distance Weighting Method
126
5.27
RMS for the Thirteen Reference Points
127
5.28(a)
Positions of Eighteen Well Distributed Reference Points
128
5.28(b)
Positions of Eighteen Random Distributed Reference Points
129
5.29(a)
Result of Eighteen Well Distributed Reference Points
using Multiquadric Method
5.29(b)
Result of Eighteen Well Distributed Reference Points
using Sphere Multiquadric Method
5.29 (c)
133
Result of Eighteen Random Distributed Reference Points
using Sphere Multiquadric Method
5.29(f)
132
Result of Eighteen Random Distributed Reference Points
using Multiquadric Method
5.29(e)
131
Results of Eighteen Well Distributed Reference Points
using Inverse Distance Weighting Method
5.29(d)
130
134
Result of Eighteen Random Distributed Reference Points
using Inverse Distance Weighting Method
135
5.30
RMS for the Eighteen Reference Points
136
5.31
RMS for All the Six Sets of Reference Points
140
xix
LIST OF ABBREVIATIONS
EUV
Extreme ultraviolet
NOAA
National Oceanic and Atmospheric Administration
GPS
Global Positioning System
GLONASS
Russian Navigational System
HF
High frequency
ELF/VLF
Extra or very low frequency
TEC
Total Electron Content
IRI-2001
International Reference Ionosphere 2001
RMS
Root Mean Square
HEO
High earth orbit
LEO
Low earth orbit
TECU
Total electron content units
SLM
Single layer model
EOF
Empirical orthogonal function
UNB
University of New Brunswick
CORS
Continuously operating reference stations
KR
Kriging
MQ
Multiquadric
GIM
Global Ionosphere Map
IGS
International GPS Service
MART
Multiplicative Algebraic Reconstruction Technique
NNSS
Naval Navigation Satellite System
LITN
Low-latitude Ionospheric Tomography Network
GPS/MET
Global Positioning System/Meteorology
NASA
National Aeronautics and Space Administration
xx
DORIS
Doppler Orbitography and Radiopositioning Integrated by Satellite
TID
Travelling Ionospheric Disturbances
CHAMP
CHAllenging Minisatellite Payload
PIM
Parameterized Ionospheric Model
GEONET
GPS Earth Observation Network
ASHA
Adjusted spherical harmonic
CIT
Computerised Ionospheric Tomography
DGPS
Differential GPS
RTK
Real-time kinematic
GIS
Geographic Information System
IDW
Inverse distance weighting
COSPAR
Committee on Space Research
URSI
International Union of Radio Science
NSSDC
National Space Science Data Center
COSMIC
Constellation Observing System for Meteorology, Ionosphere and
Climate
c
Small constant
w
Power (usually between 1 to 3)
xxi
LIST OF APPENDICES
APPENDIX
A
TITLE
Numerical results of the TEC values for the whole study
area, which were derived from Model IRI-2001.
B
160
Numerical results for the TEC values derived via three
interpolation methods for four different study areas’ size.
C
PAGE
162
Numerical results of TEC values derived from the three
interpolation methods for twelve sets of reference points
with different quantity and distribution.
168
CHAPTER 1
INTRODUCTION
1.1
Overview on the Ionosphere
1.1.1
Definition of Ionosphere
The ionosphere is the ionized part of the atmosphere that extends from an
altitude of around 50 km to more than 1000 km above the earth surface.
The
ionosphere is electrically neutral although there are a significant number of free
thermal electrons and positive ions inside it.
The term ionosphere was first used in
1926 by Sir Robert Watson-Watt in a letter to the secretary of the British Radio
Research Board.
The expression came into wide use during the period 1932-34 in
papers and books.
Before the term ionosphere gained worldwide acceptance, it was
called the Kennelly-Heaviside layer, the upper conducting layer or ionized upper
atmosphere (Hunsucker, 1991).
The activity of ionosphere will vary with altitude, latitude, longitude, universal
time, season, solar cycle and magnetic activity.
This variation is reflected in all
ionospheric properties, such as electron density, ion and electron temperatures and
ionospheric composition and dynamics.
Normally the level of ionospheric activity
is generally described in terms of electron density.
The interaction of solar
2
radiation (the ultra-violet radiation of the Sun) or charged particles (such as X-rays
and cosmic rays) with the Earth’s atmosphere drives the ionospheric behaviour.
1.1.2
Structure of Ionosphere
The structure of the ionosphere is very complex due the physical and chemical
processes within it.
The sun’s extreme ultraviolet (EUV) light, cosmic radiation
and X-ray emissions encountering gaseous atoms and molecules in the atmosphere
can impart enough energy for photo ionization to occur producing positively charged
ions and negatively charged free electrons.
Process recombination occurs in the
ionosphere when the ions and electrons join again producing neutral atoms and
molecules.
But in the lower regions of the ionosphere, a process called attachment
occurs when the free electrons combine with neutral atoms to produce negatively
charged ions.
The absorption of EUV light increases as altitude decreases.
Due to
the absorption and the increasing density of neutral molecules, a layer of maximum
electron density is formed.
However, since there are many different atoms and molecules in the ionosphere
and each of it have different rates of absorption, a series of distinct layers or regions
of electron density exist.
These are denoted by the letters D, E, F1 and F2, which
are usually are collectively referred to as the bottom side of the ionosphere.
The
part of the ionosphere between the F2 layer and the upper boundary of the
ionosphere is termed the topside of the ionosphere.
structure of the ionosphere.
Figure 1.1 below depicts the
3
Figure 1.1: Structure of Ionosphere (Komjathy, 1997).
1.1.3
Characteristics of Ionosphere Structures
According to Komjathy (1997) the D layer extends from about 75 to 90 km
above the earth.
D-layer ionization is produced by solar UV light, X-rays and
cosmic radiation at any time of day or night.
Due to this, the electrons may become
attached to molecules and atoms forming negative ions that cause the D layer to
disappear, at night time.
While during the day time, the electrons tend to detach
themselves from the ions causing the D layer to reappear, as the consequence of
sun’s radiation.
Since the electrons in D layer at the altitude of about 60 to 70 km
are present by day but not by night, it causes a distinct diurnal variation in the
electron density.
In Davies (1990), the lower part of D layer was referred to as the C layer where
the cosmic radiation is the only source of ionization compared to the middle and
4
upper part of the D layer where both the cosmic radiation and X-ray emissions are
present (Komjathy, 1997).
According to the National Oceanic and Atmospheric Administration (NOAA),
the E layer extends from about 95 to 150 km above the earth.
Since the ionization
mostly depends on the level of solar activity and the zenith angle of the sun,
ionization drops to low values at night.
Although the E layer does not completely
vanish at night, however, for practical purposes it is often assumed that its electron
density drops to zero at night.
day time.
Due to that, the E layer is said to be only present by
In that respect, the primary source of ionization is the sun’s X-ray
emissions, causing the electron densities in E layer showing distinct solar-cycle,
seasonal and diurnal variations.
to be irregular.
According to NOAA, the E-layer effects are noted
Other subdivisions of the E-layer, after isolating the irregular
occurrence within this region into separate layers, are also labelled with an E prefix.
These layers are the thick layer, E2, and a highly variable thin layer, Sporadic E.
Ions in these regions consist of mainly O2+.
The F1 layer is the lower part of the F layer, which extends from about 170 to
250 km above the earth.
The main source of ionization in the F1 layer is the EUV
light while the electron densities are primarily controlled by the zenith angle of the
sun.
Because of this, the F1 layer exists only during daylight hours and will
disappear at night, so it’s only observed during the day time.
changes rapidly in a matter of minutes.
electron densities range between 2.3x10
When it is present, it
During typical noon time, the mid-latitude
11
and 3.3x1011 electrons/m3 in according to
the solar activity (Komjathy, 1997).
From about 250 to 500 km above the earth is the region of the F2 layer.
This
layer is present 24 hours a day but varies in altitude with geographical location, solar
activity, and local time.
The critical frequency for this layer peaks after local noon
time and decreases gradually, thus showing a linear dependency of the F2 layer on
the number of solar sunspot.
Here, the typical mid-latitude noon time electron
5
densities range between 2.8x1011 and 5.2x1011 electrons/m3 in according to the solar
activity.
The global spatial distribution of this layer also reveals a strong
geomagnetic dependence rather than the solar zenith angle dependence (Komjathy,
1997).
The top side of the ionosphere starts at the height of maximum density of the F2
layer of the ionosphere and extends upward with decreasing density to a transitional
height where O+ ions become less numerous than H+ and He+.
The transition
height varies but seldom drops below 500km at night or 800km during daytime,
although
it
may
lie
as
high
as
1100km
(http://www.ngdc.noaa.gov/stp/IONO/ionostru.html).
From above, the existence of the D, E, and F1 layers are noted to be primarily
controlled by the solar zenith angle and showing a strong diurnal, seasonal and
latitudinal variation.
The diurnal variation of the D, E, and F1 layers also implies
that they tend to reduce greatly in size or even will vanish at night time.
In contrast,
the F2 layer is present for 24 hours and is where the maximum electron density
usually occurs.
This happens as a consequence of the combination of the
absorption of the EUV light and increase of neutral atmospheric density as the
altitude decreases.
Thus, this layer is commonly taken into consideration to
represent the whole layer of the ionosphere, during the calculations of the
ionospheric delay.
1.1.4
Effects of Ionosphere Delay on Satellite Applications
The ionosphere is one of the main sources of error in the vast areas of
satellite-related applications.
Those satellite applications that will be affected by
6
the ionospheric effect are those which are directly related to satellite signal
transmission system, such as navigational satellite operators example U.S. Global
Positioning System (GPS), Russian Navigational System (GLONASS) and European
Navigational System (Galileo).
Other than that, radio and television operations
utilising satellite communication; space weather forecasts; space and aero industries
and the military are also significantly affected.
In the space and aero industries, the
ionosphere may affect the spacecraft designs, its internal and surface charging,
sensor interference, satellite anomalies, loss of navigational signal phase and
amplitude lock, besides affecting the planning of the electromagnetic environment in
manned spacecraft’s travels.
In the military, the ionospheric effect made its presence felt in terms of space
communication and navigation as it causes loss of high frequency (HF)
communications and direction finding, causes clutter in the horizon radar; disrupts
targeting and extra or very low frequency (ELF/VLF) communications with
submarines, besides contributed to reduced detection of missile launch.
Furthermore, scientists using remote sensing measurement techniques -in astronomy,
biology, geology, geophysics, seismology and many more fields were very much
affected where discrepancies in their readings arises and thus compensation of the
effects of the ionosphere on their observations are needed.
Besides, those
applications which does not utilise the satellite system but only involve signal and
wave transmissions will be affected as well.
For example, phone communication
where it causes possible interference; radio communication agencies and amateur
radio operators where efficiency of communication is compromised.
Irregularities of the effect of the ionospheric delay can range from a few meters
to a few kilometres.
It will scatter satellite radio signals when it is propagated
through the ionosphere.
This will lead to rapid phase and amplitude fluctuations
and also variations in the angle of arrival and polarization of the radio signals, which
are collectively known as ionospheric scintillation.
Among the ionospheric
scintillation that is important in satellite application are the amplitude scintillation
and phase scintillation.
7
Amplitude scintillations, can reach 20 dB at 1. 5 GHz during high solar activity
times (Bishop et al., 1996).
It induces signal fading and cycle slips.
When the
signal fading exceeds the fade margin or the threshold limit of a receiving system,
message errors in satellite communications are encountered and loss of lock occurs
in navigational systems.
The amplitude scintillation typically can last for several
hours in the evening time, which is broken up with intervals of no fading in between
(Klobuchar, 1991).
Phase scintillations will cause Doppler shifts and may degrade the performance
of phase-lock loops.
For example, in GPS navigation systems, the Doppler shifts
caused by TEC variations can be up to 1-Hz/second, which may cause some
narrow-band receivers to lose lock on the signals.
This is due to the rapid
frequency changes in the received signals, which are greater than the receiver
bandwidth.
The phase scintillation also may affect the resolution of space-based
synthetic aperture radars.
The duration of strong phase scintillation effects are
limited from approximately one hour after local sunset to local midnight (Klobuchar,
1991).
Although the ionospheric scintillation is unlikely to affect all of the satellite in a
receiver's field of view, they will have impact on the accuracy of the result of the
navigation solution by degrading the geometry of the available constellation.
is the most severe test on a GPS receiver in the natural environment.
This
Consequently,
the coverage of both the satellites and the irregularities as well as the intensity of
scintillation activity will all contribute to the accuracy of the result of the final
solution (Klobuchar, 1991).
8
1.2
Problem Statement
Estimating and mapping the ionospheric delay for the whole country are being
performed on a real time basis by many developed countries in the world. The time
series of this type of map can be used to derive average monthly maps describing
major ionospheric trends as a function of local time, season and spatial location
(Weilgosz et al, 2003a).
By analyzing these maps, ionospheric forecasting and
broadcasting can be done and applied to many related fields or researches.
Unfortunately, this capability is currently absent in Malaysia where being in the
tropical region, such information are vital for many applications.
This research
work will explore and develop the basic infrastructure such as ionospheric content
computation, suitable interpolation method and finally mapping of the Total Electron
Content (TEC) of the Malaysian region.
1.3
Research Objectives
The objectives of this research are:
1.
To develop an efficient approach in mapping TEC over a regional area
using interpolation methods.
2.
To define the most suitable interpolation method for mapping the TEC over
the Malaysian region.
9
1.4
Research Scope
The scope of this research is confined to the following areas:
1.
Mapping the TEC over a regional area using an efficient interpolation
method.
The interpolation methods used here focus only on the inverse
distance weighting, multiquadric and sphere multiquadric, as both the
inverse distance weighting and multiquadric methods are among the
commonly used method. Whereas sphere multiquadric method were
included to study a method which interpolates from a spherical plane as
opposed to the commonly used flat plane in the two former methods.
2.
Producing a regional TEC map and numerical result that can be utilised for
many satellite based observation applications.
3.
TEC data from the model International Reference Ionosphere 2001
(IRI-2001) -an empirical model of the ionosphere based on all available
data sources; please refer to section 4.2 for more details- rather than real
observations were used in the interpolation processing step.
4.
The research results were analysed using the Root Mean Square (RMS)
method.
5.
1.5
The grid size of the output TEC map is 0. 5° x 0. 5°.
Significance of Research
This research has its significance in terms of establishing the superiority of
different interpolation methods in the mapping of the ionospheric effect on the
10
Malaysian region.
This research also has its significance in terms of the
development of a program to estimate the ionospheric effect for the whole of
Malaysia, using the interpolation method which was found to be more suitable in the
Malaysian context.
The program is an alternative way for the amateur satellite
users, especially Global Positioning System (GPS) single frequency users to compute
the ionosphere errors in the satellite signals.
Besides that, this program helps in
terms of cost saving, as it provides an alternative to replace the expensive
commercial software, such as Trimble Geomatics Office, Leica SKI-Pro, Waypoint
GrafNav, EZSurv and RADAN.
1.6
Study Area
The study area for this research was the whole region of Malaysia.
The
coordinate of the study area ranges from 0°N to 8°N latitude and 99°E to 120°E
longitude, which can be seen in Figure 1.2 below:
Figure 1.2: Study Area.
11
1.7
Thesis Outline
Chapter 1 generally introduces the user to the ionosphere.
Besides that, this
chapter also discusses the problem statements, research objectives and scope, the
significance of research and the area of study.
The literature reviews were discussed in Chapter 2.
Literature reviews were
very important in offering guidelines, guidance and inspirations on the ways on how
this research was to be carried out.
Chapter 3 explains about the different interpolation techniques that were used in
this research.
The research methodology is discussed in Chapter 4.
This chapter contains the
explanation of the data collection and the processing steps of this research.
Chapter 5 presents the results of this research.
The analysis of the result of this
research is also included in this chapter.
Lastly, chapter 6 consists of the conclusions of this research.
some recommendations were proposed to improve this research.
Besides that,
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
This chapter discusses the concepts and methods used to observe the ionosphere.
Besides that, previous studies on the mapping of the ionosphere are also presented in
the section below.
Lastly, the effect of ionospheric delay on the satellite positioning
is also described.
2.2
Methods of Ionospheric Observation
This section will continue from the introduction of the ionosphere discussed in
the previous chapter, where here, we will discuss about the various methods utilized
to observe the ionosphere.
Since the ionosphere is in the middle of air, which is not
easily accessible, the best way to observe it is through remote sensing methods.
In
remote sensing, the concept is to gather or observe information of a specific place or
location without going or having the need to be present there.
The remote sensing
13
method is suitable for the observation of the ionosphere since it can provide real time
information, as the ionosphere content changes dynamically over the time.
There
are few ways to observe the ionosphere using the remote sensing method, namely
through the Ionosonde, Incoherent Scatter Radars (also known as Thomson
Scattering Sounding) and satellite based techniques such as occultation, Faraday
rotation and Global Positioning System (GPS).
Among those techniques, the
popular techniques are the Ionosonde, occultation and GPS.
Ionosonde is short for ionosphere sounder.
The Ionosonde is a radar device that
sends a spectrum of radio wave pulses straight up, vertically striking the ground.
The parameters measured are the duration of time it takes for a reflection to be
returned; the strength of the reflection; and how high of a frequency can be reflected.
The reflection is governed by the electron concentration in the ionosphere, so it
varies with different height due to the existence of different layers of electron
concentration in the ionosphere.
With these three measurements, namely the time,
strength and frequency, the device can determine the altitude of the ionization and
ionization density, hence the observation of the ionosphere.
Although the
Ionosonde has been used since early 20th century, there is still no widespread
deployment of it.
Ionosonde is primarily deployed and maintained by the US Air
Force, a few universities, National Oceanic and Atmospheric Administration
(NOAA),
and
similar
organizations
in
other
countries
(http://www.amfmdx.net/fmdx/ionosonde.html).
Over the past several years, the use of calibrated GPS receivers for ionospheric
observation has become feasible with the availability of a full constellation of GPS
satellites.
The theory used in the GPS measurement is based on measuring the
travel time of a signal from the satellite to a receiver.
Measurement and observation
of the ionospheric delay can be performed due to the sufficient dispersion index of
refraction in the ionosphere on both the L1 (1575.42 MHz) and L2 (1227.6 MHz)
frequency.
Owing to the ionospheric dispersion, time delay or signal delay occurs
at the two frequencies, of which both the delay differs.
From this time delay
difference, one may deduce the ionosphere condition by forming a linear
14
combination of L1 and L2 measurements, commonly termed as L3 or ionosphere free
combination.
Besides that, the ionosphere also can be observed or measured from
the carrier phase and/or pseudorange in the GPS signal.
Occultation technique (also known as limb sounding technique) was originally
developed by National Oceanic and Atmospheric Administration (NASA) for the
study of planetary atmospheres. The concept used in occultation is similar with the
one in GPS which measures the transmission time from a satellite to a receiver.
However, in occultation, signals are sent from the high earth orbit (HEO) satellites to a
receiver, which is on board a low earth orbit (LEO) satellite, instead of to a
ground-based receiver used in GPS. Normally one occultation takes nearly four to
ten minutes depending on the relative geometry of the LEO and HEO satellites.
In
occultation, the signal also experiences the ionospheric delay, causing bending and
amplitude changes during the signal transmission, thus providing information on the
ionosphere (Hajj et al., 2000). These signal delays provide horizontal slices through
the ionosphere. The information contained in these sets of signals is then extracted by
an inversion technique known as tomographic reconstruction to estimate the vertical
profiles of the ionosphere. This technique offers not only a new data source for the
upper atmosphere but also may revolutionize the weather forecasting in the lower
atmosphere (Essex, 2002).
2.3
Determination of Total Electron Content (TEC)
Total electron content (TEC) refers to the number of electrons in a column of
one meter-squared cross-section along a path through the ionosphere, between the
satellite and the receiver.
These regions of the ionosphere are responsible in
affecting the propagation of the signals, changing their speed and direction of travel.
The TEC is a well-suited parameter for the study of ionospheric perturbed conditions
since the TEC is proportional to the delay suffered by electromagnetic signals
15
crossing the ionosphere.
The TEC values are recorded in TEC units (TECU), where
1 TECU is equivalent to 1016 el/m2 and corresponds to 0.84 cycle of phase and
0.1624 meters in equivalent range on the GPS L1 signal.
The TEC in turn depends on the geographic latitude, longitude, local time,
season and geomagnetic activity.
range from 10 to 120 TECU.
The typical diurnal variation for the TEC is in the
The TEC normally varies smoothly from day to night
as during day time the ionosphere is ionized by the sun's ultraviolet radiation, while
during night time the ionosphere electron content is reduced by deionization process.
However, the ionosphere may experience stormy weather just as the lower
atmosphere does.
When the storm occurs, smooth variations in TEC are replaced
by rapid fluctuations and some regions experience significantly lower or higher TEC
values than normal.
As mentioned in the previous section, the ionosphere electron content can be
observed and measured through the pseudorange and carrier phase from the GPS
signal.
In pseudorange measurement, the pseudorange is related to the distance
between the satellite and the receiver, implied by the time the signal took to travel
from satellite (signal emission) to receiver (signal reception).
This time is then
multiplied with the speed of light in order to get the range between satellite and
receiver.
The standard mathematical equation of pseudorange measurement is
represented by:
P = p + c (dt + dT) + I + T + Mp + εp
where,
P = measured pseudorange.
p = geometric distance (true range).
c = speed of light in vacuum.
dT = receiver clock bias.
dt = satellite clock bias.
(2.1)
16
I = ionosphere delay.
T = troposphere delay.
Mp = multipath
εp = code observation noise.
The ionospheric delay, namely TEC, can be obtained by inversing equation 2.1 above
to:
I = P – [p + c (dt + dT) + T + Mp + εp]
(2.2)
Carrier phase measurement has a similar concept with the pseudorange
measurement but it gives higher precision than the pseudorange measurement since
carrier phase’s wavelength is much shorter than pseudorange’s wavelength. The
standard mathematical equation for the carrier phase measurement is shown as below:
Φ = p + c (dt + dT) + I + T + MΦ + λN + εΦ
where,
Φ = measured range.
p = geometric distance (true range).
c = speed of light in vacuum.
dt = satellite clock bias.
dT = receiver clock bias.
I = ionosphere delay.
T = troposphere delay.
MΦ = multipath.
εΦ = carrier phase observation noise
N = ambiguity.
λ = wavelength.
(2.3)
17
Similar to the pseudorange, the ionospheric delay can also be obtained by inversing
equation 2.3 to:
I = Φ - [p + c (dt + dT) -+ T + MΦ + λN + εΦ]
(2.4)
The TEC values can be presented in graphical format, such as a map.
Normally,
this is done when a regional network of ground-based GPS receivers is used or when
the interpolation or extrapolation method is applied.
These maps show the TEC
value in the vertical direction as a function of geographic latitude and longitude.
The maps are then provided as correction information for use by single frequency
GPS receivers to obtain highly accurate corrections for their GPS data, which are
obtained by interpolating the correction planes to the location of the single frequency
receiver.
With this technique, higher accurate surveying results can be achieved
with low cost single frequency receivers in real-time or in post-processing thus even
with the result obtaining form the more expensive dual frequency receivers.
The accurate information on TEC is essential for many satellite usage
applications.
One of the important applications for TEC data is in automatically
controlling aircraft trajectories, which must be extremely accurate.
Information on
TEC also provides a valuable tool for investigating global and regional ionospheric
structures.
Through the post processing techniques, TEC measurements can be
obtained to produce the quality of data necessary for modelling applications with
rigorous error requirements.
These procedures necessitate the collection of large
volumes of GPS pseudorange and carrier phase data to address the various
abnormalities in the computation of TEC.
Besides that, by learning how to predict TEC values in advance, researchers
may also be able to set up early warning procedures that give us enough time to
protect valuable communications satellites from the sun, choosing suitable surveying
or GPS observing time, forecast future space weather and many more.
18
2.4
Ionosphere Modelling
Beginning from the late 1980’s, various research groups have been investigating
the behaviour of the ionosphere using GPS data (Fedrizzi et al., 2001).
These
investigations are based on the refractivity index of an electromagnetic signal when
passing through the ionosphere, which is proportional to ionospheric electronic
density, i.e. TEC.
Since then many ionospheric model with various algorithms and approaches
have been created.
Some of these approaches include the empirical models based
on extensive worldwide data sets; and simple analytical models for a restricted
number of ionospheric parameters.
three-dimensional,
time-dependent
Besides that, approaches such as the
physical
models
which
also
include
self-consistent coupling to other solar-terrestrial regions; models based on orthogonal
function fits to the output obtained from numerical models; and models driven by
real-time magnetospheric inputs.
To achieve simplicity, some of the models have
been restricted to certain altitude or latitude domains, while others have been
restricted to certain ionospheric parameters.
Most of the models have been
constructed to describe the climatology of the ionosphere and, in this aspect, have
been very successful in describing the characteristic ionospheric features and their
variations with universal time, season, solar cycle, and geomagnetic activity.
Recently, the development the model has focused on including the large-scale and
medium-scale density structures in global simulations in a self-consistent manner.
Furthermore, efforts have also been made towards modelling storms and substorms.
All of the ionospheric model can be grouped into two different categories,
namely grid-based and function-based (Gao and Liu, 2002).
Most of the GPS
ionospheric models are function-based model and the ionosphere-modelling
algorithms are based on the polynomial function (Komjathy, 1997) and spherical
harmonics expansion (Schaer, 1999; Wielgosz et al., 2003a), which is not very
effective in handling multi-scale phenomena and nonhomogeneous fields, due to
19
their global nature (Li, 1999; Schmidt, 2001).
Therefore, alternative method that is
more suitable for the modelling of nonhomogeneous fields is needed.
Interpolation
or prediction techniques are suitable for handling multi-scale phenomena and
unevenly distributed data (Weilgosz et al., 2003a).
Gao and Liu (2002) also pointed
out that interpolation methods might give comparable or even better results,
compared to the mathematical function representation of TEC.
The results from all the models or methods are two-dimension in nature, where
the ionosphere’s free electrons is assumed to be concentrated on a spherical shell of
infinitesimal thickness located at the altitude of about 350km above the earth’s
surface (Gao et al., 1994).
This is called the single layer model (SLM), where the
altitude can be changed according to the needs of different algorithm.
function converting slant TEC to the vertical one is needed.
A mapping
The function is the
computation of the line-of-sight between the GPS receiver and the observed satellite
on the ionosphere shell as illustrated in Figure 2.1 and formula below (Mannucci et
al., 1993):
Figure 2.1: Single Layer Model of the Ionosphere (Schaer, 1999).
20
F z = [1 - R cos(90- z) ]- 0.5
R+H
(2.5)
where,
Fz = vertical TEC.
R = Earth radius.
H = SLM height.
z = satellite zenith angle.
2.5
Previous Studies on Mapping of the Ionosphere
Many researches and studies were already done on the mapping of the
ionosphere.
Thus, this section will present some of the conclusions and findings
obtained from other studies or researches.
Schmidt et al. (2007) presented different multi-dimensional approaches for
modelling of the TEC over South America.
The different approaches utilised
include 2-D B-spline combined with 1-D empirical orthogonal function (EOF)
modelling, 3-D B-spline modelling and 4-D B-spline modelling.
The input data for
these approaches are derived from the IRI model and the results obtained from these
approaches are compared with the original electron density data sets calculated from
IRI to get the respective RMS values.
The conclusion achieved from this study is
that for each of the approaches, the same parameter estimation process can be used
and by using these methods, an update of climatological parameters of the applied
reference model, such as the IRI model can be performed.
Moeketsi et al. (2007) had performed a research to study the solar cycle
variations of TEC over Southern Africa.
The TEC is derived using the University
21
of New Brunswick (UNB) ionospheric modelling technique primed with data from
the Southern Africa GPS network.
TEC maps over South Africa were produced
during selected days and hours of different epochs of solar cycle 23.
A comparison
of the TEC values from UNB and IRI 2001 models was performed.
From the
comparison, it shows a good agreement during a geomagnetically quiet day at mid
and higher latitudes.
Wielgosz et al. (2003a) performs the concept and practical examples of
instantaneous mapping of regional ionosphere, based on GPS observations from five
of the State of Ohio continuously operating reference stations (CORS) network.
Interpolation techniques, such as kriging (KR) and the multiquadric (MQ) model,
were used to create the TEC maps.
The quality of the ionosphere representation
was tested by comparison with the IGS Global Ionosphere Maps (GIMs).
The KR
and MQ methods applied to the regional GPS data allowed the production of more
detailed TEC maps, as compared to the GIMs.
Since KR and MQ are suitable for
interpolation and extrapolation, they enable forecasting of the ionosphere in order to
support radio navigation.
Both methods seemed to be suitable for instantaneous
regional ionosphere modelling.
Wielgosz et al. (2003b) demonstrated the concept and some practical examples
of the TEC modelling using undifferenced phase-smoothed pseudorange GPS
observations.
These phase-smoothed pseudorange observations are equivalent to
the carrier phase observations, where the integer ambiguities might be biased.
The
resulting TEC estimates were tested against the International GPS Service (IGS)
TEC data for some American, European and Antarctic stations.
The
point-measurements of TEC were interpolated using the Kriging technique to create
TEC maps.
The quality of the ionosphere representation was tested by comparison
to the reference IGS Global Ionosphere Maps (GIMs) and the result shows that
phase-smoothed pseudorange observations is efficient and enables generation of the
real-time regional TEC maps, when the Kriging method is applied.
However, the
systematic bias between both TEC estimation sets needs to be further investigated.
22
Liu et al. (2000) implemented the Multiplicative Algebraic Reconstruction
Technique (MART) algorithm to the ionospheric electron density inversion from
measured TEC through observation of the GPS signals and the Naval Navigation
Satellite System (NNSS) transit signals to reconstruct two-dimensional ionospheric
structures.
The NNSS signals are observed by the Low-latitude Ionospheric
Tomography Network (LITN), which consists of a chain of six stations.
They
compare the tomography results and show good agreement for both of the GPS and
the LITN programs.
Ruffini et al. (1998) combined the Global Positioning System/Meteorology
(GPS/MET) occultation data with ground data collected from more than one hundred
International GPS Service (IGS) stations to perform stochastic tomography of the
TEC with a 3D global grid of voxels extending up to 2000 km above the mean
surface of the Earth, and thus produce temporal series of 3D images of the TEC.
A
correlation functional approach that enforces smoothness of the images is used and
Kalman filter is used to assimilate the data and propagate the solutions in the time
direction.
They compare the TEC measurements from the National Aeronautics and
Space Administration (NASA) Radar Altimeter and Doppler Orbitography and
Radiopositioning
Integrated
by
Satellite
(DORIS)
instrument
on
board
TOPEX/Poseidon with GPS TEC estimates and evaluates different GPS data analysis
strategies.
From the comparison, they verify that global tomographic GPS analysis
using a voxel grid is well suited for ionospheric calibration of altimeters.
Besides
that, the result also showed that ground and occultation GPS delay data can be
combined successfully to perform ionospheric tomography with a substantial level of
vertical resolution.
Hajj et al. (2000) provided an overview of ionospheric sensing from GPS space
measurements.
They then described and applied the different methods of
processing ionospheric data collected during an occultation in a progressive manner
starting from the simplest (Abel inversion) to the most sophisticated (data
assimilation).
The accuracy of each methods are assessed either via examination of
real data from GPS/MET or via simulation.
Besides that, they also discuss about
23
the means of making use of the extremely rich set of measurements that could
become available from Constellation Observing System for Meteorology, Ionosphere,
and Climate (COSMIC) such as obtaining continuous and global scale 3-D images of
electron density or irregularity structure or Traveling Ionospheric Disturbances (TID).
In the end, they concluded that the COSMIC GPS occultations in the ionosphere
provide accurate 3-D specification of electron density, ionospheric irregularities and
global maps of TID.
Garcia et al. (2004) presented a method of inversion of the tridimensional
structure of the electronic density in the ionosphere from GPS data.
The TEC along
the rays from the GPS receivers to GPS satellites has been used as an entry data in a
general tomographic problem.
These data are inverted for electronic density in the
ionosphere and biases in the satellites and stations.
The problem is solved by least
squares and Kalman filtering, thus leading to an estimation of the error bar and the
resolution on the model parameters at each time step.
A specific processing method
of the inversion outputs is developed in order to localise the ionospheric regions
where the error bar is low and the resolution is good enough to detect the small
postseismic signal.
Heise et al. (2001) presented some preliminary results on the reconstruction of
ionosphere electron density distribution using GPS data obtained onboard the
CHAMP (CHAllenging Minisatellite Payload).
The calibrated TEC data derived
for a full CHAMP revolution are then assimilated into the Parameterized Ionospheric
Model (PIM).
Preliminary results of this assimilation provide a 2D-reconstruction
of the ionosphere electron density in the CHAMP orbit plane from the CHAMP
altitude up to GPS orbit heights.
Validation checks on the preliminary result had
been performed where the integrated TEC values for these modelled profiles were
compared with the corresponding TEC values derived from the GPS ground based
TEC maps.
The validation result showed a reasonable agreement between these
two sets of TEC values.
24
Ducic et al. (2002) presented some approaches to monitor the TEC using a dense
ground network of GPS receivers, namely the GPS Earth Observation Network
(GEONET) and to estimate the instrumental biases which is the biggest error source
in the estimation of TEC using GPS observations.
The GPS data from GEONET
allows performing imagery of the ionospheric structure and to distinguish between
spatial and temporal variations in details.
The purposes of their work were to
provide significant improvement in mono-frequency satellite measurement and some
improvement in GPS and SAR imagery of geophysical phenomena such as the
volcano deformations or subsidence detection.
Besides that, the precise imagery of
the ionosphere make possible to detect ionospheric disturbances like geomagnetic
storms, ionospheric scintillation and post-seismic perturbations such as Rayleigh
waves and tsunamis.
From the results of their work, it showed that dense GPS
networks enable the recording of the two-dimensional structure of the ionosphere
with a sufficient resolution to detect post-seismic disturbances.
Furthermore, this
work represents a significant improvement in ionosphere imagery resolution
allowing investigation of other sources of ionospheric perturbations (namely
geomagnetic storms or ionospheric scintillation) as well as the study of
acoustic-gravity waves and coupling processes in the atmosphere.
Jakowski et al. (2001) demonstrated the power of the GPS tool to detect and to
study the dynamics of large-scale spatial structures, such as ionospheric pertubations,
through TEC estimation.
The TEC maps of Europe are derived using permanent
operating European IGS GPS ground station networks
Stanislawska et al. (2002) measured the TEC over the European area using the
data collected from fourteen IGS GPS receiver stations within Europe.
The spatial
variations of TEC are then examined using an instantaneous mapping procedure,
namely kriging technique.
The TEC maps for magnetically quiet and disturbed
days during a single month are produced and discussed in terms of the
heliogeophysical conditions (magnetically quiet and disturbed days).
From this
study, they concluded the efficiency of the kriging technique in predicting the TEC.
25
Opperman et al. (2007) had demonstrated and developed a regional GPS based,
bias-free ionospheric TEC mapping methodology for South Africa, namely the
Adjusted Spherical Harmonic (ASHA) model.
Slant TEC values along oblique
GPS signal paths are quantified from a network of GPS receivers and converted to
vertical TEC by means of the single layer mapping function.
2D regional TEC
maps at any location within the region of interest are constructed using vertical TEC
at the ionospheric pierce points.
The results from this study showed favourable
comparisons with measured ionosonde data and two independent GPS-based
methodologies.
Cilliers et al. (2005) had presented and demonstrated the current status of the
various means available for ionospheric mapping in Southern Africa.
Three
different methods are addressed, which are the statistical IRI model, ionograms as
derived from the three Digisonde radar stations in South Africa and lastly the
Computerised Ionospheric Tomography (CIT) based on TEC which derived from the
signals received by the network of dual frequency GPS receivers in Southern Africa.
The operation, merits and limitations of these three methods of ionospheric mapping
were also discussed.
Meyer et al. (2006) had studied the potential of broadband L-band Synthetic
Aperture Radar (SAR) systems for ionospheric TEC mapping.
The sensitivity of
L-band SAR to changes in the ionospheric state and to ionospheric turbulence
suggests its application for ionospheric mapping with high spatial resolution and high
accuracy.
It shows that phase advance and group delay of the SAR signal can be
measured by interferometric and correlation techniques, respectively.
The
achievable accuracy suffices in mapping small-scale ionospheric TEC disturbances.
The result of that is compared with ground-based estimations of TEC using dense
GPS networks.
The conclusion of this study was the ground-based estimations of
TEC can reach neither the accuracy of SAR method nor a comparable spatial
resolution due to the separation of radio links of several tens of kilometres on
average.
26
Tsai et al (2002) had implemented the multiplicative algebraic reconstruction
technique (MART) to reconstruct two-dimensional ionospheric structures based on
TEC.
The TEC values were measured through the receptions of the GPS signals by
a LEO satellite receiver and the Naval Navigation Satellite System (NNSS) signals
by the low-latitude ionospheric tomography network (LITN).
The daytime and
night time tomographic images and a series of ionospheric imaging had been
conducted.
The results form these two methods were compared with the originally
vertical electron density profiles retrieved from the Abel transformation on
occultation observations.
From this comparison, it concluded that the profiles
retrieved from tomographic reconstruction shows much more reasonable TEC results
than the original vertical profiles retrieved by the Abel transformation.
Escudero et al. (2001) presented preliminary results by obtaining Electronic
Density fields from ionospheric tomography using the TEC data.
The TEC data
was derived from the occultation observation data from the Danish LEO satellite,
Orsted.
In this paper, it demonstrated two techniques to process the occultation data,
namely four dimensional tomographic procedure and Abel transform to obtain the
TEC.
Then some comparisons are carried out between these two results.
Further
more, these two results are validated with ground based radar observations, namely
ionosonde data.
From the comparisons, it showed good agreement among the two
results.
2.6
Use of Ionospheric Data on Satellite Positioning
Ionospheric delay is the major error source in GPS signal in these days. Thus for
precision GPS positioning, the ionosphere effect must be estimated then eliminated
from the GPS observations (Gao and Liu, 2002).
27
2.6.1
Effects of the Ionosphere on Position Determination
The GPS signal experience delay when it passes through the ionosphere. The
delay of GPS signals in the ionosphere is inversely proportional to the square of the
carrier wave’s frequency and proportional to the total number of electrons along its
atmospheric traverse.
Besides that, the propagation speed and direction of the GPS
signal changes in proportion to the varying electron density along the line of sight
between the satellite and the receiver.
The ionosphere delay will affect the GPS range observation where a delay is
added to the code measurements and an advance to the phase measurements.
This
will degrade the signal performance, such as causing signal loss of lock and degrades
the accuracy of differential corrections. These effects are caused by irregularities of
TEC that scatters radio waves at L1 and L2 frequencies thus generating phase and
amplitude scintillation in GPS signals. Amplitude scintillation causes cycle slips and
data losses to occur while the phase scintillation generates fast variations of frequency,
namely Doppler shifts, which the receiver has to cope. In severe conditions, these
fluctuations can cause the receiver to lose lock.
Furthermore, the carrier-phase
differential GPS (DGPS) and real-time kinematic (RTK) applications are affected by
the presence of the TEC as the ionospheric term in the observation equations may not
cancel, causing unknown ambiguities difficult to resolve.
The equatorial anomaly region is the worst source of fluctuation or scintillation.
During the solar maximum periods, amplitude scintillations may exceed 20 dB for
several hours after sunset. Besides that, auroral and polar cap latitudes are some of
the potential active region.
In the central polar cap, during the years of solar
maximum, GPS receivers may experience >10 dB signal fades. When these fading
effects are strong, the refractive effects which produce range-rate errors are also
changing, often causing rapid carrier-phase changes. The Doppler shifts caused by
the TEC variations may be up to 1-Hz/sec thus inducing some narrow-band receivers
28
to lose lock on the GPS signals. Magnetic storms will also generate ionospheric
anomalies which, although rare, can extend well into the midlatitudes.
2.6.2
Method of Ionospheric Correction
There are a few methods to correct or eliminate the ionospheric error in the GPS
signal.
One of the methods to eliminate the ionospheric error in the signal GPS is
by taking advantage of the two frequency signal, namely L1 at 1575.42 Hz and L2 at
1227.6 MHz, which are transmitted by GPS satellite itself.
A linear combination
using L1 and L2 data which is known as the LC or L3 or ionosphere-free
combination is formed to calculate a total propagation delay time that is free of
ionospheric delay.
Another method to correct the ionospheric error is by combining simultaneous
observation from multiple GPS ground receiving stations.
This method is known as
the differencing observation techniques, which can be categorized into three types,
namely single differencing, double differencing and triple differencing.
Among
these three techniques, the double differencing is commonly used to eliminate the
ionospheric error in the GPS signal.
Generally, this technique is a combination of
two single differencing techniques, which consist of two receivers, and two GPS
satellites, please refer to Figure 2.2.
Double differencing technique is carried out by
measuring the difference in simultaneous measurements by two receivers from two
GPS satellite.
29
Satellite 1
Receiver 1
Satellite 2
Receiver 2
Figure 2.2: The Double Differencing Observation Technique.
CHAPTER 3
REVIEWS ON INTERPOLATION TECHNIQUES
3.1
Introduction
In the real world, it is impossible to get exhaustive values of data at every
desired point due to the practical constraints.
Thus the interpolation technique is
important since it is a procedure or process to estimate the value of properties or
variables at unsampled location or site using the existing samples or observations
made at other sites or locations.
In many of the cases the variable or property must
be interval or ratio scaled.
Interpolation is related to, but is distinct, from function approximation. Both
tasks consist of finding an approximate, but easily computable function to use in
place of a more complicated one.
In the case of interpolation, we are given the
function at points not of our own choosing.
For the case of function approximation,
we are allowed to compute the function at any desired points for the purpose of
developing our approximation (Press et al., 1992).
31
3.2
Definition of Interpolation
The concept of the interpolation is that the points which are close together in
space are more likely to have similar values and attributes as compared to points
which are far apart.
This is known as positive spatial autocorrelation.
In other
word, when given a set of sample points with known values, the value at a location
with an unmeasured attribute or value is best determined by assigning to it the value
of the closest measured value.
Another definition of interpolation is the one stated
by Martin (1996), whereby he defined interpolation as a sampling strategy when
measurement of a geographic phenomenon at all points in space is need, which is not
usually possible.
He also stated that the method for intermediate-value estimation is
the focus of attention of interpolation.
In practice, the output from the interpolation
will be on a regular grid, whereas observations will come from irregularly-positioned
stations.
Conceptually, the process of interpolation consists of two stages.
which is fitting an interpolating function to the samples provided.
The first,
The second stage
is evaluating that interpolating function at the target point to get the estimated value.
The number of samples (minus one) used in an interpolation scheme is called the
order of the interpolation.
increase the accuracy.
However, increasing the order does not necessarily
If the added samples are distant from the target point, the
resulting higher-order polynomial, with its additional constrained samples, tends to
oscillate wildly between the tabulated values.
This oscillation may have no relation
at all to the behaviour of the “true” function.
On the contrary, adding samples that
are close to the target point usually does help, but a finer mesh means a larger table
of values, which is not always available.
32
3.3
Methods of Interpolation
There are various kinds of data interpolation, for example, point or area
interpolation, global or local interpolation, exact or approximate interpolation,
stochastic or deterministic interpolation, and gradual or abrupt interpolation. These
are the various interpolation methods, but they all share one key assumption, that
unknown values can be estimated from the spatial proximity to known values
(Lammeren, 2002; Godefa, 2006).
Point interpolation is based on a given number of points whose locations and
values are known.
From which, the values of other points at predetermined
locations are then determined later.
Point interpolation is used for data which can
be collected at point locations such as spot heights.
Once the grid of points has
been determined, interpolated grid points are often used as the data input to computer
contouring algorithms.
Isolines (e.g. contours) can be threaded between them using
a linear interpolation on the straight line between each pair of grid points.
Point to
point interpolation is the most frequently performed type of spatial interpolation done
in Geographic Information System (GIS).
Whereas area interpolation of a given set
of data which is mapped out on one set of source zones determines the values of the
data for a different set of target zones (Martin, 1996; Lammeren, 2002; Godefa,
2006).
Global interpolation determines a single function that is mapped across the
whole region.
Thus, a change in one single input value (sample point), will affect
the entire map.
On the other hand, local interpolation applies an algorithm
repeatedly to a small portion of the total set of samples.
As a result, a change in an
input value only affects the result within the particular window.
Global
interpolation will be used when there is a hypothesis about the form of the surface, as
it tends to produce smoother surfaces with less abrupt changes (Lammeren, 2002;
Godefa, 2006).
33
Exact interpolation function is based on a concept that the surface passes
through all samples whose values are known.
Its interpolators are the data points
upon which the interpolation is based on. On the other hand, approximate
interpolation is used when there is some uncertainty about the given surface values.
The latter utilizes the belief that in many data sets there are global trends, which vary
slowly, but overlie by local fluctuations, which vary rapidly and produce uncertainty
(error) in the recorded values.
Thus the effect of smoothing here is to reduce the
effects of error on the resulting surface (Martin, 1996; Lammeren, 2002; Godefa,
2006).
Stochastic method incorporates the concept of randomness.
The interpolated
surface is conceptualized as one of many surfaces that might have been observed,
from which, all the surfaces could have produced the known samples.
Stochastic
interpolators include trend surface analysis, Fourier analysis and Kriging procedures.
Stochastic interpolators such as trend surface analysis allow the statistical
significance of the surface and uncertainty of the predicted values to be calculated.
Deterministic method, on the other hand, does not use probability theory (Lammeren,
2002; Godefa, 2006).
A typical example of a gradual interpolation is the distance weighted moving
average which usually produces an interpolated surface with gradual changes.
However, if the number of samples that is used in the moving average were reduced
to a small number, or even one, there would be abrupt changes in the surface.
Thus,
it may be necessary to include barriers in the interpolation process (Lammeren, 2002;
Godefa, 2006).
34
3.3.1
The Multiquadric Technique
Multiquadric method is a popular choice for interpolating scattered data in one
or more dimensions.
Besides that, multiquadric is also often used to approximate
geographical surfaces and gravitational and magnetic anomalies.
Measurements of
pressure or temperature on the earth's surface at scattered meteorological station, or
measurements on other multidimensional objects may give rise to interpolation
problem that require the scattered data.
use.
Multiquadric performs well for this type of
Moreover, multiquadric has been used in many applications, such as geodesy;
hydrology; photogrammetry; surveying and mapping; remote sensing; image
processing; geophysics and crustal movement; geology and mining; natural resource
modelling and so on (Hardy, 1990).
The basic theory on the multiquadric interpolation was originally introduced by
Hardy (1971).
The multiquadric belongs to a family of radial basis functions.
The
interpolation equation using radial basis function is
N
H(X) = ∑ αi Q(X-Xi)
(3.1)
i=1
where H(X) is a spatially varying field, such as temperature or pressure, and Q(X-Xi)
is a radial basis function.
The argument represents the vector between an
observation point Xi and any other point in the domain.
The coefficient, αi is a
weighting factor that must be determined specifically in some manner or from the
observation.
For statistical interpolation, the covariance functions between the field
at observed points and other points in the domain serve as the basic functions.
The
multiquadric method uses hyperboloid functions as the basic function in the form:
Q(X-Xi) = (│x-xi│2 + c2) 1/2
where c is an arbitrary and typically, small constant.
(3.2)
The constant c make the basic
35
function infinitely differentiable by preventing the basic functions from vanishing at
the point of the observations and affects the condition number of the coefficient
matrix by controlling the relative sizes of the diagonal and off-diagonal terms.
constant will be referred to as the multiquadric parameter.
the position vector in one, two or three dimensions.
This
Here, X may represent
For example, the hyperboloid
functions in two dimensions become:
Qi(X, Y) = (│x-xi│2 +│y-yi│2 + c2) 1/2
(3.3)
To determine the coefficients αi, a set of linear equation to the field at every
observation point (Xj, Yj) results in the following set of equations:
N
H(Xj, Yj) = ∑ αi Qi(Xj, Yj)
(3.4)
i=1
where,
Qi(Xj, Yj) = (│xj-xi│2 +│yj-yi│2 + c2) 1/2
(3.5)
Note that the observations, H(Xj, Yj) may represent either the raw observations or the
deviation of the observations from some background field.
all N observation points.
coefficients αi.
Hj = αi Qij
Equation (3.4) holds at
This results in a set of N equations with N unknown
In matrix notation,
(3.6)
and the solution for the αi in this set of equations is given mathematically as
αi = Qij-1 Hj
(3.7)
In practice, the coefficients αi as well as the inverse matrix Qij-1 is determined by
36
solving the set of linear equations.
Computational stability in solving the system of linear equations is a potential
problem.
The parameter c determines the curvature of the hyperboloids used in the
interpolation.
For small value of c, very sharp (large curvature) hyperboloids are
generated, so very tight gradients are easily represented.
For large value of c, flat
hyperboloids are used and the interpolation cannot easily represent tight gradients or
fit closely-spaced observations.
The multiquadric function relies on the Euclidian distance between points and
the multiquadric parameter, c (Ferreira et al, 2005a; Ferreira et al, 2005b).
But the
multiquadric parameter, c, has the biggest impact on the computation stability when
solving for the coefficients.
If the value of the │x-xi│2 is small and the value of c2
is large in the multiquadric function, then the matrix has nearly equal diagonal and
off-diagonal elements.
This results in an ill-conditioned matrix.
Since the choice
of the interpolation constant is very important for maintaining computational stability
in solving for the coefficients, its choice potentially influences the analysis as well.
Kansa (1990a) had suggested to vary this parameter over the set of observation and
to maintain computational stability and increase interpolation accuracy.
The interpolation solution to any desired uniform grid Hg, represented by the
grid points (Xg, Yg), is then given by
Hg = Qgi Qij-1 Hj
(3.8)
where each element in the matrix Qgi is given by
Qgi = (│xg-xi│2 +│yg-yi│2 + c2) ½
(3.9)
Since the number of grid points is not necessarily equal to the number of observation
points, the matrix Qgi is not a square matrix.
Note that, once the coefficients αi are
37
determined, the solution or approximated function can be determined on any
arbitrary grid, such as a grid with 10- or 1000-km spacing.
The resolved scales and
accuracy of the approximated function are completely determined by the number and
spacing of the observations that were used to determine the coefficients.
However,
the choice of output grid may limit the representation of these scales on the output
grid.
Since 1971, the multiquadric which is one type of radial basis function has been
investigated thoroughly (Chen and Wu, 2006).
But it was largely unknown to
mathematicians and scientist until the publication of Franke’s (1982) review paper.
In that paper, Franke compared radial basis functions against many popular
compactly supported schemes for 2D interpolation.
From that paper, he concluded
that the multiquadric was rated as one of the best methods among 29 scattered data
interpolation schemes based on their accuracy, stability, efficiency, memory
requirement, fitting ability, visual smoothness and ease of implementation.
More
recent review papers by Jin et al. (2000), McDonald et al. (2000) and Wang (2004)
have indicated that multiquadric can also be used as a basis for constructing
multivariate response surface models.
3.3.2
The Sphere Multiquadric Technique
The multiquadric method can be very flexible and can be easily modified to fix
certain condition or surface because it’s a radial basis function method. This is
because, an important feature of the radial basis function method is that it does not
require a grid.
Thus the only geometric properties needed in a radial basis function
approximation are the paired-wise distances between points.
Working with higher
dimensional problems is not difficult as distances are easy to compute in any number
of space dimensions (Ferreir, 2003).
Thus, Hardy and Goepfert (1975) purposed
the use of a spherical analogue of the reciprocal multiquadric concept.
The
38
spherical reciprocal multiquadric interpolant developed by them is shown below:
Ak
N
SRMQ = ∑
k=1
(3.10)
(1 + R2 – 2R cos sk) 1/2
Pottmann and Eck (1990) had reformulated the spherical multiquadrics to the
more generalized form, which will provide better result than the spherical reciprocal
multiquadric.
Actually what Pottmann and Eck did are inverting the spherical
reciprocal multiquadric.
The new spherical multiquadric equation became:
N
SMQ = ∑ Ak (1 + R2 – 2R cos sk) 1/2
(3.11)
k=1
For both equations, R is a user-specified tension parameter, which is equivalent
to the parameter c in the multiquadric equation.
The sk is the angular distance
between the estimated point and the observation point.
The weights, Ak is
equivalent to the αi in the multiquadric equation.
All the weights are computed so that the estimated function agrees with the
observations at the observation points.
For N observation points, this requires the
solution of N simultaneous equations and the inversion of an NxN matrix.
In
matrix notation, the formula is:
Ak = Qk -1 S
(3.12)
where each of the element in Qk is given by (1 + R2 – 2R cos sk)1/2 whereby S refers
to the matrix that contains N observation values.
The interpolation solution for any desired uniform grid Sm, which is represented
39
by the grid points (Xm, Ym), is given by the following formula:
Sm = Qmk Qk -1 S
(3.13)
Angular distance is the distance between any two points on the surface of a
sphere, which is measured along a path on the surface of the sphere.
Since
spherical geometry is different from ordinary Euclidean geometry, the equations for
distance take on a different form.
The distance between two points in Euclidean
space is the length of a straight line from one point to the other point. But on the
sphere, there are no straight lines.
replaced with geodesics.
In non-Euclidean geometry, straight lines are
Geodesics on the sphere are referring to the great circles.
The great circle is a circle on the sphere whose centres are in coincidence with
the centre of the sphere.
Between any two points on a sphere which are not directly
opposite each other, there is a unique great circle.
circle into two arcs.
between the points.
The two points separate the great
The length of the shorter arc is the great-circle distance
The great circles can be calculated easily giving the latitudes
and longitudes of two points, example the points A and B, using the following
equation from spherical trigonometry:
D = arcos [(sin a) (sin b) + (cos a) (cos b) (cos P)]
(3.14)
where,
D = angular distance or great circle distance between points A and B.
a = latitude of point A.
b = latitude of point B.
P = longitudinal difference between point A and B.
When applying the equation above, south latitudes and west longitudes are
treated as negative angles.
Beside that, theses functions may expect angle measured
40
in radians, rather than degrees.
Thus the degree of the point needs to be converted
to radians first before it can be used in the equation.
3.3.3
The Inverse Distance Weighting Technique
The inverse distance weighting (IDW) interpolation method is one of the
simplest and most readily available methods.
interpolation.
It is a deterministic and exact
Exact interpolation means that the surface passes directly through the
known points while the basis of deterministic interpolation methods is the principle
of simple averaging (Collins and Bolstad, 1996; Kravcehnko and Bullock, 1999;
Robinson and Metternicht, 2005; Meyer, 2006; Milillo and Gardella, 2006).
It
assumes that each sample point has a local influence that diminishes with distance.
When estimating the value of an unknown point, it gives greater weight to the points
which is closer to the unknown point than to those farther away from the unknown
point.
It means the weights change according to the linear distance of the known
sample points from the unsampled point, where the shorter distance will have higher
weighting, while the longer distance will have lower weighting.
Because this is a
static averaging method, the estimated values can never exceed the range of values in
the original field data.
The equation for the inverse squared distance weighted
interpolation is (http://www.esri.com/software/arcgis/):
n
z’(x) = ∑ λi ·z (xi)
(3.15)
i=1
In the above equation, the z’(x) refer to the estimated value while the z (xi) is the
value of the ith observed or sample data input and lastly the λi is the weight of the ith
observed or sample data input.
The weight of each sample point is in inverse
proportion to a power of distance, the equation for calculating the weight is
(http://www.statios.com/Training/):
41
(3.16)
where,
di = distance between ith data and the estimated point.
c = small constant.
w = power (usually between 1 to 3).
There is a limitation for the weight where the total of the weight must be equal to
one or nearing one, but should not be more than one.
Besides the limit on the weight, other limitations can also be applied to the equation.
The other limitations on the weight are the power and the number of input points to
use in the interpolation, which is collectively known as the size of the neighbourhood,
and is expressed as a radius or a barrier.
In the inverse distance weighting, the significance of the known points upon the
interpolated values can be controlled, based on their distance from the estimated
point.
By specifying a high power, more emphasis is placed on the nearest points.
Thus the output result, mainly referring to the surface, will have more details but less
smooth.
Hence defining a lower power will give more influence to the points that
are further away, resulting in a smoother output surface.
If inverse distance
weighting is run with higher powers (greater than 1), it runs with a high degree of
local influence, giving the output surface increased detail.
However, if inverse
42
distance weighting is run with a power of 1 or less, it runs with a global influence,
treating each point almost equally to create a smoother output surface.
A power of
two is most commonly used (http://www.esri.com/software/arcgis/).
The characteristics of the interpolated output also can be controlled by applying
a search radius, either fixed or variable.
This limits the number of input points that
can be used for calculating or for estimating each interpolated point.
radius requires a distance and a minimum number of points.
the radius of the circle of the neighbourhood.
A fixed search
The distance dictates
The distance of the radius is constant,
so for each interpolated point, the radius of the circle used to find input point is the
same.
The minimum number of points indicates the minimum number of measured
points to use within the neighbourhoods.
All the measured points that fall within
the radius will be used in the calculation of each interpolated point.
When there are
fewer measured points in the neighbourhood than the specified minimum, the search
radius will increase until it can encompass the minimum number of points.
The
specified fixed search radius will be used for each interpolated point in the study area.
Thus, if the observed points are not spread out equally, which they rarely are, then
there are likely to be a different number of observed points used in the different
neighbourhoods for the various predictions (http://www.esri.com/software/arcgis/).
When applying the variable search radius, the usage of the number of input
points in calculating the value of the interpolated point is specified.
This will cause
the radius distance to vary for each interpolated point, depending on how far it has to
search around each interpolated point to reach the specified number of input points.
Thus, some neighbourhoods can be small and others can be large, depending on the
density of the observed points near the interpolated point.
Besides that, a maximum
distance, in map units, can be specified so that the search radius cannot exceed it.
If
the radius for a particular neighbourhood reaches the maximum distance before
obtaining the specified number of input points, the prediction for that location will be
performed on the number of observed points within the maximum distance
(http://www.esri.com/software/arcgis/).
43
A barrier refers to a polyline dataset used as a break that limits the search for
input points.
A polyline can represent a ridge, cliff, shoreline or some other
interruptions in a landscape.
Barriers limit the number of input sample points that is
used to interpolate the unknown point's value.
Only those input sample points on
the same side of the barrier as the current processing point will be used
(http://www.esri.com/software/arcgis/).
Many studies done on the inverse distance weighting interpolation method have
found it to be more accurate than other interpolation methods.
Example, in year
1992, Weber and Englund (1992) found that squared inverse distance weighting
produces better interpolation results than any other method, including Kriging.
On
1994, when Wollenhaupt et al. (1994) compared Kriging and inverse distance
weighting for mapping soil and level sand, the result showed that inverse distance
weighting is relatively more accurate.
During 1996 Gotway et al. (1996) observed
the best results in mapping soil organic matter contents and soil levels for several
fields and he found that the accuracy of the inverse distance method increased as the
exponent value increased.
In 1999, Kravchenko and Bullock (1999) reported a
significant improvement in the accuracy of soil properties interpolated using inverse
distance weighting by manipulating the exponent value.
Again in 1994, Weber and
Englund (1994) had reported that inverse distance weighting with a power of one
resulted in a better estimation for data with skew coefficients in the range of four to
six when interpolating blocks of contaminant waste sites.
Their studies used the
mean squared error as a main criterion for comparison of the results (Weber and
Englund, 1992; Gotway et al., 1996).
Besides that, the studies also showed that the
accuracy of the results is solely influenced by the data input density and distribution.
Through various studies, the advantageous and disadvantageous of the inverse
distance weighting interpolation method can be identified.
Its advantages consisted
of the simplicity of its underlying principle; the speed in its calculation; the ease of
programming using computers; reasonable and credible results, with considerable
accuracy for many types of data.
On top of that, with simple modifications it
becomes as competitive as other more elaborated methods such as Kriging or spline
44
interpolation.
It also works well with noisy data, limited sample size and random
input points that are rather independent of their surrounding locations.
Another
advantage is that it only requires few parameter decisions and does not assess any
predictions errors (Lam, 1983).
The disadvantages of the inverse distance weighting interpolation method are its
inherently oversimplified theoretical model; sometimes its unreliability to interpolate
values that deviate significantly from reality; its emphasis on distance which is
unreliable in many cases and the choice of weighting function which may introduce
ambiguity, especially when the characteristics of underlying surface are not known.
Besides, the interpolation can be easily affected by uneven distribution of
observational data points, since an equal weight will be assigned to each of the data
points even if it is in a cluster.
It does not always reproduce the local shape implied
by the data input; and the maxima and minima in the interpolated result can only
occur at input points since inverse distance weighted interpolation is a smoothing
technique.
Other than that, it does not assume any type of spatial relationship or
spatial arrangement and neglects the statistical inter-relationships between the
actually observing points (Davis, 1986; Maguire et al., 1991).
The attributes of the inverse distance weighting, with its advantageous and
disadvantageous, have led to its wide application.
The inverse distance weighting
method can be used to interpolate climatic data, soil data and hydrological data,
atmospherical data, mining data and many other scientific fields (Legates and
Willmont, 1990; Herpin et al., 1995).
45
3.4
Accuracy of Interpolation Techniques
The quality of interpolation depends on accuracy, number and distribution of the
known points; and how well the mathematical function models the phenomenon.
For example, in exact interpolation method, the values at the data points are
preserved, while in the approximate interpolation method, the data is smoothed out,
thus affecting the quality of the interpolation differently.
Besides that, the range of
influence of the data points also plays a role in the quality of interpolation, where
global methods uses all sample points for interpolation, whereas local methods,
which is a piecewise method, only considers nearby data points (Lammeren, 2002;
Godefa, 2006).
The accuracy of the estimated results can be obtained by comparing the
estimated values with the true values.
This is normally done via two methods,
which are visualisation or statistical analysis.
CHAPTER 4
INTERPOLATION OF TOTAL ELECTRON CONTENT (TEC)
4.1
Introduction
This research estimates the Total Electron Content (TEC), using a program
written in Visual C++, for the whole region of Malaysia, which extends from 0°N to
8°N latitude and 99°E to 120°E longitude.
The estimation of the TEC for the aforementioned region was done via
interpolation methods from some sample points. The sample points used in this study
were obtained from the International Reference Ionosphere 2001 (IRI 2001) model.
Whereas the interpolation methods used here are the multiquadric, sphere
multiquadric and inverse distance weighting method. The region being studied in this
research is shown in Figure 4.1 below:
47
Figure 4.1: Study Area.
The output of this research is hoped to be benefit single frequency Global
Positioning System (GPS) users in Malaysia.
The results in this research will be
able to help them to compensate the ionospheric delay in their data.
Although there
are many ionospheric models that can be found in the market for the purpose of
estimating the TEC, it is not sufficient as the results derived from these models caters
more for global scale, which is not as accurate for local scale applications.
The first section discusses the data collection methodology in the research.
Whereas the second section shows how the data is processed via programming.
The last section explains the methods that are used in the analysis of the results.
4.2
Data Collection
The following sections will discuss about the way the data input in this study
was gathered.
48
4.2.1
Description of Test Data
The test data was obtained from the IRI 2001 model.
It was dated on year 2005,
day 211 which corresponded to 30th July 2005, at 1200 hour of the Universal Time
(the time in Greenwich, where the longitude is 0°).
The input data in this study was in the numerical form and consisted of the
coordinates (geographical latitude, geographical longitude) and their respective TEC
values.
4.2.2
The data covers the Malaysian region and its surrounding areas.
Location of Test Site
The test site in this study is the Malaysian region which ranges from 1°-7°N
100°-119°E, and its surrounding areas.
Malaysia is situated in the Southeast Asian
region, and is located very near the Equator.
Thus, Malaysian’s position in the
equatorial zone guarantees an equatorial climate which is characterised by the annual
southwest, northeast monsoons, where they have heavy rainfalls, high temperatures
and humidity levels as high as 90% perennially.
With its position in the equatorial zone, Malaysian is guaranteed to receive 12
hours of sun light everyday perennially.
Since ionospheric delay is mainly caused
by sun rays, the ionospheric delay is exaggerated in this region.
49
4.2.3
Observation of Test Data
The data input for this research, which was the reference points for the
interpolation of the TEC in the Malaysian region, was derived from the IRI 2001
model.
The IRI 2001 model is an empirical ionospheric model based on experimental
observations of the ionospheric plasma either by ground or in-situ measurements.
The major data sources for this model are the worldwide network of ionosondes, the
powerful incoherent scatter radars, the topside sounders, and in situ instruments on
several satellites and rockets. The IRI model is a joint project of by the Committee
on Space Research (COSPAR) and the International Union of Radio Science (URSI)
and it is still being improved-update by a working group from time to time.
Besides
that it is also supported by National Space Science Data Center (NSSDC, NASA).
The main purpose of IRI is to provide reliable ionospheric densities, composition and
temperatures (Bilitza, 2001). The IRI 2001 model can be downloaded from its official
web site (http://iri.gsfc.nasa.gov/).
Based on an ISO review report prepared by Technical Committee ISO/TC 20,
Aircraft and Space Vehicles, and Subcommittee SC 14, Space Systems and
Operations (2005), the accuracy of the IRI model differs according to the different
height and also the time of the day tested.
The accuracy is highest at 50-80% both
at heights 65 km to 95 km; and at heights from 200 km to 1000 km at latitudes more
than 60°.
The accuracy is at its lowest at 5-15% during daytime at heights 100 km
to 200 km.
However, during night time, for the height 100 km to 200 km, the
accuracy was 15-30%, whereas at heights from 200 km to 1000 km and latitudes less
than 60°, which includes the height and latitude used in this study, the accuracy was
15-25%.
50
Few sets of test data had been collected from the IRI 2001 model to be used in
this research.
To obtain the test data, which is the TEC value, from the IRI 2001
model, a few input data are needed. Those input data are the geographic latitude and
longitude, the date (year, month, day), local or universal time, sunspot number
(optional), magnetic kp-index (optional), the F2 layer critical frequency (optional)
and/or F2 layer peak height (optional) (Bilitza, 2001).
4.3
Flow Chart of Processing Stage
The data processing starts after all the data input, which are the coordinates of
the sample points with their corresponding real TEC values have been gathered from
the IRI 2001 model.
Thus, enables the estimation or calculation of the TEC for the
whole Malaysian region.
The results on the TEC of the Malaysian region were estimated using the three
interpolation methods -multiquadric, sphere multiquadric and inverse distance
weighting- that was discussed in the previous chapter.
The calculation of the results
or data output, which are the estimated TEC values for some predetermined
coordinates (target points) within the region of Malaysia, were done with programs
that were written with the Microsoft Visual C++.
Lastly, analysis was done to
determine the superiority in terms of accuracy of the different interpolation methods
used in this study.
Later sections will show the detailed processing steps in those programs, namely
for Multiquadric method, please refer section 4.4; Sphere Multiquadric method, refer
section 4.5; and Inverse Distance Weighting method, please refer section 4.6.
All
the formulas that was used in the programs, namely the multiquadric, sphere
51
multiquadric and inverse distance weighting program, can be found in the previous
chapter, thus will not be shown in this section.
Figure 4.2 shown below depicts the entire processing steps in this study.
Figure 4.2: Flow Chart of Processing Steps.
52
4.4
Interpolation using the Multiquadric Technique
The first step of the program was the reading of the input data, which was
obtained from the IRI 2001 model.
In this study, the input data consisted of the
sample points’ coordinates and their corresponding TEC values.
Prior to any
calculations, the value for the constant, c was determined.
After that, the distance, d (linear distance) of each sample points from one
another was calculated using the formula d2=│x-xi│2 +│y-yi│2, where x and y
stands for the first sample point’s latitude and longitude; while xi and yi represents
the latitude and longitude for the second sample point.
Then, the results of those
distances were used, in combination with the corresponding TEC values and the
constant, c, to define the weight for each sample point.
Please refer to formula 3.7
in section 3.3.1 for the above processing step.
For the purpose of this study, target points are used, and are defined as the
predetermined coordinates in the region of the whole Malaysia, of which the TEC
values will be estimated by interpolation methods.
Next, calculations of the linear
distances between every target points from each of the sample points were made via
the linear distance formula used above, d2=│x-xi│2 +│y-yi│2, where x stands for the
target points’ latitude; xi for the sample points’ latitude; y for the target points’
longitude; yi for the sample points’ longitude.
Finally, the output data, which is the estimated TEC values for each of the target
point, was computed using the results from the calculations on the linear distance
between the target points and each of the sample points; the weights, the constant, c
and the TEC values of the sample points.
3.3.1 for the calculations.
Please refer to formula 3.8 in section
53
Figure 4.3 shown below depicts the processing steps mentioned in detail above.
Figure 4.3: Flow Chart of Multiquadric Processing Steps.
54
4.5
Interpolation using the Sphere Multiquadric Technique
The processing steps in the sphere multiquadric program are the same as the
ones in the multiquadric program.
The only difference is the method of calculation
of the distance between the points, both among the data input (sample points) itself,
or between data input and target points.
In the sphere multiquadric program, the distance between the points was
calculated using the great circles formula rather than the linear formula used in the
multiquadric program.
In other words, the point-to-point distance in sphere
multiquadric is in spherical form, whereas the point-to-point distance in multiquadric
is in linear form.
The first step of the program was reading the input data, obtained from the IRI
2001 model.
After that, the constant, R value was defined first.
Then the great
circle distance of each sample points from one another was calculated, using the
formula 3.14 in section 3.3.2.
The results of those distances were then used, in
combination with the corresponding TEC and the constant, R, to define the weight
for each sample point, with the formula in 3.12 in section 3.3.2.
Subsequently, calculations of the great circle distances between every target
points from each of the sample points were also made with formula 3.14 in section
3.3.2.
Finally, the output data was computed with formula 3.13 in section 3.3.2,
using the results from the calculations on the great circle distance between the target
points and each of the sample points; the weights, the constant, R and the TEC values
of the sample points.
Figure 4.4 in the next page depicts the above described processing steps.
55
Figure 4.4: Flow Chart of Sphere Multiquadric Processing Steps.
56
4.6
Interpolation using the Inverse Distance Weighting Technique
The first step was the reading of the input data, consisting of the sample points’
coordinates and their corresponding TEC values which were obtained from the IRI
2001 model.
Secondly, the small constant, c was defined.
Next, linear distance, d between each of the sample point from each of the target
point was calculated with the formula, d2=│x-xi│2 +│y-yi│2, where x and y stands
for the first sample point’s latitude and longitude; while xi and yi represents the
latitude and longitude for the second sample point.
Then, the total of the linear
distance between the sample points and target points were tabulated. This will be
used together with the linear distance, d and the small constant, c to define the weight
of each of the sample points, using formula 3.16 from section 3.33.
This was
simply obtained according to the spatial relationship of each sample point to the
target points, where the closer the distance is, the higher the weight of the sample
point in the calculation for that particular target point.
Finally the estimated TEC value for each target point was defined from the total
of the multiplication of the TEC from each sample points with its corresponding
weight for that particular target point.
Formula 3.15 in section 3.3.3 was used in
this calculation.
The inverse distance weighting processing is simpler than the two multiquadric
programs as it consisted of fewer steps, which can be see from the flow chart above.
Thus, requires shorter time to run the processing steps.
Figure 4.5 in the following page shows the pictorial presentation of the
processing steps mentioned above.
57
Figure 4.5: Flow Chart of Inverse Distance Weighting Processing Steps.
58
4.7
Analyses Strategy
There will be two forms of result from the programs in this study, namely the
numerical result and the graphical result.
The numerical results will be shown in
the appendices, while the graphical results will be shown in chapter 5.
The accuracy of the numerical result was analysed using the root mean square
(RMS) method.
In mathematics, the RMS is a statistical measurement of the
magnitude of a varying quantity.
It can be calculated for a series of discrete values
or for a continuously varying function.
The name comes from the fact that it is the
square root of the mean of the squares of the values, which is equivalent to standard
deviation.
The RMS is a frequently used measurement of the differences between
values predicted by a model or an estimator, from the values actually observed from
the objects being modelled or estimated.
In other words, the RMS error is used as a
measurement of the accuracy of the estimated value from the interpolation methods,
indicating the discrepancies between the actual values and the estimated values.
Lower RMS error indicates a more accurate result (Walker, 1993), which in this
study, are the estimated TEC values.
There will only be one RMS value obtained from the whole set of output, instead
of multiple RMS values per each output.
The one simple RMS error calculated
from the results reflects the average discrepancy of all the output, collectively, from
their respective true values; and does not reflect that each output has the same value
of error from their respective actual values.
In fact, the values actual error can vary
across the output, depending on the number, distribution, and accuracy of the
reference points that were used.
The formula of the RMS error is shown below:
(4.1)
59
where,
xi = ith point of the real or observed.
x’i = ith point from the interpolation or estimation.
n = total number of points.
In this paper, the real TEC value for the whole Malaysian region was obtained
from the IRI 2001 model.
The estimated TEC refers to the interpolation result.
Thus, the RMS error for this research was calculated from the discrepancies between
the TEC values obtained from the IRI 2001 model and the estimated TEC from the
interpolation program in this study.
CHAPTER 5
RESULTS AND ANALYSIS
5.1
Introduction
This chapter discusses the final results from the interpolation programs.
The
results or outputs from the programming of this research consisted of the numerical
result and graphical result.
Both of the results were displayed in a window, and the
screen shot of the outputs from the programming is shown in Figure 5.1 on the
following page.
All of the numerical results derived from the interpolation programs in this
research will be used in the result analysis section and will not be presented here, but
in appendix B and C.
61
Figure 5.1: Screen Shots of Programs’ Output.
62
5.2
Results and Analysis
The analysis of the accuracy of the interpolation methods in this study were
based on statistical analysis via the RMS error of the numerical results.
Analysis
was done to compare the accuracy of the results of the three abovementioned
interpolation methods, namely the multiquadric, sphere multiquadric and inverse
distance weighting methods, in estimating and calculating the TEC values of the
Malaysian region.
Besides that, the factors that will affect the accuracy, namely the
number and distribution pattern of reference points and size of study areas on each
interpolation methods, will also be analysed.
This was done to determine the
requisites for the generation of more accurate interpolation results.
To ascertain the effects of both the quantity and the distribution of the reference
points on the accuracy of the results, an analysis of the RMS error was done for each
set of data with different number and pattern of distribution of reference points.
The RMS value is in TEC unit (TECU), of which 1 TECU is equal to 1016 el/m2.
Besides that, the effects of different study areas’ size on the accuracy of the results
were also similarly determined as well.
In this study, the distribution pattern of the reference points was classified into
well distributed and randomly distributed.
The determination of the distribution of
the reference points was done according to the definition below.
Well distributed is
defined as dissemination of reference points which are scattered accordingly to cover
most of the study area, and not just focused on one or few localized areas.
Random
or stochastic distribution refers to dissemination of reference points which are
scattered without any rules and just by chance, regardless of the outcome of the
distribution of the points.
63
5.2.1
Results and Analysis According to Study Area’s Size
To analyse the effects of different sizes of study area on the RMS error, hence
the accuracy of the interpolation, four different sized of study areas were identified
within the original study area (0°N to 8°N, 99°E to 120°E).
The identification of the coordinates of reference points according to the sizes of
the study areas was done by first determining a starting point (8°N, 99°E) at one edge
of the original study area.
Then, a smaller scale study area sized 1°x 1° grid size
was defined, starting from the identified starting point.
Next, subsequent study
areas were defined by expanding them from the same starting point and doubling the
grid size each time, from 1°x 1° to 2°x 2°, to 4°x 4, to 8°x 8° grid size.
The reference points for these newly defined study areas consisted of the
coordinates forming the four edges of the respective study areas.
The following
Figure 5.2 depicts the position and area size of these four sets data, where the black
colour point is the starting point.
Figure 5.2: Positions of Reference Points and Its’ Coverage Area.
64
In the analysis of the effect of the study area size on result accuracy, there were
four sets of data, which consisted of reference points from four different sizes of
study area, which were described above.
Thus, comparison will be made among the
four sets of data from the four different study areas statistically.
5.2.1.1 Dataset 1
Dataset 1 consists of four reference points which forms the 1º x 1º grid size
study area.
The position of the reference points and the size of the study area can
be seen in Figure 5.2, which is surrounded by the red colour points.
Below, the
Tables 5.1 shows the coordinates and the respective TEC values.
Table 5.1: Reference Points for 1º x 1º Grid Size:
Latitude Longitude
TEC
8
99
29.447
8
100
29.196
7
100
28.451
7
99
28.708
The graphical results for this dataset are shown in Figure 5.3(a) to Figure 5.3(c)
below:
65
Figure 5.3(a): Result of Reference Points within 1º x 1º Grid Size using Multiquadric
Method.
The graphical result obtained from the multiquadric method for the reference
points within the 1º x 1º grid size shows interpolated TEC values which are the least
dense in the middle with 27 TECU and surrounded by higher TEC density, especially
on the upper side, with 29 TECU and the lower side with 28 TECU.
However, the
differences in the TEC density are minimal, with TEC values ranging from 27 to 29
TECU.
66
Figure 5.3(b): Result of Reference Points within 1º x 1º Grid Size using Sphere
Multiquadric Method.
Figure 5.3(b) shows TEC density derived via the Sphere Multiquadric Method
with the least dense in the middle, with 25 TECU, but shows three-layered density
with the highest density in the uppermost region with 29 TECU, followed by the
lowermost layer, with 28 TECU and lastly the middle region, with 26 TECU.
figure shows a wider range of TEC density, ranging from 25 to 29 TECU.
This
67
Figure 5.3(c): Result of Reference Points within 1º x 1º Grid Size using Inverse
Distance Weighting Method.
Figure 5.3(c) shows TEC density derived via the IDW method, showing only
two TEC density, with the density or 28 TECU covering the lower region and 29
TECU covering the upper region.
The RMS values for all the numerical results of this dataset are presented in
Table 5.2 with a graph plotted according to it in Figure 5.4 below:
Table 5.2: RMS Error for the Numerical Results of Reference Points within 1º x 1º
Grid Size:
Interpolation Method
RMS error (TECU)
Multiquadric
0.4685
Sphere Multiquadric
1.7424
Inverse Distance Weighting
0.0649
68
RMS for Study Area Sized 1 º x 1 º
RMS error
2
1.5
1
0.5
0
Sphere
IDW
Multiquadric
Multiquadric
Interpolation Method
Figure 5.4: RMS Error for Reference Points within 1º x 1º Grid Size.
From Table 5.2 and Figure 5.4, we can notice that the inverse distance weighting
interpolation method have the lowest RMS error, which is 0.0649 TECU.
This is
followed by the multiquadric method, 0.4685 TECU and the sphere multiquadric
method with 1.7424 TECU.
Thus the inverse distance weighting method generates
the most accurate result in this dataset.
5.2.1.2 Dataset 2
Dataset 2 also consists of four reference points which forms the 2º x 2º grid size
study area.
The position of the reference points and the size of the study area can
also be seen in Figure 5.2, which is surrounded by the green colour points.
table below, Table 5.3, shows the coordinates and respective TEC values.
The
69
Table 5.3: Reference Points within 2º x 2º Grid Size:
Latitude Longitude
TEC
8
99
29.447
8
101
28.931
6
101
27.308
6
99
27.843
All of the three graphical results for this dataset are shown in Figure 5.5(a) to
Figure 5.5(c) below:
Figure 5.5(a): Result of Reference Points within 2º x 2º Grid Size using Multiquadric
Method.
Figure 5.5(a) shows only one coordinate with the highest density of 29 TECU at
the uppermost left side.
This is followed by 28 TECU scattered at the outer region,
especially at the upper layer and left side, then density of 27 TECU scattered
70
between the second dense layer. The least dense area consists of regions with 25
TECU at the middle of the study area, surrounded by 26 TECU region.
This figure shows a wider range of TEC density, ranging from 25 to 29 TECU.
Figure 5.5(b): Result of Reference Points within 2º x 2º Grid Size using Sphere
Multiquadric Method.
Figure 5.5(b) shows scattered areas of different TEC density, with the highest
density region at 30 TECU at the two ends of the middle layer, and the lowest
density region at the lowermost right coordinate of the study area, at 27 TECU.
TEC density ranges from 27 to 30 TECU.
The
71
Figure 5.5(c): Result of Reference Points within 2º x 2º Grid Size using Inverse
Distance Weighting Method.
Figure 5.5(c) shows three well-demarcated layers of three TEC densities, with
the lowest density at 27 TECU at the lower region, followed by 28 TECU at the
middle layer and lastly the highest density of 29 TECU covering the uppermost left
coordinates.
The TEC densities show a narrow range from 27 to 29 TECU.
The RMS values for all the numerical results of this dataset are presented in
Table 5.4 and a graph was plotted according to it in Figure 5.6, of which both are
shown below:
Table 5.4: RMS Error for the Numerical Result of Reference Points within 2º x 2º
Grid Size:
Interpolation Method
RMS error (TECU)
Multiquadric
1.5580
Sphere Multiquadric
0.8524
Inverse Distance Weighting
0.1471
72
RMS for Study Area Sized 2 º x 2 º
RMS error
2
1.5
1
0.5
0
Sphere
IDW
Multiquadric
Multiquadric
Interpolation Method
Figure 5.6: RMS Error for Reference Points within 2º x 2º Grid Size.
From Figure 5.6 and Table 5.4, we can notice that the inverse distance weighting
interpolation method have the lowest RMS error, which is 0.1471 TECU.
It is
followed by the sphere multiquadric method, 0.8524 TECU then the multiquadric
method with 1.580 TECU.
Thus the most accurate interpolation method in this
dataset is the inverse distance weighting method.
5.2.1.3 Dataset 3
Similar with the earlier dataset, there were four reference points forming a study
area of 4 º x 4 º grid size in dataset 3.
Again, the position of the reference points
and the size of the study area can be seen in Figure 5.2, which is surrounded by the
blue colour points.
values.
Below, Table 5.5 shows the coordinates and respective TEC
73
Table 5.5: Reference Points within 4º x 4º Grid Size:
Latitude Longitude
TEC
8
99
29.447
8
103
28.364
4
103
24.5
4
99
25.62
All the graphical results for this dataset are shown from Figure 5.7(a) to Figure
5.7(c) in the following pages.
Figure 5.7(a): Result of Reference Points within 4º x 4º Grid Size using Multiquadric
Method.
Figure 5.7(a) shows a study area with a wider TEC density range, from 21 to 29
TECU. It shows a smooth transition of density with the lowest density at the lower
third layer, which slowly increases outwardly up to the highest density at the
uppermost left coordinate at 29 TECU.
74
Figure 5.7(b): Result of Reference Points within 4º x 4º Grid Size using Sphere
Multiquadric Method.
Figure 5.7(b) shows scattered areas of different TEC density with a smaller TEC
range, from 25 to 30 TECU. However, the transition of the TEC values were noted
not to be smooth with the lowest density area of 25 TECU at the two ends of the
lowermost layer, and three scattered coordinates at the outermost region of the study
area with the highest density of 30 TECU.
75
Figure 5.7(c): Result of Reference Points within 4º x 4º Grid Size using Inverse
Distance Weighting Method.
Figure 5.7(c) shows well demarcated layers of different TEC density, ranging
from 25 to 29 TECU, with the highest density covering the uppermost left region of
the study area at 29 TECU, and smoothly decreasing in intensity down to the lowest
density of 25 TECU at the lowermost right region of the study area.
The RMS values for all the numerical results of this dataset are presented in
Table 5.6 and Figure 5.8 below:
Table 5.6: RMS Error for the Numerical Results of Reference Points within 4º x 4º
Grid Size:
Interpolation Method
RMS error (TECU)
Multiquadric
3.1099
Sphere Multiquadric
2.6009
Inverse Distance Weighting
0.3736
76
RMS error
RMS for Study Area Sized 4 º x 4 º
3.5
3
2.5
2
1.5
1
0.5
0
Sphere
IDW
Multiquadric
Multiquadric
Interpolation Method
Figure 5.8: RMS Error for Reference Points within 4º x 4º Grid Size.
According to Table 5.6 and Figure 5.8, the inverse distance weighting
interpolation method has the lowest RMS error, which is 0.3736 TECU.
It is
followed by the sphere multiquadric method, 2.6009 TECU then the multiquadric
method with 3.1099 TECU.
Again, this indicates that the most accurate
interpolation method in this dataset is the inverse distance weighting method.
5.2.1.4 Dataset 4
Dataset 4 is the last set of data in this section. As usual, it is formed by four
reference points, but here they form the edges of an 8º x 8º grid size study area.
Again, the position of the reference points and the size of the study area can be seen
in Figure 5.2, which is surrounded by the yellow colour points.
Table 5.7, shows the coordinates and their respective TEC values.
The table below,
77
Table 5.7: Reference Points within 8º x 8º Grid Size:
Latitude Longitude
TEC
8
99
29.447
8
107
27.081
0
107
17.378
0
99
19.496
All three graphical results for this dataset are shown from Figure 5.9(a) to Figure
5.9(c) below:
Figure 5.9(a): Result for Reference Points within 8º x 8º Grid Size using
Multiquadric Method.
Figure 5.9(a) shows graphical result from the study region from 8◦N to 0◦ and
from 0◦ to 107◦E.
It shows a smooth transition of TEC density, from the lowest
density of 15 TECU at the lower right region and smoothly increasing in density
78
outwardly up to the highest density at 29 TECU.
It is noted that the range of TEC
unit is wide, from 15 to 29 TECU.
Figure 5.9(b): Result for Reference Points within 8º x 8º Grid Size using Sphere
Multiquadric Method.
Figure 5.9(b) covers from 8◦N to 0◦ and from 0◦ to 107◦E.
It shows four foci of
region with highest TEC density of 39 TECU in the middle, which decreases
smoothly from the centre of the foci to the lowest density of 17 TECU.
density ranges widely from 17 to 39 TECU.
The TEC
79
Figure 5.9(c): Result of Reference Points within 8º x 8º Grid Size using Inverse
Distance Weighting Method.
Figure 5.9(c) covers from 8◦N to 0◦ and from 0◦ to 107◦E.
It shows a smooth
transition of density from the lowest density at 17 TECU at the lowermost right and
increases up to the highest density at 29 TECU at the uppermost left region.
The
range of TEC density is the smallest among the 3 methods for this grid size, from 17
to 29 TECU.
The RMS values for all the numerical results of this dataset are presented in
Table 5.8 and a bar graph was plotted in Figure 5.10 as shown below:
Table 5.8: RMS Error for the Numerical Results of Reference Points within 8º x 8º
Grid Size:
Interpolation Method
RMS error (TECU)
Multiquadric
3.9152
Sphere Multiquadric
7.6365
Inverse Distance Weighting
1.2178
80
RMS for Study Area Sized 8 º x 8 º
RMS error
10
8
6
4
2
0
Sphere
IDW
Multiquadric
Multiquadric
Interpolation Method
Figure 5.10: RMS Error for Reference Points within 8º x 8º Grid Size.
By referring to the above Table 5.8 and Figure 5.10, the inverse distance
weighting interpolation method, once again, has the lowest RMS error, which is
1.2178 TECU among the three interpolation methods.
The second lowest RMS
error, 3.9152 TECU, is from the multiquadric method.
The highest RMS error
comes from the multiquadric method with 7.6365 TECU.
Once again, this indicates
that the most accurate interpolation method in this dataset is the inverse distance
weighting method.
5.2.1.5 Summary of Results and Analysis According to Study Area’s Size
This section discusses the overall analysis of the result from the above four sets
of data.
below.
All of the RMS error from these four sets of data is shown in the Table 5.9
81
Table 5.9: RMS Error for the Four Sets Reference Points:
Area
Inverse
Sphere
Size
Distance
Multiquadric
Multiquadric
Weighting
1º x 1º
0.0649
1.7424
0.4685
2º x 2º
0.1471
0.8525
1.5580
4º x 4º
0.3736
2.6009
3.1099
8º x 8º
1.2178
7.6365
3.9152
Based on Table 5.9, two graphs were plotted according it and are shown in
Figure 5.11 and Figure 5.12 below:
82
RMS for Different Interpolation Methods
9
8
RMS error
7
6
1ºx1º
2ºx2º
4ºx4º
8ºx8º
5
4
3
2
1
0
IDW
Sphere
Multiquadric
Interpolation Method
Multiquadric
Figure 5.11: RMS Error for Three Different Interpolation Methods.
RMS of Different Size of Study Area
9
8
RMS error
7
6
Sphere Multiquadric
Multiquadric
IDW
5
4
3
2
1
0
1ºx1º
2ºx2º
4ºx4º
Area Size
8ºx8º
Figure 5.12: RMS Error for Four Different Size of Study Area.
83
From Figure 5.11, we can see that the smaller the size of the study area, the more
accurate the interpolation output, as the RMS errors are smaller.
This indicates that
the RMS error is proportional to the size of the study area, whereas the RMS errors
increase when the size of the output areas are increased.
This phenomenon is very
obvious in the results from the inverse distance weighting and multiquadric
interpolation method, but not consistent in the results from the sphere multiquadric
interpolation method.
This happens most probably due to the ill-conditioned matrix
which occurs in the sphere multiquadric interpolation method, causing the results
accuracy to be unstable or inconsistent.
Ill-conditioned matrix is a matrix which is
invertible but can become non-invertible (singular) if some of its entries are changed
ever so slightly, thus small change in the constant coefficients results in a large
change in the solution.
According to Figure 5.12, the inverse distance weighting interpolation always
generates the lowest RMS error in all the four sets of reference points. This is
because IDW is one of the simplest methods, using exact interpolation and simple
averaging principle, thus the estimated values can never exceed the range of values
in the original field data.
The graph also indicates that the inverse distance
weighting and multiquadric interpolation methods have proportional relationship
between the study area’s size and the RMS error.
On the other hand, the sphere
multiquadric method did not show this trend, as explained in the paragraph above.
5.2.2
Results and Analysis According to Quantity and Distribution of
Reference Points
The analysis of the effects of the number and distribution of reference points was
done by obtaining six sets of data with different number of reference points.
For
each sets of data with a predetermined number of reference points –which are two,
four, six, nine, thirteen and eighteen reference points-, there will be two groups of
84
different pattern of reference points’ distribution, namely well distributed and
randomly distributed, of which, each group will have the same predetermined
number of reference points.
The graphical and numerical results of the TEC estimation for the well
distributed and random distributed groups in each set of predetermined data will be
compared and analysed statistically.
Besides that, comparison will also be made
among data with different number of reference points, which will also be similarly
analysed.
5.2.2.1 Dataset 1
Dataset 1 consists of a pair of reference points, each pair showing well
distributed and randomly distributed data.
Below, the Tables 5.10(a) and 5.10(b)
show the coordinates and respective TEC values while Figures 5.13(a) and 5.13(b)
illustrate the positions of those reference points:
Table 5.10(a): Two Well Distributed Reference Points:
Latitude Longitude
TEC
4.0
104.25
24.124
4.0
114.25
21.012
85
Figure 5.13(a): Positions of Two Well Distributed Reference Points.
Table 5.10(b): Two Random Distributed Reference Points:
Latitude Longitude
TEC
6.7
100.77
27.99
7.6
107.66
26.565
Figure 5.13(b): Position of Two Random Distributed Reference Points.
86
The graphical results of these two groups of reference points are shown from
Figure 5.14(a) to Figure 5.14(f) below:
Figure 5.14(a): Result of Two Well Distributed Reference Points using Multiquadric
Method.
Figure 5.14(a) shows a graphical result with smooth transition of TEC density
with a wide range of TEC density, from 19 to 42 TECU, with the lowest density at
the middle region, which is in between the two reference points, and increasing
outwardly, with the highest density at the outermost layer.
87
Figure 5.14(b): Result of Two Well Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.14(b) shows a smooth transition of density with a wave-like focus of
the lowest TEC density of 21 TECU at the middle layer, and increases both upward
and downwardly to the highest density at 65 TECU at the lowest and highest layer.
The range of TEC density were noted to be among the widest in this setting of two
reference points, which is from 21 to 65 TECU.
88
Figure 5.14(c): Result of Two Well Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.14(c) shows 4 well-demarcated region of abrupt transition of TEC
density, ranging from 21 to 24 TECU, with the lowest density of 21 TECU covering
the right half of the study area, and increases smoothly towards the left region.
89
Figure 5.14(d): Result of Two Random Distributed Reference Points using
Multiquadric Method.
Figure 5.14(d) shows a smooth transition of TEC density, with one focus of low
TEC density at the upper right region, where the two reference points are situated,
and slowly increases in TEC density outwardly as the regions are further and further
away from the two reference points.
from 24 to 96 TECU.
However, the range of TEC values is wide,
90
Figure 5.14(e): Result of Two Random Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.14(e) shows a transition of TEC density with a wave-like focus of the
highest TEC density of 109 TECU at the middle layer and lowest layer, and increases
both upward and downwardly to the lowest density at 26 TECU.
The range of TEC
density were noted to be among the widest in this setting of two reference points,
which is from 26 to109 TECU.
91
Figure 5.14(f): Result of Two Random Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.14(f) shows only 2 regions of different TEC values, with the higher
TEC density of 27 TECU covering a quarter left of the study region, then abruptly
reduces to 28 TECU.
The IDW gives the smallest range of TEC value from 27 to
28 TECU.
The RMS values, in the unit of TECU, for all the numerical results are presented
in Table 5.11 and a graph which was plotted according to it in Figure 5.15 are shown
below:
Table 5.11: RMS Error for Two Reference Points:
Interpolation
Method
Input Data
well distributed
2
random distributed
Inverse
Distance
Weighting
3.1893
6.1681
Sphere
Multiquadric
Multiquadric
31.0062
53.4530
8.7414
35.3326
92
RMS for 2 input data
60
RMS error
50
40
Well Distributed
Random Distributed
30
20
10
0
Sphere
Multiquadric
Multiquadric
IDW
Interpolation Method
Figure 5.15: RMS for Two Reference Points.
Table 5.11 and the bar graph in Figure 5.15, illustrate that the inverse distance
weighting interpolation method have the most accurate result among all three
interpolation methods for both the well and random distributed reference points.
Besides that, it also shows that the well distributed reference points generate more
accurate results than the randomly distributed reference points.
The results showing
the highest accuracy is from the well distributed reference points using inverse
distance weighting interpolation method, where the RMS error is lowest at 3.1893
TECU.
5.2.2.2 Dataset 2
Dataset 2 consists of a pair of well distributed and randomly distributed data
with four reference points.
Below, Tables 5.12(a) and 5.12(b) show the coordinates
93
and respective TEC values while Figures 5.16(a) and 5.16(b) illustrate the positions
of those reference points:
Table 5.12(a): Four Well Distributed Reference Points:
Latitude Longitude
TEC
0.5
99.5
20.176
7.5
99.5
28.965
0.5
119.5
15.0200
7.5
119.5
21.838
Figure 5.16(a): Positions of Four Well Distributed Reference Points.
Table 5.12(b): Four Random Distributed Reference Points:
Latitude Longitude
TEC
3.5
109.0
22.076
4.5
109.0
23.303
3.5
110.0
21.772
4.5
110.0
22.982
94
Figure 5.16(b): Position of Four Random Distributed Reference Points.
The graphical results of these two groups of reference points are shown from
Figure 5.17(a) to Figure 5.17(f) below:
Figure 5.17(a): Result of Four Well Distributed Reference Points using Multiquadric
Method.
95
Figure 5.17(a) shows smooth and gradual transition of TEC densitiy, ranging
from 14 to 30 TECU, with a small focus of region with the highest TEC density at
the upper left region, and the lowest density of 14 TECU at the lower right.
Figure 5.17(b): Result of Four Well Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.17(b) shows transition of TEC density with a wave-like focus of the
lowest TEC density of 64 TECU at the lowest and middle layer, and decreases both
upward and downwardly to the highest density at 15 TECU. The range of TEC
density were noted to be among the widest in this setting of four reference points,
which is from 15 to 64 TECU.
96
Figure 5.17(c): Result of Four Well Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.17(c) shows a similar pattern of distribution of TEC values as Figure
5.17(a), but with a more abrupt and less smooth transition, as compared to the
graphical result obtained via the multiquadric method.
values is smaller here, from 15 to 29 TECU.
However, the range of TEC
97
Figure 5.17(d): Result of Four Random Distributed Reference Points using
Multiquadric Method.
Figure 5.17(d) shows a smooth and gradual transition of TEC values from the
lowest density of 22 TECU in the middle of the study region and gradually increases
towards both the left and right region to the highest TEC density of 57 TECU.
range of TEC is rather wide, from 22 to 97 TECU.
The
98
Figure 5.17(e): Result of Four Random Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.17(e) shows a smooth transition of density with a wave-like focus of the
lowest TEC density of 29 TECU at the lowest and middle layer, and increases both
upward and downwardly to the highest density at 61 TECU.
The range of TEC
density were noted to be second widest in this setting of four reference points, which
is from 29 to 61 TECU.
99
Figure 5.17(f): Result of Four Random Distributed Reference Points using Inverse
Distance Weighting Method.
The Figure 5.17(f) shows only two different regions of TEC values which
changes abruptly from the small area highest density of 23 TECU in the middle
region to 22 TECU covering the rest of the study region.
The RMS values for all the numerical results are presented in Table 5.13 and a
graph plotted according to it in Figure 5.18, both of which are shown below:
Table 5.13: RMS Error for Four Reference Points:
Interpolation
Method
Input Data
well distributed
4
random distributed
Inverse
Distance
Weighting
1.9699
3.5604
Sphere
Multiquadric
Multiquadric
24.4242
26.1586
3.0555
37.8847
100
RMS for 4 Input Data
40
35
RMS error
30
25
Well Distributed
Random Distributed
20
15
10
5
0
Sphere
Multiquadric
Multiquadric
IDW
Interpolation Method
Figure 5.18: RMS for the Four Reference Points.
Table 5.13 and Figure 5.18 show that there is a large difference (about 35 TECU)
between the results from the well distributed reference points and randomly
distributed reference points using multiquadric interpolation method.
This did not
occur with the other two interpolation methods, where their differences were just
around 2 TECU.
The RMS error of the randomly distributed reference points using
multiquadric is the highest among all the results, at 37.8847 TECU.
This is
probably due to the occurrence of ill-conditioned matrix in its calculation.
Besides that, both the table and figure also show that the inverse distance
weighting interpolation method is the most accurate in both well distributed (1.9699
TECU) and randomly distributed (3.5604 TECU) reference points.
101
5.2.2.3 Dataset 3
In Dataset 3, there was a pair of well distributed and randomly distributed data,
each with six reference points.
Below, Tables 5.14(a) and 5.14(b) show the
coordinates and respective TEC values while Figures 5.19(a) and 5.19(b) illustrate
the positions of those reference points:
Table 5.14(a): Six Well Distributed Reference Points:
Latitude Longitude
TEC
1.33
116.5
16.898
6.67
102.5
27.514
3.92
106
23.495
1.33
102.5
20.663
6.67
116.5
22.61
3.93
113
21.321
Figure 5.19(a): Positions of Six Well Distributed Reference Points.
102
Table 5.14(b): Six Random Distributed Reference Points:
Latitude Longitude
TEC
5.9
116.03
22.223
1.63
110.2
19.038
6.37
114
23.369
4.58
101.13
25.784
5.35
100.3
26.900
2.27
111.85
19.584
Figure 5.19(b): Position of Six Random Distributed Reference Points.
The graphical results of these two groups of reference points are shown in Figure
5.20(a) to Figure 5.20(f) below:
103
Figure 5.20(a): Result of Six Well Distributed Reference Points using Multiquadric
Method.
Figure 5.20(a) shows a smooth transition of TEC values, from the lowest TEC
value of 17 TECU at the lower right region to the highest density of 32 TECU at the
upper left region.
The TEC values interpolated using the multiquadric method
ranges from 19 to 32 TECU.
104
Figure 5.20(b): Result of Six Well Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.20(b) shows interpolated TEC with multiple foci of highest TEC values
at 36 TECU, which reduce as it goes outwardly from each of the focus to the lowest
TEC density of 17 TECU.
105
Figure 5.20(c): Result of Six Well Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.20(c) shows interpolated TEC densities ranging from 17 to 27 TECU.
There are three foci of different densities in this reference point distribution, where
one of the foci on the right lower region was of the lowest TEC value at 17 TECU
and slowly increases until 22 TECU outwardly.
The second foci on the right lower
region shows a small region of 19 TECU which slowly increases in TEC values and
terminates in the third foci of highest TEC density of 27 TECU in the upper left
region.
106
Figure 5.20 (d): Result of Six Random Distributed Reference Points using
Multiquadric Method.
Figure 5.20(d) shows a smooth transition of TEC values from the lowest TEC
value of 19 TECU in the lower middle region and gradually increases in TEC values
outwardly to the highest TEC value of 32 TECU.
107
Figure 5.20(e): Result of Six Random Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.20(e) shows wave-like distribution of high TEC densities which is
surrounded by low TEC densities.
The range of TEC values derived from this
method in this group is 19 to 29 TECU.
108
Figure 5.20(f): Result of Six Random Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.20(f) shows well-demarcated regions of different TEC values, ranging
from 19 to 27 TECU, with the lowest TEC value at the lower middle region, whereas
the highest TEC density at the left side.
The RMS values for all the numerical results are presented in Table 5.15 and
together with its graph in Figure 5.21, are shown below:
Table 5.15: RMS Error for Six Reference Points:
Interpolation
Method
Input Data
well distributed
6
random distributed
Inverse
Distance
Weighting
2.1558
2.8925
Sphere
Multiquadric
Multiquadric
7.6308
4.8533
1.6939
4.1912
109
RMS for 6 Input Data
9
8
RMS error
7
6
5
Well Distributed
Random Distributed
4
3
2
1
0
Sphere
Multiquadric
Multiquadric
IDW
Interpolation Method
Figure 5.21: RMS for the Six Reference Points.
From the bar graph in Figure 5.21, it is noticeable that the order of accuracy for
the result, from the most accurate to least accurate, for both the well distributed and
randomly distributed reference points varies across the different interpolation
methods.
For the well distributed reference points, the most accurate result is
generated using multiquadric interpolation method, followed by inverse distance
weighting and lastly sphere multiquadric.
Whereas for the randomly distributed
reference points, in descending order of the accuracy is the inverse distance
weighting interpolation, multiquadric then followed by the sphere multiquadric
method.
In this dataset, the results from the well distributed reference points using
multiquadric method is the most accurate among all the results.
110
5.2.2.4 Dataset 4
Dataset 4 consists of a pair of well distributed and randomly distributed data
with nine reference points.
Below, Tables 5.16(a) and 5.16(b) show the coordinates
and respective TEC values while Figures 5.22(a) and 5.22(b) illustrate the positions
of those reference points:
Table 5.16(a): Nine Well Distributed Reference Points:
Latitude Longitude
TEC
7.6
99.2
29.114
1.3
100.1
21.328
6.2
119.1
21.243
0.3
118.4
15.009
3.2
111.2
21.016
4.5
105.6
24.357
2.5
110.3
20.327
7.8
108.2
26.526
5.2
112.8
22.775
Figure 5.22(a): Positions of Nine Well Distributed Reference Points.
111
Table 5.16(b): Nine Random Distributed Reference Points:
Latitude Longitude
TEC
3.8
108.3
22.675
3.2
105.7
22.645
4.6
110.2
23.029
5.3
115.2
22.014
4.6
106.1
24.323
2.5
109.7
20.500
2.3
111.9
19.584
3.2
113.1
20.436
4.6
112.6
22.235
Figure 5.22(b): Positions of Nine Random Distributed Reference Points.
The graphical results of these two groups of reference points are shown from
Figure 5.23(a) to Figure 5.23(f) below:
112
Figure 5.23(a): Result of Nine Well Distributed Reference Points using Multiquadric
Method.
Figure 5.23(a) shows a smooth transition of TEC densities, from the lowest
density of 15 TECU in the lower right region to the highest density of 30 TECU in
the upper left region.
113
Figure 5.23(b): Result of Nine Well Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.23(b) shows ten foci with highest TEC density of 33 TECU, alternating
with eleven foci with the lowest TEC value of 16 TECU.
yielded TEC values at the range of 16 to 33 TECU.
This interpolation method
114
Figure 5.23(c): Result of Nine Well Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.23(c) shows transition of TEC values which are less smooth as
compared to the graphical derived via the multiquadric method.
The graphical
result show a region of lowest TEC density of 15 TECU at the lower region which
increases step-wise towards the upper left side to the highest TEC value of 29 TECU.
115
Figure 5.23(d): Result of Nine Random Distributed Reference Points using
Multiquadric Method.
Figure 5.23(d) shows a very smooth transition of TEC values from the lowest at
19 TECU in the middle region and increases in TEC density bilaterally up to the
highest TEC value of 44 TECU on the left region.
116
Figure 5.23(e): Result of Nine Random Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.23(e) shows a very chaotic arrangement of TEC values obtained from
the Sphere Multiquadric method.
However, the range of TEC values obtained was
not very big, ranging from 19 to 26 TECU.
117
Figure 5.23(f): Result of Nine Random Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.23(f) shows well demarcated regions of five consecutive levels of TEC
densities, namely 20, 21, 22, 23 and 24 TECU. The lower right region consists of
the TEC density of 21 TECU, with 2 isolated region of the lowest Tec value, 20
TECU in the middle of it.
The TEC values increases to 22 TECU over the rest of
the study region, with two regions of 23 TECU in the middle of it and a smaller
region of the highest TEC density, 24 TECU within the region of 23 TECU.
The RMS values for all the numerical results are presented in Table 5.17 and a
graph was plotted according to it in Figure 5.24, of which both are shown as below:
Table 5.17: RMS Error for Nine Reference Points:
Interpolation
Method
Input Data
well distributed
9
random distributed
Inverse
Distance
Weighting
2.0149
3.1562
Sphere
Multiquadric
Multiquadric
6.5335
3.8358
1.1337
6.7941
118
RMS for 9 Input Data
8
7
RMS error
6
5
Well Distributed
Random Distributed
4
3
2
1
0
Sphere
Multiquadric
Multiquadric
IDW
Interpolation Method
Figure 5.24: RMS for the Nine Reference Points.
Referring to Table 5.17 and its respective graph in Figure 5.24, the difference
between the accuracy of the well distributed and randomly distributed reference
points using multiquadric interpolation is noted to be big (about 5 TECU), as
compared with the other two methods.
This indicates that the distribution of the
reference point plays an important role in the multiquadric interpolation method.
The reason for this occurrence is different as compared with the one in Dataset 2,
which was due to the ill-conditioned matrix, as the difference of the RMS value for
this dataset is still within reasonable range.
Besides that, the order of the sequence from most accurate to least accurate for
the well distributed reference points is different from the order in the randomly
distributed reference points.
For the sequence in well distributed reference points, it
starts with the multiquadric interpolation method then the inverse distance weighting
and end with the sphere multiquadric method. While the sequence for randomly
distributed reference points starts with inverse distance weighting method, which is
followed by the sphere multiquadric method, then the multiquadric method.
119
5.2.2.5 Dataset 5
Dataset 5 consists of a pair of well distributed and randomly distributed data
with thirteen reference points.
Below, Tables 5.18(a) and 5.18(b) show the
coordinates and respective TEC values while Figures 5.25(a) and 5.25(b) illustrate
the positions of those reference points:
Table 5.18(a): Thirteen Well Distributed Reference Points:
Latitude Longitude
TEC
1.3
101.1
21.05
3.99
101
25.066
7.3
101.1
28.393
2.66
105.3
22.046
5.33
105.3
25.346
1.2
109.5
18.617
4.1
109.5
22.675
7.4
109.5
25.783
2.33
113.7
19.066
5.66
113.7
22.911
1.1
117.9
16.251
4.3
117.4
20.288
7.4
117.9
22.461
120
Figure 5.25(a): Positions of Thirteen Well Distributed Reference Points.
Table 5.18(b): Thirteen Random Distributed Reference Points:
Latitude Longitude
TEC
5.9
116.03
22.223
3.17
101.72
23.784
5.32
103.13
26.004
6.37
114
23.369
1.57
103.63
20.840
5.85
118.12
21.421
5.35
100.3
26.900
3.77
101.52
24.664
3.25
113.07
20.562
1.3
100.1
21.328
0.3
118.4
15.009
4.5
105.6
24.357
7.8
108.2
26.526
121
Figure 5.25(b): Positions of Thirteen Random Distributed Reference Points.
The graphical results of the two groups of reference points are shown in Figure
5.26(a) to Figure 5.26(f) below:
Figure 5.26(a): Result of Thirteen Well Distributed Reference Points using
Multiquadric Method.
122
Figure 5.26(a) shows a very smooth transition of TEC values from the lowest
TEC density of 16 TECU on the lowest right region to the highest TEC value of 30
TECU in upper left region.
Figure 5.26(b): Result of Thirteen Well Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.26(b) shows a chaotic distribution of TEC values, with multiple foci of
lowest TEC value of 3 TECU.
However, the transition of the TEC values to the
highest TEC density is abrupt and not smooth. Furthermore, the range of TEC
values obtained via this Sphere Multiquadric method is very wide, ranging from 3 to
34 TECU.
123
Figure 5.26(c): Result of Thirteen Well Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.26(c) shows a flow of TEC values transition from the lower TEC
density in the lower right region to the higher TEC values in the upper left region.
The TEC values interpolated via the IDW method ranges from 16 to 28 TECU.
124
Figure 5.26(d): Result of Thirteen Random Distributed Reference Points using
Multiquadric Method.
Figure 5.26(d) shows a very smooth transition of TEC values from the lowest
TEC density of 15 TECU on the lowest right region to the highest TEC value of 31
TECU in upper left region.
125
Figure 5.26(e): Result of Thirteen Random Distributed Reference Points using
Sphere Multiquadric Method.
Figure 5.26(e) shows a chaotic distribution of TEC values, with multiple foci of
lowest TEC value of 3 TECU.
However, the transition of the TEC values to the
highest TEC density is abrupt and not smooth.
The range of TEC values obtained
via this Sphere Multiquadric method ranges from 16 to 30 TECU.
126
Figure 5.26(f): Result of Thirteen Random Distributed Reference Points using
Inverse Distance Weighting Method.
Figure 5.26(f) shows a flow of TEC values transition from the lowest TEC
density of 15 TECU in the lowest right region to the higher TEC values in the upper
left region, with two small regions of the highest TEC value of 27 TECU within it.
The TEC values interpolated via the IDW method ranges from 15 to 27 TECU.
The RMS values for all the numerical results are presented in Table 5.19 and
Figure 5.27 below:
Table 5.19: RMS Error for Thirteen Reference Points:
Interpolation
Method
Input Data
well distributed
13
random distributed
Inverse
Distance
Weighting
1.7981
2.2478
Sphere
Multiquadric
Multiquadric
5.3281
4.8565
0.9800
1.3310
127
RMS for 13 Input Data
6
RMS error
5
4
Well Distributed
Random Distributed
3
2
1
0
Sphere
Multiquadric
Multiquadric
IDW
Interpolation Method
Figure 5.27: RMS for the Thirteen Reference Points.
Based on Figure 5.27 and Table 5.19, the ranking from the most accurate to least
accurate for both the distribution is the same.
Both of the ranking start with
multiquadric method and end with the sphere multiquadric method.
This implies
that the effect of distribution of the reference points is not apparent in this dataset.
5.2.2.6 Dataset 6
The last dataset, dataset 6 also consists of a pair of well distributed and randomly
distributed data with eighteen reference points.
Below, Tables 5.20(a) and 5.20(b)
show the coordinates and respective TEC values while Figures 5.28(a) and 5.28(b)
illustrate the positions of those reference points:
128
Table 5.20(a): Eighteen Well Distributed Reference Points:
Latitude Longitude
TEC
3.83
103.35
24.124
7.1
117.8
22.333
6.45
100.28
27.953
3.6
108.1
22.478
1.63
110.2
19.038
5.32
103.13
26.004
6.23
102.1
27.187
6.37
114.0
23.369
1.8
114.2
18.228
1.57
103.63
20.840
7.7
109.3
26.062
5.85
118.12
21.421
4.27
117.88
20.116
5.35
100.3
26.900
1.2
99.6
21.288
3.77
101.52
24.664
0.7
106.3
18.678
3.25
113.07
20.562
Figure 5.28(a): Positions of Eighteen Well Distributed Reference Points.
129
Table 5.20(b): Eighteen Random Distributed Reference Points:
Latitude Longitude
TEC
7.8
99.3
29.233
4.9
118.1
20.608
1.4
100.2
21.461
4.1
111.7
21.974
0.6
119.2
15.231
5.3
113.1
22.764
6.2
106.1
25.978
6.3
115.4
22.758
7.2
117.2
22.639
1.5
120.6
16.071
4.5
116.1
20.936
7.8
118.1
22.585
5.2
115.8
21.707
5.3
109.3
24.068
2.4
112.7
19.493
6.7
117.5
22.209
4.2
106.8
23.631
3.2
112.1
20.742
Figure 5.28(b): Positions of Eighteen Random Distributed Reference Points.
130
The graphical results of these two groups of reference points are shown from
Figure 5.29(a) to Figure 5.29(f) below:
Figure 5.29(a): Result of Eighteen Well Distributed Reference Points using
Multiquadric Method.
Figure 5.29(a) shows a very smooth transition of TEC values from the lowest
TEC density of 17 TECU on the lowest right region to the highest TEC value of 30
TECU in upper left region.
131
Figure 5.29(b): Result of Eighteen Well Distributed Reference Points using Sphere
Multiquadric Method.
Figure 5.29(b) shows TEC values distribution which is very chaotic without any
forms of pattern and abrupt change of TEC densities without a smooth transition of
density.
The range of TEC values interpolated ranges from 19 to 28 TECU.
132
Figure 5.29(c): Result of Eighteen Well Distributed Reference Points using Inverse
Distance Weighting Method.
Figure 5.29(c) shows a flow of TEC values transition from the lower TEC
density in the lower right region to the higher TEC values in the upper left region.
The TEC values interpolated via the IDW method ranges from 18 to 28 TECU.
133
Figure 5.29(d): Result of Eighteen Random Distributed Reference Points using
Multiquadric Method.
Figure 5.29(d) shows a very smooth transition of TEC values from the lowest
TEC density of 15 TECU on the lowest right region to the highest TEC value of 30
TECU in upper left region
134
Figure 5.29(e): Result of Eighteen Random Distributed Reference Points using
Sphere Multiquadric Method.
Figure 5.29(e) shows a chaotic distribution of TEC values, with multiple foci of
lower TEC value.
However, the transition of the TEC values to the highest TEC
density is abrupt and not smooth.
The range of TEC values obtained via this Sphere
Multiquadric method ranges from 6 to 28 TECU.
135
Figure 5.29(f): Result of Eighteen Random Distributed Reference Points using
Inverse Distance Weighting Method.
Figure 5.29(f) shows a flow of TEC values transition from the lower TEC
density in the lower right region to the higher TEC values in the upper left region.
The TEC values interpolated via the IDW method ranges from 15 to 29 TECU.
The RMS values for all the numerical results are presented in Table 5.21 and a
graph in Figure 5.30 as shown below:
Table 5.21: RMS Error for Eighteen Reference Points:
Interpolation
Method
Input Data
well distributed
18
random distributed
Inverse
Distance
Weighting
2.0886
2.2436
Sphere
Multiquadric
Multiquadric
4.3781
5.7640
1.3371
1.1259
136
RMS for 18 Input Data
7
RMS error
6
5
4
Well Distributed
Random Distributed
3
2
1
0
Sphere
Multiquadric
Multiquadric
IDW
Interpolation Method
Figure 5.30: RMS for the Eighteen Reference Points.
From Table .21 and Figure 5.30 above, we can notice that the hierarchy of
accuracy, from the most accurate to least accurate result for both the well and
randomly distributed reference points is the same.
The result with the highest
accuracy is multiquadric method, followed by the inverse distance weighting method
and then the sphere multiqudric method.
The order is the similar with the results in
previous dataset, ie. dataset 5.
However, the similarity ends here, as both datasets show difference in terms of
result with the highest accuracy.
The result from the well distributed reference
points using multiquadric method is the most accurate in this dataset while for the
Dataset 5, the result from the randomly distributed reference points using
multiquadric method is the most accurate.
137
5.2.2.7 Summary of Results and Analysis According to Quantity and
Distribution of Reference Points
In this section, all of the RMS error from the above six sets of data will be used
to analyse the effects of quantity and distribution of reference points on the three
interpolation methods.
Besides that, the most accurate result among all the six sets
of data will be defined.
All of the RMS error from these six sets of data is shown in
Table 5.22 below:
Table 5.22: RMS Error for All the Six Sets of Reference Points:
Interpolation
Inverse
Method
Distance
Sphere
Input Data
2
4
6
9
13
18
Multiquadric
Multiquadric
Weighting
well distributed
3.1894
31.0062
8.7414
random distributed
6.1681
53.4531
35.3326
well distributed
1.9699
24.4242
3.0555
random distributed
3.5604
26.1586
37.8447
well distributed
2.1558
7.6308
1.6939
random distributed
2.8925
4.8533
4.1912
well distributed
2.0149
6.5335
1.1337
random distributed
3.1563
3.8358
6.7941
well distributed
1.7981
5.3281
0.9800
random distributed
2.2478
4.8565
1.3310
well distributed
2.0886
4.3781
1.3371
random distributed
2.2436
5.7640
1.1259
According to Global Positioning System Precise Positioning Service
Performance Stance, normally the ionospheric delay model errors vary from 9.8 m to
19.6 m at 95% confident level.
Based on that, a standard RMS error of 46.2 TECU
138
is set as the benchmark to determine the efficiency of the interpolation methods that
is used in this research.
From Table 5.22, most of all of the interpolation results are
below this benchmark, except for the sphere multiquadric interpolation method with
two random distributed references points, where the RMS values at 53.4531 TECU,
hence the least accurate method.
This shows that all the interpolation methods,
except for the sphere multiquadric interpolation method can be used to interpolate
the TEC for Malaysia region, regardless of the number and distribution of reference
points.
Based on Table 5.22, the most accurate result is from the thirteen well
distributed reference points, using the multiquadric interpolation method, where the
RMS values at 0.98 TECU.
For the inverse distance weighting method, the RMS error ranges from
1.7981 to 6.1681 TECU.
This is low in comparison with the other two methods.
The RMS error for the multiquadric interpolation method ranges from 3.8358 to
53.4531 TECU while for the sphere multiquadric, the RMS error ranges from 0.98 to
37.8447 TECU.
Overall, the inverse distance weighting method consistently has
small RMS values in all the different settings, in terms of number of reference points
and distribution.
Furthermore, the difference between the RMS error of the well
distributed and random distribution is small in this method as compared to other
interpolation methods.
On the other hand, the sphere multiquadric interpolation method has the highest
RMS error, which is translated as giving the least accurate results, among the three
interpolation methods, regardless of the quantity and distribution of reference points.
Besides that, the difference between the RMS error of the result between the well
distributed and the random distributed reference points was not consistent. This can
be seen in the result of dataset with two reference points who showed very big
difference in the RMS values, whereas in the thirteen reference points dataset, the
difference in the RMS values were small.
Based on this, we can say that the results
139
from the sphere multiquadric interpolation greatly depend on the number of reference
points and its distribution.
Thus, it can be concluded that this interpolation method
is rather inferior when used to estimate the TEC values of the whole Malaysian
region, as compared to the other two interpolation methods.
Similar to the sphere multiquadric interpolation method, the multiquadric
interpolation method also has the same attributes where its RMS error is dependent
on the number and distribution of the reference points.
However, the distribution of
the reference points has more influence on the results of the multiquadric
interpolation method.
A graph was plotted according to Table 5.22 and is shown in Figure 5.31.
From the graph, the difference between all the results and the effect of different
quantity and distribution on the accuracy of the results, for different interpolation
methods can be easily seen and compared.
140
RMS Error All Results
60
50
RMS error
40
IDW (Well)
IDW (Random)
Multiquadric (Well)
Multiquadric (Random)
Sphere Multiquadric (Well)
Sphere Multiqudric (Random)
30
20
10
0
0
3
6
9
12
Reference Points
15
18
Figure 5.31: RMS for All the Six Sets of Reference Points.
Figure 5.31 shows that the RMS error correlates inversely with the quantity of
reference points.
In other words, the RMS error reduces as the quantity of reference
points increases.
Furthermore, this graph also shows that reference points which
were well distributed will generate more accurate results as compared to randomly
distributed reference points.
From the graph, we can see that the random distributed reference point in the
multiquadric method will produce unstable RMS error resulting in a wave-like trend.
While with well distributed reference points, it produces consistently low RMS
values.
From the graph also, results from the sphere multiquadric interpolation
greatly depend on the number of reference points and its distribution when the
141
amount of well distributed reference points used in the interpolation is more than
nine points.
The effects of both aforementioned factors were not obviously seen in inverse
distance weighting method as compared to the other two interpolation methods, as
the IDW uses both deterministic and exact interpolation, where interpolation surfaces
passes directly through the known sample points, and the use of simple averaging
principle which gives heavier weight to the local influence by sample points which
are nearer to the interpolated points.
Thus, this static averaging method generates
interpolated values which are within the range of values in the original field data.
On the other hand, the effects of the quantity and distribution of reference points
were conspicuous in the results obtained via both multiquadric and sphere
multiquadric methods, especially in the first few datasets, namely the four randomly
distributed reference points for multiquadric method, and two reference points of
either distribution for sphere multiquadric method.
Lastly, this study found that, as a rule of thumb, the quantity of reference points
plays a bigger role in affecting the accuracy of the interpolated results as compared
to the distribution of the reference points, which by itself also plays a role.
This can
be seen from the graph above where datasets with high quantity of reference points,
tends to produce lower RMS values which translate to producing more accurate
results, regardless of the distribution.
Nevertheless, to obtain the best result
accuracy, both factors, namely high quantity and well distributed reference points are
needed.
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1
Conclusions
This study discusses the way to estimate and map the TEC over a regional area
by using some interpolation methods and the most suitable interpolation method will
be determined. A number of programs had been written on different interpolation
methods (formula) to estimate the TEC for Malaysian region using the Microsoft
Visual C++.
Since the GPS receivers, especially the dual frequency receiver, are expensive,
thus high cost is needed to observe the TEC for the whole Malaysian region. A more
cost-effective way would be to map the TEC via interpolation as it is much lower in
cost and simple to implement.
Analysis of the interpolation results in this study was performed by using the
RMS error. From the analysis, it is concluded that for all the interpolation methods,
the accuracy is dependent on the quantity of the reference points, the distribution of
the input data and the size of the study area.
Besides that, the user-defined
143
parameters such as the power, w and the small constant, c which were used in the
inverse distance weighting method; the constant, c in the multiquadric method; and
the user-specified tension parameter, R in the sphere multiquadric method, will affect
the accuracy of the result as well. The user-defined parameters can be found in the
formulas listed in Chapter 3.
Besides that, the analysis from this research had shown that the most suitable
interpolation method is the inverse distance weighting method. This is because it
produces high accuracy (according to the Global Positioning System Precise
Positioning Service Performance Stance) in all condition regardless of the quantity of
the reference points, the distribution of the reference points and the size of the study
area.
The multiquadric method is also suitable to be used in the estimation of TEC.
However, unlike the inverse distance weighting method, it requires some requisites.
The requisites are the quantity of reference points should be more than nine points
and the distribution of those reference points should be well distributed. Only when
these two requisites are fulfilled, then the multiquadric method can produce better
accuracy as compared to the inverse distance weighting method. One thing to be
cautious about when using this interpolation method is the occurrence of the illconditioned matrix. This is because the existence of the ill-conditioned matrix will
affect the accuracy of the result.
As for the sphere multiquadric method, it yielded results with the highest RMS
error, ranging from 3.8358 to 53.4531 TECU, almost in all condition, as compared to
the other two interpolation methods. Based on this, it can be concluded that the
sphere multiquadric method is not suitable to be applied in the estimation of the TEC
over the Malaysian region.
144
As a conclusion, interpolation especially the inverse distance weighting method
is suitable and good enough to be used in estimating and mapping the TEC over a
regional area. Thus, with all the conclusions reached here, all the objectives of this
research were fulfilled.
6.2
Recommendations
Interpolation can be applied to estimate the TEC over a regional area. However,
there is still room for improvement and the following recommendations can be
applied to improve this kind of study:
1. The user-defined parameters, c, w and R will affect the accuracy of the
interpolation result. Thus, the optimum value of c, w and R for Malaysia region can
be defined with another research so a more accurate TEC map can be produced.
2. Interpolation formulas can be modified by adding more parameters to produce
better results. This can be done by having more studies on the interpolation methods.
3. There are many other interpolation methods, such as the Kriging and spline
line interpolation.
All these interpolation methods can be applied in the TEC
estimation application and maybe some of it will produce a better result.
4. The GPS observation can provide information in three-dimensional, so a
three-dimensional map can be produce, when using the GPS data as input. This is
because when compared to the two-dimensional map, more information can be
shown in the three-dimensional map.
145
5. All programs that were written in this research are post-processed while the
TEC condition varies all the time. Thus, these programs can be updated or modified
to process near real-time or real-time data. In this sense, it may produce near realtime or real-time result. Besides that, these results can be published on the internet
for the access of satellite application users, especially the single frequency GPS users.
6. Improvements also can be applied to the interpolation programs so it will have
user-friendly interface and will be easier to use.
7. A TEC map with a colourful scale can be used in place of the black and white
scale used in this study to facilitate easier interpretation and provide a TEC map
which is more attractive and nice-looking.
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APPENDIX A
Numerical results of the TEC values for the whole study area, which were
derived from Model IRI-2001.
TEC generated using Model IRI-2001
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
19.496
19.355
19.216
19.094
18.957
18.821
18.686
18.551
18.418
18.286
18.154
18.023
17.893
17.763
17.634
17.506
17.378
17.251
17.124
16.998
16.872
16.747
16.622
16.498
16.374
16.25
16.127
16.004
15.881
15.759
15.638
15.517
15.396
15.275
15.155
15.036
14.917
14.798
14.68
14.562
14.445
14.328
14.212
0.50
20.317
20.176
20.035
19.914
19.776
19.639
19.503
19.367
19.232
19.098
18.964
18.832
18.699
18.568
18.437
18.306
18.175
18.046
17.916
17.787
17.658
17.529
17.401
17.273
17.145
17.018
16.891
16.764
16.637
16.511
16.254
16.259
16.134
16.009
15.884
15.759
15.635
15.511
15.388
15.265
15.142
15.02
14.898
1.00
21.134
20.992
20.851
20.731
20.592
20.454
20.317
20.18
20.044
19.908
19.773
19.638
19.504
19.37
19.236
19.103
18.97
18.837
18.705
18.572
18.44
18.308
18.176
18.045
17.913
17.782
17.65
17.519
17.388
17.257
17.126
16.996
16.865
16.735
16.605
16.475
16.345
16.216
16.087
15.958
15.829
15.701
15.573
1.50
21.939
21.798
21.678
21.538
21.398
21.259
21.121
20.983
20.846
20.709
20.572
20.435
20.299
20.163
20.027
19.891
19.755
19.619
19.484
19.348
19.212
19.077
18.941
18.805
18.67
18.534
18.398
18.262
18.127
17.991
17.855
17.719
17.583
17.448
17.312
17.176
17.041
16.906
16.771
16.636
16.501
16.366
16.232
2.00
22.727
22.608
22.468
22.328
22.188
22.049
21.91
21.771
21.632
21.493
21.355
21.217
21.078
20.94
20.801
20.663
20.524
20.385
20.246
20.107
19.968
19.829
19.689
19.549
19.409
19.269
19.128
18.988
18.847
18.706
18.565
18.424
18.282
18.141
17.999
17.858
17.716
17.575
17.433
17.292
17.151
17.01
16.869
2.50
23.516
23.375
23.235
23.095
22.956
22.816
22.676
22.536
22.396
22.256
22.116
21.976
21.835
21.695
21.554
21.412
21.271
21.129
20.986
20.844
20.701
20.557
20.413
20.269
20.125
19.98
19.834
19.689
19.543
19.397
19.25
19.103
18.956
18.809
18.661
18.513
18.365
18.218
18.07
17.922
17.774
17.626
17.478
3.00
24.253
24.114
23.974
23.834
23.695
23.554
23.414
23.273
23.132
22.991
22.849
22.707
22.565
22.421
22.278
22.134
21.989
21.844
21.698
21.552
21.405
21.257
21.109
20.961
20.811
20.662
20.511
20.361
20.209
20.057
19.905
19.753
19.6
19.446
19.292
19.138
18.984
18.83
18.675
18.52
18.365
18.211
18.056
3.50
24.956
24.818
24.679
24.539
24.4
24.259
24.118
23.977
23.835
23.692
23.549
23.405
23.26
23.115
22.969
22.822
22.674
22.526
22.377
22.227
22.076
21.924
21.772
21.618
21.465
21.31
21.155
20.998
20.842
20.684
20.526
20.368
20.209
20.049
19.889
19.729
19.568
19.407
19.246
19.084
18.923
18.761
18.599
4.00
25.62
25.483
25.345
25.206
25.066
24.926
24.785
24.643
24.5
24.356
24.211
24.065
23.919
23.771
23.623
23.473
23.322
23.171
23.018
22.864
22.709
22.554
22.397
22.239
22.081
21.921
21.761
21.599
21.437
21.274
21.111
20.946
20.781
20.616
20.449
20.283
20.115
19.948
19.78
19.611
19.443
19.274
19.105
4.50
26.242
26.106
25.969
25.831
25.692
25.551
25.41
25.267
25.124
24.979
24.833
24.685
24.537
24.387
24.236
24.084
23.93
23.775
23.619
23.462
23.303
23.143
22.982
22.82
22.657
22.493
22.327
22.161
21.993
21.825
21.656
21.486
21.315
21.143
20.971
20.798
20.624
20.45
20.275
20.1
19.925
19.75
19.574
5.00
26.819
26.685
26.549
26.412
26.274
26.134
25.992
25.849
25.705
25.559
25.412
25.263
25.113
24.961
24.808
24.653
24.496
24.338
24.179
24.018
23.856
23.692
23.527
23.36
23.193
23.024
22.853
22.682
22.509
22.336
22.161
21.985
21.808
21.631
21.453
21.273
21.094
20.913
20.732
20.551
20.369
20.187
20.004
5.50
27.353
27.22
27.086
26.95
26.812
26.672
26.531
26.388
26.243
26.096
25.948
25.789
25.646
25.492
25.337
25.18
25.021
24.86
24.697
24.533
24.367
24.2
24.031
23.86
23.688
23.514
23.339
23.163
22.986
22.807
22.627
22.445
2.263
22.08
21.896
21.71
21.525
21.338
21.151
20.963
20.775
20.586
20.397
6.00
27.843
27.712
27.579
27.445
27.308
27.169
27.028
26.885
26.739
26.592
26.443
26.292
26.138
25.983
25.825
25.666
25.504
25.341
25.175
25.008
24.839
24.668
24.495
24.32
24.144
23.966
23.786
23.605
23.423
23.239
23.054
22.867
22.679
22.491
22.301
22.11
21.918
21.726
21.533
21.339
21.144
20.949
20.754
6.50
28.293
28.164
28.033
27.9
27.764
27.625
27.485
27.342
27.196
27.049
26.898
26.746
26.591
26.434
26.275
26.113
25.949
25.783
25.615
25.444
25.272
25.097
24.921
24.742
24.562
24.38
24.196
24.01
23.823
23.634
23.444
23.252
23.06
22.865
22.67
22.474
22.276
22.078
21.879
21.679
21.479
21.278
21.076
7.00
28.708
28.581
28.451
28.319
28.184
28.046
27.906
27.763
27.617
27.469
27.318
27.164
27.008
26.85
26.688
26.525
26.359
26.19
26.019
25.845
25.669
25.492
25.311
25.129
24.945
24.759
24.57
24.38
24.189
23.995
23.8
23.603
23.405
23.206
23.005
22.803
22.601
22.397
22.192
21.983
21.78
21.573
21.366
7.50
29.091
28.965
28.837
28.706
28.571
28.434
28.294
28.151
28.005
27.856
27.704
27.55
27.392
37.232
27.069
26.903
26.735
26.564
26.39
26.213
26.034
25.583
25.669
25.483
25.295
25.105
24.912
24.718
24.521
24.323
24.123
23.922
23.719
23.514
23.308
23.101
22.893
22.684
22.473
22.262
22.05
21.838
21.625
8.00
29.447
29.323
29.196
29.065
28.931
28.794
28.654
28.105
28.364
28.214
28.062
27.906
27.747
27.585
27.42
27.252
27.081
26.907
26.73
26.551
26.368
26.184
25.996
25.807
25.614
25.42
25.223
25.024
24.824
24.621
24.416
24.21
24.002
23.792
23.581
23.369
23.155
22.94
22.725
22.508
22.29
22.072
21.854
161
APPENDIX B
Numerical results for the TEC values derived via three interpolation methods
for four different study areas’ size.
Numerical results for 1°x 1° grid size using multiquadric method
Coor.
99.00
99.50
100.00
7.00
28.708
28.0859
28.451
7.50
28.5919
27.9678
28.3338
8.00
29.447
28.8398
29.196
Numerical results for 1°x 1° grid size using sphere multiquadric method
Coor.
99.00
99.50
100.00
7.00
28.708
28.4799
28.451
7.50
26.2926
25.3484
26.312
8.00
29.447
29.4896
29.196
Numerical results for 1°x 1° grid size using IDW method
Coor.
99.00
99.50
100.00
7.00
28.7098
28.7063
28.4525
7.50
29.0045
28.9369
28.8345
8.00
29.4455
29.2049
29.1954
163
Numerical results for 2°x 2° grid size using multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
6.00
28.0052
26.8386
26.3277
26.4961
27.342
6.50
27.3857
26.1993
25.6774
25.8451
26.7011
7.00
27.4435
26.258
25.7343
25.8981
26.7484
7.50
28.1619
26.997
26.4806
26.6378
27.4683
8.00
29.4988
28.372
27.8712
28.0204
28.8195
Numerical results for 2°x 2° grid size using sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
6.00
28.2545
28.9438
29.3746
28.7313
27.4324
6.50
29.4223
28.6355
28.7164
28.5101
29.0733
7.00
30.0174
29.0866
28.8777
29.1039
30.0437
7.50
29.2155
28.9189
28.874
29.0881
29.5534
8.00
29.3754
29.5269
29.5074
29.2375
28.8658
Numerical results for 2°x 2° grid size using IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
6.00
27.844
27.9016
27.8473
27.5141
27.3088
6.50
27.9781
28.0422
28.0146
27.7372
27.528
7.00
28.5245
28.4767
28.3672
28.2408
28.1731
7.50
29.1879
29.0096
28.7365
28.6866
28.7541
8.00
29.4462
29.2671
28.9268
28.8577
28.9307
164
Numerical results for 4°x 4° grid size using multiquadric method
Coor.
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
99.00
25.7108
25.1747
24.9698
25.0755
25.4652
26.1152
27.009
28.1365
29.489
99.50
24.5672
24.0157
23.8026
23.9075
24.3036
24.9671
25.8806
27.0329
28.4147
100.00
23.7112
23.1451
22.9206
23.0193
23.4158
24.0863
25.013
26.1835
27.5871
100.50
23.1332
22.5547
22.3188
22.4093
22.8022
23.4746
24.4082
25.5897
27.0073
101.00
22.8223
22.2345
21.9901
22.0734
22.4615
23.1317
24.0661
25.2511
26.6749
101.50
22.7753
22.1823
21.9333
22.0123
22.3956
23.0605
23.9896
25.1706
26.5926
102.00
23.0011
22.4068
22.1573
22.2341
22.6122
23.2684
24.1863
25.3557
26.7679
102.50
23.5173
22.9257
22.6775
22.7522
23.1228
23.7662
24.6673
25.818
27.2123
103.00
24.342
23.7561
23.5085
23.5779
23.9369
24.5628
25.4418
26.5677
27.9361
Numerical results for 4°x 4° grid size using sphere multiquadric method
Coor.
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
99.00
25.5986
26.9182
28.1476
30.3462
32.7848
33.9183
33.239
30.766
29.3906
99.50
28.3568
27.5685
27.0446
27.5877
30.3896
32.0316
31.8532
29.8593
29.8207
100.00
30.8124
28.2774
26.2004
25.0656
28.5815
30.5605
30.7511
29.1547
30.1908
100.50
32.3267
28.7974
25.9208
25.6796
28.1224
29.9097
30.2144
28.9454
30.3875
101.00
32.7918
28.9651
25.9856
26.2865
28.3591
29.9595
30.2665
29.1576
30.368
101.50
32.1865
28.7292
26.1673
26.3807
28.7129
30.466
30.7936
29.6028
30.1245
102.00
30.5713
28.1429
26.543
26.0311
29.3822
31.4286
31.6996
30.1979
29.6834
102.50
28.0838
27.3707
27.3193
27.8845
31.0533
32.9222
32.8771
30.9013
29.1074
103.00
25.0294
26.681
28.3305
30.6281
33.3014
34.6469
34.0924
31.5805
28.5349
Numerical results for 2°x 2° grid size using IDW method
Coor.
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
99.00
25.6203
25.6978
25.9975
26.5622
27.335
28.1673
28.8734
29.3106
29.4465
99.50
25.6712
25.7577
26.048
26.5768
27.2927
28.0701
28.7487
29.1899
29.343
100.00
25.788
25.8971
26.1653
26.6185
27.218
27.869
28.4501
28.8536
29.0279
100.50
25.8476
25.978
26.2265
26.6126
27.107
27.6335
28.1012
28.4395
28.6182
101.00
25.7376
25.8856
26.1426
26.5147
26.9677
27.4294
27.8237
28.1066
28.2735
101.50
25.4348
25.5958
25.8994
26.3271
26.8222
27.3018
27.6905
27.9543
28.1049
102.00
25.0261
25.1858
25.5547
26.0894
26.697
27.2684
27.7138
27.9935
28.126
102.50
24.6699
24.8093
25.2247
25.868
26.6114
27.3069
27.8353
28.1421
28.2523
103.00
24.5051
24.6235
25.0457
25.7411
26.5708
27.3536
27.9389
28.2608
28.3534
Numerical results for 8°x 8° grid size using multiquadric method
Coor.
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
99.00
19.5471
19.4659
19.5435
19.7632
20.1046
20.5484
21.0788
21.6835
22.3532
23.0807
23.8607
24.6889
25.562
26.4779
27.4346
28.4309
29.4655
99.50
18.811
18.7262
18.8007
19.0187
19.3601
19.806
20.3406
20.9512
21.6284
22.3649
23.1548
23.9939
24.8788
25.807
26.7766
27.7861
28.8342
100.00
18.1989
18.1087
18.1754
18.3849
18.7192
19.1602
19.6926
20.3037
20.9838
21.7252
22.5218
23.369
24.2632
25.2016
26.1822
27.2032
28.2632
100.50
17.696
17.5994
17.6556
17.8527
18.175
18.6063
19.1318
19.7393
20.4185
21.1615
21.9619
22.8146
23.7157
24.6623
25.652
26.6828
27.7529
101.00
17.2839
17.1808
17.2258
17.4092
17.7179
18.1372
18.6535
19.2546
19.9305
20.6727
21.4744
22.3304
23.2365
24.1892
25.186
26.2248
27.3034
101.50
16.9459
16.8368
16.8716
17.0423
17.3379
17.7453
18.2519
18.846
19.5172
20.2571
21.0586
21.9161
22.8251
23.7821
24.7843
25.8292
26.9146
102.00
16.6695
16.5551
16.5814
16.7419
17.0267
17.4242
17.9223
18.5098
19.1764
19.9134
20.7136
21.5713
22.4816
23.4411
24.4468
25.4961
26.5868
102.50
16.4466
16.3277
16.3479
16.5012
16.7786
17.1691
17.6612
18.2436
18.9064
19.6406
20.4391
21.2958
22.2062
23.1665
24.174
25.2261
26.3204
103.00
16.2728
16.1505
16.167
16.3166
16.5905
16.9777
17.4668
18.0465
18.7068
19.4389
20.2353
21.0904
21.9995
22.9591
23.9667
25.0198
26.1163
103.50
16.1477
16.0229
16.0384
16.188
16.4624
16.8503
17.3397
17.9193
18.5788
19.3093
20.1037
20.9563
21.8629
22.8203
23.8262
24.8787
25.9758
104.00
16.0741
15.948
15.965
16.1184
16.3974
16.7897
17.2828
17.8646
18.5247
19.2544
20.0466
20.896
21.7987
22.7521
23.7545
24.8045
25.9005
104.50
16.0585
15.9322
15.9535
16.114
16.4013
16.8016
17.3009
17.8868
18.5487
19.2777
20.0673
20.9124
21.8098
22.7574
23.7543
24.7998
25.8931
105.00
16.1118
15.9863
16.0141
16.1847
16.4832
16.8937
17.401
17.9919
18.6557
19.3838
20.1699
21.0095
21.8999
22.8398
23.8292
24.8682
25.9568
105.50
16.2497
16.1259
16.1617
16.3439
16.6548
17.0761
17.5913
18.1867
18.8516
19.5777
20.359
21.1916
22.0733
23.0037
23.9835
25.014
26.096
106.00
16.4924
16.3708
16.4144
16.6075
16.9293
17.3595
17.8804
18.4782
19.1421
19.8642
20.639
21.463
22.3346
23.2538
24.2223
25.2425
26.3161
106.50
16.8624
16.7425
16.7916
16.9917
17.3198
17.754
18.2761
18.8722
19.5318
20.2473
21.0135
21.8273
22.6874
23.5945
24.5507
25.5592
26.6226
107.00
17.3782
17.2589
17.3088
17.5089
17.8356
18.2666
18.7836
19.3727
20.0237
20.7293
21.4846
22.2866
23.1344
24.0287
24.9722
25.9684
27.02
165
Numerical results for 8°x 8° grid size using sphere multiquadric method
Coor.
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
99.00
19.7796
22.0298
24.3162
26.7423
31.0717
33.3583
34.8325
35.3773
34.9002
33.3258
30.6361
26.9034
22.3179
20.5403
23.0794
25.2006
29.3273
99.50
19.6674
20.5044
23.3434
26.7915
31.659
35.2611
37.4397
37.9354
36.7095
33.9083
29.8736
25.1949
20.9699
19.6016
21.6238
24.7526
29.1442
100.00
19.2927
20.0935
23.2937
26.9765
31.159
35.3384
37.8527
38.4654
37.1474
34.0686
29.6387
24.6299
20.4677
19.2115
21.3145
24.9176
28.4436
100.50
17.9271
20.2769
24.2053
27.288
29.8534
33.7571
36.1956
37.0195
36.1853
33.7736
29.9898
25.1703
19.9545
18.3032
22.0047
25.7443
27.4759
101.00
21.4303
23.2587
26.2011
27.6813
28.2041
30.8581
32.7047
33.802
34.017
33.0986
30.8768
27.386
23.1161
21.6824
24.6105
27.1763
26.78
101.50
28.555
28.4365
28.8698
28.0693
26.5674
27.1277
27.6736
29.183
31.0906
32.2104
32.0979
30.8664
29.2048
28.3545
28.6344
28.9109
26.4577
102.00
33.9323
32.8972
31.2746
28.3213
25.194
23.5076
21.608
24.1388
28.2011
31.3284
33.3302
34.2464
34.2514
33.5547
32.2673
30.3882
26.2354
102.50
37.2242
35.6252
32.6453
28.3072
24.3657
21.4688
19.5081
21.7039
26.2442
30.665
34.2498
36.5903
37.4423
36.7163
34.4841
31.0348
26.1718
103.00
38.3115
36.3745
32.6984
28.0227
24.2482
20.8846
19.3532
21.1167
25.4249
30.3711
34.6345
37.4904
38.5602
37.7017
34.9749
30.6778
26.3484
103.50
37.259
35.2352
31.5766
27.591
24.9001
21.0909
18.3601
20.6444
25.6465
30.5152
34.4029
36.8584
37.6211
36.5943
33.8364
29.5512
26.7998
104.00
34.2606
32.4811
29.6658
27.1836
26.3401
23.1058
19.3976
22.3892
27.2545
31.076
33.6172
34.8332
34.7942
33.6176
31.387
28.1266
27.4935
104.50
29.5777
28.5049
27.4077
26.912
28.3324
27.2839
26.56
27.8298
30.1757
31.9286
32.4695
31.7898
30.3734
29.0687
28.0743
26.8018
28.3194
105.00
23.5129
24.051
25.2683
26.7705
30.2693
31.5119
32.3958
33.0796
33.3682
32.858
31.2458
28.4724
24.9523
23.414
24.6265
25.6822
29.0773
105.50
19.4687
21.0882
23.7778
26.7475
31.4652
34.4071
36.2337
36.7311
35.8412
33.6236
30.2483
25.9937
21.354
19.7294
22.255
24.9368
29.3376
106.00
19.6274
20.285
23.2115
26.8549
31.5655
35.5145
37.8845
38.4152
37.0748
34.0342
29.7014
24.832
20.7884
19.5123
21.3891
24.7447
28.8875
106.50
18.8161
20.0247
23.5602
27.0977
30.6662
34.8391
37.3762
38.0722
36.8958
33.9946
29.7189
24.6973
20.1654
18.8325
21.447
25.1943
28.0391
107.00
17.453
21.0877
24.943
27.4526
29.1541
32.6378
34.8909
35.825
35.3737
33.5195
30.3167
25.9081
20.5428
18.6033
22.8627
26.3017
27.0969
166
Numerical results for 8°x 8° grid size using IDW method
Coor.
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
99.00
19.4962
19.5452
19.7185
20.0456
20.5452
21.2205
22.0569
23.0234
24.075
25.1572
26.2105
27.1766
28.004
28.6546
29.1082
29.3658
29.4467
99.50
19.5354
19.5888
19.7646
20.0912
20.5857
21.2497
22.0684
23.0119
24.0379
25.0955
26.1293
27.0838
27.9084
28.5637
29.0264
29.2935
29.3818
100.00
19.6554
19.7223
19.9049
20.2289
20.7088
21.3451
22.1235
23.0165
23.9861
24.9868
25.9688
26.8818
27.679
28.322
28.7858
29.0638
29.1682
100.50
19.8309
19.9172
20.1084
20.4263
20.8832
21.479
22.201
23.0251
23.9178
24.8392
25.7459
26.5937
27.3415
27.9546
28.4086
28.6944
28.8198
101.00
20.022
20.1297
20.3287
20.6375
21.0664
21.6157
22.2748
23.0231
23.8314
24.6646
25.4847
26.254
26.9375
27.5061
27.9386
28.2258
28.3719
101.50
20.1813
20.3089
20.5145
20.8134
21.2149
21.7201
22.3204
22.9981
23.7271
24.476
25.2112
25.9001
26.5142
27.0303
27.4324
27.7129
27.875
102.00
20.2636
20.4074
20.6192
20.9115
21.2927
21.7643
22.3191
22.9411
23.6064
24.2857
24.9485
25.5665
26.116
26.5799
26.9476
27.2152
27.3862
102.50
20.234
20.3898
20.609
20.9019
21.2754
21.7305
22.26
22.8485
23.4728
24.1049
24.7161
25.2808
25.7792
26.1991
26.5346
26.7862
26.959
103.00
20.0741
20.2374
20.4667
20.77
21.1519
21.6114
22.1401
22.7213
23.3317
23.9435
24.5286
25.0632
25.5299
25.9196
26.2305
26.4665
26.6352
103.50
19.7858
19.9515
20.1933
20.517
20.9241
21.4098
21.9629
22.5644
23.1894
23.8093
24.396
24.9259
25.3829
25.7594
26.056
26.2793
26.4393
104.00
19.3908
19.553
19.8077
20.1594
20.6056
21.1371
21.738
22.3856
23.0524
23.7077
24.3226
24.8726
25.3413
25.7215
26.0143
26.2282
26.3757
104.50
18.9288
19.0804
19.3454
19.7277
20.2217
20.813
21.4799
22.1949
22.9262
23.6405
24.3063
24.8974
25.3959
25.7933
26.0907
26.2975
26.4288
105.00
18.4515
18.5859
18.8553
19.2653
19.8082
20.465
21.2081
22.0038
22.8153
23.6049
24.3376
24.9844
25.5244
25.9474
26.2538
26.4539
26.5659
105.50
18.015
18.1278
18.3944
18.8239
19.4089
20.1273
20.946
21.8253
22.7221
23.5934
24.3996
25.1075
25.6929
26.1435
26.459
26.6517
26.743
106.00
17.67
17.7611
18.0189
18.4573
19.071
19.8374
20.7198
21.673
22.6477
23.5949
24.4694
25.2334
25.8596
26.3337
26.656
26.8407
26.9129
106.50
17.4526
17.5269
17.7736
18.2107
18.8367
19.6306
20.5545
21.5597
22.5917
23.5959
24.5217
25.3272
25.9823
26.4721
26.7979
26.9761
27.0346
107.00
17.3783
17.4449
17.6822
18.1108
18.7331
19.531
20.4681
21.4944
22.5528
23.5845
24.5355
25.3607
26.0288
26.5249
26.8518
27.0274
27.0809
167
APPENDIX C
Numerical results of TEC values derived from the three interpolation
methods for twelve sets of reference points with different quantity and distribution.
TEC generated using two well distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
42.3383
40.8347
39.3629
37.9285
36.5374
35.1965
33.9134
32.696
31.5522
30.4891
29.5123
28.6254
27.8294
27.1226
26.5017
25.9618
25.4973
25.1032
24.775
24.5093
24.3043
24.1594
24.0757
24.0559
24.1041
24.2261
24.4287
24.7193
25.1056
25.5945
26.1911
26.8978
27.7137
28.635
29.6547
30.7644
31.9543
33.2147
34.5363
35.9108
37.3305
38.789
40.2807
0.50
41.6838
40.149
38.6441
37.1749
35.7476
34.3699
33.0503
31.7981
30.6226
29.5326
28.5351
27.6343
26.831
26.1229
25.5049
24.9703
24.512
24.1232
23.7984
23.5334
23.3257
23.1747
23.0814
23.0488
23.0818
23.1869
23.3723
23.6474
24.0221
24.5053
25.104
25.8218
26.6579
27.6074
28.6617
29.8103
31.0415
32.3439
33.707
35.1214
36.5792
38.0735
39.5987
1.00
41.101
39.5363
37.9995
36.496
35.0328
33.618
32.2611
30.9728
29.7645
28.6469
27.6287
26.7153
25.9073
25.2012
24.5899
24.0644
23.6155
23.2348
22.9155
22.6526
22.4431
22.2861
22.1826
22.1361
22.1516
22.237
22.4018
22.6575
23.0164
23.4903
24.0887
24.8165
25.6732
26.6523
27.7433
28.9328
30.2068
31.5521
32.9568
34.4108
35.9057
37.4345
38.9916
1.50
40.5953
39.003
37.4361
35.9001
34.402
32.9506
31.5563
30.2315
28.9895
27.8437
26.8051
25.8806
25.0707
24.3702
23.7694
23.2566
22.8203
22.4501
22.1382
21.8786
21.668
21.5054
21.3917
21.3303
21.3271
21.3906
21.5318
21.7642
22.1033
22.5642
23.1595
23.8962
24.7737
25.7839
26.9131
28.1448
29.4623
30.8502
32.2956
33.7876
35.3176
36.8786
38.4652
2.00
40.1723
38.5554
36.9613
35.3955
33.8652
32.3791
30.9488
29.5879
28.3124
27.1384
26.0802
25.1462
24.3372
23.6456
23.0588
22.5617
22.1401
21.7822
21.4788
21.2235
21.0126
20.8448
20.7211
20.6451
20.6229
20.6634
20.7792
20.9858
21.3018
21.7463
22.3359
23.0801
23.9783
25.0202
26.1882
27.4619
28.8217
30.2504
31.7338
33.2608
34.8226
36.4124
38.025
2.50
39.837
38.1994
36.5825
34.9912
33.4326
31.9159
30.4528
29.0586
27.7514
26.5507
25.4741
24.5327
23.7268
23.0467
22.4758
21.9957
21.5897
21.2444
20.9497
20.6989
20.4882
20.316
20.1835
20.0941
20.0539
20.0725
20.1632
20.3435
20.635
21.0611
21.6428
22.393
23.3111
24.3836
25.5886
26.9017
28.3003
29.7654
31.2822
32.8393
34.4281
36.0421
37.6763
3.00
39.5938
37.9408
36.3063
34.6953
33.1146
31.5733
30.0836
28.6617
27.3275
26.1039
25.0118
24.0649
23.2635
22.5952
22.0396
21.5753
21.1834
20.8492
20.5622
20.3155
20.1052
19.9298
19.7902
19.6898
19.6348
19.6348
19.7038
19.8606
20.1294
20.5377
21.1111
21.8656
22.8008
23.9001
25.137
26.4831
27.9134
29.4077
30.9508
32.5313
34.1408
35.7732
37.4237
3.50
39.4464
37.7836
36.1381
34.5147
32.9198
31.3626
29.8553
28.4147
27.0621
25.8224
24.7197
23.7695
22.9721
22.3128
21.7687
21.3158
20.9337
20.6072
20.3256
20.0818
19.8718
19.6943
19.5501
19.4426
19.3777
19.3652
19.4193
19.5596
19.812
20.207
20.7737
21.5309
22.4781
23.5961
24.8549
26.2234
27.6748
29.1882
30.7482
32.3436
33.9662
35.61
37.2706
4.00
39.397
37.7309
36.0817
34.4539
32.8542
31.2914
29.7779
28.3307
26.9715
25.7261
24.6195
23.6681
22.8723
22.2166
21.6767
21.2279
20.8495
20.5258
20.246
20.0032
19.7934
19.6152
19.4694
19.3594
19.2911
19.2741
19.3228
19.4571
19.7035
20.0935
20.6577
21.4158
22.3673
23.4921
24.7589
26.1353
27.5941
29.1141
30.68
32.2805
33.9075
35.5552
37.2193
4.50
39.4464
37.7836
36.1381
34.5147
32.9198
31.3626
29.8553
28.4147
27.0621
25.8224
24.7197
23.7695
22.9721
22.3128
21.7687
21.3158
20.9337
20.6072
20.3256
20.0818
19.8718
19.6943
19.5501
19.4426
19.3777
19.3652
19.4193
19.5596
19.812
20.207
20.7737
21.5309
22.4781
23.5961
24.8549
26.2234
27.6748
29.1882
30.7482
32.3436
33.9662
35.61
37.2706
5.00
39.5938
37.9408
36.3063
34.6953
33.1146
31.5733
30.0836
28.6617
27.3275
26.1039
25.0118
24.0649
23.2635
22.5952
22.0396
21.5753
21.1834
20.8492
20.5622
20.3155
20.1052
19.9298
19.7902
19.6898
19.6348
19.6348
19.7038
19.8606
20.1294
20.5377
21.1111
21.8656
22.8008
23.9001
25.137
26.4831
27.9134
29.4077
30.9508
32.5313
34.1408
35.7732
37.4237
5.50
39.837
38.1994
36.5825
34.9912
33.4326
31.9159
30.4528
29.0586
27.7514
26.5507
25.4741
24.5327
23.7268
23.0467
22.4758
21.9957
21.5897
21.2444
20.9497
20.6989
20.4882
20.316
20.1835
20.0941
20.0539
20.0725
20.1632
20.3435
20.635
21.0611
21.6428
22.393
23.3111
24.3836
25.5886
26.9017
28.3003
29.7654
31.2822
32.8393
34.4281
36.0421
37.6763
6.00
40.1723
38.5554
36.9613
35.3955
33.8652
32.3791
30.9488
29.5879
28.3124
27.1384
26.0802
25.1462
24.3372
23.6456
23.0588
22.5617
22.1401
21.7822
21.4788
21.2235
21.0126
20.8448
20.7211
20.6451
20.6229
20.6634
20.7792
20.9858
21.3018
21.7463
22.3359
23.0801
23.9783
25.0202
26.1882
27.4619
28.8217
30.2504
31.7338
33.2608
34.8226
36.4124
38.025
6.50
40.5953
39.003
37.4361
35.9001
34.402
32.9506
31.5563
30.2315
28.9895
27.8437
26.8051
25.8806
25.0707
24.3702
23.7694
23.2566
22.8203
22.4501
22.1382
21.8786
21.668
21.5054
21.3917
21.3303
21.3271
21.3906
21.5318
21.7642
22.1033
22.5642
23.1595
23.8962
24.7737
25.7839
26.9131
28.1448
29.4623
30.8502
32.2956
33.7876
35.3176
36.8786
38.4652
7.00
41.101
39.5363
37.9995
36.496
35.0328
33.618
32.2611
30.9728
29.7645
28.6469
27.6287
26.7153
25.9073
25.2012
24.5899
24.0644
23.6155
23.2348
22.9155
22.6526
22.4431
22.2861
22.1826
22.1361
22.1516
22.237
22.4018
22.6575
23.0164
23.4903
24.0887
24.8165
25.6732
26.6523
27.7433
28.9328
30.2068
31.5521
32.9568
34.4108
35.9057
37.4345
38.9916
7.50
41.6838
40.149
38.6441
37.1749
35.7476
34.3699
33.0503
31.7981
30.6226
29.5326
28.5351
27.6343
26.831
26.1229
25.5049
24.9703
24.512
24.1232
23.7984
23.5334
23.3257
23.1747
23.0814
23.0488
23.0818
23.1869
23.3723
23.6474
24.0221
24.5053
25.104
25.8218
26.6579
27.6074
28.6617
29.8103
31.0415
32.3439
33.707
35.1214
36.5792
38.0735
39.5987
8.00
42.3383
40.8347
39.3629
37.9285
36.5374
35.1965
33.9134
32.696
31.5522
30.4891
29.5123
28.6254
27.8294
27.1226
26.5017
25.9618
25.4973
25.1032
24.775
24.5093
24.3043
24.1594
24.0757
24.0559
24.1041
24.2261
24.4287
24.7193
25.1056
25.5945
26.1911
26.8978
27.7137
28.635
29.6547
30.7644
31.9543
33.2147
34.5363
35.9108
37.3305
38.789
40.2807
169
TEC generated using two well distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
43.0572
43.6736
44.349
44.7637
45.6632
47.929
50.8374
52.8878
53.2073
51.6122
48.5281
45.1419
43.2116
43.2497
44.0044
44.5389
45.0232
46.4759
49.2062
51.9012
53.2635
52.7405
50.4082
46.9956
44.0398
43.0433
43.5681
44.279
44.706
45.4732
47.5577
50.4723
52.7041
53.2771
51.9256
48.9897
45.5445
43.3402
43.1717
43.9075
44.4858
44.9284
46.1959
0.50
53.3255
53.3295
53.7477
54.3977
55.4747
57.1227
58.9497
60.2178
60.3672
59.2683
57.2669
55.1245
53.6826
53.2481
53.4809
53.9958
54.7953
56.1281
57.9348
59.6096
60.4384
60.0345
58.4743
56.3011
54.3769
53.3808
53.2962
53.6795
54.2933
55.2977
56.8792
58.7232
60.1056
60.4212
59.4784
57.5604
55.3841
53.8145
53.2564
53.4286
53.9154
54.6635
55.9163
1.00
60.6898
60.5228
60.722
61.2166
61.9725
62.9079
63.8123
64.3944
64.4268
63.8653
62.8828
61.8085
60.9767
60.5666
60.5695
60.9025
61.5147
62.3653
63.3206
64.1207
64.4836
64.2509
63.4739
62.4067
61.4026
60.7441
60.5219
60.6775
61.1352
61.8589
62.7796
63.7044
64.3453
64.458
63.9699
63.0265
61.9434
61.0646
60.5956
60.5484
60.8416
61.4183
62.242
1.50
64.5625
64.525
64.5466
64.6219
64.7335
64.8555
64.9587
65.0167
65.014
64.9503
64.8422
64.7175
64.6077
64.5391
64.5271
64.5734
64.6672
64.7868
64.9043
64.9906
65.0234
64.9932
64.9075
64.7883
64.6663
64.5717
64.5266
64.5404
64.6093
64.7174
64.8398
64.9471
65.0123
65.018
64.9619
64.8582
64.7339
64.6204
64.5452
64.5252
64.5642
64.6527
64.7704
2.00
64.6765
64.9887
64.877
64.3589
63.5946
62.8241
62.2617
62.0132
62.0772
62.4083
62.9587
63.6545
64.3537
64.8588
64.9948
64.6957
64.0444
63.2469
62.5455
62.1136
62.005
62.1907
62.6232
63.249
63.9682
64.6084
64.9702
64.9172
64.4466
63.7019
62.9182
62.3193
62.0274
62.0522
62.3507
62.8751
63.558
64.2676
64.81
65.0019
64.759
64.1446
63.3522
2.50
61.0595
61.8842
61.6874
60.4792
58.6682
56.9378
55.8842
55.6226
55.8791
56.4346
57.3362
58.6867
60.2682
61.5265
61.9332
61.2724
59.7313
57.8655
56.3779
55.6855
55.6887
56.0861
56.7737
57.8692
59.3723
60.8894
61.829
61.7762
60.6869
58.9201
57.1378
55.9753
55.6202
55.8257
56.3442
57.191
58.4849
60.0633
61.3994
61.9399
61.419
59.9697
58.1058
3.00
54.0606
55.4982
55.2682
53.361
50.3786
47.5789
46.2726
46.4291
47.0372
47.5615
48.356
50.1463
52.7154
54.8639
55.6172
54.6268
52.1402
49.0507
46.7898
46.2178
46.6892
47.2734
47.8258
48.988
51.2276
53.77
55.3964
55.401
53.6959
50.7972
47.8848
46.3438
46.3609
46.9588
47.4922
48.2054
49.8439
52.3706
54.6442
55.6161
54.8559
52.5315
49.446
3.50
44.4701
46.488
46.2753
43.8206
39.643
35.4124
34.2444
35.5646
36.6944
36.8398
36.7256
38.6752
42.525
45.5987
46.6807
45.4706
42.1625
37.6425
34.4112
34.7109
36.1616
36.8725
36.7136
37.1925
40.2921
44.0563
46.3429
46.4369
44.2639
40.2561
35.8617
34.1835
35.3625
36.5994
36.8685
36.6798
38.246
42.0141
45.2918
46.6679
45.7611
42.7013
38.2458
4.00
34.023
36.0921
35.927
33.5376
29.0811
22.9396
22.8179
25.7488
27.1398
26.8664
24.9962
26.7122
31.9071
35.1891
36.2976
35.1583
31.8442
26.5828
20.9926
24.2589
26.5529
27.2267
26.2362
24.0769
29.1681
33.5861
35.9445
36.0787
33.9787
29.7819
23.8152
22.3381
25.4431
27.0501
26.9986
25.3224
25.9213
31.3186
34.8752
36.2798
35.4378
32.4029
27.3799
4.50
26.1815
26.7816
26.6756
25.8612
24.6047
23.4258
22.8314
22.8329
23.0694
23.3315
23.7405
24.5378
25.6191
26.5175
26.8285
26.4002
25.345
24.048
23.081
22.7782
22.9264
23.1799
23.4744
24.0325
24.9958
26.06
26.7395
26.7331
26.0034
24.7802
23.5563
22.87
22.8111
23.0354
23.2938
23.6676
24.408
25.4749
26.4256
26.8292
26.4983
25.5101
24.2138
5.00
22.4475
22.8162
23.1877
23.3869
23.8412
25.0743
26.6759
27.8023
27.9803
27.112
25.423
23.5584
22.5111
22.5693
23.0019
23.2828
23.5111
24.2783
25.7778
27.2606
28.009
27.7269
26.4539
24.5799
22.954
22.4346
22.7558
23.151
23.3603
23.7412
24.8701
26.4751
27.7014
28.018
27.283
25.6765
23.7801
22.5778
22.5218
22.9481
23.257
23.4647
24.1266
5.50
24.9617
27.5172
28.4712
27.7305
25.7535
29.7105
34.5205
37.2931
37.7818
35.948
31.9207
26.0708
23.0828
26.2473
28.139
28.3546
26.927
26.5287
32.0154
35.9937
37.7916
37.2681
34.4572
29.5681
23.3988
24.5254
27.2648
28.4427
27.9229
25.9798
28.9549
33.9903
37.0538
37.8514
36.3223
32.5723
26.9213
22.7315
25.8798
27.9821
28.4243
27.1986
25.9742
6.00
36.3478
37.5948
38.4217
38.4718
38.8874
41.5124
45.1495
47.6274
48.0448
46.2393
42.5834
38.3373
36.1577
36.8539
38.0583
38.5101
38.4789
39.7342
43.124
46.4427
48.0831
47.5263
44.8359
40.6876
36.974
36.2382
37.4287
38.363
38.4863
38.7293
41.0459
44.7008
47.4071
48.119
46.5997
43.1437
38.8493
36.2451
36.6831
37.9316
38.4984
38.461
39.4204
6.50
47.8121
48.0955
48.6554
49.2304
50.2869
52.2927
54.7066
56.4125
56.6544
55.2624
52.648
49.8319
48.0999
47.852
48.3387
48.8887
49.5877
51.0447
53.3555
55.5911
56.7204
56.241
54.2328
51.3724
48.8898
47.8399
48.0269
48.583
49.1416
50.0946
51.98
54.4039
56.2599
56.7185
55.5326
53.0347
50.1683
48.2376
47.8216
48.2628
48.817
49.465
50.792
7.00
56.9182
56.8042
57.1224
57.7445
58.7299
60.0822
61.4936
62.4478
62.5378
61.6724
60.1262
58.4627
57.2702
56.7994
56.9019
57.3541
58.1217
59.2813
60.716
61.9931
62.6067
62.272
61.0572
59.381
57.8622
56.9796
56.7892
57.0623
57.6432
58.5755
59.8892
61.3211
62.3647
62.5826
61.836
60.3523
58.6672
57.3876
56.8232
56.8647
57.2774
57.9983
59.1054
7.50
62.8203
62.6781
62.7951
63.1344
63.6443
64.2382
64.7801
65.112
65.118
64.781
64.1994
63.5511
63.0202
62.7253
62.6988
62.9175
63.3385
63.8984
64.489
64.9584
65.1583
65.0107
64.5495
63.9149
63.2975
62.8596
62.6815
62.7658
63.0782
63.5694
64.159
64.717
65.085
65.1378
64.843
64.2848
63.634
63.0787
62.7489
62.6874
62.8758
63.2729
63.8194
8.00
65.0787
65.1694
65.1276
64.9623
64.7185
64.462
64.2581
64.1528
64.1652
64.2891
64.4977
64.7464
64.978
65.1333
65.1679
65.0692
64.8626
64.6047
64.3638
64.1985
64.1435
64.2064
64.3714
64.6037
64.8526
65.0579
65.1647
65.1408
64.9901
64.7531
64.4943
64.2802
64.1601
64.1568
64.267
64.4665
64.713
64.9505
65.1189
65.1711
65.0894
64.8944
64.6394
170
TEC generated using two well distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
23.6599
23.683
23.7052
23.7261
23.745
23.7612
23.7737
23.7813
23.7827
23.776
23.7595
23.7308
23.6877
23.6277
23.5488
23.4491
23.3281
23.186
23.025
22.8488
22.6627
22.4733
22.2872
22.111
21.95
21.8079
21.6869
21.5872
21.5083
21.4483
21.4052
21.3765
21.36
21.3533
21.3547
21.3623
21.3748
21.391
21.4099
21.4308
21.453
21.4761
21.4996
0.50
23.6887
23.7146
23.7399
23.7643
23.7869
23.8072
23.8241
23.8363
23.8424
23.8405
23.8284
23.8037
23.7636
23.7051
23.6257
23.5229
23.3954
23.2435
23.0691
22.8766
22.6723
22.4637
22.2594
22.0669
21.8925
21.7406
21.6131
21.5103
21.4309
21.3724
21.3323
21.3076
21.2955
21.2936
21.2997
21.3119
21.3288
21.3491
21.3717
21.3961
21.4214
21.4473
21.4734
1.00
23.7149
23.7435
23.7718
23.7994
23.8258
23.85
23.8712
23.8881
23.8991
23.9021
23.8949
23.8747
23.8382
23.782
23.7028
23.5975
23.4643
23.3027
23.1149
22.9056
22.6822
22.4538
22.2304
22.0211
21.8333
21.6717
21.5385
21.4332
21.354
21.2978
21.2613
21.2411
21.2339
21.2369
21.2479
21.2648
21.286
21.3102
21.3366
21.3642
21.3925
21.4211
21.4496
1.50
23.738
23.7691
23.8001
23.8308
23.8606
23.8886
23.914
23.9354
23.9511
23.9592
23.957
23.9415
23.909
23.8557
23.7774
23.6705
23.5321
23.3616
23.1608
22.9348
22.6922
22.4438
22.2012
21.9752
21.7744
21.6039
21.4655
21.3586
21.2803
21.227
21.1945
21.179
21.1768
21.1849
21.2006
21.222
21.2474
21.2754
21.3052
21.3359
21.3669
21.398
21.4287
2.00
23.7577
23.7909
23.8243
23.8578
23.8905
23.922
23.9511
23.9766
23.9968
24.0096
24.0122
24.0014
23.9732
23.923
23.8462
23.7383
23.5958
23.4173
23.2044
22.9628
22.7018
22.4342
22.1732
21.9316
21.7187
21.5402
21.3977
21.2898
21.213
21.1628
21.1346
21.1238
21.1264
21.1392
21.1594
21.1849
21.214
21.2455
21.2782
21.3117
21.3451
21.3783
21.4109
2.50
23.7734
23.8083
23.8438
23.8795
23.9148
23.9491
23.9814
24.0105
24.0345
24.0514
24.0584
24.0518
24.0274
23.9804
23.9054
23.7972
23.6515
23.4663
23.2431
22.9876
22.7104
22.4256
22.1484
21.8929
21.6697
21.4845
21.3388
21.2306
21.1556
21.1086
21.0842
21.0776
21.0846
21.1015
21.1255
21.1546
21.1869
21.2212
21.2565
21.2922
21.3277
21.3626
21.3967
3.00
23.7849
23.8212
23.8581
23.8955
23.9327
23.9692
24.0039
24.0357
24.0627
24.0828
24.0931
24.09
24.0688
24.0245
23.9511
23.8429
23.6951
23.5049
23.2737
23.0073
22.7173
22.4187
22.1287
21.8623
21.6311
21.4409
21.2931
21.1849
21.1115
21.0672
21.046
21.0429
21.0532
21.0733
21.1003
21.1321
21.1668
21.2033
21.2405
21.2779
21.3148
21.3511
21.3864
3.50
23.7919
23.829
23.8669
23.9053
23.9437
23.9815
24.0178
24.0512
24.0801
24.1023
24.1148
24.1138
24.0948
24.0523
23.9801
23.8721
23.723
23.5298
23.2934
23.0201
22.7217
22.4143
22.1159
21.8426
21.6062
21.413
21.2639
21.1559
21.0837
21.0412
21.0222
21.0212
21.0337
21.0559
21.0848
21.1182
21.1545
21.1923
21.2307
21.2691
21.307
21.3441
21.3801
4.00
23.7943
23.8316
23.8698
23.9086
23.9474
23.9857
24.0224
24.0565
24.086
24.1089
24.1221
24.122
24.1037
24.0618
23.99
23.8821
23.7326
23.5383
23.3002
23.0245
22.7232
22.4128
22.1115
21.8358
21.5977
21.4034
21.2539
21.146
21.0742
21.0323
21.014
21.0139
21.0271
21.05
21.0795
21.1136
21.1503
21.1886
21.2274
21.2662
21.3044
21.3417
21.378
4.50
23.7919
23.829
23.8669
23.9053
23.9437
23.9815
24.0178
24.0512
24.0801
24.1023
24.1148
24.1138
24.0948
24.0523
23.9801
23.8721
23.723
23.5298
23.2934
23.0201
22.7217
22.4143
22.1159
21.8426
21.6062
21.413
21.2639
21.1559
21.0837
21.0412
21.0222
21.0212
21.0337
21.0559
21.0848
21.1182
21.1545
21.1923
21.2307
21.2691
21.307
21.3441
21.3801
5.00
23.7849
23.8212
23.8581
23.8955
23.9327
23.9692
24.0039
24.0357
24.0627
24.0828
24.0931
24.09
24.0688
24.0245
23.9511
23.8429
23.6951
23.5049
23.2737
23.0073
22.7173
22.4187
22.1287
21.8623
21.6311
21.4409
21.2931
21.1849
21.1115
21.0672
21.046
21.0429
21.0532
21.0733
21.1003
21.1321
21.1668
21.2033
21.2405
21.2779
21.3148
21.3511
21.3864
5.50
23.7734
23.8083
23.8438
23.8795
23.9148
23.9491
23.9814
24.0105
24.0345
24.0514
24.0584
24.0518
24.0274
23.9804
23.9054
23.7972
23.6515
23.4663
23.2431
22.9876
22.7104
22.4256
22.1484
21.8929
21.6697
21.4845
21.3388
21.2306
21.1556
21.1086
21.0842
21.0776
21.0846
21.1015
21.1255
21.1546
21.1869
21.2212
21.2565
21.2922
21.3277
21.3626
21.3967
6.00
23.7577
23.7909
23.8243
23.8578
23.8905
23.922
23.9511
23.9766
23.9968
24.0096
24.0122
24.0014
23.9732
23.923
23.8462
23.7383
23.5958
23.4173
23.2044
22.9628
22.7018
22.4342
22.1732
21.9316
21.7187
21.5402
21.3977
21.2898
21.213
21.1628
21.1346
21.1238
21.1264
21.1392
21.1594
21.1849
21.214
21.2455
21.2782
21.3117
21.3451
21.3783
21.4109
6.50
23.738
23.7691
23.8001
23.8308
23.8606
23.8886
23.914
23.9354
23.9511
23.9592
23.957
23.9415
23.909
23.8557
23.7774
23.6705
23.5321
23.3616
23.1608
22.9348
22.6922
22.4438
22.2012
21.9752
21.7744
21.6039
21.4655
21.3586
21.2803
21.227
21.1945
21.179
21.1768
21.1849
21.2006
21.222
21.2474
21.2754
21.3052
21.3359
21.3669
21.398
21.4287
7.00
23.7149
23.7435
23.7718
23.7994
23.8258
23.85
23.8712
23.8881
23.8991
23.9021
23.8949
23.8747
23.8382
23.782
23.7028
23.5975
23.4643
23.3027
23.1149
22.9056
22.6822
22.4538
22.2304
22.0211
21.8333
21.6717
21.5385
21.4332
21.354
21.2978
21.2613
21.2411
21.2339
21.2369
21.2479
21.2648
21.286
21.3102
21.3366
21.3642
21.3925
21.4211
21.4496
7.50
23.6887
23.7146
23.7399
23.7643
23.7869
23.8072
23.8241
23.8363
23.8424
23.8405
23.8284
23.8037
23.7636
23.7051
23.6257
23.5229
23.3954
23.2435
23.0691
22.8766
22.6723
22.4637
22.2594
22.0669
21.8925
21.7406
21.6131
21.5103
21.4309
21.3724
21.3323
21.3076
21.2955
21.2936
21.2997
21.3119
21.3288
21.3491
21.3717
21.3961
21.4214
21.4473
21.4734
8.00
23.6599
23.683
23.7052
23.7261
23.745
23.7612
23.7737
23.7813
23.7827
23.776
23.7595
23.7308
23.6877
23.6277
23.5488
23.4491
23.3281
23.186
23.025
22.8488
22.6627
22.4733
22.2872
22.111
21.95
21.8079
21.6869
21.5872
21.5083
21.4483
21.4052
21.3765
21.36
21.3533
21.3547
21.3623
21.3748
21.391
21.4099
21.4308
21.453
21.4761
21.4996
171
TEC generated using two random distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
53.511
52.1871
50.9814
49.8997
48.9466
48.1259
47.4403
46.8914
46.4803
46.2072
46.072
46.0742
46.2131
46.4879
46.8973
47.44
48.1141
48.9171
49.8461
50.8974
52.0666
53.3485
54.7378
56.2283
57.8137
59.4876
61.2437
63.0756
64.9773
66.9431
68.9674
71.0453
73.1721
75.3435
77.5557
79.805
82.0882
84.4025
86.7451
89.1137
91.5061
93.9204
96.3547
0.50
51.4127
50.0408
48.7916
47.6713
46.6851
45.837
45.1295
44.5641
44.1416
43.8617
43.7241
43.7281
43.8727
44.1573
44.5806
45.1416
45.8385
46.6689
47.6299
48.7177
49.9274
51.2537
52.6904
54.2308
55.868
57.5948
59.4044
61.2898
63.2445
65.2624
67.3377
69.4653
71.6401
73.858
76.1148
78.407
80.7314
83.0851
85.4655
87.8701
90.297
92.7442
95.21
1.00
49.3721
47.9496
46.6546
45.4941
44.4737
43.5976
42.8682
42.2867
41.8532
41.5671
41.4274
41.4331
41.5834
41.8773
42.3143
42.8932
43.6128
44.4709
45.4647
46.59
47.842
49.2145
50.7008
52.2934
53.9846
55.7666
57.6316
59.5722
61.5814
63.6526
65.7799
67.9576
70.1809
72.4452
74.7466
77.0815
79.4466
81.8391
84.2565
86.6964
89.1569
91.6361
94.1325
1.50
47.3966
45.9207
44.5776
43.3751
42.3197
41.4154
40.6645
40.0676
39.624
39.3323
39.1909
39.1983
39.3537
39.6564
40.106
40.7021
41.4439
42.3297
43.3566
44.5207
45.8164
47.2372
48.7753
50.4226
52.1701
54.0094
55.9318
57.9292
59.9942
62.1197
64.2994
66.5277
68.7994
71.1101
73.4557
75.8326
78.2376
80.6682
83.1216
85.5958
88.0889
90.5991
93.1248
2.00
45.4948
43.9627
42.569
41.3231
40.2319
39.2996
38.5281
37.9171
37.4646
37.1682
37.0255
37.0345
37.1943
37.5044
37.9653
38.5771
39.34
40.2528
41.313
42.5166
43.8577
45.3288
46.9212
48.6254
50.4318
52.3305
54.3121
56.3678
58.4896
60.67
62.9025
65.1813
67.5012
69.8576
72.2465
74.6646
77.1086
79.576
82.0643
84.5716
87.0959
89.6357
92.1895
2.50
43.6774
42.0859
40.6394
39.3485
38.221
37.2615
36.4709
35.8475
35.388
35.0882
34.9447
34.9548
35.1176
35.4333
35.903
36.5283
37.3104
38.249
39.3424
40.5862
41.9741
43.4976
45.1466
46.9105
48.7779
50.7381
52.7805
54.8957
57.0749
59.3105
61.5957
63.9245
66.2917
68.6929
71.1241
73.582
76.0636
78.5664
81.0882
83.6269
86.181
88.7488
91.3292
3.00
41.9569
40.3032
38.8013
37.464
36.3004
35.315
34.5075
33.8745
33.4102
33.1086
32.9646
32.975
33.1389
33.4571
33.9324
34.5678
35.3662
36.3289
37.4545
38.739
40.1752
41.7532
43.4614
45.2873
47.2181
49.2415
51.3459
53.5212
55.7581
58.0486
60.3858
62.7636
65.177
67.6215
70.0934
72.5894
75.1068
77.6432
80.1965
82.7649
85.3469
87.9411
90.5463
3.50
40.3491
38.6301
37.0706
35.6859
34.4867
33.4774
32.6563
32.0169
31.5507
31.249
31.1047
31.114
31.276
31.5928
32.069
32.7099
33.5207
34.5045
35.6612
36.9865
38.4723
40.1071
41.877
43.7673
45.7633
47.8512
50.0184
52.2539
54.5479
56.8923
59.2801
61.7053
64.1629
66.6487
69.1592
71.6912
74.2422
76.8101
79.3928
81.9887
84.5966
87.215
89.8431
4.00
38.8729
37.0866
35.4676
34.0349
32.8012
31.7708
30.9399
30.2982
29.8332
29.5328
29.388
29.3939
29.5501
29.8603
30.3314
30.9718
31.7897
32.7909
33.9766
35.3427
36.8795
38.5731
40.4069
42.3636
44.4262
46.5792
48.809
51.1037
53.4535
55.85
58.2862
60.7563
63.2557
65.7802
68.3265
70.8919
73.4739
76.0706
78.6802
81.3013
83.9326
86.5731
89.2218
4.50
37.5516
35.6971
34.0179
32.5373
31.2709
30.2231
29.3867
28.7467
28.2857
27.9876
27.8411
27.8404
27.9858
28.283
28.7416
29.3741
30.1927
31.2064
32.4185
33.8248
35.4137
37.1679
39.0674
41.0917
43.2212
45.4387
47.7297
50.0817
52.4846
54.9302
57.4117
59.9235
62.4613
65.0212
67.6001
70.1957
72.8056
75.4282
78.0618
80.7053
83.3576
86.0176
88.6845
5.00
36.4132
34.4924
32.754
31.2271
29.9308
28.8692
28.0312
27.3961
26.9405
26.6443
26.4936
26.4822
26.611
26.8878
27.3258
27.9419
28.7534
29.7739
31.0092
32.4547
34.0961
35.9121
37.8779
39.9694
42.1645
44.4443
46.7934
49.199
51.6511
54.1416
56.6642
59.2135
61.7855
64.3768
66.9846
69.6066
72.2409
74.886
77.5405
80.2034
82.8736
85.5505
88.2331
5.50
35.4889
33.5081
31.7156
30.1463
28.8236
27.7513
26.914
26.2843
25.8329
25.5359
25.3772
25.35
25.4561
25.7053
26.1145
26.7056
27.502
28.5228
29.7772
31.2601
32.9534
34.8304
36.8611
39.0172
41.2741
43.6115
46.0134
48.4671
50.9628
53.4928
56.0509
58.6326
61.2339
63.8518
66.4839
69.1282
71.783
74.4469
77.1188
79.7977
82.4829
85.1736
87.8692
6.00
34.8109
32.7824
30.9461
29.3421
27.9974
26.9158
26.0777
25.4498
24.998
24.6948
24.5227
24.4746
24.5526
24.7685
25.1423
25.7013
26.4754
27.4903
28.759
30.2758
32.0179
33.952
36.0425
38.257
40.5685
42.956
45.403
47.8972
50.4291
52.9914
55.5786
58.1863
60.8112
63.4504
66.1018
68.7637
71.4346
74.1133
76.7988
79.4903
82.187
84.8885
87.5941
6.50
34.4064
32.3492
30.4856
28.8584
27.4972
26.4054
25.5607
24.9264
24.4655
24.1485
23.9572
23.8836
23.9306
24.1107
24.4467
24.9702
25.7176
26.7215
27.9989
29.5435
31.327
33.3093
35.4493
37.7111
40.0662
42.4926
44.9743
47.4991
50.0581
52.6444
55.2529
57.8796
60.5214
63.176
65.8412
68.5157
71.198
73.8871
76.5822
79.2825
81.9874
84.6963
87.4089
7.00
34.2913
32.2285
30.3581
28.7226
27.3508
26.2462
25.3865
24.735
24.2546
23.9159
23.6999
23.5988
23.6151
23.7618
24.0632
24.554
25.2754
26.2656
27.5455
29.1075
30.9189
32.9339
35.107
37.3998
39.7828
42.234
44.7372
47.2808
49.8562
52.4569
55.078
57.7159
60.3677
63.0311
65.7044
68.386
71.0748
73.7698
76.4702
79.1755
81.8849
84.598
87.3145
7.50
34.4652
32.4196
30.5629
28.9336
27.5579
26.4388
25.5567
24.8785
24.37
24.0032
23.7598
23.632
23.622
23.7427
24.0188
24.4861
25.188
26.1653
27.4404
29.0055
30.825
32.8506
35.0347
37.3377
39.7297
42.1886
44.6984
47.2476
49.8277
52.4324
55.0569
57.6977
60.352
63.0175
65.6926
68.3758
71.066
73.7622
76.4637
79.1699
81.8802
84.594
87.3112
8.00
34.912
32.902
31.0751
29.4641
28.0909
26.9585
26.0513
25.3419
24.8011
24.4039
24.1337
23.9831
23.9543
24.0599
24.3238
24.781
25.4736
26.4408
27.7039
29.255
31.0597
33.0706
35.2407
37.531
39.9115
42.36
44.8606
47.4015
49.9741
52.572
55.1904
57.8256
60.4748
63.1356
65.8063
68.4854
71.1719
73.8646
76.5629
79.266
81.9734
84.6845
87.3991
172
TEC generated using two random distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
86.6151
75.5822
62.718
50.9784
48.7966
57.4141
68.8488
80.1202
89.5971
96.0697
98.7303
97.1953
91.5108
82.1598
70.1171
57.1783
48.2114
51.828
62.2619
73.8636
84.5298
92.8298
97.7239
98.5871
95.2218
87.8615
77.1897
64.4565
52.2467
48.2438
56.0046
67.2984
78.6966
88.4897
95.4167
98.6147
97.6433
92.4914
83.5829
71.8193
58.8369
48.79
50.7403
0.50
72.2063
61.0251
47.4202
32.9152
29.8497
40.8173
52.9187
64.6206
74.4273
81.1438
83.9984
82.6328
77.0761
67.7273
55.3511
41.1127
27.6708
34.3482
46.0157
58.1334
69.1853
77.7743
82.8861
83.9314
80.7229
73.4514
62.6741
49.3197
34.7988
28.6456
39.261
51.3016
63.1458
73.2817
80.4621
83.8586
83.0598
78.0443
69.1629
57.1311
43.0544
28.9771
32.9127
1.00
55.5453
47.2877
37.8166
29.5701
26.477
30.2675
38.5611
47.9059
55.9978
61.6204
64.1399
63.304
59.1887
52.2102
43.2251
33.8801
27.3784
27.3521
33.5253
42.6525
51.6576
58.7864
63.1166
64.1924
61.9061
56.4761
48.4888
39.0743
30.4579
26.4765
29.4284
37.3322
46.7015
55.0467
61.0432
63.9966
63.6087
59.9125
53.2763
44.4862
35.0465
27.9224
26.9471
1.50
39.2444
37.7198
36.0782
34.6932
33.9602
34.1818
35.3344
37.0154
38.7184
40.0424
40.7358
40.6911
39.9353
38.6193
37.0015
35.4227
34.2732
33.9303
34.5845
36.0292
37.778
39.3572
40.43
40.8085
40.4445
39.4205
37.9364
36.2899
34.848
34.0069
34.0937
35.1398
36.7806
38.5069
39.899
40.6853
40.7399
40.0723
38.818
37.2221
35.6163
34.3867
33.919
2.00
37.6451
45.668
52.2191
56.4376
57.891
56.4601
52.3225
45.9862
38.4
31.1768
26.6345
27.0453
33.0499
41.2231
48.7525
54.368
57.4211
57.6212
54.9768
49.8013
42.7738
35.0991
28.7327
26.0885
29.1044
36.546
44.6621
51.4703
56.0308
57.8645
56.8128
53.0131
46.9255
39.4295
32.0359
26.9965
26.6397
32.0385
40.1361
47.844
53.7601
57.1769
57.7615
2.50
51.8629
62.8395
71.653
77.2184
78.9068
76.4887
70.1027
60.2492
47.8333
34.504
27.0016
34.2179
45.2654
56.7983
67.0019
74.5118
78.4488
78.3626
74.1858
66.2131
55.1089
42.0121
29.5323
29.1476
38.8159
50.3221
61.4777
70.6514
76.6934
78.9178
77.0447
71.1646
61.7291
49.5827
36.2155
26.9781
32.9074
43.7272
55.3085
65.7779
73.7061
78.152
78.6117
3.00
67.749
78.9993
87.9741
93.5865
95.1523
92.4076
85.5058
75.0162
61.9659
48.2084
40.9826
49.0774
60.8954
72.8223
83.243
90.8705
94.7875
94.4919
89.9015
81.349
69.5916
55.9145
43.246
43.4522
54.0631
66.1572
77.609
86.9566
93.0638
95.191
93.0188
86.6451
76.5836
63.7936
49.9507
40.8847
47.6364
59.2802
71.2942
81.9959
90.0558
94.5034
94.7808
3.50
82.5129
91.8912
99.5249
104.304
105.554
103.035
96.9605
88.0435
77.6616
68.3781
64.5326
68.4842
77.014
86.7039
95.4909
101.997
105.304
104.923
100.808
93.3805
83.608
73.2844
65.7644
65.4022
71.8617
81.2159
90.7174
98.6562
103.863
105.604
103.584
97.9516
89.35
79.0496
69.4054
64.5768
67.6021
75.7581
85.4336
94.4308
101.302
105.071
105.192
4.00
94.2633
100.31
105.418
108.65
109.449
107.645
103.482
97.6506
91.3578
86.32
84.3382
86.163
90.9061
96.9251
102.704
107.091
109.314
108.982
106.1
101.1
94.8883
88.9054
85.0026
84.6817
87.9541
93.456
99.5367
104.831
108.353
109.493
108.03
104.15
98.483
92.1625
86.8472
84.3807
85.7204
90.1665
96.1105
101.996
106.62
109.162
109.177
4.50
101.71
103.592
105.261
106.341
106.593
105.96
104.572
102.735
100.888
99.5053
98.9659
99.4165
100.722
102.523
104.366
105.819
106.559
106.424
105.437
103.807
101.907
100.205
99.1528
99.0413
99.8946
101.468
103.344
105.067
106.241
106.611
106.092
104.79
102.99
101.116
99.6466
98.9808
99.3018
100.51
102.272
104.136
105.662
106.51
106.494
5.00
104.101
101.551
99.1466
97.534
97.1777
98.1715
100.208
102.726
105.103
106.807
107.476
106.966
105.37
103.02
100.451
98.3161
97.2098
97.4527
98.956
101.278
103.808
105.95
107.238
107.4
106.393
104.416
101.896
99.4334
97.6827
97.145
97.9694
99.8966
102.386
104.816
106.635
107.454
107.101
105.635
103.358
100.782
98.5514
97.2821
97.3418
5.50
101.182
94.4939
87.6995
82.834
81.829
84.9976
90.8618
97.5427
103.514
107.676
109.331
108.182
104.347
98.4025
91.4525
85.2214
81.8537
82.7508
87.3243
93.7584
100.293
105.591
108.728
109.18
106.826
101.977
95.4259
88.5391
83.2898
81.7059
84.3797
89.998
96.6681
102.805
107.256
109.271
108.496
104.995
99.2795
92.3776
85.9303
82.0676
82.3876
6.00
93.1697
83.2643
72.2745
63.3567
61.6502
67.8762
77.5487
87.5767
96.1512
102.032
104.416
102.932
97.6547
89.1325
78.4975
67.876
61.4721
63.6351
71.8738
81.9766
91.5565
99.0891
103.527
104.254
101.089
94.3069
84.6868
73.7067
64.24
61.3407
66.7591
76.1955
86.297
95.1457
101.44
104.319
103.354
98.5591
90.4172
79.9695
69.163
61.8715
62.8851
6.50
80.7565
69.3305
55.6057
41.6447
38.9893
49.6727
61.9267
73.6993
83.5342
90.2479
93.0433
91.5397
85.769
76.1664
63.5769
49.3686
37.532
43.1824
54.9445
67.1806
78.2794
86.885
91.9731
92.9267
89.5451
82.0357
71.0087
57.5051
43.3455
38.0279
48.0973
60.294
72.2186
82.3862
89.5691
92.9156
91.9898
86.7692
77.6357
65.3781
51.274
38.4313
41.7875
7.00
65.1436
54.8189
42.4658
30.5567
27.6241
35.4676
46.3283
57.3547
66.7097
73.152
75.9445
74.7625
69.6481
61.0009
49.6197
36.9786
27.4178
30.3476
40.0137
51.2112
61.7024
69.9146
74.839
75.9257
73.0125
66.2957
56.337
44.1612
31.9118
27.1501
34.1643
44.83
55.9536
65.6142
72.4954
75.7994
75.1502
70.5428
62.3282
51.2459
38.6378
28.114
29.3635
7.50
48.1856
42.2634
35.6153
29.6961
26.1976
27.4241
33.9365
41.365
47.7489
52.2121
54.285
53.7909
50.8263
45.7804
39.3948
32.8597
27.7838
25.934
29.8973
37.2036
44.325
49.955
53.4211
54.3866
52.793
48.8594
43.1175
36.4918
30.3789
26.4607
26.8701
32.95
40.4133
46.998
51.7502
54.1565
54.0036
51.3513
46.5475
40.282
33.6807
28.3129
25.9049
8.00
34.6979
38.3455
41.4956
43.6274
44.466
43.9381
42.1609
39.4371
36.2399
33.172
30.936
30.5318
32.7433
36.2938
39.8098
42.5661
44.1586
44.4024
43.3072
41.0718
38.0758
34.8551
32.0533
30.458
31.2056
34.2194
37.8751
41.1276
43.415
44.4337
44.0845
42.4597
39.8378
36.671
33.548
31.1547
30.4332
32.3325
35.8032
39.3751
42.2608
44.0229
44.4492
173
TEC generated using two random distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
27.6115
27.6021
27.5897
27.5739
27.5545
27.5314
27.5045
27.4741
27.4406
27.4046
27.3667
27.3278
27.289
27.2509
27.2146
27.1806
27.1494
27.1215
27.0969
27.0758
27.0579
27.0431
27.0311
27.0217
27.0145
27.0093
27.0058
27.0038
27.0029
27.0031
27.0041
27.0058
27.0081
27.0108
27.0139
27.0172
27.0208
27.0245
27.0284
27.0323
27.0362
27.0402
27.0441
0.50
27.6352
27.6266
27.6145
27.5985
27.5784
27.5538
27.5249
27.4916
27.4546
27.4144
27.3719
27.3283
27.2847
27.2422
27.2019
27.1645
27.1306
27.1007
27.0748
27.0528
27.0347
27.0201
27.0086
26.9999
26.9937
26.9895
26.9871
26.9861
26.9863
26.9876
26.9896
26.9923
26.9955
26.9991
27.0029
27.007
27.0113
27.0157
27.0201
27.0245
27.029
27.0334
27.0378
1.00
27.6608
27.6531
27.6416
27.6257
27.605
27.5791
27.5479
27.5115
27.4704
27.4254
27.3776
27.3284
27.2793
27.2316
27.1867
27.1455
27.1088
27.0767
27.0496
27.0271
27.009
26.9948
26.9841
26.9765
26.9714
26.9685
26.9673
26.9676
26.9691
26.9716
26.9748
26.9785
26.9827
26.9872
26.9919
26.9968
27.0018
27.0068
27.0119
27.0169
27.0219
27.0268
27.0316
1.50
27.688
27.6817
27.6712
27.6557
27.6347
27.6075
27.574
27.5341
27.4884
27.4378
27.3837
27.328
27.2723
27.2187
27.1686
27.1232
27.0833
27.0493
27.021
26.9982
26.9805
26.9672
26.9576
26.9514
26.9478
26.9464
26.9468
26.9486
26.9515
26.9553
26.9597
26.9646
26.9698
26.9753
26.981
26.9867
26.9924
26.9981
27.0038
27.0094
27.0149
27.0203
27.0255
2.00
27.7168
27.7123
27.7032
27.6886
27.6676
27.6393
27.6034
27.5597
27.5088
27.4517
27.3903
27.3267
27.2634
27.2028
27.1468
27.0969
27.0538
27.0178
26.9888
26.9661
26.9492
26.9371
26.9292
26.9247
26.9229
26.9234
26.9255
26.929
26.9335
26.9387
26.9445
26.9507
26.957
26.9636
26.9701
26.9767
26.9832
26.9896
26.9959
27.0021
27.0081
27.014
27.0197
2.50
27.7469
27.7447
27.7375
27.7243
27.7037
27.6747
27.6365
27.5887
27.5319
27.4673
27.3972
27.3244
27.2521
27.1834
27.1207
27.0659
27.0196
26.982
26.9526
26.9307
26.9151
26.9049
26.899
26.8967
26.8971
26.8997
26.9038
26.9092
26.9154
26.9222
26.9294
26.9369
26.9444
26.952
26.9595
26.967
26.9743
26.9814
26.9883
26.9951
27.0016
27.008
27.0141
3.00
27.7778
27.7784
27.7737
27.7625
27.7429
27.7136
27.6733
27.6212
27.5578
27.4846
27.4042
27.3205
27.2376
27.1596
27.0896
27.0296
26.9803
26.9416
26.9125
26.8919
26.8784
26.8706
26.8674
26.8677
26.8707
26.8756
26.882
26.8894
26.8974
26.9059
26.9146
26.9234
26.9322
26.9408
26.9493
26.9576
26.9657
26.9735
26.9811
26.9884
26.9954
27.0022
27.0088
3.50
27.8088
27.8127
27.8112
27.8025
27.7847
27.7557
27.7136
27.6572
27.5866
27.5034
27.411
27.3145
27.2193
27.1308
27.0528
26.9875
26.9357
26.8965
26.8686
26.8502
26.8395
26.8348
26.8348
26.8381
26.844
26.8515
26.8603
26.8699
26.8799
26.8901
26.9003
26.9104
26.9204
26.9301
26.9396
26.9487
26.9575
26.966
26.9742
26.9821
26.9896
26.9968
27.0038
4.00
27.839
27.8466
27.8487
27.8434
27.8282
27.8002
27.7568
27.6962
27.6177
27.5232
27.417
27.3056
27.1964
27.0961
27.0097
26.9395
26.8858
26.8472
26.8215
26.8063
26.7992
26.7983
26.8018
26.8086
26.8176
26.828
26.8393
26.851
26.863
26.8749
26.8867
26.8982
26.9093
26.9201
26.9304
26.9404
26.95
26.9591
26.9678
26.9762
26.9842
26.9919
26.9992
4.50
27.8673
27.8787
27.885
27.8836
27.8715
27.8453
27.8014
27.7367
27.6501
27.5432
27.4214
27.2932
27.1682
27.0553
26.9605
26.886
26.8316
26.7947
26.7724
26.7612
26.7585
26.7619
26.7695
26.7799
26.7922
26.8055
26.8193
26.8333
26.8472
26.8608
26.874
26.8868
26.8991
26.9108
26.922
26.9328
26.943
26.9527
26.962
26.9709
26.9793
26.9873
26.995
5.00
27.8922
27.9076
27.918
27.9208
27.9124
27.8887
27.8448
27.7765
27.6817
27.5617
27.4229
27.2763
27.1345
27.0088
26.9061
26.8285
26.7747
26.7409
26.7229
26.7167
26.719
26.727
26.7388
26.753
26.7685
26.7846
26.8009
26.817
26.8328
26.8479
26.8625
26.8765
26.8898
26.9025
26.9145
26.9259
26.9368
26.947
26.9568
26.9661
26.9749
26.9833
26.9912
5.50
27.9124
27.9312
27.9455
27.9523
27.9477
27.9266
27.8832
27.8119
27.7092
27.576
27.4199
27.2546
27.0961
26.9582
26.849
26.7699
26.7181
26.6885
26.6757
26.6749
26.6823
26.695
26.711
26.7287
26.7473
26.7661
26.7847
26.8027
26.8201
26.8367
26.8525
26.8675
26.8817
26.8952
26.9079
26.92
26.9313
26.9421
26.9523
26.9619
26.971
26.9797
26.9879
6.00
27.9264
27.9479
27.9652
27.9753
27.9737
27.9549
27.912
27.8381
27.7282
27.583
27.4109
27.2284
27.0551
26.9072
26.7934
26.7145
26.6659
26.6412
26.6338
26.6383
26.6505
26.6675
26.6872
26.7081
26.7294
26.7505
26.771
26.7907
26.8095
26.8273
26.8441
26.86
26.875
26.8891
26.9024
26.915
26.9268
26.9379
26.9485
26.9584
26.9678
26.9767
26.9852
6.50
27.933
27.9561
27.9751
27.9869
27.9871
27.9695
27.9264
27.85
27.7343
27.5795
27.3949
27.1994
27.0153
26.861
26.7452
26.6678
26.6229
26.6028
26.6002
26.6092
26.6255
26.646
26.6686
26.6921
26.7155
26.7384
26.7604
26.7813
26.8012
26.8199
26.8376
26.8541
26.8697
26.8843
26.8981
26.911
26.9232
26.9346
26.9454
26.9556
26.9652
26.9743
26.9829
7.00
27.9316
27.9547
27.9737
27.9855
27.9855
27.9672
27.9228
27.8439
27.7242
27.5636
27.3724
27.1705
26.9819
26.8255
26.7103
26.6352
26.5936
26.577
26.5778
26.5899
26.6089
26.6317
26.6563
26.6814
26.7061
26.7302
26.7531
26.7749
26.7955
26.8148
26.833
26.85
26.8659
26.8809
26.8949
26.9081
26.9205
26.9322
26.9432
26.9535
26.9633
26.9725
26.9813
7.50
27.9218
27.9434
27.9607
27.9705
27.9681
27.9473
27.9003
27.819
27.6974
27.5361
27.3454
27.1452
26.9591
26.8056
26.6931
26.6205
26.5809
26.5661
26.5684
26.5817
26.6017
26.6253
26.6506
26.6763
26.7016
26.7261
26.7494
26.7716
26.7924
26.812
26.8304
26.8476
26.8638
26.8789
26.8931
26.9064
26.9189
26.9307
26.9417
26.9522
26.962
26.9713
26.9802
8.00
27.9041
27.9228
27.9368
27.9428
27.9363
27.9115
27.8611
27.7779
27.6573
27.5004
27.3173
27.1265
26.9495
26.803
26.695
26.6245
26.5857
26.5706
26.5722
26.5848
26.604
26.627
26.6518
26.6771
26.702
26.7262
26.7494
26.7714
26.7921
26.8116
26.8299
26.8471
26.8632
26.8783
26.8925
26.9058
26.9183
26.9301
26.9412
26.9516
26.9615
26.9708
26.9796
174
TEC generated using four well distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
20.606
20.0454
19.5769
19.1954
18.887
18.6347
18.4227
18.2383
18.0722
17.9178
17.7705
17.6274
17.4862
17.3457
17.2051
17.0638
16.9215
16.7782
16.634
16.4888
16.3428
16.1964
16.0497
15.9032
15.7572
15.6121
15.4686
15.3271
15.1886
15.054
14.9244
14.8014
14.6871
14.5842
14.4962
14.4282
14.3869
14.3818
14.4251
14.532
14.719
14.9994
15.3788
0.50
20.7578
20.1965
19.7284
19.3481
19.0411
18.7898
18.5779
18.3928
18.2251
18.0683
17.918
17.7713
17.6263
17.4817
17.3368
17.1911
17.0445
16.8968
16.7481
16.5986
16.4484
16.2978
16.147
15.9964
15.8464
15.6974
15.5499
15.4045
15.2621
15.1234
14.9898
14.8627
14.7441
14.6366
14.5439
14.4708
14.4243
14.4135
14.4512
14.5529
14.7355
15.0134
15.3923
1.00
21.0263
20.4668
19.9974
19.6131
19.3001
19.0416
18.822
18.6289
18.4532
18.2884
18.1304
17.9762
17.8239
17.6723
17.5208
17.3688
17.2161
17.0628
16.9088
16.7542
16.5994
16.4444
16.2895
16.1352
15.9816
15.8294
15.679
15.5311
15.3863
15.2457
15.1104
14.982
14.8624
14.7545
14.6618
14.5892
14.5436
14.5344
14.5738
14.6769
14.8603
15.1374
15.5137
1.50
21.4054
20.85
20.378
19.9852
19.6597
19.3867
19.1521
18.9443
18.7545
18.5766
18.4063
18.2407
18.0779
17.9166
17.7561
17.5959
17.4357
17.2755
17.1152
16.9551
16.7951
16.6355
16.4767
16.3189
16.1624
16.0078
15.8555
15.7062
15.5607
15.4201
15.2855
15.1585
15.0414
14.9368
14.8485
14.7816
14.7429
14.7415
14.7891
14.8997
15.088
15.3657
15.7375
2.00
21.8803
21.3305
20.8552
20.4512
20.109
19.8165
19.5614
19.3335
19.1247
18.9292
18.7427
18.5623
18.386
18.2125
18.041
17.8709
17.7018
17.5337
17.3664
17.1999
17.0346
16.8704
16.7076
16.5466
16.3877
16.2314
16.0782
15.9289
15.7842
15.6453
15.5135
15.3905
15.2786
15.1807
15.1006
15.0436
15.0163
15.0274
15.0876
15.2094
15.405
15.6841
16.0503
2.50
22.433
21.8894
21.4108
20.9947
20.634
20.3192
20.0404
19.7889
19.5576
19.341
19.1352
18.9373
18.7452
18.5575
18.3732
18.1917
18.0126
17.8356
17.6605
17.4875
17.3164
17.1475
16.981
16.8171
16.6563
16.4991
16.3459
16.1976
16.0551
15.9195
15.7922
15.6752
15.5709
15.4822
15.4131
15.3688
15.3557
15.3819
15.4569
15.5913
15.795
16.0754
16.4356
3.00
23.0462
22.5092
22.0276
21.5997
21.2203
20.8824
20.5786
20.3017
20.0457
19.806
19.5787
19.3613
19.1515
18.9481
18.7497
18.5558
18.3657
18.1792
17.9959
17.8158
17.6389
17.4653
17.2952
17.1289
16.9666
16.809
16.6567
16.5104
16.3711
16.24
16.1188
16.0094
15.9142
15.8365
15.7801
15.75
15.7524
15.7944
15.8845
16.0312
16.2425
16.5241
16.8781
3.50
23.7055
23.1752
22.6912
22.2522
21.8549
21.4945
21.1655
20.8627
20.5812
20.3172
20.0674
19.8292
19.6008
19.3805
19.1672
18.9601
18.7585
18.562
18.3702
18.1829
18.0002
17.822
17.6485
17.4799
17.3167
17.1593
17.0084
16.8649
16.7297
16.6042
16.49
16.3891
16.3042
16.2383
16.1953
16.1799
16.1978
16.2553
16.3594
16.5173
16.7351
17.0172
17.3652
4.00
24.3994
23.8757
23.3897
22.9407
22.5268
22.1449
21.7915
21.4631
21.1562
20.8677
20.595
20.3357
20.0881
19.8506
19.622
19.4014
19.1881
18.9813
18.7809
18.5865
18.3979
18.2153
18.0386
17.8682
17.7044
17.5478
17.3989
17.2587
17.1282
17.0089
16.9023
16.8106
16.7364
16.6826
16.653
16.6519
16.6844
16.7561
16.8728
17.0403
17.2633
17.5453
17.8875
4.50
25.1181
24.6011
24.1137
23.6557
23.2262
22.8241
22.4476
22.0946
21.7631
21.4508
21.1555
20.8754
20.6088
20.3542
20.1104
19.8763
19.6512
19.4344
19.2255
19.024
18.8299
18.643
18.4635
18.2916
18.1276
17.972
17.8255
17.6891
17.5638
17.451
17.3524
17.27
17.2064
17.1645
17.1477
17.16
17.2059
17.2902
17.4177
17.5931
17.8202
18.1015
18.438
5.00
25.8533
25.3431
24.8547
24.3884
23.9447
23.5237
23.1255
22.7495
22.3947
22.0597
21.7429
21.4429
21.158
20.8869
20.6283
20.3813
20.1448
19.9183
19.7012
19.493
19.2936
19.1029
18.9208
18.7476
18.5837
18.4295
18.2858
18.1534
18.0334
17.9273
17.8367
17.7635
17.7102
17.6796
17.6747
17.6992
17.757
17.8522
17.9888
18.1705
18.4005
18.6806
19.0117
5.50
26.5969
26.0934
25.6045
25.1308
24.6739
24.2356
23.8175
23.4203
23.0441
22.6882
22.3516
22.033
21.7311
21.4445
21.1721
20.9128
20.6657
20.43
20.2052
19.9908
19.7865
19.5923
19.408
19.234
19.0705
18.918
18.7772
18.6489
18.5344
18.4349
18.352
18.2877
18.2442
18.224
18.23
18.2654
18.3336
18.438
18.582
18.7687
19.0005
19.279
19.6048
6.00
27.3403
26.8436
26.3547
25.8745
25.4058
24.952
24.5162
24.1003
23.7051
23.3307
22.9763
22.641
22.3237
22.0231
21.7381
21.4676
21.2107
20.9667
20.7349
20.5148
20.3062
20.1089
19.9229
19.7483
19.5854
19.4348
19.2971
19.1731
19.0639
18.9708
18.8954
18.8394
18.8049
18.7943
18.81
18.855
18.9321
19.0443
19.1943
19.3847
19.6175
19.894
20.2146
6.50
28.0747
27.5847
27.0962
26.6107
26.1322
25.6655
25.2149
24.7832
24.3721
23.9818
23.6123
23.2626
22.9319
22.619
22.3229
22.0425
21.777
21.5255
21.2876
21.0626
20.8502
20.6504
20.463
20.2882
20.1262
19.9777
19.8431
19.7233
19.6193
19.5324
19.464
19.4157
19.3895
19.3875
19.4119
19.4652
19.5498
19.6684
19.8232
20.0163
20.2495
20.5236
20.8391
7.00
28.7911
28.3072
27.8199
27.331
26.8455
26.3693
25.9076
25.4638
25.0401
24.6373
24.2554
23.894
23.5522
23.229
22.9234
22.6346
22.3617
22.104
21.8608
21.6316
21.4162
21.2144
21.026
20.8514
20.6906
20.5442
20.4128
20.2972
20.1982
20.1171
20.0553
20.0141
19.9954
20.001
20.033
20.0934
20.1845
20.3083
20.4669
20.6619
20.8947
21.1662
21.4767
7.50
29.4821
29.0036
28.5185
28.0288
27.5399
27.0583
26.5896
26.1379
25.7055
25.2936
24.9026
24.5321
24.1816
23.8502
23.5371
23.2415
22.9626
22.6997
22.4522
22.2197
22.0019
21.7987
21.6099
21.4357
21.2764
21.1323
21.0041
20.8925
20.7983
20.7227
20.6669
20.6322
20.6202
20.6327
20.6712
20.7378
20.8343
20.9623
21.1237
21.3199
21.552
21.8207
22.1263
8.00
30.1445
29.6703
29.1883
28.7006
28.2122
27.7296
27.2585
26.803
26.3658
25.9484
25.5513
25.1746
24.8178
24.4803
24.1616
23.8608
23.5772
23.3104
23.0597
22.8248
22.6054
22.4013
22.2125
22.0392
21.8815
21.7399
21.6148
21.5071
21.4175
21.347
21.2967
21.2679
21.262
21.2804
21.3247
21.3965
21.4974
21.629
21.7925
21.9893
22.2202
22.486
22.7867
175
TEC generated using four well distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
39.6231
30.4905
25.9039
25.364
30.6144
39.7167
48.7382
55.9365
60.3959
61.6012
59.3487
53.7355
45.2483
35.3175
27.9113
25.1561
26.8438
34.3885
43.7706
52.1485
58.2445
61.3369
61.0505
57.31
50.3588
40.9636
31.4897
26.2622
25.1629
29.5795
38.4577
47.6196
55.1235
59.9834
61.6388
59.8464
54.6619
46.5063
36.6085
28.5908
25.3148
26.2503
33.1853
0.50
32.9697
20.5196
17.8314
15.2517
21.7088
32.3868
41.9131
49.3051
53.8821
55.2325
53.1808
47.7558
39.1461
27.6739
19.0212
16.7344
15.7884
26.4051
36.7238
45.4272
51.6655
54.8793
54.7632
51.2345
44.398
34.4962
22.0546
18.1385
15.5831
20.2717
31.0109
40.7532
48.4741
53.4539
55.2475
53.6498
48.6646
40.4624
29.3424
19.2703
17.082
14.9503
24.9721
1.00
32.083
25.9231
20.9722
18.7041
21.646
28.3341
35.2946
40.9445
44.5667
45.8123
44.5868
41.0409
35.6332
29.3318
23.5637
19.5218
19.2627
24.3398
31.4432
37.9588
42.7911
45.4097
45.5814
43.3157
38.8829
32.9285
26.6936
21.5184
18.7564
20.9451
27.3781
34.4243
40.3003
44.2179
45.7896
44.889
41.6326
36.4305
30.1674
24.2573
19.9048
18.9678
23.4635
1.50
32.2077
31.3074
30.5745
30.2338
30.4245
31.0956
32.0315
32.9675
33.679
34.0215
33.9414
33.4708
32.7112
31.8111
30.9555
30.3669
30.2494
30.6666
31.4846
32.4521
33.3141
33.8781
34.0386
33.7806
33.169
32.3282
31.4223
30.6538
30.2498
30.3684
30.9856
31.9017
32.852
33.6035
34.0001
33.976
33.5526
32.8237
31.9324
31.0588
30.4215
30.2335
30.5835
2.00
35.2562
39.5384
42.0815
42.636
41.2003
38.0412
33.7828
29.4219
24.7028
21.0952
21.5653
26.5055
32.2507
37.2997
40.8753
42.5719
42.2489
40.0151
36.2768
31.8489
27.49
22.8356
20.5397
23.4531
29.0104
34.5819
39.0616
41.8556
42.6794
41.4989
38.5418
34.3772
29.9822
25.3419
21.4181
21.1358
25.7566
31.5054
36.7019
40.5029
42.4623
42.4068
40.4106
2.50
42.19
48.6085
52.1998
52.6438
49.8434
43.894
35.0502
24.0693
18.283
15.644
18.1818
27.9812
37.5101
45.2897
50.5373
52.7893
51.8263
47.6387
40.3937
30.4356
20.3266
17.0896
15.1737
22.2906
32.2598
41.1532
47.9094
51.8997
52.7716
50.4002
44.8574
36.3768
25.5408
18.6623
15.95
17.0899
26.6469
36.3241
44.3895
50.0057
52.6729
52.1415
48.3758
3.00
49.231
55.9077
59.585
59.8614
56.6113
49.9771
40.4642
29.8303
23.7099
21.8163
25.2595
34.6328
44.3774
52.4565
57.9008
60.1359
58.8831
54.1314
46.1543
35.7664
26.3351
22.5603
22.2702
29.0278
38.9763
48.1535
55.1819
59.2868
60.0276
57.2435
51.0397
41.8566
31.1372
24.1765
21.8942
24.3113
33.2954
43.1524
51.5194
57.3536
60.0367
59.2532
54.9571
3.50
54.8352
60.4767
63.5938
63.7353
60.8117
55.1288
47.5726
40.0191
35.0158
33.7632
36.7221
43.2197
50.8303
57.5466
62.1734
64.0341
62.8361
58.6512
52.0003
44.1433
37.4202
33.9901
34.5098
39.2357
46.5235
53.9374
59.8589
63.3453
63.8947
61.3698
56.0182
48.6288
40.9252
35.4723
33.6982
36.0841
42.2381
49.8377
56.7556
61.7079
63.9604
63.1725
59.3656
4.00
58.133
61.8426
63.9164
63.968
61.9605
58.2335
53.5524
49.0807
46.0672
45.3489
47.1356
50.9144
55.5718
59.9034
62.9734
64.1974
63.3396
60.5209
56.2601
51.5104
47.5321
45.4465
45.8284
48.5862
52.9005
57.553
61.4319
63.7526
64.0825
62.3374
58.8044
54.19
49.6152
46.3471
45.2978
46.7649
50.3348
54.9481
59.3842
62.663
64.1532
63.5727
60.9937
4.50
58.671
59.8571
60.5304
60.5372
59.8737
58.689
57.2612
55.9402
55.0613
54.8523
55.3665
56.4679
57.8729
59.2329
60.2243
60.619
60.3264
59.4101
58.08
56.6541
55.488
54.8808
54.9903
55.786
57.0599
58.4887
59.7242
60.4775
60.5763
59.9964
58.8673
57.4524
56.0966
55.1428
54.8376
55.2596
56.297
57.6813
59.0673
60.1233
60.6057
60.4041
59.5615
5.00
56.3279
54.6602
53.6991
53.6983
54.6559
56.3147
58.2452
59.9735
61.0995
61.3721
60.7282
59.305
57.4253
55.5429
54.1365
53.5747
54.0057
55.3117
57.1468
59.0457
60.5545
61.3307
61.202
60.1917
58.5214
56.5804
54.849
53.7745
53.6405
54.4805
56.0685
57.9906
59.7714
60.9955
61.3893
60.8635
59.5289
57.6857
55.7753
54.2807
53.5927
53.8929
55.0986
5.50
51.2961
46.6785
44.0009
43.9962
46.6951
51.292
56.4339
60.8604
63.6803
64.3842
62.8245
59.2322
54.28
49.1311
45.2202
43.6517
44.8618
48.5302
53.5361
58.5027
62.3188
64.2623
63.9815
61.488
57.1945
51.9878
47.2038
44.2115
43.834
46.2016
50.6197
55.7686
60.3499
63.4204
64.4215
63.1577
59.8069
54.9786
49.7741
45.6218
43.7027
44.5437
47.9361
6.00
44.1501
36.6546
32.4794
32.3229
36.7051
44.2088
52.0928
58.564
62.6052
63.6604
61.5337
56.3926
48.8981
40.6277
34.3626
31.8902
33.6726
39.75
47.7099
55.1449
60.6562
63.4488
63.128
59.6499
53.3677
45.2646
37.4967
32.8081
32.0902
35.8818
43.1391
51.0986
57.8282
62.2324
63.7027
61.9972
57.2315
49.9852
41.677
34.9867
31.9904
33.1636
38.7696
6.50
36.2998
25.7622
21.4697
20.222
26.125
36.3245
45.8671
53.3439
57.9617
59.2514
57.0147
51.3016
42.431
31.3766
23.2323
20.5748
21.5989
30.4777
40.6483
49.418
55.7315
58.9472
58.7172
54.9526
47.8114
37.7872
26.8826
21.8072
20.1593
24.8862
34.964
44.6975
52.5024
57.533
59.2815
57.5153
52.2519
43.7687
32.8774
23.8421
20.8134
20.9545
29.1154
7.00
31.8467
22.1568
17.7712
15.679
20.7024
30.0796
38.899
45.8152
50.1372
51.4845
49.7116
44.879
37.2347
27.4096
19.7221
16.5617
16.637
24.6904
34.0753
42.1811
48.0362
51.1003
51.0998
47.9815
41.8878
33.165
23.2206
18.1816
15.7505
19.5736
28.8235
37.8181
45.0352
49.729
51.4843
50.1264
45.6896
38.3969
28.7764
20.3218
16.9066
16.1108
23.4393
7.50
32.667
29.2757
24.8557
22.0034
23.6926
28.294
33.132
37.2064
39.9162
40.9537
40.2563
38.0108
34.7041
31.1689
27.3584
23.3295
21.9304
25.5731
30.4324
35.0355
38.573
40.5806
40.8595
39.4519
36.6659
33.1413
29.7443
25.3975
22.2323
23.1801
27.6421
32.5167
36.7343
39.6486
40.9169
40.4448
38.384
35.1774
31.6172
27.9869
23.7547
21.7985
24.9709
8.00
32.6331
34.409
35.574
35.9498
35.519
34.4091
32.8512
31.086
29.3565
28.1901
28.2287
29.5253
31.4818
33.4598
35.0035
35.8385
35.8577
35.1091
33.7733
32.0992
30.3101
28.739
28.0352
28.6641
30.3338
32.368
34.2027
35.4626
35.9476
35.6194
34.5878
33.0746
31.325
29.569
28.2866
28.1432
29.2997
31.2087
33.2143
34.8352
35.7739
35.9018
35.2473
176
TEC generated using four well distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
20.2515
20.2126
20.2453
20.345
20.4991
20.69
20.8986
21.107
21.3003
21.4677
21.6018
21.6982
21.7548
21.7712
21.7481
21.687
21.5899
21.4592
21.2977
21.1083
20.8941
20.6582
20.4037
20.1335
19.8502
19.5561
19.253
18.9423
18.625
18.3015
17.9723
17.6375
17.2982
16.9561
16.6147
16.28
15.9607
15.6688
15.4187
15.2259
15.1038
15.061
15.0987
0.50
20.2215
20.1761
20.2147
20.3315
20.5105
20.7296
20.9655
21.1974
21.4091
21.5892
21.731
21.8308
21.8875
21.9015
21.8742
21.8076
21.7044
21.5672
21.3992
21.2035
20.9836
20.7427
20.484
20.2107
19.9254
19.6305
19.3277
19.0183
18.7029
18.3816
18.0542
17.7203
17.3799
17.0337
16.6844
16.3371
16.0007
15.6882
15.4162
15.2036
15.0677
15.02
15.0631
1.00
20.2775
20.2255
20.2695
20.4024
20.6038
20.8469
21.1042
21.3523
21.5742
21.7591
21.9009
21.9972
22.0479
22.0543
22.0186
21.9432
21.8311
21.6855
21.5096
21.3069
21.081
20.8352
20.5731
20.2978
20.0121
19.7184
19.4185
19.1135
18.8039
18.4894
18.1693
17.8425
17.508
17.1656
16.8166
16.4651
16.1192
15.7924
15.503
15.2731
15.1241
15.0711
15.1182
1.50
20.4611
20.4038
20.4518
20.5963
20.8129
21.07
21.3367
21.5883
21.808
21.9858
22.1172
22.2011
22.2384
22.2312
22.1821
22.094
21.9702
21.814
21.6288
21.4182
21.1858
20.9353
20.6702
20.394
20.1094
19.8189
19.5245
19.2271
18.9272
18.6243
18.3173
18.0047
17.6845
17.3555
17.0177
16.6737
16.3304
16.0005
15.7031
15.4628
15.3046
15.247
15.2957
2.00
20.8193
20.7599
20.8088
20.9557
21.1732
21.4265
21.6836
21.9198
22.1199
22.2755
22.3838
22.4448
22.4602
22.4325
22.3647
22.2599
22.1213
21.9522
21.756
21.5365
21.2973
21.0421
20.7747
20.4983
20.2162
19.9308
19.6442
19.3574
19.0709
18.7843
18.4963
18.2049
17.9081
17.6034
17.2899
16.9684
16.6441
16.328
16.0385
15.8005
15.6411
15.5814
15.6283
2.50
21.3944
21.3385
21.383
21.5171
21.7132
21.9369
22.1581
22.3547
22.514
22.6299
22.7008
22.7275
22.7121
22.6571
22.5653
22.4397
22.2832
22.099
21.8904
21.6611
21.4146
21.1548
20.8853
20.6097
20.3311
20.0524
19.7755
19.5019
19.2321
18.9658
18.7021
18.4389
18.174
17.9048
17.6294
17.3475
17.0619
16.7813
16.5213
16.3046
16.1571
16.1
16.1408
3.00
22.2062
22.1613
22.1944
22.2959
22.4422
22.605
22.7599
22.8901
22.9863
23.0446
23.064
23.0455
22.9908
22.9021
22.7814
22.6312
22.4541
22.2529
22.0306
21.7906
21.5365
21.272
21.0008
20.7265
20.4524
20.1814
19.9159
19.6573
19.4067
19.1641
18.9288
18.6995
18.474
18.2501
18.0257
17.7995
17.573
17.3513
17.1455
16.9729
16.854
16.8064
16.8361
3.50
23.2317
23.2059
23.2204
23.2692
23.3377
23.4092
23.4695
23.5092
23.5228
23.508
23.4641
23.3913
23.2905
23.1627
23.0092
22.8316
22.6317
22.4119
22.1749
21.9236
21.6616
21.3924
21.1197
20.8471
20.5781
20.3156
20.0623
19.8201
19.5902
19.3733
19.1692
18.9773
18.7963
18.6247
18.4607
18.3032
18.1518
18.0087
17.8792
17.772
17.6981
17.6669
17.6814
4.00
24.3942
24.3933
24.3848
24.3674
24.3395
24.3
24.2476
24.1812
24.0997
24.002
23.8871
23.7543
23.603
23.4328
23.2439
23.0369
22.8129
22.5735
22.3211
22.0583
21.7882
21.5144
21.2403
20.9697
20.7061
20.4525
20.2119
19.9863
19.7776
19.587
19.415
19.2619
19.1274
19.0108
18.9115
18.8284
18.7605
18.7065
18.6654
18.6359
18.6168
18.6068
18.6044
4.50
25.5759
25.6014
25.5703
25.486
25.3603
25.2075
25.04
24.8651
24.6861
24.5035
24.316
24.1215
23.9183
23.7047
23.4795
23.2426
22.994
22.7349
22.467
22.1927
21.9147
21.6363
21.3611
21.0926
20.8344
20.5897
20.3614
20.1522
19.9641
19.799
19.6581
19.5424
19.4528
19.3896
19.3529
19.342
19.355
19.3878
19.4329
19.4795
19.5144
19.5259
19.5079
5.00
26.6537
26.7021
26.6535
26.5147
26.3071
26.0576
25.7891
25.5172
25.2493
24.9879
24.732
24.4789
24.2258
23.9702
23.7099
23.4438
23.1714
22.8931
22.6102
22.3248
22.0392
21.7567
21.4805
21.2141
20.9611
20.7248
20.5082
20.3142
20.1452
20.0035
19.8909
19.8091
19.7597
19.7437
19.7618
19.8132
19.8949
19.9999
20.1155
20.2234
20.3013
20.33
20.3005
5.50
27.5369
27.6012
27.5429
27.3696
27.1073
26.7896
26.4465
26.0992
25.7596
25.4323
25.1175
24.8128
24.5152
24.2213
23.9288
23.6356
23.341
23.0449
22.7482
22.4525
22.1601
21.8738
21.5969
21.3327
21.0846
20.8559
20.6499
20.4695
20.3174
20.196
20.1075
20.0542
20.0378
20.0598
20.1208
20.2193
20.3511
20.5064
20.669
20.8158
20.9202
20.9596
20.9239
6.00
28.1857
28.2584
28.1974
28.01
27.7219
27.3679
26.9805
26.5844
26.1947
25.8186
25.4581
25.1118
24.777
24.4508
24.1303
23.8136
23.4995
23.1876
22.8787
22.574
22.2757
21.9864
21.709
21.4469
21.2033
20.9816
20.7848
20.616
20.4779
20.373
20.3039
20.2725
20.2808
20.3301
20.4201
20.5488
20.71
20.8924
21.0775
21.241
21.3557
21.3994
21.3622
6.50
28.6057
28.68
28.6215
28.4358
28.1456
27.7827
27.3789
26.9595
26.5418
26.1352
25.7436
25.3671
25.0043
24.6526
24.3097
23.9737
23.6435
23.3186
22.9996
22.6876
22.3847
22.0931
21.8158
21.5558
21.3164
21.1006
20.9116
20.7521
20.6251
20.5328
20.4777
20.4616
20.4861
20.5517
20.6576
20.8004
20.9726
21.1619
21.3496
21.5122
21.625
21.668
21.6327
7.00
28.8296
28.9007
28.8472
28.6729
28.3962
28.0443
27.6454
27.2239
26.7975
26.3771
25.9685
25.5736
25.1921
24.8226
24.4633
24.113
23.7705
23.4358
23.1092
22.7919
22.4857
22.193
21.9163
21.6586
21.423
21.2123
21.0295
20.8774
20.7584
20.6749
20.6288
20.6217
20.6544
20.7269
20.8372
20.9809
21.15
21.3316
21.5082
21.6587
21.7619
21.8013
21.7697
7.50
28.8999
28.9646
28.9167
28.7582
28.5035
28.1742
27.7944
27.3858
26.9656
26.5453
26.1322
25.7294
25.3383
24.9584
24.589
24.2294
23.8789
23.5377
23.2062
22.8858
22.5781
22.2853
22.0099
21.7548
21.5226
21.3163
21.1384
20.9916
20.878
20.7997
20.7583
20.7546
20.7891
20.8606
20.9667
21.102
21.2582
21.4231
21.5808
21.7135
21.8036
21.8379
21.8105
8.00
28.8571
28.9138
28.8708
28.7291
28.4992
28.1979
27.8448
27.4585
27.0548
26.6451
26.2372
25.8357
25.4428
25.0595
24.686
24.322
23.9677
23.6234
23.2899
22.9685
22.661
22.3694
22.0962
21.8439
21.6152
21.4125
21.2385
21.0953
20.9849
20.9089
20.8683
20.8638
20.8949
20.96
21.0558
21.1767
21.3145
21.4581
21.5938
21.7066
21.7826
21.8113
21.7881
177
TEC generated using four random distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
93.852
90.1144
86.4029
82.7209
79.0729
75.4641
71.9005
68.3898
64.9412
61.5659
58.2776
55.0936
52.0348
49.127
46.4011
43.8942
41.6483
39.7093
38.1235
36.9327
36.1682
35.8464
35.9665
36.5123
37.4565
38.7655
40.4036
42.335
44.5255
46.9431
49.5585
52.3453
55.2799
58.342
61.5137
64.7797
68.1272
71.545
75.0238
78.5555
82.1335
85.752
89.406
0.50
92.7203
88.9351
85.1718
81.4337
77.7247
74.0491
70.4125
66.8218
63.2851
59.8131
56.4185
53.1179
49.9317
46.8862
44.0137
41.3543
38.9553
36.8709
35.1575
33.8677
33.0419
32.7007
32.8421
33.4439
34.471
35.882
37.6348
39.6884
42.0046
44.5482
47.2871
50.193
53.2411
56.4102
59.6821
63.0415
66.4757
69.9739
73.527
77.1276
80.7693
84.4468
88.1556
1.00
91.7547
87.9281
84.1198
80.3328
76.5701
72.8358
69.1346
65.4724
61.8568
58.297
54.8049
51.3958
48.0895
44.9114
41.8945
39.0811
36.5236
34.2841
32.4311
31.0307
30.1351
29.7708
29.934
30.5946
31.7077
33.2235
35.0929
37.2703
39.7129
42.3821
45.2431
48.2657
51.4237
54.6955
58.0625
61.5099
65.0249
68.5975
72.219
75.8825
79.5821
83.313
87.071
1.50
90.9605
87.0994
83.2537
79.4258
75.6183
71.8346
68.0788
64.3562
60.6731
57.0378
53.4609
49.9564
46.5425
43.2435
40.0921
37.1312
34.4169
32.0191
30.0185
28.4974
27.5228
27.1292
27.3104
28.027
29.2231
30.8402
32.8232
35.1211
37.6868
40.4777
43.4561
46.5896
49.8512
53.2184
56.6731
60.2006
63.7888
67.4281
71.1106
74.8297
78.5803
82.3578
86.1588
2.00
90.3419
86.454
82.5792
78.7193
74.8768
71.0545
67.2559
63.4855
59.749
56.0535
52.4086
48.8265
45.3241
41.924
38.6571
35.5662
32.709
30.161
28.0144
26.3678
25.3055
24.8717
25.0589
25.8181
27.0837
28.7898
30.876
33.2856
35.9663
38.8706
41.9574
45.1922
48.5471
51.9996
55.5317
59.1292
62.7807
66.4773
70.2117
73.978
77.7714
81.5882
85.4249
2.50
89.9024
85.9959
82.1007
78.2186
74.3517
70.5025
66.6741
62.8705
59.0967
55.3591
51.6663
48.0294
44.4636
40.9899
37.6375
34.4474
31.4769
28.8043
26.5291
24.7635
23.6075
23.1165
23.2842
24.0568
25.3637
27.1355
29.3062
31.8124
34.594
37.5978
40.779
44.1009
47.5351
51.0589
54.655
58.3098
62.0128
65.7555
69.5313
73.335
77.1623
81.0098
84.8745
3.00
89.6444
85.7276
81.8213
77.9271
74.047
70.1834
66.3391
62.5179
58.7244
54.9648
51.2469
47.5812
43.9821
40.4693
37.0703
33.8244
30.787
28.0354
25.6703
23.8093
22.5608
21.9895
22.0965
22.8352
24.1406
25.9439
28.1725
30.7524
33.614
36.6969
39.9522
43.3419
46.8366
50.4143
54.0581
57.7551
61.4955
65.2714
69.0769
72.9072
76.7584
80.6274
84.5116
3.50
89.5689
85.6504
81.7425
77.8466
73.9648
70.0995
66.2536
62.4309
58.6361
54.8753
51.1563
47.4897
43.8896
40.3755
36.9742
33.7236
30.6767
27.9067
25.5087
23.5932
22.2644
21.5905
21.5886
22.2368
23.4899
25.2832
27.5351
30.1576
33.0694
36.203
39.5057
42.9379
46.4702
50.0807
53.7531
57.475
61.2371
65.0321
68.8543
72.6994
76.5638
80.4445
84.3393
4.00
89.676
85.7644
81.8641
77.9769
74.1048
70.2505
66.4173
62.609
58.8309
55.0893
51.3928
47.7525
44.1831
40.7046
37.3442
34.1391
31.1398
28.4133
26.0428
24.1212
22.7358
21.9516
21.8082
22.3217
23.4771
25.2171
27.4501
30.0742
32.9971
36.1448
39.4616
42.9063
46.4493
50.0687
53.7483
57.476
61.2429
65.0417
68.8671
72.7146
76.581
80.4633
84.3593
4.50
89.9646
86.0681
82.1846
78.316
74.4647
70.6336
66.8265
63.0477
59.3032
55.6
51.9476
48.3581
44.8473
41.4363
38.1529
35.0338
32.1267
29.4906
27.1939
25.3073
23.8964
23.0208
22.7407
23.1091
24.1405
25.7877
27.9551
30.5323
33.4198
36.5392
39.832
43.256
46.7804
50.3829
54.0473
57.7611
61.515
65.302
69.1164
72.9538
76.8108
80.6843
84.5722
5.00
90.4322
86.559
82.7009
78.8603
75.04
71.2435
67.4749
63.7394
60.0436
56.3955
52.8056
49.2871
45.8572
42.5377
39.3568
36.3502
33.5615
31.0411
28.8425
27.0175
25.6148
24.6897
24.3141
24.5619
25.4665
26.9931
29.0517
31.5333
34.338
37.3857
40.6161
43.9854
47.4618
51.0219
54.6485
58.3285
62.0521
65.8116
69.6011
73.4159
77.2521
81.1067
84.9771
5.50
91.0757
87.233
83.4084
79.6046
75.8248
72.073
68.354
64.6737
61.0394
57.4603
53.9475
50.5156
47.1822
43.97
40.9066
38.0254
35.3653
32.9684
30.8765
29.1288
27.7652
26.8384
26.4213
26.5895
27.3822
28.7765
30.6967
33.0448
35.7268
38.6648
41.7983
45.0823
48.4836
51.9773
55.5449
59.1724
62.849
66.5663
70.3176
74.0977
77.9023
81.728
85.5719
6.00
91.8907
88.0855
84.3017
80.5425
76.8115
73.1133
69.4533
65.8381
62.2759
58.7763
55.3517
52.017
48.7904
45.6941
42.7546
40.0026
37.4719
35.1976
33.214
31.5539
30.2538
29.3633
28.948
29.0738
29.7766
31.0425
32.8128
35.0061
37.5395
40.3404
43.3504
46.5243
49.8277
53.2345
56.7247
60.283
63.8975
67.5589
71.2597
74.9939
78.7567
82.5442
86.3531
6.50
92.8723
89.1107
85.3742
81.6663
77.9914
74.3543
70.7611
67.2191
63.7368
60.3249
56.9959
53.765
50.6505
47.6738
44.8595
42.2353
39.8308
37.6762
35.801
34.2352
33.0136
32.1813
31.7932
31.9014
32.5349
33.6855
35.3098
37.3435
39.7169
42.3657
45.2353
48.2817
51.4703
54.774
58.1717
61.6469
65.1864
68.78
72.4193
76.0976
79.8094
83.5501
87.3161
7.00
94.0148
90.3022
86.6186
82.968
79.355
75.7852
72.265
68.8021
65.4058
62.0868
58.858
55.7347
52.7343
49.8774
47.1866
44.687
42.4046
40.3661
38.5985
37.13
35.9932
35.2274
34.8768
34.9808
35.561
36.6123
38.103
39.9837
42.1978
44.6902
47.4117
50.3209
53.3837
56.573
59.8669
63.248
66.7022
70.2181
73.7867
77.4004
81.053
84.7393
88.4552
7.50
95.3119
91.653
88.0272
84.4387
80.8926
77.3948
73.9523
70.573
67.2664
64.0437
60.9175
57.9029
55.0166
52.2778
49.7074
47.3281
45.1633
43.2373
41.5749
40.2027
39.1503
38.4511
38.1395
38.245
38.783
39.7499
41.1223
42.8627
44.9259
47.2655
49.8385
52.607
55.5387
58.6069
61.7897
65.0688
68.4298
71.8603
75.3507
78.8925
82.479
86.1044
89.7639
8.00
96.7573
93.156
89.5918
86.0693
82.5939
79.1718
75.8102
72.5174
69.303
66.1781
63.1552
60.2488
57.4749
54.8513
52.3975
50.1338
48.0819
46.2638
44.7026
43.4227
42.4503
41.8131
41.538
41.6466
42.15
43.045
44.3144
45.929
47.853
50.0482
52.4775
55.1069
57.9066
60.851
63.9185
67.091
70.3533
73.6929
77.0992
80.5634
84.0782
87.6372
91.2351
178
TEC generated using four random distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
39.3324
31.4416
27.6559
27.6592
31.6425
39.2658
46.5873
52.3034
55.7821
56.6643
54.8318
50.4091
43.7852
35.7794
29.0513
27.3778
28.6565
34.825
42.5818
49.3075
54.1133
56.496
56.2014
53.2158
47.7731
40.4059
32.3791
27.8469
27.5173
30.7829
38.2255
45.6901
51.6628
55.4645
56.7033
55.2294
51.1343
44.7688
36.8668
29.6541
27.4164
28.2447
33.81
0.50
46.6165
41.3448
38.3562
38.3871
41.4084
46.5947
52.1647
56.7647
59.6191
60.3226
58.7621
55.1132
49.8978
44.1651
39.6867
38
39.3417
43.494
49.0587
54.3343
58.2478
60.2013
59.9206
57.4148
52.9977
47.3875
41.9491
38.5797
38.2094
40.8484
45.8463
51.4588
56.2421
59.3583
60.3599
59.0964
55.7033
50.6498
44.8987
40.1388
38.0487
38.9889
42.8196
1.00
52.4773
49.7062
48.0966
48.1028
49.7124
52.4588
55.5725
58.2821
60.0117
60.431
59.4569
57.2578
54.2674
51.1794
48.8285
47.8908
48.6214
50.8051
53.8123
56.8364
59.1775
60.365
60.1758
58.6346
56.023
52.892
50.0221
48.2225
48.0047
49.4189
52.0551
55.1673
57.9688
59.8528
60.4563
59.663
57.6075
54.6874
51.5649
49.0703
47.92
48.4313
50.4509
1.50
55.9701
55.6365
55.4453
55.4445
55.634
55.9662
56.3583
56.7143
56.9482
57.0044
56.8692
56.5747
56.1914
55.8127
55.5323
55.4204
55.5051
55.7648
56.1344
56.5226
56.8349
56.9963
56.9684
56.7576
56.4142
56.0209
55.6741
55.4603
55.4331
55.5992
55.9166
56.3062
56.6724
56.9266
57.0081
56.8974
56.6207
56.2441
55.8592
55.561
55.4241
55.4828
55.7222
2.00
56.7126
58.6206
59.6903
59.7048
58.6559
56.7496
54.3997
52.1799
50.6859
50.3325
51.2126
53.0754
55.4092
57.6207
59.2048
59.8315
59.3734
57.9149
55.7541
53.3845
51.4122
50.379
50.5699
51.9254
54.0648
56.4162
58.4085
59.6064
59.7661
58.8512
57.0392
54.7177
52.4448
50.8246
50.3068
51.0305
52.7882
55.0939
57.3538
59.0445
59.8101
59.4958
58.1575
2.50
54.6658
58.4154
60.4721
60.5211
58.5349
54.7856
49.9152
45.07
41.7806
41.0379
42.9708
47.0754
52.0195
56.4668
59.5404
60.748
59.9011
57.0977
52.7572
47.7236
43.3691
41.1263
41.5566
44.5493
49.2045
54.0708
58.0048
60.3108
60.634
58.9093
55.3662
50.591
45.6568
42.0808
40.9806
42.5684
46.4489
51.3674
55.9409
59.2324
60.7048
60.1313
57.5711
3.00
50.0889
55.0372
57.7115
57.8102
55.287
50.3587
43.5695
36.1554
31.2114
30.3522
32.9289
39.3387
46.4862
52.4836
56.4997
58.0791
57.0317
53.4224
47.5951
40.3081
33.4664
30.4486
30.9478
35.4035
42.4996
49.2885
54.5016
57.5008
57.9496
55.768
51.136
44.5456
37.0893
31.5994
30.2927
32.3271
38.3802
45.579
51.7883
56.0998
58.0191
57.3222
54.0398
3.50
43.5356
48.7635
51.5922
51.7513
49.1871
44.0611
36.7404
27.7913
21.6688
21.5615
22.9305
31.7114
39.6829
46.0712
50.3055
51.9972
50.9692
47.262
41.1275
33.0186
23.6522
21.6436
21.4699
26.7576
35.3201
42.6845
48.1993
51.3667
51.888
49.6806
44.8778
37.8203
29.0462
21.6915
21.5868
21.9437
30.5704
38.7018
45.3364
49.8834
51.9276
51.263
47.9013
4.00
35.8379
40.1566
42.5645
42.784
40.7767
36.7368
31.1581
25.1368
20.9335
19.8531
21.7974
26.8117
32.7499
37.9162
41.4576
42.9359
42.1812
39.2539
34.4626
28.4982
22.9368
20.115
20.2757
23.6981
29.4
35.1477
39.6842
42.3674
42.8845
41.1669
37.3763
31.9577
25.8918
21.3047
19.8358
21.3368
26.0415
31.9806
37.3107
41.0998
42.8669
42.4101
39.7594
4.50
28.3493
30.2969
31.4529
31.6577
30.9052
29.343
27.2688
25.1029
23.3468
22.5528
22.7285
24.5231
27.0084
29.2745
30.9083
31.6624
31.4438
30.3131
28.484
26.3133
24.2561
22.8806
22.4969
23.2984
25.5925
28.0463
30.0787
31.3523
31.687
31.0565
29.5878
27.5595
25.3787
23.5326
22.6037
22.634
24.2099
26.6799
29.0029
30.7382
31.6178
31.5282
30.5096
5.00
26.9137
24.2207
22.3448
21.787
22.7259
25.393
28.5049
31.1694
32.9134
33.488
32.8332
31.0722
28.5211
25.6944
23.2611
21.9395
21.9748
23.7341
26.7552
29.7489
32.0578
33.3138
33.352
32.1915
30.0372
27.2926
24.548
22.5204
21.7842
22.4902
24.9849
28.1041
30.8609
32.7458
33.483
32.9884
31.3604
28.8887
26.0626
23.5346
22.0367
21.8864
23.3918
5.50
30.0057
23.6427
20.1703
19.9406
23.1207
29.2012
35.4449
40.4701
43.5968
44.4743
42.9962
39.2818
33.7078
27.107
21.6432
19.7437
20.8106
25.59
31.9949
37.823
42.0858
44.265
44.1209
41.6448
37.0593
30.8925
24.3898
20.4101
19.8115
22.467
28.34
34.6663
39.9016
43.3062
44.4934
43.3261
39.8932
34.5322
27.9875
22.175
19.8209
20.4642
24.7913
6.00
35.3103
26.0903
22.5947
22.47
26.4452
35.1185
42.7519
48.6136
52.1741
53.1004
51.2762
46.8051
40.0042
31.4053
23.0066
22.5399
22.676
30.2691
38.6051
45.5464
50.4645
52.9111
52.646
49.6487
44.1161
36.4562
27.3338
22.6173
22.4816
25.2961
34.0074
41.8271
47.9583
51.848
53.1354
51.6752
47.5417
41.0244
32.6241
23.5997
22.5568
22.522
29.1007
6.50
42.5662
35.8398
32.2581
32.2926
35.9649
42.5325
49.2291
54.5797
57.8574
58.6767
56.9198
52.7345
46.5822
39.4707
33.7674
31.8907
33.3787
38.6413
45.5342
51.7671
56.2846
58.5275
58.2288
55.3843
50.2669
43.5224
36.6169
32.4969
32.1044
35.2484
41.6056
48.3965
53.9771
57.5583
58.7163
57.2988
53.4171
47.4846
40.4057
34.3184
31.9403
32.9645
37.7783
7.00
49.4061
45.2236
42.8078
42.8272
45.2559
49.3859
53.9432
57.7985
60.219
60.8107
59.4695
56.3796
52.0597
47.4542
43.899
42.5068
43.6065
46.9081
51.3849
55.7529
59.0544
60.7127
60.4626
58.3224
54.6129
50.0251
45.7021
42.9939
42.68
44.8116
48.7843
53.3582
57.3571
59.9975
60.844
59.7552
56.8757
52.675
48.0361
44.2628
42.5487
43.3204
46.3733
7.50
54.3142
52.6131
51.6285
51.6288
52.6098
54.2996
56.2499
57.9801
59.0989
59.3688
58.7314
57.3146
55.426
53.5151
52.0767
51.5013
51.9442
53.2792
55.1424
57.0532
58.5582
59.3279
59.2006
58.1986
56.5298
54.5706
52.8062
51.7058
51.5693
52.4305
54.0495
55.9937
57.7785
58.9959
59.3859
58.8656
57.5382
55.6888
53.7519
52.2245
51.5196
51.8285
53.0619
8.00
56.6391
57.3126
57.6951
57.6983
57.3207
56.6489
55.8415
55.096
54.6004
54.4821
54.7712
55.3922
56.1867
56.958
57.5213
57.7453
57.5782
57.0576
56.3043
55.4988
54.841
54.4985
54.5595
55.0075
55.7267
56.5357
57.2371
57.6651
57.7207
57.3905
56.7499
55.9496
55.1842
54.6463
54.4739
54.7111
55.2957
56.0782
56.864
57.4639
57.7378
57.6224
57.1435
179
TEC generated using four random distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.5185
22.517
22.5153
22.5134
22.5112
22.5086
22.5057
22.5023
22.4983
22.4938
22.4884
22.4823
22.4751
22.4669
22.4576
22.4472
22.4359
22.4241
22.4125
22.4019
22.3932
22.3873
22.3849
22.3865
22.3919
22.4003
22.4108
22.4221
22.4334
22.444
22.4538
22.4625
22.4701
22.4767
22.4825
22.4875
22.4919
22.4957
22.499
22.5019
22.5045
22.5067
22.5087
0.50
22.5205
22.5191
22.5175
22.5157
22.5137
22.5112
22.5084
22.5051
22.5013
22.4967
22.4913
22.4849
22.4773
22.4683
22.4578
22.4457
22.4321
22.4174
22.4025
22.3885
22.3766
22.3684
22.365
22.3672
22.3749
22.3867
22.4009
22.4157
22.4298
22.4426
22.4538
22.4635
22.4718
22.4788
22.4848
22.4899
22.4942
22.498
22.5012
22.5041
22.5065
22.5087
22.5106
1.00
22.5226
22.5214
22.52
22.5184
22.5165
22.5143
22.5117
22.5086
22.5049
22.5005
22.4952
22.4887
22.4808
22.4713
22.4596
22.4457
22.4294
22.411
22.3916
22.3727
22.3563
22.3444
22.3392
22.3422
22.3535
22.3708
22.3905
22.41
22.4276
22.4427
22.4554
22.466
22.4747
22.4819
22.4879
22.4929
22.4972
22.5008
22.5039
22.5066
22.5089
22.5109
22.5126
1.50
22.5249
22.5238
22.5226
22.5212
22.5196
22.5177
22.5154
22.5126
22.5093
22.5052
22.5001
22.4939
22.4861
22.4762
22.4638
22.4482
22.4288
22.4058
22.38
22.354
22.331
22.3134
22.3043
22.3082
22.326
22.3525
22.3807
22.4064
22.4279
22.4453
22.4592
22.4702
22.4791
22.4862
22.492
22.4968
22.5008
22.5041
22.507
22.5094
22.5115
22.5133
22.5149
2.00
22.5273
22.5265
22.5255
22.5244
22.523
22.5214
22.5195
22.5172
22.5143
22.5108
22.5063
22.5007
22.4934
22.4838
22.4712
22.4544
22.4322
22.4034
22.3687
22.3318
22.2991
22.2726
22.2545
22.2587
22.2897
22.333
22.374
22.4073
22.4325
22.4515
22.4658
22.4767
22.4851
22.4918
22.4971
22.5015
22.505
22.508
22.5105
22.5126
22.5144
22.516
22.5173
2.50
22.5298
22.5292
22.5285
22.5277
22.5267
22.5255
22.5241
22.5223
22.5201
22.5173
22.5137
22.509
22.5028
22.4944
22.4827
22.4662
22.4423
22.4078
22.3603
22.304
22.2567
22.2208
22.1765
22.1782
22.2429
22.3181
22.3763
22.4163
22.4435
22.4623
22.4757
22.4856
22.493
22.4987
22.5032
22.5069
22.5098
22.5123
22.5143
22.5161
22.5176
22.5188
22.52
3.00
22.5324
22.5321
22.5317
22.5312
22.5306
22.5299
22.529
22.5279
22.5264
22.5246
22.5222
22.5189
22.5144
22.5082
22.499
22.4851
22.4631
22.4268
22.3655
22.2709
22.1857
22.1685
22.0326
22.0369
22.2006
22.3262
22.3976
22.4381
22.4626
22.4784
22.4891
22.4968
22.5025
22.5068
22.5102
22.5129
22.5151
22.517
22.5185
22.5198
22.5209
22.5219
22.5227
3.50
22.5351
22.535
22.5349
22.5348
22.5346
22.5344
22.5341
22.5337
22.5332
22.5324
22.5314
22.5299
22.5278
22.5247
22.5198
22.5118
22.4979
22.4714
22.4156
22.2885
22.088
22.1841
21.8601
21.9241
22.2549
22.3929
22.4483
22.475
22.4899
22.4992
22.5054
22.5099
22.5133
22.5158
22.5179
22.5195
22.5208
22.522
22.5229
22.5237
22.5244
22.525
22.5256
4.00
22.5378
22.538
22.5382
22.5384
22.5387
22.539
22.5393
22.5397
22.5401
22.5405
22.541
22.5416
22.5422
22.5429
22.5435
22.544
22.5441
22.543
22.5388
22.53
22.5662
22.6474
22.4206
22.4995
22.5353
22.5269
22.523
22.522
22.5222
22.5228
22.5235
22.5242
22.5248
22.5254
22.5259
22.5263
22.5268
22.5271
22.5275
22.5278
22.528
22.5283
22.5285
4.50
22.5404
22.5409
22.5414
22.542
22.5427
22.5436
22.5445
22.5456
22.547
22.5486
22.5506
22.5532
22.5565
22.561
22.5673
22.5767
22.5917
22.6185
22.6744
22.814
23.1489
23.2136
22.8791
22.9703
22.7736
22.6487
22.5939
22.5679
22.5542
22.5463
22.5415
22.5385
22.5364
22.535
22.534
22.5332
22.5327
22.5323
22.532
22.5318
22.5317
22.5315
22.5315
5.00
22.543
22.5438
22.5446
22.5456
22.5467
22.548
22.5495
22.5514
22.5536
22.5563
22.5597
22.5641
22.5698
22.5775
22.5883
22.6042
22.6288
22.6697
22.7418
22.8688
23.0344
23.038
22.8962
22.8757
22.7916
22.6986
22.6382
22.6024
22.5807
22.567
22.558
22.5518
22.5474
22.5442
22.5418
22.54
22.5385
22.5374
22.5365
22.5358
22.5352
22.5348
22.5344
5.50
22.5456
22.5465
22.5477
22.5489
22.5504
22.5522
22.5542
22.5567
22.5597
22.5633
22.5678
22.5736
22.5811
22.591
22.6044
22.6234
22.6508
22.6912
22.7499
22.8257
22.8909
22.8917
22.845
22.8075
22.76
22.7042
22.6573
22.6232
22.5996
22.5832
22.5717
22.5634
22.5572
22.5526
22.549
22.5463
22.5441
22.5423
22.5409
22.5397
22.5387
22.5379
22.5372
6.00
22.548
22.5492
22.5505
22.5521
22.5539
22.5561
22.5586
22.5615
22.5651
22.5694
22.5748
22.5815
22.59
22.6009
22.6153
22.6344
22.6599
22.6934
22.7347
22.7783
22.8093
22.8128
22.7936
22.7663
22.7332
22.6964
22.6619
22.6334
22.6114
22.5948
22.5823
22.5728
22.5656
22.5599
22.5555
22.552
22.5492
22.5469
22.545
22.5434
22.5421
22.5409
22.54
6.50
22.5502
22.5516
22.5532
22.555
22.5571
22.5596
22.5624
22.5658
22.5698
22.5746
22.5804
22.5876
22.5965
22.6076
22.6215
22.639
22.6607
22.6865
22.7149
22.7415
22.7591
22.7627
22.753
22.7349
22.7116
22.6855
22.6599
22.6369
22.6177
22.6022
22.5898
22.5801
22.5723
22.5661
22.5611
22.5571
22.5538
22.551
22.5487
22.5468
22.5452
22.5438
22.5426
7.00
22.5523
22.5539
22.5557
22.5577
22.56
22.5627
22.5658
22.5694
22.5736
22.5787
22.5847
22.592
22.6008
22.6114
22.6241
22.6393
22.657
22.6766
22.6964
22.7136
22.7248
22.7276
22.722
22.7099
22.6933
22.6743
22.6548
22.6365
22.6203
22.6064
22.5949
22.5853
22.5775
22.5711
22.5658
22.5614
22.5578
22.5547
22.5521
22.5499
22.5481
22.5464
22.5451
7.50
22.5543
22.556
22.5579
22.56
22.5625
22.5653
22.5686
22.5723
22.5767
22.5818
22.5879
22.5949
22.6032
22.6129
22.6242
22.6371
22.6513
22.6661
22.6803
22.6921
22.6996
22.7017
22.6981
22.6896
22.6777
22.6635
22.6486
22.6339
22.6204
22.6083
22.5979
22.5889
22.5814
22.575
22.5696
22.5651
22.5612
22.5579
22.5551
22.5527
22.5507
22.5489
22.5473
8.00
22.556
22.5578
22.5598
22.5621
22.5646
22.5676
22.5709
22.5747
22.5791
22.5841
22.5899
22.5966
22.6043
22.613
22.6227
22.6335
22.6448
22.6561
22.6665
22.675
22.6803
22.6817
22.6792
22.6732
22.6643
22.6536
22.642
22.6302
22.619
22.6086
22.5993
22.5911
22.584
22.5778
22.5725
22.568
22.5641
22.5607
22.5578
22.5552
22.553
22.5511
22.5494
180
TEC generated using six well distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
25.316
24.4327
23.5891
22.7986
22.0776
21.4457
20.922
20.5205
20.2441
20.0823
20.0138
20.0123
20.0518
20.1102
20.1698
20.218
20.2463
20.2493
20.2244
20.1704
20.0869
19.9738
19.8311
19.6584
19.4555
19.2226
18.961
18.6735
18.366
18.0481
17.734
17.4431
17.1998
17.0321
16.9685
17.032
17.2345
17.5734
18.0351
18.5998
19.2477
19.9612
20.7264
0.50
25.2875
24.3952
23.5416
22.7402
22.0094
21.371
20.8479
20.4572
20.2031
20.0733
20.0422
20.0791
20.1546
20.2442
20.3291
20.3965
20.4379
20.4493
20.4288
20.3764
20.2926
20.1778
20.032
19.8547
19.645
19.402
19.1256
18.8177
18.4831
18.1311
17.7765
17.4402
17.1493
16.9356
16.8326
16.8677
17.0547
17.3902
17.8568
18.4312
19.0907
19.8162
20.5928
1.00
25.3445
24.4513
23.5962
22.7934
22.0618
21.4251
20.9083
20.5311
20.2984
20.1963
20.1963
20.2644
20.3684
20.482
20.5853
20.6651
20.7137
20.7279
20.7074
20.6533
20.5671
20.4499
20.3019
20.1221
19.909
19.6603
19.3747
19.0524
18.697
18.3174
17.929
17.554
17.2221
16.9683
16.8296
16.8371
17.0061
17.3323
17.796
18.3714
19.0338
19.7631
20.5436
1.50
25.4896
24.6045
23.7582
22.9652
22.2446
21.6203
21.1179
20.7572
20.5433
20.4618
20.483
20.5716
20.694
20.8223
20.9354
21.0199
21.0685
21.0794
21.0538
20.9943
20.9036
20.7833
20.6337
20.4537
20.2408
19.9916
19.7029
19.3731
19.0044
18.6052
18.1916
17.7875
17.4245
17.14
16.9727
16.955
17.103
17.4124
17.8629
18.4281
19.0827
19.806
20.5822
2.00
25.7218
24.8537
24.0266
23.2546
22.5566
21.9555
21.475
21.1334
20.9348
20.8653
20.8966
20.994
21.1238
21.2567
21.3707
21.4515
21.4928
21.4941
21.4585
21.3901
21.2926
21.1683
21.0178
20.8396
20.6304
20.3855
20.0999
19.7697
19.3956
18.9853
18.5558
18.1329
17.7502
17.4458
17.2583
17.2191
17.3439
17.6292
18.0564
18.6004
19.2367
19.9446
20.7082
2.50
26.0363
25.193
24.3934
23.6515
22.985
22.4147
21.9611
21.6394
21.4522
21.3871
21.4184
21.5141
21.6409
21.7691
21.8755
21.9453
21.9727
21.959
21.9091
21.8289
21.7229
21.5939
21.4427
21.2675
21.0645
20.8278
20.5504
20.2261
19.8537
19.4403
19.0037
18.5718
18.1795
17.865
17.6651
17.6085
17.7099
17.9669
18.3639
18.8788
19.4887
20.1737
20.9177
3.00
26.4254
25.6122
24.8458
24.1394
23.5091
22.9727
22.5471
22.2439
22.0644
21.9976
22.0212
22.1063
22.2215
22.3371
22.4288
22.4815
22.4902
22.4579
22.3914
22.2976
22.182
22.0478
21.8956
21.7238
21.5279
21.3012
21.0349
20.721
20.3559
19.9459
19.5099
19.0774
18.6841
18.3675
18.1615
18.0919
18.1719
18.4006
18.7655
19.2478
19.827
20.4844
21.2042
3.50
26.8793
26.0994
25.3687
24.6994
24.1057
23.6023
23.2025
22.9146
22.7388
22.6654
22.6752
22.7428
22.8391
22.9352
23.0067
23.0384
23.0261
22.9742
22.8907
22.7834
22.6581
22.5182
22.3644
22.195
22.0052
21.7877
21.5327
21.2306
20.8762
20.4752
20.0467
19.621
19.2341
18.9217
18.7151
18.6373
18.7003
18.9042
19.2393
19.6898
20.2379
20.8663
21.5598
4.00
27.3878
26.6417
25.9466
25.3132
24.7535
24.2795
23.9012
23.6243
23.4479
23.3634
23.3544
23.3986
23.4696
23.5403
23.5874
23.5964
23.5634
23.4935
23.3948
23.2754
23.1412
22.9956
22.8391
22.67
22.4835
22.2722
22.026
21.7346
21.3924
21.0046
20.5899
20.1782
19.8043
19.5019
19.2999
19.2191
19.2707
19.4556
19.7661
20.1889
20.7084
21.3088
21.9758
4.50
27.9409
27.2276
26.5658
25.9651
25.4352
24.9856
24.6235
24.3527
24.1715
24.072
24.0399
24.0559
24.0964
24.1373
24.1574
24.1434
24.0916
24.0065
23.8956
23.7665
23.6247
23.4734
23.3131
23.142
22.9554
22.7461
22.5047
22.2215
21.8918
21.5203
21.125
20.7337
20.3788
20.0916
19.8991
19.8208
19.8671
20.0397
20.332
20.7327
21.2277
21.8028
22.4448
5.00
28.5295
27.8467
27.2152
26.643
26.1379
25.7073
25.3563
25.087
24.8971
24.7793
24.721
24.7055
24.7125
24.7211
24.713
24.6765
24.608
24.5105
24.3903
24.2538
24.1057
23.949
23.784
23.6088
23.4193
23.2086
22.9687
22.6918
22.3742
22.0215
21.6495
21.2833
20.9519
20.6843
20.5057
20.4346
20.4816
20.6482
20.9288
21.313
21.7881
22.3413
22.9604
5.50
29.1461
28.4909
27.8859
27.3377
26.8526
26.436
26.0914
25.8197
25.6181
25.4798
25.3938
25.3457
25.3182
25.2941
25.258
25.2
25.1162
25.0083
24.8806
24.7382
24.5849
24.4231
24.2529
24.0728
23.8787
23.6651
23.4254
23.154
22.8491
22.5164
22.17
21.8315
21.5267
21.2818
21.1205
21.0608
21.1131
21.2791
21.5533
21.9259
22.3852
22.9194
23.5178
6.00
29.7846
29.1537
28.5714
28.043
27.5734
27.1665
26.8245
26.5475
26.3322
26.1726
26.0588
25.9787
25.918
25.8624
25.7996
25.721
25.6228
25.5051
25.3708
25.2232
25.0654
24.8989
24.7239
24.5388
24.3403
24.124
23.8851
23.6201
23.3288
23.0171
22.6974
22.3881
22.1116
21.8916
21.7502
21.705
21.766
21.9349
22.2061
22.5703
23.0165
23.5341
24.1134
6.50
30.44
29.8304
29.2673
28.7549
28.2969
27.8962
27.554
27.2696
27.0399
26.859
26.7187
26.6085
26.517
26.4323
26.3446
26.2465
26.1342
26.007
25.8661
25.7137
25.5517
25.3811
25.202
25.0129
24.8113
24.594
24.3579
24.1011
23.8249
23.5351
23.2426
22.9632
22.7164
22.5231
22.4038
22.375
22.4466
22.6199
22.8896
23.2466
23.6809
24.1831
24.7443
7.00
31.1089
30.5176
29.9704
29.4708
29.0214
28.6243
28.2799
27.987
27.7426
27.5416
27.3767
27.2392
27.1197
27.0088
26.8983
26.7819
26.656
26.5192
26.3716
26.2144
26.0485
25.8745
25.6924
25.5008
25.2982
25.0823
24.8514
24.6051
24.3456
24.0786
23.8138
23.565
23.3488
23.1838
23.0882
23.0773
23.1599
23.3375
23.6052
23.9549
24.3775
24.8645
25.4081
7.50
31.7885
31.2129
30.679
30.1895
29.7463
29.3508
29.0028
28.7012
28.4427
28.223
28.0358
27.874
27.7298
27.5955
27.4643
27.331
27.1921
27.0458
26.8915
26.7295
26.5601
26.3836
26.1996
26.0075
25.806
25.594
25.3708
25.1372
24.8959
24.6525
24.4158
24.1978
24.0128
23.8769
23.8059
23.8132
23.9067
24.0878
24.3525
24.694
25.1044
25.576
26.1022
8.00
32.4769
31.9147
31.3919
30.9103
30.4716
30.0764
29.7243
29.4138
29.1423
28.9057
28.6988
28.5155
28.3495
28.1946
28.045
27.8963
27.7452
27.5897
27.4289
27.2623
27.0899
26.9117
26.7273
26.5364
26.3381
26.1323
25.919
25.6998
25.4778
25.2585
25.0499
24.8623
24.7081
24.6011
24.5547
24.5799
24.6835
24.8673
25.1282
25.4609
25.8586
26.3149
26.8236
181
TEC generated using six well distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
30.0707
32.6195
34.3762
35.0732
34.6093
33.0513
30.6345
27.6182
24.4202
22.7953
23.4395
25.5964
28.4352
31.2491
33.498
34.8183
35.0146
34.058
32.0897
29.3976
26.1579
23.4407
22.8216
24.2419
26.7884
29.6943
32.319
34.1999
35.047
34.7371
33.3142
30.993
28.0534
24.7901
22.8772
23.2454
25.2541
28.046
30.8982
33.2468
34.7052
35.056
34.248
0.50
27.476
29.8779
31.6096
32.3914
32.1341
30.9353
29.0932
26.9389
23.8979
22.1436
22.2371
23.6258
25.9965
28.5734
30.7321
32.0747
32.406
31.7172
30.1905
28.2084
25.5794
22.9146
21.9806
22.6753
24.5794
27.1305
29.5892
31.4304
32.3473
32.2265
31.1401
29.3588
27.2772
24.2576
22.2682
22.1466
23.3687
25.6537
28.2442
30.4861
31.9524
32.4225
31.8628
1.00
23.5083
25.4845
26.9258
27.634
27.5423
26.6967
25.2232
23.2729
21.1413
19.5081
19.1433
20.2785
22.2805
24.4121
26.1901
27.3296
27.6921
27.2621
26.1261
24.4262
22.3389
20.3236
19.1585
19.4752
21.0891
23.2227
25.247
26.7738
27.5858
27.5999
26.8483
25.4496
23.5525
21.4134
19.6668
19.1
20.0595
21.9939
24.1413
25.9862
27.2214
27.6905
27.3626
1.50
20.0233
20.5227
20.9063
21.1104
21.1056
20.8943
20.5098
20.0171
19.5157
19.1416
19.0422
19.2714
19.7266
20.2484
20.7078
21.0193
21.1345
21.0381
20.7458
20.3044
19.7936
19.3287
19.0579
19.1043
19.4506
19.9533
20.4612
20.8647
21.095
21.1185
20.9334
20.5688
20.0856
19.5782
19.1783
19.036
19.2246
19.659
20.1804
20.6539
20.9886
21.1314
21.0628
2.00
23.3863
21.5534
19.6473
18.229
18.2263
19.7159
21.6952
23.5628
25.0033
25.8341
25.973
25.4257
24.2678
22.6247
20.7104
18.9255
18.0019
18.751
20.5595
22.5411
24.2531
25.4454
25.9808
25.8168
24.9923
23.6055
21.8096
19.888
18.3582
18.1212
19.4711
21.4299
23.3342
24.8443
25.7628
25.9949
25.5357
24.4527
22.8645
20.9682
19.1337
18.0366
18.5648
2.50
27.6412
25.2566
22.6673
21.3966
21.7446
23.375
25.7624
28.1763
30.0718
31.1238
31.1977
30.3339
28.744
26.7097
24.043
21.9091
21.3736
22.3116
24.3626
26.8433
29.0857
30.6436
31.2775
30.9297
29.7156
27.9094
25.6237
22.9556
21.4661
21.62
23.0984
25.4295
27.8763
29.8637
31.0393
31.2445
30.4966
28.9855
27.0064
24.4086
22.1094
21.3493
22.1127
3.00
29.7122
26.7713
23.8032
22.741
23.694
25.8987
28.6971
31.3716
33.3968
34.442
34.3583
33.1763
31.1192
28.5492
25.3306
23.0617
22.9643
24.5264
27.0852
29.9076
32.3533
33.9832
34.5467
33.9722
32.3714
30.0522
27.218
24.1098
22.75
23.4857
25.5545
28.3189
31.0446
33.1791
34.3668
34.4351
33.3905
31.4294
28.9164
25.7576
23.2443
22.8587
24.2481
3.50
29.6128
25.9677
23.0331
22.3042
24.1914
27.1289
30.1602
32.8052
34.7012
35.5902
35.3339
33.9165
31.4307
28.0646
24.4952
22.3767
22.8822
25.4136
28.4637
31.3781
33.7371
35.2213
35.6234
34.8586
32.9613
30.0622
26.4537
23.3193
22.2327
23.8468
26.721
29.7711
32.4904
34.5031
35.5364
35.4356
34.1691
31.8167
28.5496
24.9207
22.5288
22.6551
25.0271
4.00
28.8229
25.2987
22.7515
22.0108
24.7576
27.6552
30.2889
32.4427
33.9085
34.5178
34.1662
32.8215
30.518
27.3601
23.8342
22.1152
23.1008
26.0324
28.8423
31.2945
33.1739
34.2857
34.4869
33.7044
31.9363
29.2435
25.7894
22.9641
21.8405
24.3656
27.2811
29.9622
32.1921
33.7602
34.4907
34.27
33.0566
30.8762
27.8214
24.2319
22.2983
22.7299
25.644
4.50
29.0053
28.0169
27.3649
27.2841
27.7914
28.6772
29.6665
30.535
31.125
31.3372
31.1282
30.5167
29.5964
28.5554
27.6755
27.2526
27.4404
28.1456
29.1083
30.0686
30.8321
31.2673
31.2988
30.9089
30.1469
29.145
28.1354
27.4219
27.2586
27.6962
28.548
29.538
30.4329
31.0668
31.3329
31.1802
30.6185
29.7306
28.6911
27.7717
27.2746
27.3812
28.031
5.00
30.1174
31.1573
31.7918
31.9229
31.5135
30.5967
29.2993
27.8874
26.7865
26.4234
26.9469
28.0819
29.4062
30.6094
31.4893
31.9141
31.8116
31.1734
30.0691
28.6793
27.3436
26.5203
26.5489
27.3901
28.6543
29.9566
31.0398
31.735
31.9365
31.5986
30.7442
29.4857
28.0674
26.8977
26.4194
26.8328
27.912
29.232
30.4648
31.3965
31.8871
31.8566
31.2874
5.50
31.0405
33.1277
34.4436
34.8254
34.184
32.5053
29.8364
26.2893
22.9231
21.3495
23.6618
26.7365
29.5964
32.0274
33.8042
34.7309
34.6753
33.5819
31.465
28.3953
24.5525
22.2079
21.9287
25.0085
28.015
30.7166
32.8908
34.3199
34.8325
34.3292
32.7867
30.2447
26.8031
23.1586
21.5195
23.249
26.3363
29.2365
31.7375
33.6135
34.6623
34.742
33.7868
6.00
30.8444
33.3428
35.0111
35.6138
35.0473
33.3389
30.6295
27.1743
23.8868
22.3928
23.5037
26.1594
29.1927
32.0094
34.185
35.4125
35.5131
34.4407
32.2756
29.1982
25.6253
22.9451
22.5749
24.5558
27.4691
30.4682
33.0524
34.8472
35.6002
35.1901
33.6273
31.0395
27.6571
24.2495
22.4443
23.2307
25.7687
28.7919
31.6644
33.9453
35.3119
35.5676
34.6489
6.50
29.1356
31.6543
33.4287
34.1771
33.8029
32.3959
30.2539
27.7082
24.4738
22.7561
23.1474
24.915
27.5526
30.2931
32.536
33.889
34.1518
33.3072
31.5319
29.2113
26.252
23.4678
22.6994
23.7613
25.9988
28.7685
31.3544
33.248
34.1421
33.9159
32.6337
30.5644
28.0973
24.851
22.8579
23.005
24.6134
27.181
29.9471
32.283
33.7697
34.1822
33.4788
7.00
25.8945
28.1505
29.7954
30.5703
30.3938
29.3482
27.6594
25.4905
22.9245
21.2189
21.0696
22.3215
24.5131
26.9232
28.9584
30.2469
30.6095
30.0366
28.6784
26.7865
24.3647
22.0134
20.961
21.4579
23.1982
25.5714
27.8784
29.6234
30.5222
30.4707
29.53
27.9108
25.8142
23.2438
21.3599
21.0021
22.0867
24.1941
26.6142
28.7252
30.1271
30.6166
30.1627
7.50
21.6046
23.233
24.4044
24.9921
24.947
24.2888
23.0923
21.4871
19.6934
18.0525
17.4469
18.6921
20.5557
22.3554
23.8063
24.7355
25.0506
24.7336
23.8301
22.4358
20.7167
18.9334
17.5691
17.8239
19.4816
21.3642
23.0395
24.2805
24.9502
24.9894
24.4093
23.2783
21.7167
19.9323
18.2409
17.4102
18.4658
20.3038
22.1319
23.6409
24.6463
25.0455
24.811
8.00
20.8597
19.8972
18.8846
18.0799
18.0427
18.8527
19.9104
20.8988
21.6645
22.1164
22.2077
21.9329
21.3253
20.4588
19.4538
18.4851
17.9335
18.3287
19.3058
20.3584
21.2646
21.9027
22.2015
22.1325
21.707
20.9754
20.0314
19.015
18.1575
17.9866
18.7203
19.7696
20.7779
21.5794
22.0765
22.217
21.9897
21.4229
20.5849
19.5898
18.6018
17.9587
18.2269
182
TEC generated using six well distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.0607
21.8984
21.7199
21.5326
21.3498
21.1915
21.0841
21.0542
21.119
21.2747
21.4941
21.735
21.9573
22.1341
22.2539
22.3157
22.3236
22.2833
22.2008
22.0821
21.9335
21.7618
21.5731
21.3721
21.1609
20.9375
20.6948
20.4215
20.1031
19.7273
19.2917
18.8144
18.3393
17.9301
17.6484
17.5279
17.5632
17.7199
17.9528
18.2217
18.4972
18.7615
19.0055
0.50
22.1024
21.92
21.7131
21.4883
21.26
21.0534
20.9043
20.8535
20.9304
21.134
21.4244
21.7392
22.021
22.2369
22.377
22.4458
22.4519
22.4042
22.3103
22.1778
22.0145
21.8289
21.629
21.4218
21.2105
20.9931
20.7608
20.4973
20.1802
19.7862
19.3027
18.7443
18.1669
17.6618
17.3209
17.1926
17.2641
17.4811
17.7791
18.106
18.4277
18.7262
18.9941
1.00
22.1806
21.984
21.7544
21.4965
21.225
20.9691
20.7751
20.7001
20.79
21.0475
21.4167
21.8085
22.146
22.3916
22.5414
22.6075
22.6041
22.5429
22.433
22.2828
22.1014
21.8992
21.687
21.4742
21.2662
21.062
20.8518
20.615
20.3204
19.9312
19.4188
18.7889
18.1074
17.4981
17.0911
16.9531
17.0611
17.3364
17.6938
18.0697
18.427
18.749
19.0311
1.50
22.3049
22.105
21.8647
21.5871
21.2861
20.9938
20.7658
20.6748
20.7815
21.0906
21.5288
21.9802
22.3517
22.6058
22.7479
22.7986
22.777
22.6964
22.5659
22.3942
22.1915
21.9702
21.744
21.5255
21.3233
21.1384
20.9615
20.7693
20.5228
20.1707
19.6655
18.9984
18.2394
17.5412
17.0711
16.9147
17.0414
17.3517
17.7431
18.1438
18.5153
18.8428
19.1243
2.00
22.4827
22.2946
22.0629
21.7889
21.4855
21.1869
20.9546
20.87
20.9989
21.3406
21.8077
22.2715
22.6355
22.8679
22.9828
23.0068
22.9607
22.8569
22.7032
22.5077
22.2815
22.0391
21.7972
21.5722
21.3761
21.2135
21.077
20.943
20.7672
20.4864
20.0351
19.3893
18.6165
17.8815
17.3697
17.1803
17.2864
17.5842
17.9642
18.351
18.7057
19.0146
19.2773
2.50
22.7169
22.5591
22.3599
22.1196
21.8503
21.586
21.388
21.3341
21.4793
21.81
22.2372
22.6453
22.9525
23.1358
23.212
23.2065
23.1366
23.011
22.8353
22.6168
22.3672
22.1034
21.8451
21.6121
21.4203
21.2779
21.1807
21.1071
21.0111
20.8215
20.4616
19.8985
19.1948
18.5041
17.9966
17.7712
17.8176
18.0491
18.3656
18.6946
18.9981
19.2626
19.4874
3.00
23.004
22.8955
22.7537
22.5786
22.3801
22.187
22.05
22.0289
22.1577
22.4133
22.7247
23.0127
23.2248
23.3467
23.3884
23.3636
23.2803
23.1415
22.9501
22.7133
22.4442
22.1616
21.8881
21.6463
21.455
21.3255
21.2569
21.2303
21.2008
21.0954
20.8359
20.3921
19.8234
19.2554
18.8163
18.5847
18.565
18.7009
18.9166
19.1527
19.3761
19.5743
19.7451
3.50
23.3339
23.2907
23.2278
23.1444
23.0456
22.9472
22.8773
22.8669
22.9289
23.0458
23.1816
23.3043
23.3981
23.4577
23.4785
23.4527
23.3723
23.2331
23.0363
22.7899
22.5086
22.2135
21.9289
21.6792
21.4848
21.3583
21.3005
21.2951
21.3006
21.25
21.0756
20.7593
20.3571
19.9607
19.6478
19.4616
19.4062
19.452
19.5563
19.6827
19.8099
19.9281
20.0346
4.00
23.6896
23.7226
23.7528
23.7786
23.7978
23.8074
23.8041
23.7836
23.7424
23.6805
23.6056
23.5366
23.4959
23.4892
23.4947
23.4776
23.4108
23.2815
23.0892
22.8429
22.559
22.26
21.9712
21.7174
21.5187
21.3871
21.3235
21.313
21.3207
21.2934
21.1843
20.9905
20.7601
20.5505
20.3928
20.2906
20.2347
20.2129
20.2151
20.2333
20.262
20.2973
20.3367
4.50
24.0498
24.1622
24.29
24.4312
24.5764
24.7037
24.7761
24.7519
24.6085
24.3628
24.0685
23.7971
23.6093
23.5211
23.4961
23.4764
23.4175
23.2978
23.1141
22.8748
22.597
22.3032
22.0184
21.7663
21.5655
21.4264
21.3486
21.3192
21.3117
21.2918
21.2363
21.1556
21.0856
21.0517
21.044
21.0307
20.9877
20.9156
20.832
20.7552
20.6953
20.6547
20.6317
5.00
24.3916
24.5778
24.7964
25.0458
25.3121
25.5595
25.7243
25.729
25.5232
25.1271
24.6336
24.1673
23.8257
23.6341
23.5476
23.4961
23.4242
23.3028
23.1238
22.8935
22.627
22.3453
22.0717
21.8275
21.6293
21.4854
21.3951
21.3482
21.3274
21.3159
21.3104
21.3292
21.3958
21.506
21.6154
21.6656
21.626
21.5111
21.36
21.209
21.079
20.977
20.9023
5.50
24.6934
24.9401
25.2318
25.5675
25.9318
26.2824
26.5408
26.6036
26.3903
25.9075
25.2697
24.6438
24.1585
23.8498
23.6746
23.5621
23.4535
23.3146
23.1322
22.9082
22.6543
22.3883
22.1301
21.8986
21.7076
21.5643
21.4684
21.4133
21.3901
21.3949
21.4364
21.535
21.7014
21.9078
22.0847
22.1612
22.1114
21.9629
21.7672
21.5684
21.3921
21.2479
21.136
6.00
24.9388
25.2266
25.5655
25.9541
26.3761
26.7879
27.1076
27.2231
27.0364
26.5373
25.8393
25.1239
24.5358
24.123
23.8543
23.668
23.5089
23.3412
23.1477
22.9258
22.683
22.4329
22.1918
21.9751
21.7944
21.6561
21.5609
21.5061
21.4892
21.5134
21.5916
21.7405
21.959
22.2048
22.3999
22.4756
22.4152
22.2525
22.0405
21.8229
21.6256
21.4594
21.3259
6.50
25.1185
25.4259
25.7831
26.1869
26.6195
27.0379
27.3652
27.4969
27.3396
26.8764
26.2037
25.4855
24.8598
24.3832
24.0414
23.7889
23.5796
23.3801
23.1717
22.9488
22.7147
22.4791
22.2543
22.0525
21.8831
21.752
21.661
21.6102
21.6007
21.6387
21.7353
21.9
22.1229
22.3588
22.5376
22.6026
22.543
22.3898
22.1886
21.978
21.7821
21.6121
21.4713
7.00
25.2306
25.5376
25.8874
26.2736
26.677
27.0567
27.3456
27.4578
27.3196
26.9178
26.3259
25.6718
25.0701
24.5778
24.1967
23.8988
23.6503
23.4235
23.2012
22.9761
22.7489
22.5257
22.3154
22.1272
21.9687
21.845
21.7586
21.7112
21.7056
21.747
21.8427
21.9951
22.1897
22.3874
22.5338
22.587
22.5387
22.4109
22.2384
22.052
21.8731
21.7128
21.5757
7.50
25.2802
25.5712
25.8945
26.2414
26.5915
26.9082
27.137
27.2138
27.0875
26.7517
26.2585
25.6987
25.1583
24.688
24.2996
23.9802
23.7081
23.4631
23.2311
23.005
22.7839
22.5713
22.3735
22.1971
22.0481
21.9308
21.8479
21.8016
21.7945
21.8301
21.9115
22.0362
22.1894
22.3408
22.4521
22.4942
22.4595
22.3614
22.2234
22.0687
21.9147
21.772
21.646
8.00
25.2765
25.5414
25.8275
26.1246
26.4131
26.662
26.8298
26.8715
26.7551
26.4785
26.0777
25.6137
25.1474
24.7198
24.347
24.0262
23.7459
23.4928
23.2569
23.0322
22.8173
22.6143
22.4273
22.261
22.1199
22.0077
21.9267
21.879
21.8664
21.8905
21.9514
22.0443
22.1561
22.2649
22.345
22.3763
22.3524
22.2801
22.1742
22.0508
21.9234
21.8014
21.6901
183
TEC generated using six random distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
31.5436
30.7073
29.9055
29.1378
28.4031
27.6997
27.0257
26.3791
25.758
25.1607
24.5859
24.0326
23.5006
22.99
22.5021
22.0392
21.6048
21.2046
20.8464
20.5403
20.2987
20.1347
20.0588
20.0756
20.1813
20.3645
20.6101
20.9035
21.2338
21.5943
21.983
22.4006
22.8503
23.3364
23.8632
24.4346
25.0535
25.7214
26.4385
27.2035
28.0144
28.8681
29.7614
0.50
31.0833
30.2432
29.4405
28.6745
27.9437
27.2459
26.5787
25.9394
25.3256
24.7353
24.1667
23.6186
23.0903
22.5819
22.0942
21.6292
21.1904
20.7832
20.4156
20.0988
19.8468
19.675
19.5968
19.6179
19.7333
19.9283
20.1836
20.4819
20.8107
21.1636
21.5395
21.9411
22.3733
22.8423
23.3542
23.9144
24.5266
25.1925
25.9123
26.6843
27.5056
28.3725
29.2809
1.00
30.657
29.814
29.0118
28.2495
27.5252
26.8361
26.1789
25.5503
24.9474
24.3677
23.8091
23.2702
22.7501
22.2485
21.7661
21.3046
20.8672
20.4594
20.0891
19.768
19.5113
19.3363
19.2585
19.2846
19.4084
19.6118
19.8717
20.1682
20.4879
20.8249
21.1795
21.5564
21.9627
22.4071
22.8978
23.4417
24.0435
24.7053
25.4267
26.2054
27.0374
27.918
28.842
1.50
30.2664
29.421
28.6205
27.8641
27.1492
26.4721
25.8284
25.2141
24.6257
24.0604
23.5158
22.9903
22.4829
21.9932
21.5217
21.0701
20.6414
20.2408
19.8766
19.5602
19.3074
19.1363
19.0631
19.0948
19.2237
19.4293
19.686
19.9719
20.2733
20.585
20.9087
21.2511
21.6224
22.0337
22.4961
23.0183
23.6061
24.2617
24.984
25.7695
26.6128
27.5078
28.4482
2.00
29.9133
29.0657
28.2683
27.5199
26.8173
26.1555
25.529
24.9327
24.3626
23.8154
23.2887
22.7808
22.2907
21.818
21.3633
20.9281
20.5157
20.1311
19.7825
19.4812
19.2425
19.0837
19.0201
19.0574
19.1871
19.3874
19.6319
19.8981
20.172
20.4488
20.7316
21.0295
21.3556
21.7248
22.1513
22.6463
23.2166
23.8644
24.5874
25.3802
26.2357
27.1461
28.1036
2.50
29.6008
28.7508
27.9571
27.2188
26.5314
25.8884
25.2827
24.7081
24.1598
23.6344
23.1293
22.6431
22.1746
21.7237
21.291
20.8785
20.4893
20.1288
19.8048
19.5282
19.313
19.1743
19.1247
19.1679
19.2944
19.4829
19.7079
19.9468
20.1855
20.4193
20.6521
20.8954
21.1661
21.4835
21.8661
22.3284
22.8783
23.5173
24.2413
25.0426
25.9115
26.8381
27.8132
3.00
29.3335
28.4801
27.6904
26.9635
26.2941
25.6732
25.0918
24.5423
24.0191
23.5187
23.0387
22.5774
22.1342
21.7092
21.3032
20.9184
20.5583
20.2282
19.9357
19.6908
19.5055
19.3921
19.3598
19.4095
19.5312
19.705
19.9066
20.1144
20.3134
20.4983
20.6736
20.853
21.058
21.3139
21.6448
22.0691
22.5961
23.2261
23.9522
24.7633
25.6468
26.5903
27.583
3.50
29.1183
28.2602
27.4738
26.7591
26.1095
25.5135
24.9594
24.4378
23.9426
23.4699
23.0174
22.5838
22.1688
21.7725
21.3965
21.0429
20.7157
20.4201
20.1631
19.9536
19.8015
19.7159
19.7025
19.7601
19.8781
20.038
20.2173
20.3943
20.5531
20.6867
20.7993
20.9071
21.0371
21.2221
21.4939
21.8758
22.3784
22.9999
23.7293
24.5515
25.4501
26.4104
27.4199
4.00
28.9658
28.1016
27.3171
26.614
25.9846
25.4149
24.8899
24.3982
23.9327
23.4894
23.0662
22.6619
22.2766
21.9109
21.5665
21.2461
20.9535
20.6939
20.4737
20.3004
20.1818
20.1242
20.1306
20.1977
20.315
20.4652
20.6266
20.7773
20.8994
20.9832
21.0316
21.063
21.1108
21.2174
21.4241
21.7603
22.2378
22.8515
23.5853
24.4187
25.3318
26.3073
27.3314
4.50
28.8899
28.0191
27.2351
26.5418
25.9312
25.3867
24.8904
24.4286
23.9931
23.5796
23.1859
22.8112
22.4559
22.121
21.8085
21.5213
21.2632
21.039
20.8546
20.7161
20.6293
20.5984
20.6243
20.7026
20.8229
20.9686
21.1187
21.2505
21.343
21.3828
21.3703
21.3254
21.2884
21.3128
21.4513
21.7405
22.1928
22.7988
23.5361
24.3789
25.3035
26.2906
27.3252
5.00
28.906
28.0307
27.2471
26.5611
25.9653
25.442
24.9708
24.5361
24.1285
23.743
23.3774
23.031
22.7046
22.3993
22.1175
21.862
21.6366
21.4458
21.2944
21.1876
21.1296
21.123
21.1673
21.2576
21.3836
21.5296
21.675
21.7958
21.8681
21.8736
21.8091
21.6951
21.5784
21.5241
21.5966
21.8399
22.2668
22.863
23.5998
24.4467
25.3767
26.3691
27.4082
5.50
29.027
28.1522
27.3708
26.6901
26.1038
25.5946
25.1417
24.7282
24.3436
23.9822
23.6414
23.3206
23.0204
22.7424
22.4887
22.2623
22.0666
21.9056
21.7835
21.7044
21.6713
21.6856
21.7461
21.8475
21.9801
22.129
22.2741
22.3905
22.4516
22.4348
22.3327
22.1652
21.9845
21.8651
21.8814
22.0832
22.4836
23.0645
23.7929
24.6346
25.5609
26.5498
27.5854
6.00
29.2582
28.3906
27.6148
26.9383
26.3562
25.8532
25.41
25.0098
24.6414
24.2984
23.9778
23.6784
23.401
23.1467
22.9177
22.7167
22.5468
22.4115
22.3143
22.2582
22.2454
22.2765
22.3497
22.4598
22.5975
22.7489
22.8944
23.0094
23.0658
23.0381
22.9159
22.7183
22.4998
22.3399
22.3176
22.4858
22.8583
23.4161
24.1249
24.9497
25.8608
26.836
27.8591
6.50
29.5955
28.7409
27.9741
27.3018
26.7203
26.2172
25.7758
25.3811
25.0218
24.6909
24.3849
24.1023
23.8432
23.6085
23.4002
23.2205
23.0721
22.9578
22.8806
22.8426
22.8453
22.8885
22.9701
23.085
23.2243
23.3748
23.5183
23.6308
23.6849
23.655
23.5304
23.3292
23.105
22.9353
22.8975
23.0435
23.3883
23.9158
24.5942
25.3902
26.2748
27.2261
28.2277
7.00
30.0272
29.1895
28.4342
27.7666
27.1841
26.6771
26.2325
25.8371
25.4807
25.1563
24.8596
24.5889
24.3435
24.1241
23.9321
23.7693
23.6379
23.5401
23.478
23.4532
23.4664
23.517
23.6023
23.7173
23.8536
23.9987
24.1357
24.2425
24.2941
24.2681
24.1557
23.9747
23.7741
23.6239
23.5934
23.7306
24.0518
24.5459
25.187
25.9454
26.7947
27.7137
28.6862
7.50
30.5387
29.7197
28.9771
28.3149
27.7314
27.2195
26.769
26.3694
26.0117
25.689
25.3972
25.1339
24.898
24.6897
24.5098
24.3596
24.2407
24.1548
24.1033
24.087
24.1062
24.1595
24.2442
24.355
24.4838
24.6193
24.7457
24.844
24.893
24.8752
24.7855
24.6412
24.4846
24.3744
24.3691
24.5104
24.8154
25.2787
25.881
26.5981
27.4071
28.2884
29.2264
8.00
31.1158
30.3159
29.5863
28.9302
28.3465
27.8301
27.3734
26.968
26.6064
26.2825
25.992
25.7324
25.5022
25.3012
25.1295
24.988
24.8776
24.7995
24.7544
24.7425
24.7636
24.8159
24.8961
24.9993
25.1176
25.2406
25.3547
25.4438
25.4915
25.4856
25.4248
25.3254
25.2223
25.1625
25.1928
25.3484
25.6459
26.0845
26.6514
27.3283
28.0961
28.9376
29.8384
184
TEC generated using six random distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
28.451
28.5955
28.0074
26.8562
25.2633
23.5949
23.1535
22.6816
22.3131
22.6479
24.5739
26.6059
28.0082
28.6117
28.4214
27.5675
26.2164
24.4574
23.3978
22.9478
22.4973
22.283
23.3614
25.5095
27.3064
28.3709
28.6216
28.1218
27.0359
25.498
23.7134
23.214
22.7422
22.3471
22.5033
24.2812
26.3658
27.8665
28.5788
28.4887
27.7125
26.4207
24.709
0.50
26.7844
26.8768
26.3196
25.2207
23.7416
22.3157
21.457
21.0581
21.3874
22.3104
23.7736
25.3076
26.4277
26.9087
26.7098
25.9017
24.6124
23.0688
21.8886
21.2056
21.1211
21.7128
22.8972
24.4647
25.8627
26.7204
26.9037
26.4275
25.3928
23.9502
22.4721
21.5487
21.0692
21.3089
22.1522
23.5621
25.1201
26.3131
26.8845
26.7736
26.0398
24.8055
23.2708
1.00
23.7356
23.7178
23.2805
22.5145
21.5704
20.634
19.8423
19.4921
20.1291
21.027
22.011
22.9163
23.5504
23.7823
23.5758
22.9811
22.1163
21.153
20.2681
19.5801
19.7058
20.5008
21.4509
22.4251
23.2343
23.7046
23.7454
23.3601
22.6302
21.6993
20.7519
19.9358
19.4704
20.0223
20.9003
21.8806
22.8079
23.4875
23.7769
23.6274
23.0787
22.2409
21.2797
1.50
19.6242
19.5221
19.3452
19.1438
19.0037
18.962
18.991
19.0746
19.2026
19.3549
19.5008
19.6064
19.6422
19.5907
19.4526
19.2563
19.0708
18.9749
18.9673
19.021
19.1255
19.2673
19.421
19.5535
19.6319
19.6311
19.5406
19.3717
19.169
19.0163
18.9629
18.9838
19.0606
19.1837
19.3343
19.4831
19.5959
19.6423
19.6028
19.4753
19.2837
19.0914
18.9818
2.00
19.4574
19.4823
20.0352
20.789
21.5649
22.2129
22.5987
22.6442
22.3461
21.772
21.0427
20.3029
19.6879
19.3869
19.6799
20.3499
21.1314
21.8703
22.4186
22.6622
22.5547
22.125
21.4665
20.7148
20.0132
19.4999
19.4411
19.945
20.6844
21.4659
22.1394
22.5661
22.6586
22.4037
21.8602
21.1433
20.3967
19.7574
19.3961
19.6106
20.2508
21.0268
21.7801
2.50
20.7423
20.5825
21.2685
22.3792
23.7788
25.0743
25.9222
26.1658
25.7947
24.8921
23.6066
22.2313
21.1828
20.53
20.8218
21.6996
22.9705
24.3778
25.5102
26.1053
26.0771
25.4614
24.37
22.994
21.7275
20.8345
20.5366
21.1521
22.209
23.5895
24.9226
25.8427
26.1698
25.877
25.038
23.7914
22.4015
21.3008
20.5759
20.737
21.5593
22.7848
24.1988
3.00
22.5579
22.1857
22.1497
23.0738
25.0049
26.7986
27.9425
28.3023
27.9077
26.8892
25.3768
23.4814
22.8173
22.3712
22.1098
22.3776
23.8631
25.8436
27.387
28.1961
28.2177
27.5336
26.289
24.5872
23.0547
22.6189
22.2214
22.1204
22.8695
24.7372
26.5923
27.8349
28.2999
27.9994
27.0549
25.6031
23.7375
22.8753
22.4254
22.1256
22.2827
23.6065
25.5946
3.50
24.0711
23.42
22.624
23.0006
25.4949
27.4106
28.5791
28.9357
28.5367
27.621
26.4491
25.2048
24.4101
23.8021
23.0963
22.2446
24.1348
26.4095
28.015
28.8335
28.8462
28.1831
27.1383
25.8908
24.7976
24.1507
23.5133
22.7398
22.6528
25.1918
27.1969
28.4703
28.9347
28.6266
27.7604
26.6161
25.3536
24.4925
23.8863
23.1986
22.3556
23.7936
26.1424
4.00
25.1515
24.6095
24.2439
24.627
25.8501
27.1015
27.9339
28.1739
27.7802
27.0016
26.6109
26.0565
25.4712
24.911
24.4071
24.2763
25.1038
26.4253
27.5278
28.1158
28.0791
27.4354
26.8453
26.3848
25.7996
25.2258
24.6779
24.2662
24.5129
25.6708
26.9537
27.8553
28.1788
27.8671
27.0747
26.6727
26.1351
25.5472
24.9841
24.4646
24.2467
24.9442
26.2525
4.50
25.7417
25.5766
25.5076
25.572
25.7753
26.0986
26.4058
26.5675
26.5616
26.442
26.2722
26.0728
25.8581
25.6616
25.532
25.5182
25.6433
25.9055
26.2441
26.4973
26.5836
26.5192
26.3725
26.1889
25.9801
25.768
25.5941
25.5096
25.5554
25.7404
26.0526
26.3718
26.5562
26.5706
26.4617
26.2966
26.1007
25.8865
25.685
25.5435
25.5122
25.6187
25.8633
5.00
26.7303
26.8334
26.7199
26.5109
26.2853
26.0274
25.7526
25.5123
25.3824
25.444
25.7226
26.1497
26.5661
26.8054
26.8054
26.6329
26.4157
26.1777
25.9079
25.6402
25.4373
25.382
25.54
25.897
26.3429
26.6982
26.8338
26.7437
26.5397
26.3168
26.0634
25.7884
25.5397
25.3902
25.4229
25.6747
26.0894
26.5182
26.7873
26.8181
26.6606
26.4451
26.2114
5.50
28.2446
28.3127
27.7392
27.0188
26.466
25.8082
25.1898
24.5976
24.0669
24.122
25.3698
26.8422
27.9075
28.3579
28.1345
27.3743
26.7983
26.1829
25.533
24.9325
24.3477
23.955
24.558
26.0346
27.3708
28.1845
28.3428
27.8453
27.0874
26.5487
25.895
25.2691
24.6758
24.124
24.0411
25.1678
26.6631
27.7988
28.3368
28.2017
27.4842
26.8679
26.2709
6.00
28.7572
28.8942
28.3138
27.2679
25.9444
24.6867
24.0286
23.4301
22.7259
22.358
24.7753
26.9043
28.3165
28.915
28.7184
27.9015
26.7225
25.3382
24.3598
23.779
23.14
22.3939
23.345
25.7755
27.6128
28.6778
28.9212
28.424
27.4247
26.1316
24.8153
24.1037
23.5147
22.8265
22.227
24.4495
26.6596
28.1748
28.8831
28.7858
28.0354
26.8947
25.5201
6.50
27.9049
28.0361
27.4519
26.2845
24.6514
22.9748
22.437
22.0348
21.9782
22.6394
24.3325
26.1731
27.4867
28.0559
27.8636
27.0093
25.6277
23.8385
22.7145
22.236
21.9557
22.1361
23.2833
25.1677
26.8264
27.8293
28.0622
27.5661
26.4684
24.8911
23.111
22.5017
22.0731
21.9577
22.4859
24.0763
25.9509
27.353
28.0252
27.9302
27.1557
25.8376
24.0899
7.00
25.6234
25.6732
25.1561
24.1723
22.8963
21.6465
20.6806
20.2003
20.8294
21.843
23.1284
24.4045
25.3325
25.7181
25.5142
24.7787
23.6405
22.3273
21.1941
20.3528
20.4005
21.2292
22.3781
23.7051
24.8649
25.572
25.7006
25.2545
24.3246
23.0729
21.7971
20.7939
20.1885
20.7188
21.6898
22.9502
24.2489
25.238
25.701
25.5739
24.903
23.8082
22.4989
7.50
22.0352
21.9608
21.6055
21.0511
20.4185
19.8343
19.4199
19.3476
19.7087
20.315
20.9793
21.5621
21.9424
22.0403
21.8377
21.383
20.7787
20.1523
19.6256
19.3344
19.4585
19.9544
20.6045
21.2497
21.7578
22.0222
21.9879
21.6664
21.132
20.5023
19.9048
19.4598
19.3308
19.6416
20.2279
20.893
21.494
21.907
22.0449
21.8808
21.4546
20.863
20.2322
8.00
19.0631
19.1744
19.4007
19.6896
19.9715
20.179
20.2593
20.1852
19.9653
19.6553
19.3546
19.1478
19.0583
19.0953
19.2608
19.5222
19.8169
20.0742
20.2318
20.2466
20.1057
19.8368
19.5174
19.2509
19.0942
19.0582
19.1523
19.3656
19.6501
19.937
20.1579
20.2573
20.204
20.0014
19.6983
19.3902
19.1686
19.0632
19.0828
19.2322
19.4841
19.7784
20.0446
185
TEC generated using six random distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
25.004
24.9731
24.922
24.847
24.7441
24.609
24.4375
24.2264
23.9737
23.6798
23.3478
22.9833
22.5948
22.1925
21.7874
21.3906
21.0123
20.6614
20.3463
20.0752
19.8575
19.7045
19.6275
19.6295
19.6946
19.7924
19.9016
20.0204
20.155
20.307
20.4713
20.6395
20.8031
20.9555
21.0926
21.2129
21.3164
21.4047
21.4795
21.5428
21.5966
21.6427
21.6825
0.50
25.1685
25.1479
25.1069
25.0414
24.9468
24.818
24.6496
24.4369
24.177
23.8693
23.5167
23.1255
22.7053
22.2678
21.8258
21.3918
20.9767
20.5899
20.2393
19.9327
19.6801
19.497
19.4059
19.4247
19.534
19.6708
19.7961
19.9223
20.0704
20.2445
20.4358
20.6308
20.8172
20.9868
21.1354
21.262
21.368
21.4559
21.5285
21.5886
21.6388
21.6812
21.7173
1.00
25.3319
25.322
25.2916
25.2366
25.152
25.0319
24.8695
24.6585
24.3944
24.0757
23.7049
23.289
22.8388
22.368
21.8911
21.4223
20.9735
20.5541
20.171
19.8304
19.5403
19.3172
19.1955
19.2266
19.4041
19.5909
19.7148
19.8346
19.995
20.197
20.4218
20.6481
20.859
21.0451
21.2026
21.3323
21.4372
21.5215
21.5892
21.6439
21.6886
21.7256
21.757
1.50
25.4913
25.4915
25.4711
25.4265
25.3528
25.2435
25.0902
24.8845
24.6199
24.2937
23.9082
23.4708
22.994
22.4936
21.9862
21.4879
21.0117
20.5671
20.1604
19.7957
19.4783
19.2214
19.0632
19.0935
19.3537
19.5732
19.6536
19.7553
19.9352
20.1757
20.4421
20.703
20.9377
21.1366
21.2982
21.4258
21.525
21.6016
21.661
21.7077
21.7449
21.7753
21.8007
2.00
25.6438
25.6523
25.6398
25.6037
25.5405
25.4433
25.3021
25.1056
24.8447
24.5153
24.1193
23.6651
23.1669
22.6425
22.1113
21.5911
21.0964
20.6374
20.2204
19.8493
19.5291
19.2731
19.1204
19.1649
19.4371
19.5896
19.601
19.6985
19.9146
20.205
20.5172
20.8109
21.0634
21.2671
21.4245
21.5427
21.6301
21.6945
21.7423
21.7783
21.8063
21.8287
21.8474
2.50
25.7877
25.8017
25.7922
25.7595
25.7038
25.6194
25.4935
25.3104
25.0578
24.7299
24.3287
23.8634
23.3502
22.8094
22.2625
21.7296
21.2267
20.7651
20.3518
19.992
19.6928
19.4704
19.3604
19.4109
19.5645
19.6078
19.603
19.7235
19.9837
20.323
20.6735
20.9875
21.2432
21.4381
21.58
21.68
21.7492
21.7967
21.8298
21.8533
21.8707
21.8844
21.8957
3.00
25.9235
25.9397
25.9251
25.8847
25.8288
25.7572
25.6512
25.4868
25.2472
24.9256
24.5246
24.0549
23.5345
22.9858
22.4325
21.8966
21.3954
20.9413
20.5421
20.2039
19.9341
19.7458
19.6568
19.6681
19.7159
19.7226
19.7491
19.904
20.1987
20.5675
20.9316
21.2399
21.4755
21.6433
21.7565
21.8295
21.875
21.9026
21.9191
21.929
21.9355
21.9401
21.9441
3.50
26.0551
26.0731
26.0426
25.9708
25.897
25.8398
25.7631
25.6243
25.4021
25.091
24.6956
24.2285
23.7091
23.1615
22.6113
22.0814
21.5904
21.1512
20.772
20.4583
20.2154
20.0492
19.9628
19.9436
19.9569
19.9828
20.064
20.2623
20.5794
20.9483
21.2889
21.5559
21.7431
21.8644
21.9375
21.9779
21.9974
22.0043
22.0045
22.0015
21.9976
21.9938
21.9909
4.00
26.1885
26.2205
26.1721
26.0211
25.8834
25.8539
25.8256
25.7191
25.5164
25.2182
24.8328
24.3745
23.864
23.3265
22.7879
22.2721
21.7979
21.3785
21.0218
20.7324
20.5129
20.3646
20.285
20.2647
20.2908
20.364
20.5114
20.76
21.0907
21.4325
21.7125
21.902
22.013
22.0717
22.099
22.1072
22.1036
22.0935
22.0804
22.0669
22.0543
22.0435
22.0347
4.50
26.3222
26.4027
26.3959
26.1307
25.8015
25.8306
25.8608
25.7794
25.5906
25.3041
24.931
24.4867
23.9921
23.4722
22.9528
22.4576
22.0051
21.6084
21.2752
21.0094
20.8121
20.6832
20.6205
20.6204
20.6817
20.8117
21.0247
21.321
21.6588
21.9586
22.1551
22.2384
22.247
22.2299
22.2132
22.1987
22.1822
22.1628
22.1422
22.122
22.1036
22.0876
22.0743
5.00
26.4307
26.5824
26.7299
26.6333
26.0287
25.9265
25.9167
25.8207
25.6302
25.3502
24.9898
24.5629
24.0895
23.5933
23.099
22.6291
22.2018
21.8296
21.52
21.2767
21.101
20.9929
20.9523
20.98
21.08
21.2601
21.5248
21.8574
22.2006
22.4668
22.5856
22.5482
22.4212
22.3095
22.2585
22.2409
22.2276
22.2096
22.1881
22.1657
22.1445
22.1255
22.1092
5.50
26.474
26.6479
26.8279
26.837
26.4314
26.1327
25.9926
25.8459
25.6392
25.3604
25.0118
24.6044
24.1558
23.6875
23.2223
22.7811
22.3809
22.0339
21.7473
21.5252
21.3693
21.2806
21.2605
21.312
21.4405
21.6516
21.9435
22.2928
22.6413
22.9023
22.9892
22.8501
22.548
22.3103
22.2407
22.2427
22.2464
22.2378
22.2204
22.1991
22.1774
22.1572
22.1394
6.00
26.4399
26.581
26.6866
26.661
26.4531
26.215
26.0258
25.8402
25.6168
25.338
25.0014
24.6149
24.1932
23.7553
23.3215
22.9108
22.5387
22.2166
21.952
21.7489
21.6098
21.5362
21.5303
21.5954
21.7356
21.9533
22.2431
22.5817
22.9206
23.1881
23.2934
23.1258
22.6792
22.313
22.2248
22.2414
22.2579
22.2571
22.244
22.2248
22.2038
22.1835
22.165
6.50
26.3506
26.4504
26.5045
26.473
26.3469
26.1735
25.9904
25.7927
25.5621
25.2865
24.9635
24.599
24.2054
23.799
23.3976
23.0178
22.6738
22.376
22.1317
21.9452
21.8191
21.7553
21.7557
21.8225
21.9577
22.1601
22.4216
22.7204
23.018
23.2579
23.3605
23.2143
22.7951
22.4153
22.2846
22.274
22.2801
22.2769
22.264
22.2457
22.2254
22.2054
22.1869
7.00
26.2312
26.3
26.3277
26.2969
26.2049
26.0676
25.9006
25.7061
25.4779
25.2104
24.9032
24.5619
24.1968
23.8221
23.4528
23.1035
22.7867
22.5121
22.2863
22.1138
21.9971
21.938
21.9376
21.9967
22.1146
22.2873
22.5043
22.7453
22.9776
23.1551
23.2169
23.0982
22.8123
22.5311
22.3839
22.3329
22.3144
22.3002
22.2833
22.2639
22.2437
22.2239
22.2056
7.50
26.0969
26.1438
26.1562
26.1249
26.0476
25.9293
25.7762
25.5904
25.3706
25.1153
24.8262
24.5087
24.1721
23.8282
23.49
23.1701
22.8794
22.6264
22.4174
22.2566
22.1463
22.088
22.0818
22.1271
22.2213
22.3584
22.5268
22.7079
22.8745
22.9917
23.0212
22.9375
22.7639
22.5814
22.4554
22.3868
22.3494
22.3238
22.3015
22.2801
22.2594
22.2398
22.2218
8.00
25.9552
25.9861
25.9875
25.9538
25.8825
25.7746
25.6321
25.4564
25.2479
25.0074
24.7377
24.4442
24.1353
23.821
23.5125
23.2203
22.954
22.7211
22.5273
22.3764
22.2705
22.2104
22.1958
22.2248
22.2938
22.3957
22.5196
22.6493
22.7639
22.8395
22.8549
22.8022
22.6985
22.5822
22.4864
22.42
22.3755
22.3434
22.3172
22.2941
22.2729
22.2535
22.2359
186
TEC generated using nine well distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
21.9899
21.4972
21.0926
20.7807
20.5566
20.4072
20.3147
20.2604
20.2277
20.2024
20.1727
20.1298
20.0667
19.9791
19.8647
19.7237
19.5584
19.3729
19.1732
18.9661
18.7587
18.5572
18.3653
18.1825
18.0043
17.8228
17.6294
17.417
17.1814
16.9225
16.6429
16.3483
16.0468
15.7487
15.4671
15.2184
15.0225
14.9028
14.8828
14.9808
15.2029
15.5416
15.9796
0.50
22.0135
21.5212
21.1239
20.8277
20.627
20.5063
20.4449
20.4221
20.4194
20.4216
20.4163
20.3936
20.3462
20.2692
20.1604
20.0201
19.8514
19.6596
19.4518
19.2366
19.0232
18.8196
18.6308
18.4564
18.2897
18.1198
17.9346
17.7251
17.4865
17.2188
16.9261
16.6151
16.2949
15.977
15.6751
15.4062
15.1909
15.0529
15.0162
15.0994
15.3089
15.6369
16.066
1.00
22.1321
21.6448
21.2572
20.9764
20.7963
20.6999
20.6647
20.6683
20.6914
20.7178
20.7341
20.7298
20.6965
20.6288
20.5242
20.3835
20.2103
20.0111
19.7947
19.5714
19.3523
19.1478
18.9643
18.8013
18.6496
18.494
18.3187
18.1126
17.8708
17.5946
17.2895
16.9639
16.6283
16.295
15.9788
15.6969
15.4697
15.3204
15.2716
15.3408
15.5339
15.8441
16.2554
1.50
22.3539
21.878
21.5032
21.2368
21.0727
20.9937
20.9771
21.0003
21.0434
21.0894
21.1241
21.1357
21.1149
21.0551
20.9536
20.8113
20.6329
20.4263
20.2018
19.9717
19.7489
19.5458
19.3704
19.2215
19.0869
18.9466
18.7808
18.5766
18.3303
18.0447
17.7274
17.3886
17.0402
16.6956
16.3701
16.0811
15.8482
15.6929
15.6355
15.6911
15.8652
16.1525
16.5393
2.00
22.6779
22.2196
21.8604
21.6069
21.4536
21.3845
21.3784
21.4134
21.4699
21.5305
21.58
21.6052
21.5951
21.542
21.4424
21.2978
21.114
20.9008
20.6702
20.4361
20.2132
20.0152
19.8509
19.718
19.6005
19.4736
19.3142
19.1091
18.8558
18.5595
18.23
17.8792
17.5202
17.1674
16.8364
16.5441
16.3092
16.1508
16.0864
16.1288
16.2829
16.5448
16.9037
2.50
23.0933
22.6569
22.3149
22.0727
21.9256
21.86
21.8571
21.897
21.9608
22.031
22.0916
22.1277
22.1266
22.0789
21.9803
21.8328
21.644
21.4256
21.1918
20.9579
20.7397
20.5512
20.4005
20.2832
20.1798
20.0619
19.9045
19.695
19.4328
19.1254
18.7843
18.4228
18.0552
17.6965
17.3622
17.0688
16.8334
16.6728
16.6019
16.6315
16.7658
17.0023
17.3326
3.00
23.5831
23.1701
22.8453
22.6128
22.4688
22.4021
22.397
22.436
22.5016
22.5765
22.6442
22.6884
22.6943
22.6506
22.5521
22.4015
22.2083
21.9868
21.7531
21.5238
21.3146
21.1387
21.002
20.8974
20.8028
20.6883
20.529
20.3135
20.0427
19.7254
19.3745
19.0045
18.6306
18.2679
17.9321
17.6386
17.403
17.2401
17.1627
17.1798
17.2955
17.5082
17.8115
3.50
24.1287
23.7383
23.4294
23.2048
23.0616
22.9909
22.9798
23.0133
23.0756
23.1503
23.2206
23.2691
23.2792
23.2376
23.1384
22.9847
22.7885
22.5662
22.3357
22.1141
21.9164
21.7535
21.6284
21.5315
21.4397
21.3242
21.1617
20.9416
20.6652
20.3417
19.9846
19.6093
19.2317
18.8675
18.5316
18.2388
18.0032
17.8378
17.7538
17.7592
17.858
18.0495
18.3286
4.00
24.7133
24.3433
24.048
23.8295
23.6852
23.6083
23.5882
23.6123
23.6665
23.7355
23.8026
23.8502
23.8603
23.8183
23.7173
23.5615
23.3643
23.144
22.9193
22.7071
22.521
22.3691
22.2514
22.1566
22.0631
21.9446
21.7801
21.5591
21.2821
20.9575
20.599
20.2228
19.8454
19.4825
19.1487
18.8578
18.6227
18.4551
18.365
18.3599
18.4439
18.617
18.8753
4.50
25.3234
24.9709
24.6865
24.4718
24.3247
24.2395
24.2078
24.2187
24.2599
24.3172
24.3746
24.4146
24.4191
24.3731
24.2696
24.1132
23.9179
23.7026
23.486
23.284
23.1081
22.9641
22.8497
22.7533
22.6556
22.534
22.3696
22.1518
21.8792
21.559
21.2048
20.833
20.4604
20.1027
19.7739
19.487
19.2538
19.085
18.99
18.9761
19.0477
19.2055
19.4463
5.00
25.949
25.6106
25.3343
25.1211
24.9691
24.8737
24.8279
24.8222
24.8457
24.8853
24.9262
24.9516
24.9444
24.8906
24.7837
24.6283
24.4379
24.2305
24.0238
23.8321
23.6651
23.5265
23.4127
23.313
23.2104
23.0861
22.9233
22.7112
22.4471
22.1366
21.7926
21.4311
21.0687
20.7208
20.4008
20.1209
19.8919
19.7239
19.6259
19.6054
19.6672
19.8127
20.0391
5.50
26.5825
26.255
25.9841
25.7701
25.6114
25.504
25.4417
25.4166
25.4184
25.4356
25.4542
25.4591
25.4352
25.3702
25.2589
25.1054
24.9218
24.724
24.5281
24.3467
24.1876
24.0529
23.9387
23.8351
23.7279
23.6012
23.4405
23.2354
22.9824
22.6861
22.3576
22.0123
21.6659
21.3328
21.0259
20.7565
20.5349
20.3707
20.2726
20.2482
20.303
20.439
20.6537
6.00
27.2188
26.8994
26.6312
26.4144
26.2472
26.1263
26.046
25.9993
25.9769
25.9684
25.9612
25.9422
25.8986
25.8203
25.7034
25.5514
25.3746
25.1867
25.0014
24.8296
24.6776
24.5465
24.4318
24.3248
24.2135
24.0847
23.926
23.7283
23.4881
23.209
22.9007
22.5765
22.251
21.9374
21.6479
21.393
21.1826
21.0258
20.931
20.9061
20.9569
21.0857
21.2906
6.50
27.8546
27.5406
27.273
27.0516
26.8748
26.7392
26.64
26.5707
26.5231
26.4876
26.4535
26.4095
26.3452
26.2527
26.1291
25.9776
25.8064
25.6271
25.4513
25.2881
25.1425
25.0145
24.8997
24.7901
24.6756
24.5451
24.3885
24.1985
23.9721
23.7121
23.4266
23.1271
22.8261
22.5358
22.2674
22.0308
21.8353
21.6896
21.6021
21.5802
21.6299
21.7537
21.95
7.00
28.4876
28.1769
27.9082
27.681
27.4936
27.343
27.2248
27.1329
27.0603
26.9984
26.9381
26.87
26.7856
26.6791
26.5483
26.3959
26.2287
26.0561
25.888
25.7321
25.592
25.4669
25.3522
25.2407
25.1237
24.9924
24.8386
24.6566
24.4444
24.2042
23.9428
23.6695
23.3952
23.1306
22.886
22.6706
22.4933
22.3622
22.2853
22.2698
22.321
22.4416
22.6303
7.50
29.1167
28.8076
28.5365
28.3026
28.1044
27.9389
27.8022
27.6889
27.5925
27.506
27.4214
27.3311
27.2284
27.1089
26.971
26.8169
26.6522
26.4848
26.3228
26.1725
26.0366
25.9136
25.7988
25.6859
25.5674
25.4362
25.2859
25.1125
24.9144
24.6939
24.4563
24.2095
23.9625
23.7248
23.5055
23.3133
23.1563
23.0423
22.9787
22.9718
23.0266
23.1456
23.3278
8.00
29.7416
29.4328
29.1583
28.9175
28.7085
28.5289
28.3747
28.2415
28.1235
28.0146
27.9083
27.7984
27.6797
27.5487
27.4043
27.2484
27.0856
26.9221
26.7648
26.6187
26.4855
26.3635
26.2482
26.134
26.0146
25.8843
25.7383
25.5736
25.3895
25.1879
24.9732
24.752
24.5318
24.3209
24.1274
23.9592
23.8238
23.7282
23.6792
23.6826
23.7424
23.8611
24.0381
187
TEC generated using nine well distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.9805
17.9686
19.2361
21.0344
21.0656
20.9831
23.108
27.6322
31.0188
32.8187
32.7002
30.4632
26.1465
20.4622
17.7743
20.6208
21.0564
21.0503
20.9949
25.1714
29.2701
32.016
33.0183
31.9956
28.8302
23.7517
18.3748
18.8113
21.0186
21.0655
21.0032
22.4656
27.0853
30.6521
32.6841
32.8353
30.8843
26.8265
21.2194
17.6575
20.2373
21.0516
21.058
0.50
23.4623
17.4238
17.8204
19.5165
20.6597
22.0282
24.6102
28.2041
31.29
33.049
33.0535
31.0179
26.7811
20.6344
16.8887
18.6494
20.0351
21.1781
22.9436
26.1449
29.6674
32.2454
33.2854
32.4346
29.4526
24.2899
18.0066
17.5586
19.3369
20.5114
21.8016
24.1755
27.7299
30.9448
32.909
33.1651
31.4132
27.4694
21.5099
16.8486
18.407
19.8846
21.0119
1.00
27.1963
23.2381
20.2514
19.7876
21.0732
23.083
25.5042
28.0642
30.2894
31.7343
32.1061
31.2447
29.0526
25.5222
21.6812
19.7437
20.2118
21.8834
24.0927
26.6225
29.0995
31.0326
32.0391
31.8901
30.4632
27.6695
23.7629
20.5114
19.7168
20.8481
22.789
25.1662
27.7326
30.0307
31.5995
32.1252
31.4336
29.4236
26.0515
22.1246
19.8443
20.0549
21.6243
1.50
27.6664
26.8826
26.0869
25.6262
25.6166
25.9558
26.4917
27.0923
27.6494
28.0779
28.3134
28.3028
27.9916
27.351
26.5162
25.8322
25.5698
25.73
26.1723
26.751
27.3447
27.8552
28.2069
28.3421
28.208
27.7521
26.9955
26.1793
25.6609
25.5945
25.8962
26.4142
27.0129
27.5812
28.0309
28.2952
28.3203
28.0521
27.4528
26.6267
25.9018
25.578
25.6891
2.00
26.267
28.4213
30.1828
31.2683
31.5141
30.8738
29.2618
26.0207
21.8149
20.0686
21.0317
22.8601
24.9989
27.2279
29.2523
30.7492
31.483
31.3454
30.3128
28.1104
24.1244
20.5994
20.2977
21.7689
23.7621
25.9694
28.1508
29.9828
31.1704
31.5324
31.0101
29.5472
26.5655
22.3042
20.0924
20.8308
22.5943
24.7047
26.9365
29.0074
30.5906
31.4346
31.4147
2.50
25.8739
29.1653
31.767
33.0401
32.6134
30.2383
25.8395
20.3437
18.1599
19.0627
20.2829
21.8023
24.1098
27.3258
30.4247
32.5078
33.0806
31.8337
28.5687
23.4363
18.7111
18.4393
19.5801
20.8846
22.6698
25.4398
28.7492
31.4879
32.9625
32.7778
30.6718
26.5293
21.016
18.1607
18.9076
20.113
21.5693
23.7392
26.8797
30.0576
32.31
33.1037
32.1124
3.00
24.7267
28.9164
31.9069
33.2137
32.5131
29.6104
24.5347
18.0176
17.429
20.2518
20.8148
21.0718
22.3322
26.6448
30.3944
32.7019
33.1713
31.5303
27.6611
21.7743
16.2441
18.9227
20.6013
20.9317
21.2542
24.1298
28.4154
31.5985
33.1499
32.7302
30.1248
25.3217
18.8678
16.991
20.0517
20.7737
21.0371
21.9182
26.0688
29.9693
32.4941
33.2258
31.8759
3.50
24.5029
28.1004
30.7507
31.9121
31.306
28.9052
25.1427
21.5157
20.6738
21.711
21.6765
21.5789
22.6124
26.1223
29.4062
31.4582
31.875
30.4745
27.3882
23.4028
20.7066
21.1762
21.756
21.6116
21.7112
24.0152
27.6605
30.4762
31.8557
31.4925
29.3186
25.6835
21.8903
20.5893
21.6414
21.6979
21.5758
22.2924
25.6294
29.0296
31.2734
31.9227
30.7647
4.00
24.7637
26.7319
28.4256
29.2687
28.9865
27.626
25.6053
23.7025
22.6255
22.3548
22.4596
22.816
23.8218
25.6026
27.5406
28.9189
29.2895
28.5136
26.7917
24.7134
23.1164
22.4318
22.3788
22.5654
23.147
24.5232
26.4706
28.2402
29.2187
29.0905
27.8578
25.8862
23.9172
22.7142
22.3587
22.4361
22.7416
23.6377
25.3395
27.3023
28.7873
29.3065
28.6792
4.50
24.0925
24.5961
25.2851
25.7122
25.7764
25.5025
25.0028
24.4354
23.9505
23.6569
23.5852
23.6903
23.9216
24.2563
24.9117
25.512
25.7855
25.6942
25.3047
24.7556
24.2075
23.7955
23.6005
23.6122
23.778
24.0498
24.5031
25.2044
25.6757
25.7889
25.555
25.0766
24.5089
24.0057
23.6827
23.5833
23.6681
23.8854
24.2003
24.8157
25.4489
25.7705
25.7258
5.00
24.9406
24.1873
23.6147
23.3547
23.3878
23.6238
24.034
24.6554
25.5203
26.1554
26.3285
26.0273
25.3801
24.602
23.9081
23.459
23.3404
23.4675
23.7815
24.2664
25.0274
25.8446
26.2916
26.2514
25.7777
25.0451
24.2802
23.6751
23.3696
23.3707
23.582
23.9701
24.5529
25.4095
26.0955
26.3342
26.0912
25.4787
24.7046
23.9892
23.4997
23.3396
23.4393
5.50
24.934
23.0529
22.2983
22.2611
22.3893
22.8564
24.219
26.3637
28.3957
29.6069
29.6282
28.4078
26.2705
24.0018
22.589
22.24
22.3024
22.5185
23.3142
25.1023
27.3088
29.0505
29.7728
29.2422
27.5585
25.2413
23.2418
22.34
22.2514
22.3632
22.7542
23.9775
26.0658
28.1616
29.5097
29.6991
28.6341
26.5835
24.2723
22.7064
22.2476
22.2884
22.4702
6.00
23.7699
20.3796
20.6846
21.6716
21.5028
21.4047
23.3106
27.248
30.365
32.0374
31.9355
29.9321
26.2536
21.9858
20.0554
21.4161
21.6071
21.4307
21.6959
25.0432
28.7485
31.2909
32.2241
31.298
28.5088
24.3533
20.6473
20.465
21.6726
21.5267
21.3935
22.8211
26.7514
30.0252
31.9121
32.0582
30.3046
26.8139
22.5011
20.0659
21.2188
21.6309
21.4513
6.50
22.7386
15.8643
18.065
20.2404
20.8185
21.3335
23.7117
27.92
31.2807
33.1023
33.0096
30.7502
26.2309
19.7099
16.0508
19.3548
20.5467
21.0078
21.905
25.5553
29.5356
32.2847
33.3147
32.3062
29.0647
23.6104
16.6233
17.6004
20.103
20.7598
21.2367
23.1911
27.3862
30.9133
32.9638
33.1424
31.1804
26.9573
20.6614
15.6596
19.0103
20.4683
20.9489
7.00
24.8216
20.0527
18.6701
19.4055
20.7028
22.5064
25.1136
28.2668
31.0241
32.6767
32.8117
31.1641
27.5944
22.5584
18.9883
18.8777
19.9166
21.409
23.5265
26.4674
29.5617
31.9053
32.9395
32.3283
29.8515
25.5052
20.5463
18.6668
19.2651
20.5051
22.2276
24.7186
27.8509
30.7101
32.5376
32.8916
31.4924
28.176
23.2447
19.224
18.7891
19.7522
21.1824
7.50
29.2916
25.6435
21.2424
20.5127
21.876
23.7043
25.7059
27.6865
29.397
30.5973
31.1366
30.9863
30.1818
28.087
23.5417
20.4098
21.007
22.6358
24.5612
26.581
28.4768
29.9916
30.9169
31.1536
30.7202
29.5506
26.2758
21.6885
20.4134
21.6572
23.4478
25.4366
27.4334
29.1947
30.4739
31.1053
31.0441
30.3305
28.5231
24.1771
20.5583
20.8343
22.3968
8.00
26.4457
27.5203
28.4383
29.0966
29.4352
29.4199
28.9176
27.4345
25.2192
23.9417
24.022
24.7821
25.818
26.9228
27.9446
28.7602
29.2847
29.4748
29.2809
28.4289
26.4696
24.4739
23.8508
24.2994
25.2117
26.2982
27.384
28.3296
29.0267
29.4098
29.4445
29.0263
27.7021
25.4938
24.0206
23.9592
24.6596
25.6729
26.7779
27.8185
28.6673
29.2337
29.4699
188
TEC generated using nine well distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
21.8137
21.6963
21.6466
21.6778
21.7875
21.9558
22.1516
22.3426
22.5044
22.6234
22.6945
22.7179
22.6957
22.631
22.5269
22.388
22.2208
22.0344
21.8403
21.6518
21.4822
21.3427
21.2396
21.1717
21.129
21.095
21.0506
20.9765
20.8531
20.6601
20.3763
19.9804
19.4544
18.7901
18.0011
17.1371
16.2933
15.5986
15.1725
15.0713
15.2653
15.6645
16.167
0.50
21.6949
21.5429
21.4748
21.5109
21.6498
21.8651
22.114
22.3542
22.5558
22.7039
22.7948
22.8303
22.8134
22.7467
22.6328
22.4753
22.2809
22.06
21.8269
21.599
21.3949
21.2319
21.1224
21.0676
21.0538
21.0566
21.0504
21.0129
20.9235
20.7609
20.503
20.1268
19.6122
18.9478
18.1436
17.247
16.3565
15.6122
15.1513
15.0429
15.2561
15.6884
16.2237
1.00
21.6284
21.4416
21.3547
21.3956
21.5636
21.8241
22.1226
22.4068
22.6426
22.8154
22.9238
22.971
22.9604
22.8933
22.77
22.5924
22.3664
22.1037
21.8217
21.542
21.2891
21.0886
20.9643
20.9258
20.9534
21.0053
21.0451
21.0499
21.0002
20.8754
20.6535
20.3126
19.8333
19.2046
18.4354
17.5694
16.699
15.9593
15.4882
15.3618
15.5562
15.9708
16.4877
1.50
21.6569
21.4435
21.3433
21.3898
21.5812
21.8749
22.2066
22.5183
22.7747
22.9632
23.0845
23.1431
23.1412
23.077
22.947
22.7493
22.4888
22.1783
21.8386
21.4955
21.1779
20.9192
20.7611
20.7412
20.8346
20.9525
21.0421
21.0904
21.0834
21.0009
20.8218
20.527
20.101
19.5372
18.8466
18.07
17.2872
16.613
16.1669
16.0212
16.1636
16.5102
16.9556
2.00
21.823
21.5995
21.4964
21.5482
21.7491
22.0509
22.3865
22.6985
22.9549
23.1463
23.2751
23.3455
23.3568
23.3019
23.1706
22.9557
22.66
22.299
21.898
21.4871
21.0969
20.7602
20.5317
20.5207
20.7316
20.9286
21.0543
21.1408
21.1775
21.1391
21.0045
20.759
20.3937
19.9092
19.3213
18.6687
18.017
17.4538
17.0682
16.917
16.9963
17.2457
17.5832
2.50
22.1559
21.9412
21.8442
21.8948
22.0822
22.358
22.6607
22.9414
23.1748
23.3551
23.4859
23.5697
23.6011
23.5651
23.4413
23.2149
22.8872
22.4785
22.0219
21.5536
21.1067
20.7093
20.4032
20.3737
20.7659
20.9709
21.0879
21.2096
21.2937
21.2984
21.2034
21.0012
20.692
20.2845
19.8002
19.2766
18.7667
18.3324
18.0309
17.8967
17.926
18.0781
18.2974
3.00
22.6613
22.4684
22.3772
22.4104
22.5551
22.7694
23.0048
23.2255
23.4148
23.571
23.6981
23.7964
23.8551
23.8488
23.7435
23.5141
23.1619
22.7166
22.2218
21.7214
21.2564
20.867
20.6139
20.6724
20.9827
21.0227
21.1372
21.3187
21.4579
21.497
21.4257
21.2503
20.9816
20.636
20.2393
19.8282
19.4458
19.1339
18.9237
18.8264
18.8301
18.9052
19.0183
3.50
23.3231
23.154
23.0566
23.0483
23.1199
23.2425
23.3844
23.5238
23.6524
23.772
23.8869
23.9958
24.0829
24.1121
24.0339
23.8118
23.4504
22.9915
22.4875
21.9862
21.5333
21.1794
20.9834
20.9808
21.0287
21.0689
21.2651
21.5332
21.7153
21.7573
21.6775
21.5024
21.2521
20.9471
20.615
20.2904
20.0094
19.8001
19.6743
19.6235
19.6236
19.6477
19.6784
4.00
24.1121
23.9609
23.8384
23.7624
23.7342
23.7424
23.773
23.8167
23.872
23.9424
24.0317
24.137
24.2392
24.295
24.2434
24.0412
23.6983
23.2651
22.7927
22.3217
21.8931
21.553
21.3372
21.2415
21.2262
21.3271
21.6077
21.9311
22.0949
22.0787
21.9477
21.7451
21.4926
21.2088
20.9192
20.6551
20.4474
20.3157
20.2588
20.2528
20.2616
20.257
20.2312
4.50
24.9945
24.8538
24.6891
24.5231
24.3743
24.2522
24.1598
24.0988
24.0716
24.0814
24.1292
24.2086
24.2985
24.355
24.319
24.1521
23.8688
23.5133
23.1191
22.7086
22.3126
21.9745
21.7327
21.6049
21.603
21.7662
22.1018
22.4213
22.5057
22.3929
22.1924
21.9529
21.6899
21.4164
21.1533
20.9284
20.7686
20.6888
20.6801
20.7082
20.7284
20.7105
20.6521
5.00
25.9309
25.7987
25.5822
25.3128
25.0302
24.7674
24.5454
24.375
24.261
24.2036
24.1985
24.2341
24.2869
24.3195
24.2894
24.1756
23.9925
23.761
23.4829
23.1547
22.7951
22.4507
22.1768
22.0157
21.998
22.1507
22.4479
22.7075
22.7385
22.5826
22.3521
22.0975
21.8332
21.5697
21.3249
21.1238
20.9908
20.9384
20.9546
21.0008
21.0287
21.0074
20.9368
5.50
26.8682
26.7498
26.4835
26.1091
25.6895
25.2836
24.9312
24.6523
24.4526
24.3285
24.2695
24.2582
24.2707
24.2792
24.2628
24.2204
24.1625
24.0802
23.9366
23.6959
23.3622
22.9892
22.6541
22.4207
22.3256
22.3811
22.5511
22.7117
22.7312
22.6064
22.4042
22.1694
21.9217
21.6746
21.4459
21.2588
21.1363
21.0903
21.1092
21.1564
21.1854
21.1669
21.1
6.00
27.7328
27.6375
27.3345
26.8683
26.323
25.7835
25.3093
24.9297
24.6516
24.4677
24.3624
24.315
24.3035
24.3106
24.3327
24.3821
24.4639
24.5418
24.5362
24.3717
24.0357
23.5969
23.1623
22.8187
22.6083
22.5354
22.5667
22.6252
22.6266
22.54
22.3844
22.1871
21.9678
21.7428
21.5304
21.3526
21.2305
21.1761
21.1811
21.2151
21.2389
21.2257
21.1719
6.50
28.4364
28.37
28.0502
27.5205
26.8791
26.2325
25.6581
25.1949
24.8516
24.6189
24.4785
24.4096
24.3942
24.4246
24.509
24.6665
24.8975
25.1407
25.2703
25.1624
24.7901
24.2502
23.6898
23.2201
22.8891
22.6972
22.6134
22.5836
22.5486
22.4719
22.3465
22.1816
21.9909
21.789
21.5931
21.423
21.2975
21.2283
21.2112
21.2244
21.2377
21.2282
21.1895
7.00
28.9006
28.8595
28.5424
27.9874
27.2962
26.5863
25.9475
25.4272
25.0374
24.7693
24.6049
24.5254
24.518
24.5821
24.7326
24.9912
25.3533
25.7394
25.9828
25.9135
25.495
24.8565
24.1833
23.6055
23.1742
22.8871
22.714
22.6107
22.5313
22.4412
22.324
22.1775
22.008
21.8261
21.6459
21.4836
21.3556
21.2723
21.233
21.2239
21.2236
21.2139
21.1864
7.50
29.0887
29.0603
28.7599
28.2182
27.5294
26.8091
26.1505
25.606
25.1922
24.9035
24.7246
24.6403
24.6419
24.7327
24.9284
25.2467
25.676
26.1283
26.4237
26.3774
25.9492
25.2775
24.5578
23.9257
23.4347
23.0839
22.8464
22.6852
22.563
22.4496
22.3265
22.1863
22.0297
21.863
21.6965
21.5428
21.4148
21.3217
21.2649
21.2362
21.2217
21.2076
21.1854
8.00
29.0211
28.9911
28.7143
28.215
27.5731
26.8905
26.2547
25.719
25.3042
25.0094
24.824
24.7366
24.7413
24.8414
25.0476
25.368
25.7813
26.2013
26.4702
26.431
26.0473
25.4326
24.7547
24.1375
23.6363
23.257
22.9808
22.779
22.622
22.4849
22.3506
22.2098
22.0599
21.904
21.7489
21.6038
21.4785
21.3804
21.3116
21.2679
21.2405
21.2195
21.1976
189
TEC generated using nine random distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
39.8042
38.3428
36.8986
35.4754
34.0777
32.7114
31.3837
30.1034
28.8808
27.7282
26.6583
25.6836
24.8146
24.0565
23.408
22.8602
22.3975
22.0014
21.6542
21.3428
21.0615
20.8124
20.6043
20.451
20.3684
20.3712
20.4701
20.669
20.9653
21.3523
21.8223
22.3692
22.9896
23.6821
24.4459
25.2805
26.1841
27.1538
28.1859
29.2755
30.4177
31.607
32.8385
0.50
39.4881
38.0085
36.5441
35.0985
33.6761
32.2828
30.926
29.6149
28.3612
27.1787
26.0832
25.0907
24.2151
23.4646
22.8382
22.3241
21.9012
21.5437
21.2272
20.934
20.6567
20.3982
20.1705
19.9913
19.8811
19.8586
19.9373
20.1215
20.4065
20.7828
21.241
21.775
22.3827
23.0647
23.8224
24.656
25.5641
26.5436
27.5898
28.6969
29.8588
31.0694
32.3227
1.00
39.2474
37.753
36.2721
34.8078
33.3644
31.9477
30.565
29.226
27.9433
26.7324
25.612
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23.7224
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22.5372
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24.1062
25.0149
26.0018
27.0607
28.1846
29.3658
30.5972
31.8718
1.50
39.0853
37.5803
36.0872
34.609
33.1497
31.7148
30.3114
28.9496
27.6423
26.4067
25.2645
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25.5321
26.603
27.7432
28.9434
30.195
31.4902
2.00
39.0044
37.4935
35.9935
34.5071
33.0382
31.5919
30.1754
28.7983
27.4742
26.2213
25.0637
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19.547
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21.7665
22.45
23.2434
24.1427
25.1392
26.2216
27.378
28.5968
29.8681
31.1829
2.50
39.0064
37.4948
35.9937
34.5057
33.0346
31.5854
30.1649
28.783
27.4533
26.1947
25.0329
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21.5245
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22.9359
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24.8287
25.923
27.0954
28.3324
29.6222
30.9551
3.00
39.0919
37.585
36.0889
34.6065
33.1413
31.6985
30.2849
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27.589
26.3398
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29.4637
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39.2603
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36.2787
34.8089
33.3579
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30.5354
29.1813
27.8828
26.6596
25.5383
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24.4899
25.6085
26.8109
28.0793
29.3994
30.7604
4.00
39.5099
38.0284
36.5607
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33.6808
32.2786
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21.3747
21.8826
22.5893
23.468
24.4867
25.6151
26.8283
28.1068
29.4359
30.8045
4.50
39.8381
38.3764
36.9309
35.5052
34.1041
32.7337
31.4023
30.1208
28.9039
27.7705
26.7444
25.8533
25.124
24.575
24.2053
23.9894
23.8787
23.813
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23.4189
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22.9621
22.7584
22.5936
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21.6581
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21.5506
22.0259
22.7181
23.5936
24.6147
25.7476
26.9653
28.2475
29.5792
30.9494
5.00
40.241
38.8029
37.3837
35.9875
34.6193
33.2858
31.9957
30.7599
29.5928
28.5121
27.5387
26.6953
26.002
25.4698
25.0942
24.8512
24.7004
24.5928
24.4821
24.3368
24.1494
23.9349
23.72
23.527
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22.8146
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21.8782
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23.006
23.8731
24.8886
26.0168
27.2298
28.5071
29.8334
31.198
5.50
40.7142
39.3027
37.913
36.5492
35.2171
33.9234
32.6768
31.4882
30.371
29.3409
28.4156
27.6125
26.9456
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26.0293
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25.5546
25.3997
25.251
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23.73
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22.2439
22.1965
22.3802
22.8108
23.4696
24.3187
25.3169
26.4286
27.6259
28.8881
30.2003
31.5514
6.00
41.253
39.8702
38.5117
37.1823
35.8876
34.6345
33.4314
32.2887
31.2183
30.2337
29.3491
28.5773
27.9272
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24.1098
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25.8991
26.982
28.1522
29.3893
30.6784
32.0082
6.50
41.8523
40.4993
39.1732
37.8787
36.6215
35.4082
34.2469
33.1468
32.1185
31.173
30.3212
29.5724
28.9318
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27.9653
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24.5181
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23.903
24.3039
24.9104
25.6949
26.6244
27.6685
28.802
30.0052
31.2631
32.5647
7.00
42.507
41.1844
39.8909
38.6309
37.4102
36.2349
35.1125
34.0511
33.0596
32.1468
31.3211
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24.8748
25.2657
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26.5893
27.4746
28.4737
29.5639
30.7266
31.9474
33.2149
7.50
43.2124
41.9202
40.6586
39.4323
38.2463
37.1067
36.0199
34.9929
34.0332
33.1477
32.3426
31.622
30.9873
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26.328
26.8811
27.5881
28.4284
29.3803
30.424
31.5425
32.722
33.9515
8.00
43.964
42.7015
41.4711
40.2769
39.1238
38.0171
36.9626
35.9662
35.0339
34.1712
33.3825
32.6707
32.0361
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30.9856
30.5563
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29.8416
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28.9877
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27.7853
27.5503
27.3186
27.1013
26.9179
26.7954
26.7641
26.8525
27.0821
27.4632
27.995
28.6675
29.4652
30.3709
31.3677
32.4407
33.577
34.7661
190
TEC generated using nine random distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
23.6462
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23.506
23.7039
24.2391
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23.5907
22.6499
21.5339
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22.7694
21.6681
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21.0978
22.3481
23.2855
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23.8711
24.3286
0.50
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2.00
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22.0625
22.13
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21.4965
21.2012
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20.4617
20.9384
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22.3088
3.00
22.9305
22.022
21.2099
20.8083
21.79
22.8797
23.5322
23.5963
23.1921
23.04
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3.50
23.8856
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4.50
26.3886
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5.00
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22.9794
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21.9444
21.964
21.7622
21.4485
21.2325
21.1591
21.0297
20.7514
20.5353
20.6912
21.0916
21.5106
21.8351
21.9815
21.9005
21.6283
21.3324
21.1928
21.1212
8.00
21.0068
21.0183
21.1164
21.269
21.4219
21.5274
21.5573
21.5103
21.4133
21.3045
21.2053
21.1136
21.0341
21.001
21.0511
21.179
21.3384
21.4757
21.5504
21.5453
21.4721
21.3657
21.2601
21.1649
21.0763
21.0114
21.0116
21.0992
21.2476
21.4035
21.5174
21.558
21.5203
21.4277
21.3186
21.2179
21.1254
21.043
21.0011
21.0393
21.159
21.3175
21.4604
191
TEC generated using nine random distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.3299
22.3416
22.3533
22.3646
22.3753
22.3849
22.3928
22.398
22.3997
22.3963
22.386
22.3666
22.3353
22.2889
22.2241
22.1391
22.0336
21.9102
21.7741
21.6328
21.4954
21.3686
21.2534
21.1465
21.0485
20.97
20.9256
20.9217
20.9514
21.0018
21.0617
21.1243
21.1856
21.2435
21.2965
21.344
21.386
21.4228
21.455
21.483
21.5076
21.5293
21.5485
0.50
22.3521
22.3664
22.381
22.3957
22.4102
22.424
22.4366
22.4471
22.4544
22.457
22.453
22.4398
22.4138
22.3707
22.3053
22.2136
22.0942
21.9492
21.7846
21.6107
21.443
21.2953
21.1679
21.0453
20.919
20.8099
20.7545
20.7668
20.8275
20.9091
20.9944
21.0769
21.1539
21.2238
21.2858
21.3397
21.386
21.4255
21.4591
21.4879
21.5128
21.5344
21.5534
1.00
22.3737
22.3907
22.4083
22.4265
22.445
22.4634
22.4812
22.4975
22.5111
22.5206
22.5239
22.5183
22.5002
22.4639
22.4017
22.3061
22.1732
22.0042
21.8039
21.5832
21.368
21.1933
21.0653
20.9366
20.7651
20.5928
20.5165
20.5683
20.6885
20.816
20.932
21.0366
21.1307
21.2136
21.2846
21.3443
21.3938
21.4348
21.4688
21.4974
21.5216
21.5426
21.5608
1.50
22.3945
22.414
22.4347
22.4565
22.4792
22.5024
22.5257
22.5482
22.5686
22.5852
22.5959
22.598
22.5888
22.5628
22.5099
22.4164
22.2741
22.0834
21.8444
21.5577
21.2567
21.0311
20.9318
20.8373
20.5979
20.2897
20.1717
20.3247
20.5545
20.7375
20.8822
21.0088
21.1209
21.217
21.2963
21.3603
21.4112
21.4519
21.4848
21.5118
21.5345
21.5539
21.5708
2.00
22.4138
22.436
22.4597
22.485
22.5119
22.5401
22.5692
22.5981
22.6255
22.6491
22.6657
22.6723
22.6674
22.6513
22.6163
22.5376
22.396
22.196
21.9341
21.5745
21.1215
20.7681
20.7424
20.7811
20.4802
19.9401
19.7383
20.1056
20.4825
20.6898
20.8488
20.998
21.1305
21.2398
21.3254
21.3907
21.44
21.4778
21.5074
21.5313
21.5512
21.5682
21.5832
2.50
22.4315
22.456
22.4826
22.5114
22.5424
22.5756
22.6105
22.6463
22.6811
22.7117
22.7326
22.7366
22.72
22.6964
22.6878
22.6531
22.5313
22.3442
22.1118
21.7405
21.1266
20.5613
20.6064
20.8304
20.5672
19.9409
19.6879
20.1812
20.5148
20.6507
20.8274
21.0121
21.169
21.2896
21.3769
21.4384
21.4816
21.5129
21.5366
21.5556
21.5715
21.5853
21.5977
3.00
22.447
22.4737
22.5029
22.5349
22.5698
22.6078
22.6486
22.6916
22.735
22.7746
22.8021
22.8016
22.7521
22.6715
22.6896
22.7608
22.6765
22.509
22.3768
22.1459
21.5729
20.9902
20.9572
21.1139
20.9295
20.5293
20.3785
20.5296
20.473
20.5752
20.8386
21.0742
21.2522
21.3761
21.4558
21.5051
21.5358
21.5564
21.5715
21.5838
21.5946
21.6045
21.6139
3.50
22.4601
22.4886
22.52
22.5547
22.5931
22.6355
22.6821
22.7327
22.7862
22.8395
22.8847
22.9034
22.8594
22.7435
22.8092
22.9844
22.8624
22.6474
22.6035
22.5668
22.1628
21.7756
21.7108
21.6817
21.4515
21.1691
21.031
20.885
20.5838
20.6977
20.9844
21.2222
21.3972
21.5069
21.5639
21.5894
21.6004
21.6059
21.6101
21.6145
21.6195
21.6251
21.6312
4.00
22.4704
22.5003
22.5334
22.5703
22.6114
22.6575
22.7092
22.7671
22.8317
22.903
22.9799
23.0611
23.1531
23.3182
23.6063
23.5446
23.1373
22.7553
22.6481
22.6329
22.4097
22.3187
22.4864
22.4022
21.99
21.6601
21.6086
21.6602
21.411
21.2242
21.2933
21.4552
21.6024
21.6778
21.6934
21.6837
21.6691
21.6572
21.6495
21.6456
21.6447
21.646
21.6488
4.50
22.4778
22.5085
22.5427
22.581
22.624
22.6726
22.728
22.7916
22.8656
22.9536
23.0628
23.2112
23.4476
23.8632
24.2879
24.0535
23.4047
22.8826
22.6523
22.563
22.4837
22.6127
22.9602
22.8841
22.3451
21.9553
21.9701
22.209
22.0263
21.6697
21.5873
21.6991
21.8262
21.8563
21.8203
21.7719
21.7322
21.7043
21.6861
21.675
21.6689
21.6663
21.6662
5.00
22.482
22.513
22.5476
22.5864
22.6301
22.6798
22.7368
22.8032
22.8821
22.9786
23.1026
23.2736
23.5243
23.8671
24.1276
23.9539
23.4351
22.961
22.6879
22.5554
22.5154
22.6332
22.8437
22.7777
22.3906
22.069
22.0242
22.1212
22.0253
21.8164
21.7559
21.8643
21.979
21.9758
21.9061
21.8343
21.7796
21.7418
21.7167
21.7006
21.6907
21.6852
21.6827
5.50
22.4831
22.5139
22.5481
22.5865
22.6297
22.6787
22.7351
22.8006
22.8781
22.9723
23.09
23.2409
23.4301
23.6305
23.7341
23.606
23.281
22.9407
22.6978
22.5564
22.501
22.5303
22.5804
22.5084
22.2931
22.0855
21.9971
21.9817
21.9251
21.839
21.8253
21.912
21.9974
21.9916
21.9286
21.8604
21.806
21.7667
21.7396
21.7213
21.7095
21.7021
21.698
6.00
22.4811
22.5111
22.5443
22.5814
22.6229
22.6698
22.7231
22.7843
22.8554
22.9389
23.0375
23.1517
23.2737
23.3748
23.3995
23.2996
23.0946
22.8635
22.6715
22.5396
22.4652
22.4345
22.4085
22.3339
22.2032
22.0693
21.9801
21.9291
21.8832
21.8437
21.8439
21.8928
21.9421
21.944
21.9064
21.8579
21.8144
21.7803
21.7552
21.7373
21.725
21.7169
21.7118
6.50
22.4762
22.5049
22.5366
22.5716
22.6104
22.6538
22.7023
22.7569
22.8184
22.8873
22.9632
23.0423
23.1145
23.1596
23.1508
23.0711
22.9325
22.7716
22.624
22.508
22.4255
22.367
22.3119
22.239
22.1453
22.05
21.973
21.9174
21.876
21.8491
21.846
21.8663
21.8891
21.8919
21.8728
21.843
21.8126
21.7862
21.7652
21.7494
21.7378
21.7297
21.7242
7.00
22.4687
22.4958
22.5254
22.5577
22.5932
22.6322
22.675
22.7218
22.7725
22.8265
22.8817
22.9333
22.973
22.9884
22.9665
22.9016
22.8012
22.6838
22.569
22.4692
22.3877
22.3197
22.2557
22.1866
22.111
22.0363
21.9712
21.9196
21.8811
21.8563
21.8469
21.8505
21.8574
21.8572
21.8464
21.8283
21.8079
21.7886
21.772
21.7587
21.7484
21.7408
21.7354
7.50
22.459
22.4841
22.5113
22.5406
22.5724
22.6066
22.6432
22.682
22.7224
22.7631
22.8015
22.8336
22.8531
22.8529
22.8266
22.7726
22.6956
22.6057
22.5141
22.4288
22.3528
22.2848
22.2204
22.156
22.0911
22.0285
21.9726
21.9262
21.8902
21.8651
21.8508
21.845
21.8429
21.8391
21.8309
21.8187
21.8045
21.7903
21.7775
21.7665
21.7577
21.7508
21.7457
8.00
22.4474
22.4704
22.4949
22.5211
22.5489
22.5783
22.6089
22.6403
22.6716
22.7012
22.727
22.7455
22.7527
22.7443
22.7173
22.6714
22.6097
22.538
22.4631
22.39
22.3213
22.2572
22.1962
22.137
22.0794
22.025
21.976
21.9341
21.9003
21.875
21.8576
21.8466
21.8392
21.8324
21.8244
21.8147
21.8039
21.793
21.7828
21.7738
21.7662
21.76
21.7552
192
TEC generated using thirteen well distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.5988
21.9103
21.2841
20.7405
20.2964
19.9591
19.7221
19.5667
19.4682
19.4015
19.3451
19.282
19.1999
19.091
18.9519
18.783
18.5885
18.376
18.156
17.9413
17.7453
17.5787
17.446
17.3438
17.2625
17.1898
17.114
17.0257
16.9183
16.788
16.6343
16.4601
16.2722
16.0815
15.9039
15.7606
15.6769
15.6792
15.7886
16.0138
16.3493
16.7793
17.2844
0.50
22.7811
22.0934
21.4678
20.9275
20.4928
20.173
19.9607
19.8342
19.7652
19.7262
19.6941
19.6509
19.5838
19.4847
19.3503
19.1815
18.9834
18.7642
18.5356
18.3117
18.1076
17.936
17.8019
17.7013
17.6229
17.5526
17.4778
17.3881
17.2765
17.1385
16.9733
16.7834
16.5753
16.3602
16.1542
15.9792
15.8629
15.8348
15.9191
16.1263
16.4497
16.8712
17.3692
1.00
23.0724
22.3984
21.7854
21.2574
20.8364
20.5329
20.3392
20.2323
20.1823
20.1609
20.1444
20.1144
20.0575
19.9652
19.8343
19.6662
19.4666
19.2447
19.0124
18.7843
18.5761
18.4008
18.2641
18.1616
18.0812
18.0086
17.9307
17.8373
17.7208
17.5764
17.4029
17.2026
16.9819
16.7516
16.5276
16.3317
16.1917
16.1384
16.1975
16.3806
16.6814
17.0816
17.5593
1.50
23.4736
22.8288
22.2431
21.739
21.3371
21.0476
20.8633
20.7625
20.7171
20.7001
20.6883
20.6632
20.6107
20.5219
20.3932
20.2269
20.0293
19.8101
19.5808
19.3554
19.1484
18.9718
18.8308
18.7213
18.6324
18.5509
18.4648
18.3642
18.2415
18.0919
17.9135
17.7085
17.4835
17.2488
17.0195
16.816
16.6641
16.5928
16.6272
16.7795
17.0457
17.4099
17.8527
2.00
23.9738
23.3727
22.8287
22.3596
21.9818
21.7031
21.5183
21.4096
21.3539
21.3275
21.3091
21.2803
21.2264
21.1377
21.0105
20.8474
20.6556
20.4445
20.2253
20.0097
19.8095
19.6339
19.487
19.3657
19.2618
19.1651
19.0655
18.9541
18.8238
18.6695
18.4891
18.285
18.0634
17.8346
17.6121
17.4135
17.2607
17.1785
17.1889
17.3048
17.5259
17.8416
18.2371
2.50
24.5508
24.0033
23.5104
23.0835
22.7324
22.4619
22.2687
22.1416
22.064
22.0174
21.9831
21.9433
21.8829
21.7914
21.6651
21.5067
21.3236
21.1253
20.9213
20.7206
20.5311
20.3584
20.2047
20.0686
19.9457
19.8294
19.7125
19.5878
19.4486
19.2899
19.1096
18.9101
18.6978
18.4822
18.275
18.0902
17.9442
17.8556
17.8429
17.9193
18.0895
18.3496
18.6904
3.00
25.1741
24.6829
24.2433
23.8597
23.535
23.2706
23.0656
22.9153
22.8105
22.7382
22.6827
22.6272
22.5568
22.4607
22.3347
22.1817
22.009
21.8254
21.6387
21.455
21.2779
21.1089
20.9486
20.7974
20.6544
20.5175
20.3826
20.2438
20.0953
19.9322
19.7527
19.5593
19.3583
19.1587
18.9701
18.8024
18.666
18.5731
18.5383
18.5757
18.6951
18.8994
19.1851
3.50
25.8116
25.3715
24.9797
24.6346
24.3332
24.074
23.8581
23.6862
23.5557
23.4581
23.3809
23.3087
23.227
23.1252
22.9991
22.8511
22.6881
22.5181
22.3474
22.1791
22.0132
21.8478
21.6822
21.5179
21.3577
21.2029
21.052
20.9007
20.7436
20.5761
20.3967
20.2078
20.016
19.8298
19.657
19.5038
19.3752
19.2778
19.223
19.2259
19.3007
19.456
19.693
4.00
26.4354
26.0351
25.6798
25.3637
25.0802
24.8262
24.6038
24.4171
24.2675
24.1502
24.055
23.9683
23.8763
23.7688
23.6415
23.4967
23.3408
23.1807
23.0214
22.864
22.706
22.5432
22.3741
22.2012
22.0292
21.8619
21.6996
21.539
21.375
21.2031
21.0216
20.8332
20.6448
20.4645
20.2993
20.153
20.0267
19.9234
19.8522
19.8289
19.8708
19.9898
20.1902
4.50
27.0267
26.652
26.3189
26.0202
25.7484
25.4999
25.2769
25.0843
24.9248
24.7958
24.6888
24.5916
24.4915
24.3787
24.2494
24.1054
23.9527
23.7974
23.6435
23.4909
23.336
23.1743
23.0039
22.8274
22.6503
22.4771
22.3088
22.1428
21.9739
21.7972
21.6108
21.4176
21.2246
21.0403
20.8715
20.7212
20.5896
20.4784
20.396
20.358
20.3821
20.4811
20.6604
5.00
27.5782
27.2152
26.8907
26.5986
26.3325
26.0894
25.8706
25.6799
25.5192
25.3862
25.2733
25.1697
25.0638
24.9466
24.8144
24.6691
24.5161
24.3608
24.2064
24.0529
23.8969
23.7346
23.5645
23.389
23.2125
23.039
22.8694
22.701
22.5284
22.3463
22.1523
21.9491
21.7441
21.5463
21.3631
21.1986
21.0544
20.9339
20.846
20.8053
20.8273
20.9233
21.0975
5.50
28.0923
27.7299
27.4039
27.1101
26.8449
26.606
26.3939
26.2099
26.0537
25.9218
25.8071
25.7
25.5899
25.4689
25.3336
25.1858
25.0301
24.8714
24.7127
24.5542
24.3941
24.2301
24.0613
23.8891
23.7167
23.5463
23.3779
23.2084
23.0323
22.8437
22.64
22.4237
22.2022
21.9849
21.7804
21.5949
21.4337
21.3037
21.2154
21.1819
21.2151
21.3224
21.5053
6.00
28.5785
28.2098
27.8758
27.5753
27.3073
27.071
26.8655
26.6893
26.5394
26.4107
26.296
26.1864
26.0727
25.9483
25.81
25.6593
25.5
25.3363
25.1714
25.0063
24.8408
24.6744
24.5067
24.3386
24.1711
24.0046
23.8377
23.6668
23.4862
23.2903
23.0763
22.8464
22.6077
22.3698
22.1423
21.9345
21.7559
21.6179
21.5332
21.5135
21.5667
21.6949
21.8959
6.50
29.0493
28.6711
28.3266
28.0172
27.7443
27.5082
27.3072
27.1372
26.9925
26.8662
26.7509
26.6384
26.521
26.393
26.2517
26.0981
25.9353
25.7667
25.5955
25.4237
25.2529
25.0838
24.9168
24.7518
24.5882
24.4245
24.2579
24.0844
23.8984
23.695
23.4715
23.2301
22.9772
22.7221
22.4755
22.2491
22.0568
21.914
21.836
21.8335
21.9101
22.0632
22.2865
7.00
29.5171
29.1297
28.7751
28.4568
28.1781
27.9401
27.7403
27.5727
27.4296
27.3031
27.1852
27.0686
26.9467
26.8146
26.6702
26.5138
26.3478
26.175
25.9987
25.8215
25.6461
25.4745
25.3073
25.1439
24.9821
24.8192
24.6513
24.4741
24.2826
24.0726
23.8421
23.5931
23.3314
23.0658
22.8076
22.5706
22.3716
22.2292
22.1605
22.1755
22.2745
22.4509
22.695
7.50
29.9921
29.5977
29.2357
28.9104
28.626
28.384
28.1814
28.0115
27.8655
27.7349
27.6118
27.4893
27.3617
27.2249
27.0769
26.9178
26.7492
26.5734
26.3936
26.2128
26.0342
25.8603
25.6922
25.5285
25.3665
25.2023
25.0318
24.8506
24.6544
24.4398
24.2058
23.9541
23.6902
23.4226
23.1627
22.9253
22.7288
22.5932
22.5361
22.5667
22.6835
22.8774
23.1369
8.00
30.4808
30.0829
29.7166
29.3867
29.0972
28.8496
28.6408
28.4641
28.3107
28.1723
28.0411
27.9108
27.7763
27.634
27.482
27.3201
27.1493
26.9718
26.7901
26.6075
26.4272
26.2517
26.0819
25.9164
25.7523
25.5855
25.4118
25.2271
25.0279
24.8117
24.578
24.329
24.0698
23.8086
23.5568
23.3294
23.1447
23.0223
22.9787
23.0221
23.1504
23.3542
23.6217
193
TEC generated using thirteen well distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
15.5148
16.847
20.3315
23.5649
25.1052
24.7168
23.717
24.5253
26.0926
25.9379
23.5037
19.6996
16.325
15.6796
18.2465
21.8759
24.4849
25.1362
24.2167
23.7769
25.2991
26.313
25.133
21.936
18.0466
15.6041
16.492
19.8382
23.2134
25.0205
24.8501
23.7911
24.3029
25.9491
26.096
23.9354
20.2277
16.662
15.5556
17.7873
21.4194
24.2425
25.1646
0.50
8.53923
12.1264
19.0146
24.2806
26.7734
25.7442
22.7779
24.0016
26.5705
26.1202
22.2176
16.3886
10.2188
9.16206
15.1439
21.5877
25.7632
26.733
24.5413
22.2367
25.3246
26.8577
24.7654
19.8438
13.5772
8.69925
11.2825
18.149
23.722
26.642
26.0509
23.1897
23.5711
26.3522
26.4058
22.8795
17.2277
10.9165
8.7886
14.2004
20.8443
25.3683
0.5
1.00
3.07986
15.249
21.8631
25.2106
28.2916
25.69
23.2156
23.3633
26.666
26.0799
22.3472
19.0406
11.6557
6.76319
18.8915
23.4737
26.5031
27.953
24.3338
22.925
24.3803
27.9542
24.244
21.0073
16.8593
4.74137
13.7137
21.2795
24.8202
27.8935
26.1843
23.4064
23.1743
26.0588
26.6966
22.7632
19.5553
13.2475
4.45612
17.9514
23.019
26.0992
28.4029
1.50
25.8739
25.7274
25.0059
24.0273
23.1038
22.4319
22.0392
21.9039
22.0956
22.7126
23.6991
24.7988
25.6448
25.8959
25.4683
24.5932
23.6048
22.7764
22.2298
21.9473
21.9397
22.309
23.1063
24.1821
25.2198
25.84
25.7856
25.1239
24.16
23.2144
22.5042
22.0767
21.9056
22.047
22.6059
23.5545
24.6589
25.5609
25.9035
25.5579
24.7229
23.7315
22.8708
2.00
21.9466
21.827
23.4848
22.5842
22.4521
22.7524
25.7706
24.8798
24.1846
24.6687
25.1609
24.2816
22.5162
21.7541
22.1869
23.2867
22.4665
22.5122
23.2603
29.505
24.1463
24.3863
24.8802
25.1617
23.4192
22.0482
21.7755
23.0838
22.6643
22.4467
22.6704
24.7804
25.4863
24.1384
24.6036
25.0999
24.5481
22.6996
21.7904
22.0388
23.5936
22.4874
22.4859
2.50
22.7841
24.9514
27.0902
25.3396
20.4419
13.987
7.21198
8.99776
17.0441
23.2912
26.9157
26.7725
23.9009
23.3312
26.176
26.8696
23.4775
17.8144
10.7539
6.47966
12.4449
20.0798
25.2064
27.3977
25.6277
22.8972
24.5496
26.9831
25.8048
21.2032
14.937
7.85969
8.12112
16.0169
22.612
26.6106
27.0312
24.2961
23.0454
25.8279
27.0323
24.0969
18.6384
3.00
23.3739
24.9835
26.4192
25.3923
21.9271
17.3409
13.9339
14.5337
18.5459
22.79
25.2902
25.3628
23.8403
23.8107
25.826
26.3183
24.1297
19.9719
15.5319
13.619
16.0444
20.512
24.1536
25.6147
24.7794
23.3887
24.6945
26.3478
25.6876
22.4878
17.9464
14.2016
14.1951
17.9364
22.2999
25.0949
25.4827
24.0517
23.607
25.5934
26.4053
24.5614
20.5855
3.50
23.761
24.843
25.8393
25.5602
23.8936
21.661
20.0877
19.9161
21.0996
22.7727
23.8193
23.8532
23.5881
24.1411
25.3758
25.9077
24.9767
22.9234
20.8344
19.8267
20.2962
21.836
23.3529
23.9368
23.7049
23.687
24.6699
25.7645
25.686
24.1724
21.9451
20.2233
19.8518
20.8886
22.5658
23.7426
23.8899
23.5963
24.0043
25.2227
25.9169
25.1817
23.2263
4.00
22.3764
23.6609
24.7276
25.1821
25.0725
24.7241
24.8076
23.9201
22.8714
22.5226
22.2751
21.7788
21.8432
22.9185
24.1828
25.0075
25.187
24.9002
24.6972
24.6776
23.3875
22.6218
22.4571
22.063
21.6697
22.2277
23.4898
24.617
25.1598
25.111
24.7538
24.7772
24.1046
22.9752
22.5365
22.3288
21.8381
21.7659
22.7462
24.0307
24.9354
25.1956
24.9542
4.50
21.9162
22.6154
23.29
23.8026
24.1237
24.2558
24.1655
23.8001
23.2368
22.6267
22.0484
21.6103
21.6351
22.2058
22.9226
23.5354
23.9652
24.2046
24.2481
24.0404
23.5705
22.9716
22.369
21.8275
21.5422
21.8376
22.519
23.2082
23.7456
24.0919
24.2496
24.1929
23.8634
23.317
22.7069
22.1212
21.6507
21.5942
22.1132
22.8303
23.4639
23.9193
24.1836
5.00
24.4265
23.8452
23.0819
22.3515
21.6337
21.0346
21.3455
22.3314
23.2493
23.9268
24.3482
24.5613
24.5711
24.2188
23.5177
22.759
22.0416
21.3326
21.0105
21.7558
22.7535
23.5757
24.1389
24.463
24.5963
24.4731
23.9402
23.1831
22.4462
21.7292
21.0858
21.2381
22.1973
23.1398
23.8522
24.3055
24.5433
24.586
24.291
23.6197
22.8566
22.1367
21.4218
5.50
24.1623
23.1886
22.5986
22.5902
22.3969
22.0504
22.3932
23.5326
24.6968
25.2718
25.1306
24.5599
24.2647
23.7879
22.8494
22.5607
22.5584
22.2209
22.0717
22.8315
24.0792
25.039
25.2861
24.9065
24.3647
24.216
23.3173
22.6371
22.5864
22.4455
22.076
22.2887
23.3625
24.567
25.2397
25.1814
24.636
24.2741
23.9274
22.9397
22.5601
22.5764
22.2748
6.00
19.021
19.485
21.3296
23.2584
24.1769
23.9932
23.7254
24.5466
25.7688
25.8419
24.2882
21.7662
19.5981
18.9942
20.1837
22.2353
23.8153
24.1939
23.7998
23.9328
25.1319
26.0004
25.3504
23.2451
20.697
19.1025
19.3215
21.0495
23.0442
24.1293
24.0534
23.7124
24.3774
25.6466
25.9288
24.5734
22.1127
19.8148
18.9635
19.9468
21.9636
23.6696
24.209
6.50
12.5919
14.7226
19.6021
23.8189
25.7983
25.1566
23.3082
24.2605
26.2766
25.9828
22.8819
18.1026
13.6561
12.9252
16.7442
21.637
25.0034
25.8088
24.3365
23.1968
25.2914
26.5145
24.938
20.923
15.9599
12.6959
14.1913
18.9392
23.3666
25.6922
25.3641
23.5026
23.9472
26.1044
26.1951
23.423
18.7747
14.1119
12.7151
16.0919
21.0409
24.6909
25.8584
7.00
5.37128
10.9466
19.2939
24.7797
27.6407
26.2105
23.4016
24.1602
26.89
26.3492
21.9987
15.9944
8.19282
6.39562
14.8904
21.9883
26.4136
27.5358
24.8659
23.1191
25.4216
27.284
24.7528
19.5131
12.7997
5.67095
9.73004
18.3554
24.1915
27.4759
26.5953
23.672
23.8219
26.6108
26.7067
22.6986
16.8658
9.24173
5.76739
13.717
21.2203
25.9636
27.6725
7.50
34.2782
28.4798
25.5577
24.397
23.1003
22.2802
21.4741
20.703
19.0247
20.0477
22.4555
24.4725
29.3586
32.8217
26.7288
25.008
23.8799
22.6585
21.9421
21.1384
20.2517
17.8709
21.3342
23.2306
25.9209
33.4083
29.2779
25.7678
24.5413
23.2807
22.3723
21.582
20.8112
19.4211
19.5067
22.2171
24.1368
28.3256
33.8599
27.1526
25.1609
24.0476
22.7661
8.00
20.8302
20.4522
20.56
21.848
24.0017
26.3865
28.2043
28.2124
26.6082
24.5669
22.6747
21.5282
21.0547
20.6527
20.3883
20.9656
22.7194
25.0387
27.3206
28.4718
27.6366
25.7317
23.6994
22.0551
21.2872
20.884
20.4917
20.486
21.6106
23.6913
26.0774
28.0447
28.3306
26.8661
24.8386
22.8976
21.6253
21.1064
20.7067
20.3945
20.8145
22.4394
24.7188
194
TEC generated using thirteen well distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.4153
22.2051
21.9876
21.8063
21.7199
21.765
21.917
22.1024
22.2532
22.3374
22.3552
22.3202
22.2452
22.1328
21.9741
21.7527
21.4529
21.0693
20.6187
20.1563
19.7846
19.6161
19.6831
19.8945
20.1147
20.2543
20.2894
20.2393
20.1412
20.0281
19.9109
19.7717
19.5703
19.2636
18.8272
18.2828
17.7237
17.3059
17.163
17.3072
17.6395
18.0422
18.4382
0.50
22.4213
22.1491
21.8414
21.5597
21.4136
21.4886
21.7431
22.0384
22.2626
22.3799
22.4046
22.3675
22.2939
22.1909
22.0434
21.8219
21.4963
21.0476
20.4807
19.853
19.3174
19.0906
19.2559
19.6388
19.996
20.2007
20.2398
20.1583
20.0228
19.894
19.7954
19.6975
19.5324
19.2273
18.7347
18.0636
17.3282
16.7663
16.6048
16.854
17.3321
17.8576
18.3371
1.00
22.4937
22.1713
21.7705
21.3625
21.1286
21.2412
21.6261
22.039
22.3227
22.451
22.4605
22.4038
22.3247
22.2387
22.1218
21.9248
21.6004
21.1178
20.4673
19.6916
18.975
18.6685
18.944
19.5052
19.977
20.2116
20.2177
20.0656
19.8564
19.6942
19.6276
19.6079
19.5228
19.2651
18.7685
18.0273
17.1555
16.4578
16.2744
16.6208
17.2188
17.8281
18.3525
1.50
22.6673
22.3419
21.9024
21.4088
21.1021
21.2492
21.7242
22.1848
22.4641
22.5573
22.5163
22.4099
22.308
22.2456
22.1863
22.0479
21.7642
21.306
20.667
19.8762
19.1031
18.7537
19.0629
19.6638
20.1263
20.3111
20.2341
19.9678
19.6381
19.4124
19.3902
19.4924
19.5348
19.3756
18.9537
18.2682
17.4132
16.6844
16.4739
16.8238
17.422
18.0134
18.5114
2.00
22.9565
22.7071
22.3561
21.9367
21.6626
21.7904
22.1792
22.5222
22.6963
22.7001
22.5713
22.3764
22.2183
22.1792
22.2101
22.1685
21.9648
21.5912
21.0743
20.4578
19.8642
19.5784
19.7719
20.1711
20.4544
20.5053
20.3127
19.9163
19.4406
19.1221
19.1445
19.3908
19.5797
19.5447
19.2589
18.7556
18.1129
17.531
17.3108
17.5256
17.9572
18.4078
18.8032
2.50
23.3329
23.2279
23.0941
22.9389
22.8214
22.8275
22.9229
23.002
22.9994
22.887
22.6606
22.3579
22.1079
22.0778
22.2166
22.29
22.1816
21.917
21.5695
21.2135
20.9204
20.7688
20.7844
20.8687
20.8958
20.7851
20.4931
20.0187
19.4582
19.0723
19.1094
19.4367
19.7122
19.7688
19.6186
19.3337
18.9843
18.6513
18.4602
18.4868
18.6728
18.9222
19.1766
3.00
23.7298
23.7747
23.8735
24.0115
24.0675
23.928
23.7039
23.5119
23.3404
23.1374
22.8613
22.5094
22.1983
22.1549
22.3453
22.4769
22.4246
22.2399
22.0263
21.8795
21.8359
21.815
21.7091
21.5442
21.3607
21.1273
20.7957
20.3477
19.846
19.4928
19.4985
19.7596
19.9887
20.0504
19.9731
19.8432
19.7203
19.5938
19.4502
19.3515
19.3506
19.4342
19.5642
3.50
24.0815
24.2151
24.4345
24.7126
24.8579
24.6678
24.2896
23.9478
23.6835
23.4559
23.2211
22.9557
22.7156
22.6563
22.7583
22.8073
22.7188
22.5458
22.3851
22.3295
22.4035
22.4642
22.3275
22.0546
21.7694
21.4874
21.1824
20.8445
20.5068
20.2672
20.2236
20.3173
20.3915
20.3688
20.2757
20.1885
20.1561
20.1304
20.0394
19.923
19.8572
19.8614
19.9165
4.00
24.3651
24.5092
24.711
24.9434
25.0659
24.9213
24.5923
24.2604
23.9975
23.8097
23.6907
23.6265
23.5893
23.5397
23.4416
23.2789
23.0637
22.8359
22.6533
22.5737
22.6148
22.6715
22.5773
22.3447
22.0769
21.8187
21.5832
21.3844
21.2347
21.1316
21.0539
20.9699
20.8519
20.6912
20.511
20.3638
20.296
20.2855
20.2638
20.2213
20.1916
20.1918
20.2191
4.50
24.6099
24.7252
24.8447
24.9507
24.9952
24.9191
24.7284
24.4912
24.2787
24.151
24.1581
24.3155
24.5215
24.514
24.2047
23.7952
23.4222
23.1177
22.8895
22.7424
22.677
22.6643
22.6228
22.4973
22.3088
22.1075
21.9471
21.8744
21.8978
21.9359
21.8521
21.6172
21.3152
21.0095
20.725
20.4861
20.3335
20.2975
20.3425
20.3995
20.4392
20.4648
20.4859
5.00
24.8699
24.9779
25.0532
25.0849
25.0806
25.0388
24.9265
24.7425
24.5501
24.4439
24.5129
24.7931
25.1423
25.1785
24.7628
24.2042
23.7329
23.3909
23.1543
22.9875
22.8682
22.8005
22.7635
22.6874
22.5427
22.3718
22.2514
22.2564
22.4047
22.5656
22.5013
22.1647
21.7277
21.3205
20.9782
20.7034
20.5154
20.4581
20.5256
20.6292
20.7009
20.7325
20.7403
5.50
25.1839
25.3486
25.4848
25.5703
25.5891
25.5229
25.3516
25.0977
24.8397
24.6803
24.7081
24.9462
25.2479
25.2826
24.9162
24.3923
23.9449
23.6424
23.4666
23.3695
23.3034
23.2421
23.1646
23.0335
22.8408
22.6333
22.4913
22.4958
22.6683
22.8685
22.8285
22.4797
22.0118
21.5887
21.2634
21.0356
20.9016
20.8724
20.9306
21.0025
21.0341
21.0254
20.9963
6.00
25.5446
25.8297
26.1315
26.3999
26.5223
26.389
26.0287
25.5767
25.1629
24.8834
24.7952
24.8881
25.0367
25.0291
24.7721
24.3933
24.063
23.8663
23.8144
23.8725
23.9648
23.9785
23.8331
23.5531
23.2184
22.9053
22.6845
22.6158
22.706
22.8364
22.7988
22.5215
22.1328
21.7783
21.5285
21.4001
21.3838
21.4426
21.4988
21.4897
21.4233
21.335
21.2485
6.50
25.8962
26.3191
26.8157
27.3088
27.5785
27.3914
26.8085
26.1087
25.5015
25.0777
24.8559
24.7975
24.8023
24.7451
24.5682
24.3287
24.1332
24.0651
24.165
24.4241
24.7399
24.8769
24.6516
24.1683
23.6388
23.1849
22.8605
22.6913
22.6612
22.6814
22.6214
22.4238
22.1489
21.8968
21.7411
21.7186
21.8256
21.9844
22.0487
21.9582
21.789
21.6183
21.475
7.00
26.1642
26.6786
27.2927
27.9106
28.2685
28.0773
27.3847
26.5312
25.7871
25.2512
24.9222
24.7493
24.6534
24.5561
24.4215
24.2762
24.1874
24.2273
24.4514
24.8684
25.3565
25.5928
25.3169
24.684
24.0036
23.4371
23.0272
22.7727
22.6425
22.5709
22.4795
22.328
22.1395
21.9746
21.8953
21.9441
22.1181
22.3203
22.3843
22.2579
22.0408
21.8271
21.651
7.50
26.2972
26.8232
27.429
28.0116
28.3383
28.1692
27.528
26.698
25.9403
25.3655
24.9783
24.7352
24.5774
24.4529
24.3384
24.2479
24.2251
24.3261
24.599
25.0456
25.5378
25.7723
25.5141
24.8931
24.2006
23.6078
23.1627
22.8586
22.6642
22.5321
22.4133
22.2805
22.1416
22.0317
21.9947
22.0633
22.2284
22.4023
22.4539
22.3436
22.1459
21.941
21.765
8.00
26.29
26.7605
27.2689
27.721
27.9495
27.8018
27.2914
26.6034
25.936
25.3947
24.9997
24.7268
24.5373
24.3975
24.292
24.2287
24.2351
24.3474
24.593
24.9553
25.3212
25.479
25.2766
24.7859
24.2024
23.6696
23.2435
22.9282
22.7033
22.5375
22.4001
22.2731
22.1585
22.0755
22.0508
22.1024
22.2168
22.3316
22.3652
22.289
22.1417
21.9762
21.8238
195
TEC generated using thirteen random distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
21.3074
20.8194
20.4249
20.1236
19.9017
19.7367
19.6063
19.4959
19.4015
19.3258
19.2733
19.2447
19.2354
19.2375
19.2424
19.2423
19.2319
19.2074
19.1668
19.1089
19.0331
18.9386
18.8247
18.6901
18.5332
18.3519
18.1443
17.9089
17.6449
17.3534
17.0374
16.7021
16.3555
16.008
15.6735
15.3697
15.119
14.9473
14.8814
14.9421
15.1368
15.4575
15.8852
0.50
21.515
21.0441
20.6749
20.406
20.219
20.0841
19.9734
19.8706
19.7741
19.692
19.6334
19.6016
19.5917
19.5943
19.5993
19.5984
19.5859
19.5583
19.5143
19.4531
19.3747
19.2786
19.1643
19.0303
18.8747
18.695
18.4883
18.2521
17.985
17.6873
17.3619
17.0144
16.6531
16.289
15.9366
15.6142
15.3445
15.1542
15.0708
15.1155
15.2962
15.6048
16.0222
1.00
21.8481
21.405
21.0695
20.8382
20.6875
20.5808
20.4847
20.382
20.2747
20.1769
20.1033
20.0595
20.0405
20.0355
20.0331
20.0241
20.003
19.9668
19.9146
19.8464
19.7625
19.663
19.5473
19.4142
19.2612
19.0851
18.8822
18.649
18.3828
18.0835
17.7539
17.3999
17.0306
16.6578
16.2962
15.9647
15.6857
15.4854
15.3901
15.4199
15.5827
15.8715
16.2689
1.50
22.3087
21.9046
21.6102
21.4192
21.3031
21.2197
21.1319
21.0223
20.8973
20.7768
20.6803
20.616
20.579
20.5577
20.5394
20.5148
20.4782
20.4273
20.3618
20.2825
20.1901
20.0851
19.967
19.8345
19.6848
19.5141
19.3178
19.0909
18.8298
18.5335
18.2049
17.8504
17.4799
17.1057
16.7432
16.4108
16.1305
15.9268
15.8238
15.8397
15.982
16.2454
16.6156
2.00
22.8818
22.524
22.2739
22.1216
22.0347
21.9681
21.8826
21.7619
21.6162
21.4702
21.3471
21.2568
21.1951
21.15
21.1085
21.061
21.0025
20.9313
20.8479
20.7537
20.6499
20.5371
20.4152
20.2826
20.1364
19.9722
19.7843
19.5667
19.3144
19.0256
18.7031
18.3541
17.9889
17.6203
17.2635
16.9365
16.66
16.4567
16.3481
16.3506
16.4712
16.7069
17.0463
2.50
23.5371
23.2256
23.0157
22.8943
22.8276
22.7698
22.6822
22.5501
22.3865
22.2186
22.0711
21.9548
21.8662
21.7936
21.7242
21.649
21.5638
21.4679
21.3628
21.2506
21.1328
21.0104
20.8831
20.7492
20.6058
20.4479
20.2693
20.0628
19.8222
19.545
19.234
18.8966
18.5433
18.1866
17.841
17.5233
17.2531
17.0513
16.9377
16.927
17.0265
17.2348
17.5431
3.00
24.2381
23.9648
23.7838
23.6798
23.6202
23.562
23.4694
23.3294
23.1557
22.9752
22.8115
22.6751
22.5629
22.4638
22.3657
22.261
22.1467
22.0238
21.895
21.763
21.6298
21.4963
21.362
21.2254
21.0832
20.9304
20.7603
20.5652
20.3383
20.0766
19.7826
19.4633
19.1286
18.7896
18.4595
18.1536
17.8904
17.6899
17.5707
17.5473
17.6271
17.81
18.0895
3.50
24.9523
24.7043
24.5368
24.4342
24.3672
24.2989
24.1987
24.0558
23.8818
23.7001
23.5312
23.3841
23.2552
23.1342
23.0102
22.8772
22.7346
22.5851
22.4328
22.281
22.132
21.9867
21.8445
21.7035
21.5606
21.4106
21.2471
21.0625
20.8503
20.6072
20.3354
20.0407
19.7312
19.4156
19.1047
18.8123
18.556
18.3557
18.2303
18.1947
18.2571
18.418
18.6722
4.00
25.6578
25.4218
25.2536
25.1387
25.0525
24.9661
24.8557
24.7126
24.545
24.3709
24.2059
24.0563
23.918
23.7811
23.6362
23.4792
23.3117
23.1387
22.9653
22.7956
22.632
22.4753
22.3247
22.1784
22.0329
21.8835
21.7243
21.5487
21.351
21.1288
20.8834
20.6188
20.3402
20.0529
19.7646
19.4869
19.2373
19.0363
18.9045
18.8581
18.9057
19.0486
19.2818
4.50
26.3437
26.109
25.9305
25.795
25.6836
25.5748
25.4517
25.3076
25.1476
24.9839
24.8266
24.6789
24.5358
24.3879
24.2275
24.0523
23.8658
23.6745
23.4844
23.3002
23.1244
22.9578
22.7995
22.6475
22.4984
22.3481
22.1914
22.0232
21.8396
21.639
21.4221
21.1911
20.9472
20.6919
20.4286
20.1671
19.9245
19.7231
19.5859
19.5308
19.5671
19.696
19.9124
5.00
27.007
26.767
26.5732
26.4148
26.2772
26.1455
26.0079
25.8599
25.7043
25.5482
25.3971
25.2511
25.1043
24.9483
24.777
24.5896
24.3906
24.1871
23.9856
23.7913
23.6067
23.4326
23.268
23.111
22.9585
22.8067
22.6516
22.4899
22.3193
22.1394
21.9509
21.7536
21.5457
21.3238
21.0875
20.8439
20.6102
20.4108
20.2709
20.2103
20.239
20.3578
20.5611
5.50
27.6493
27.4006
27.1904
27.0099
26.8484
26.6953
26.5429
26.388
26.2319
26.0782
25.9287
25.7811
25.6293
25.4664
25.2874
25.0926
24.8866
24.6764
24.4688
24.2687
24.0789
23.9002
23.7316
23.5712
23.4161
23.2634
23.1102
22.9544
22.7956
22.6343
22.4713
22.3052
22.1308
21.9413
21.7326
21.5095
21.2888
21.0963
20.9588
20.8974
20.9223
21.034
21.2269
6.00
28.2742
28.0155
27.7897
27.5896
27.4074
27.2356
27.069
26.9051
26.7443
26.5876
26.4345
26.2816
26.123
25.953
25.7681
25.5689
25.3598
25.1471
24.9373
24.7353
24.5437
24.3633
24.1932
24.0314
23.8755
23.7231
23.5725
23.4227
23.2743
23.1289
22.9872
22.8469
22.701
22.5403
22.3584
22.1586
21.9568
21.7783
21.6501
21.5932
21.6179
21.725
21.9091
6.50
28.8855
28.6169
28.377
28.1602
27.9605
27.7726
27.5927
27.4189
27.2504
27.0869
26.9264
26.7653
26.5984
26.4212
26.2312
26.0292
25.8191
25.6065
25.3973
25.1961
25.0055
24.8259
24.6566
24.4955
24.3407
24.1904
24.0434
23.8999
23.7611
23.6287
23.5036
23.3827
23.2586
23.1216
22.9648
22.7907
22.6135
22.4564
22.3445
22.2973
22.3253
22.4297
22.6062
7.00
29.4867
29.209
28.9568
28.7257
28.5114
28.3097
28.1176
27.9333
27.7556
27.583
27.4132
27.2425
27.0668
26.8825
26.688
26.484
26.274
26.0629
25.8559
25.6574
25.4696
25.2928
25.126
24.9674
24.8153
24.6686
24.5266
24.3898
24.2598
24.1381
24.0253
23.9182
23.8098
23.6915
23.5575
23.41
23.2611
23.1307
23.0403
23.0072
23.0414
23.145
23.3152
7.50
30.081
29.7951
29.5323
29.2892
29.0623
28.8486
28.6453
28.4507
28.2631
28.0806
27.9008
27.7205
27.5363
27.3456
27.1472
26.942
26.7328
26.524
26.3203
26.1255
25.9415
25.7685
25.6053
25.4503
25.3023
25.1602
25.0239
24.8942
24.7723
24.6596
24.5559
24.4586
24.3617
24.2585
24.145
24.0234
23.9037
23.802
23.7356
23.7193
23.762
23.8668
24.0324
8.00
30.6708
30.3776
30.1058
29.8524
29.6149
29.3905
29.1769
28.9724
28.7751
28.583
28.3937
28.2045
28.0128
27.8166
27.6152
27.4094
27.2018
26.996
26.7962
26.6055
26.4257
26.2568
26.0976
25.9468
25.8032
25.6663
25.5362
25.4134
25.299
25.1939
25.0976
25.0078
24.9201
24.8299
24.7349
24.6374
24.5454
24.4714
24.4292
24.4305
24.4833
24.5912
24.7541
196
TEC generated using thirteen random distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
20.4647
17.7979
20.007
22.8635
23.926
23.8395
26.3518
26.7473
24.884
21.5674
21.7934
23.2343
22.7287
18.9105
18.2771
21.4029
23.5802
23.7541
25.1082
26.8119
26.199
23.5104
20.9257
22.4954
23.6325
20.9886
17.9057
19.5648
22.5703
23.9057
23.5859
26.1235
26.8297
25.2476
22.0019
21.564
23.0814
23.2296
19.3495
18.0065
20.9925
23.4015
23.8415
0.50
18.079
15.8083
18.5814
22.1587
24.4428
25.941
27.586
27.6611
25.8643
23.3395
21.857
21.1578
19.6046
16.8424
16.4908
20.2479
23.3266
25.0749
26.7353
27.8711
27.073
24.7478
22.5143
21.5519
20.6785
18.4599
15.9102
18.0602
21.747
24.2189
25.7157
27.4276
27.7695
26.1822
23.6456
21.9757
21.2641
19.9058
17.2105
16.1321
19.7501
22.9987
24.891
1.00
17.5099
17.8563
19.9739
23.0775
26.0603
28.269
29.2449
28.6264
26.5842
23.8759
21.3367
19.3469
17.9462
17.4509
18.5753
21.273
24.4336
27.1399
28.8712
29.1788
27.8807
25.4367
22.7185
20.4026
18.6616
17.5804
17.7073
19.6085
22.6531
25.6985
28.0366
29.2027
28.8013
26.9138
24.2407
21.6447
19.578
18.0929
17.4385
18.3186
20.8621
24.0257
26.8273
1.50
18.0187
18.8055
20.3655
22.5253
24.9653
27.0642
27.7507
26.4923
24.1993
21.8111
19.8209
18.4868
17.9474
18.2581
19.3947
21.2428
23.5757
25.9712
27.6026
27.4106
25.5576
23.1388
20.8805
19.1515
18.1503
17.9773
18.6541
20.119
22.2134
24.643
26.8405
27.7775
26.7452
24.5241
22.1128
20.0514
18.6202
17.9705
18.168
19.1994
20.9632
23.2503
25.6737
2.00
29.5434
28.2789
25.8029
22.9254
20.3615
18.4979
17.5589
17.8729
19.6821
22.5588
25.6583
28.2077
29.5244
29.1861
27.3095
24.5557
21.745
19.4543
17.9615
17.5184
18.4791
20.8493
23.9219
26.8746
28.964
29.5889
28.5318
26.1732
23.3016
20.6669
18.6973
17.62
17.7458
19.3628
22.1467
25.2622
27.9269
29.4401
29.3286
27.6272
24.9412
22.097
19.7168
2.50
28.2339
27.5928
25.4416
23.0193
21.4332
20.2056
18.3751
16.5669
17.8853
21.3643
24.2551
26.2092
27.7943
28.184
26.7906
24.3324
22.222
20.9237
19.5088
17.4536
16.5993
19.3671
22.7487
25.1802
26.9531
28.179
27.7819
25.7768
23.3024
21.5993
20.3888
18.6574
16.7089
17.4882
20.9086
23.9344
25.9768
27.6232
28.2372
27.0633
24.6694
22.4454
21.0778
3.00
26.9307
26.6473
24.2761
21.5838
22.0745
22.8317
20.7927
17.0148
18.1308
21.7254
23.6666
23.5338
26.0156
27.0997
25.8291
22.912
21.5377
22.4937
22.5803
19.0707
16.4117
19.8158
22.8191
23.8408
24.3642
26.7868
26.819
24.6772
21.782
21.9358
22.7875
21.2986
17.4433
17.6192
21.3215
23.5302
23.6295
25.6891
27.0966
26.1192
23.3278
21.4737
22.3745
3.50
26.4029
26.1278
24.0605
21.795
23.102
24.258
22.9549
20.8353
21.8728
23.8968
24.851
24.9681
25.9155
26.4891
25.4553
22.7036
22.1685
23.7543
24.0903
21.7995
21.0007
22.7906
24.4837
24.9042
25.2707
26.3213
26.2638
24.4359
21.8338
22.8802
24.1949
23.2871
20.917
21.6193
23.6657
24.8017
24.9299
25.7627
26.494
25.6986
23.1293
21.9911
23.5705
4.00
26.0088
26.0102
25.7484
24.719
24.6434
24.8764
24.5607
24.3904
25.337
26.6695
26.3625
26.0416
25.9795
26.023
25.9706
25.2531
24.5727
24.777
24.8032
24.3873
24.6601
26.0169
26.5917
26.1978
25.9842
26.0018
26.0167
25.8434
24.8105
24.6096
24.8701
24.6235
24.3563
25.151
26.605
26.4168
26.0704
25.9755
26.0205
25.9865
25.4166
24.5944
24.7358
4.50
24.5542
24.4027
24.7112
24.9094
25.0272
25.138
25.2704
25.4451
25.6348
25.7164
25.5817
25.2593
24.8223
24.3888
24.538
24.8134
24.9646
25.074
25.1914
25.3405
25.5308
25.6925
25.6857
25.4603
25.0802
24.6158
24.3733
24.6742
24.8899
25.0129
25.1226
25.2508
25.4195
25.6124
25.717
25.6121
25.3101
24.8846
24.4296
24.4941
24.7851
24.9488
25.0596
5.00
25.3267
25.5769
25.8846
25.9862
25.7552
25.3447
24.8807
24.6107
24.8458
25.0062
25.0529
25.1261
25.2363
25.4199
25.7151
25.9709
25.9198
25.5901
25.1439
24.7057
24.6841
24.9415
25.0283
25.0796
25.169
25.3027
25.5369
25.8487
25.9934
25.7999
25.4044
24.941
24.6125
24.8091
24.996
25.0464
25.1141
25.219
25.3888
25.6722
25.9504
25.9466
25.6433
5.50
24.1422
24.0994
25.3785
26.356
26.136
25.9696
26.0776
26.1095
25.7352
24.6085
24.3403
24.7615
24.5363
23.9511
24.5348
26.0291
26.2962
26.0283
25.9963
26.1247
26.0157
25.2967
24.325
24.5207
24.7937
24.2311
24.0188
25.1651
26.3396
26.1745
25.9733
26.058
26.123
25.824
24.7494
24.3063
24.7165
24.6189
23.9875
24.3763
25.85
26.3258
26.057
6.00
21.8654
20.2825
21.923
23.9646
24.6489
24.888
26.2051
26.4358
24.766
21.6885
22.3524
23.9364
23.4917
20.7175
20.7362
22.9242
24.4383
24.6395
25.4536
26.5184
25.9557
23.4597
21.4133
23.1406
24.1928
22.2658
20.2639
21.614
23.7607
24.6335
24.7738
26.0548
26.5091
25.101
22.0235
22.0987
23.7835
23.7817
21.022
20.5402
22.6273
24.3247
24.6429
6.50
19.2583
15.6846
18.9326
22.3338
23.8653
24.2647
26.7357
27.0974
25.2547
22.4096
21.8053
22.3898
21.3121
17.5543
16.5527
20.5959
23.2535
23.9134
25.4882
27.1883
26.5343
23.9987
21.7495
22.0914
22.3547
19.7744
16
18.3824
21.9779
23.7821
24.0106
26.5069
27.1866
25.6009
22.739
21.7374
22.3411
21.6864
18.0727
16.0504
20.1127
23.0127
23.9289
7.00
17.6627
16.8217
19.0381
22.4091
25.1256
27.0705
28.3416
28.1158
26.2762
23.7574
21.74
20.2973
18.6884
17.0246
17.4322
20.5159
23.7028
26.035
27.7477
28.4632
27.4806
25.1881
22.7819
21.0855
19.6538
17.8959
16.7762
18.6107
21.9816
24.8187
26.8406
28.2419
28.2487
26.5877
24.0822
21.9618
20.4829
18.9267
17.1916
17.1728
20.0577
23.3251
25.7698
7.50
17.5068
18.3925
20.6284
23.6105
26.6368
28.9248
29.7522
28.8288
26.5132
23.589
20.8302
18.7441
17.6202
17.714
19.2173
21.8753
24.9601
27.7674
29.494
29.5603
27.9545
25.27
22.3357
19.8232
18.1243
17.4957
18.1919
20.2703
23.1973
26.2595
28.6922
29.7433
29.0455
26.8743
23.9823
21.1658
18.9709
17.7051
17.6223
18.9383
21.4836
24.5492
27.4402
8.00
29.4586
27.6476
24.8064
21.8927
19.5062
17.9884
17.529
18.208
19.9709
22.5703
25.5755
28.2819
29.6312
28.8726
26.4776
23.5091
20.7686
18.7275
17.652
17.683
18.849
21.0169
23.8561
26.8419
29.0991
29.5626
27.9718
25.2048
22.2589
19.7785
18.1319
17.525
18.0526
19.6813
22.1907
25.1744
27.9757
29.5679
29.0895
26.8506
23.9035
21.0998
18.9472
197
TEC generated using thirteen random distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.4232
22.254
22.1807
22.2474
22.4066
22.541
22.5636
22.4648
22.3061
22.1901
22.193
22.3108
22.4853
22.6593
22.7999
22.8946
22.9417
22.9436
22.9042
22.8272
22.7169
22.5777
22.415
22.2352
22.0453
21.8521
21.6605
21.4711
21.2771
21.0631
20.8048
20.471
20.0263
19.4367
18.6793
17.7636
16.7662
15.8552
15.2508
15.1018
15.3851
15.9447
16.6085
0.50
22.2562
21.9715
21.8212
21.9402
22.2535
22.508
22.544
22.351
22.0358
21.8087
21.8302
22.0592
22.355
22.6197
22.8171
22.9437
23.0064
23.0138
22.9728
22.8892
22.768
22.6144
22.4343
22.2356
22.0275
21.8202
21.6229
21.4401
21.267
21.0868
20.8705
20.5803
20.175
19.6143
18.8671
17.933
16.8817
15.893
15.2243
15.0605
15.3767
15.9854
16.6884
1.00
22.1587
21.7269
21.441
21.6209
22.1653
22.5726
22.6115
22.2768
21.701
21.285
21.3712
21.7978
22.2618
22.6279
22.8775
23.0274
23.0978
23.1043
23.0572
22.9635
22.8284
22.657
22.4554
22.2322
21.9987
21.7691
21.5585
21.3784
21.2291
21.0932
20.9357
20.7114
20.3749
19.8854
19.2123
18.3512
17.3605
16.4048
15.735
15.5441
15.8189
16.3787
17.0295
1.50
22.2555
21.7627
21.4018
21.6425
22.3529
22.8244
22.8367
22.3778
21.5229
20.881
21.0634
21.7005
22.3034
22.7338
23.0056
23.1576
23.2215
23.218
23.1591
23.0517
22.9
22.7082
22.4815
22.2282
21.9606
21.6968
21.4593
21.2712
21.1433
21.0605
20.9785
20.8406
20.5968
20.2119
19.6643
18.9542
18.1294
17.3191
16.723
16.5051
16.6724
17.0906
17.6029
2.00
22.6142
22.2616
22.0673
22.3563
22.9395
23.2787
23.2475
22.8067
21.9515
21.2641
21.3996
22.0002
22.5725
22.9734
23.2153
23.3392
23.3789
23.3551
23.2788
23.1548
22.9852
22.7719
22.5184
22.2312
21.9221
21.6104
21.3265
21.1099
20.9928
20.9688
20.9798
20.9468
20.8119
20.548
20.1485
19.6232
19.0117
18.4028
17.9286
17.703
17.7468
17.9857
18.3175
2.50
23.1387
23.0017
23.0152
23.2696
23.5876
23.727
23.6836
23.4015
22.8407
22.3482
22.3248
22.6566
23.0419
23.3297
23.4956
23.564
23.5634
23.5112
23.4141
23.2728
23.0861
22.853
22.5745
22.2547
21.9023
21.5347
21.1857
20.9131
20.7851
20.8207
20.9416
21.0286
21.0081
20.8636
20.6048
20.2518
19.8383
19.4207
19.0743
18.8652
18.8157
18.8974
19.0592
3.00
23.6822
23.6793
23.75
23.8914
23.9894
23.8656
23.8526
23.8156
23.559
23.2948
23.2237
23.356
23.5655
23.7317
23.8075
23.8078
23.7599
23.6771
23.5604
23.4049
23.2051
22.9571
22.6598
22.3155
21.93
21.5159
21.1031
20.7602
20.5981
20.6825
20.9159
21.1202
21.2013
21.1549
21.0071
20.7854
20.5197
20.2464
20.0049
19.8268
19.7269
19.7016
19.7351
3.50
24.1892
24.2522
24.2967
24.3123
24.3426
24.3773
24.1178
24.1075
24.0416
23.9397
23.8726
23.8986
24.0005
24.0867
24.0915
24.0326
23.9451
23.8402
23.7123
23.5504
23.3446
23.089
22.7824
22.4279
22.0319
21.605
21.1709
20.7943
20.6062
20.7143
21.0155
21.2875
21.4245
21.4353
21.3553
21.2136
21.0365
20.8526
20.684
20.5398
20.4237
20.3404
20.2934
4.00
24.6766
24.8229
24.8708
24.7473
24.5947
24.6158
24.4765
24.4437
24.5089
24.4829
24.3567
24.2573
24.2625
24.3042
24.2789
24.1956
24.0961
23.9905
23.8678
23.7116
23.5089
23.2533
22.9461
22.5956
22.2146
21.819
21.4327
21.1085
20.9537
21.0606
21.3353
21.5759
21.6951
21.7107
21.6548
21.5453
21.4025
21.2582
21.1325
21.0199
20.9097
20.8053
20.7186
4.50
25.1456
25.459
25.6792
25.5231
25.0367
24.7536
24.7196
24.8983
25.1424
25.0919
24.7861
24.4913
24.3608
24.3562
24.3402
24.2809
24.2086
24.1315
24.0349
23.8984
23.7066
23.455
23.1505
22.8104
22.4578
22.1193
21.8248
21.6154
21.5489
21.6507
21.8295
21.9529
21.9858
21.963
21.9042
21.7951
21.6405
21.4907
21.3838
21.3015
21.2131
21.1145
21.0193
5.00
25.5181
26.0149
26.5251
26.5383
25.7788
25.1831
25.0856
25.4129
25.8215
25.679
25.1601
24.6917
24.4382
24.3675
24.3532
24.3343
24.3141
24.2897
24.2383
24.1322
23.9534
23.7018
23.3935
23.057
22.7271
22.4403
22.2315
22.1331
22.1622
22.2798
22.3699
22.3453
22.2419
22.1528
22.0937
21.9829
21.7799
21.5768
21.4694
21.4228
21.3714
21.2987
21.2171
5.50
25.6873
26.2055
26.729
26.7853
26.1091
25.4715
25.3142
25.593
25.9418
25.8055
25.3099
24.8446
24.5627
24.4459
24.4168
24.4281
24.4668
24.5111
24.5186
24.4458
24.2715
24.0039
23.6733
23.3216
22.9936
22.7316
22.5723
22.5431
22.6459
22.8121
22.8809
22.7259
22.4352
22.2433
22.2023
22.1189
21.8566
21.5618
21.4437
21.4395
21.4337
21.3972
21.3409
6.00
25.6482
26.0365
26.3552
26.348
25.9419
25.5113
25.3548
25.4695
25.624
25.5362
25.2255
24.8956
24.6684
24.5589
24.5403
24.5941
24.7076
24.8409
24.9196
24.8738
24.6808
24.3672
23.9856
23.5933
23.2416
22.9734
22.8225
22.8126
22.945
23.1574
23.2712
23.0652
22.597
22.2745
22.2224
22.1657
21.8972
21.5623
21.4293
21.4405
21.4619
21.4539
21.4219
6.50
25.4937
25.7407
25.9021
25.8744
25.6591
25.4159
25.2921
25.298
25.3259
25.2556
25.0785
24.8781
24.7302
24.666
24.6933
24.819
25.0371
25.2885
25.4523
25.4195
25.1731
24.7762
24.3142
23.8596
23.4653
23.1684
22.9949
22.9605
23.0621
23.2462
23.3584
23.1769
22.7163
22.3513
22.2257
22.1361
21.9197
21.6532
21.5129
21.4934
21.505
21.5044
21.4861
7.00
25.3103
25.4624
25.5465
25.5258
25.4135
25.279
25.1883
25.1514
25.1257
25.0629
24.9565
24.842
24.7643
24.757
24.8469
25.0588
25.3943
25.7754
26.0267
25.9925
25.6692
25.1708
24.6197
24.0996
23.6595
23.327
23.117
23.0338
23.0639
23.1553
23.1941
23.0464
22.7266
22.4303
22.2561
22.1244
21.9529
21.7653
21.6387
21.5879
21.5739
21.5647
21.5488
7.50
25.1392
25.2365
25.2865
25.2766
25.2173
25.14
25.0747
25.0288
24.9879
24.9347
24.8683
24.8081
24.7835
24.8265
24.9704
25.2477
25.6614
26.1222
26.4252
26.3869
26.0124
25.4491
24.8431
24.2839
23.8152
23.456
23.2121
23.0785
23.0349
23.0359
23.0087
22.8873
22.6786
22.4622
22.2903
22.1469
22.002
21.8614
21.7537
21.6897
21.656
21.6345
21.6147
8.00
24.9915
25.0581
25.0924
25.0904
25.0586
25.012
24.9652
24.9237
24.8844
24.843
24.8029
24.7777
24.7895
24.8655
25.0369
25.3308
25.7425
26.1835
26.4684
26.4321
26.0745
25.5296
24.9381
24.3882
23.922
23.5557
23.291
23.1193
23.0201
22.9588
22.8909
22.7822
22.6317
22.4688
22.3189
22.1842
22.0582
21.9433
21.85
21.7835
21.7393
21.7084
21.6833
198
TEC generated using eighteen well distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
21.0102
20.5934
20.2788
20.0549
19.898
19.7796
19.6728
19.5563
19.4158
19.2445
19.0427
18.8184
18.5853
18.3611
18.1629
18.0024
17.8814
17.7923
17.7229
17.6625
17.6053
17.5505
17.4999
17.4553
17.4155
17.377
17.3363
17.2931
17.2529
17.2274
17.2319
17.281
17.3846
17.5463
17.7652
18.0381
18.3615
18.7325
19.1488
19.608
20.1075
20.6445
21.2156
0.50
21.2004
20.8052
20.5208
20.3333
20.2146
20.1314
20.0538
19.9591
19.833
19.6693
19.4696
19.2435
19.0067
18.7788
18.5785
18.418
18.2979
18.2084
18.1351
18.0662
17.9961
17.9258
17.8597
17.8007
17.7472
17.6933
17.6321
17.5605
17.4835
17.4146
17.3732
17.3782
17.4425
17.5701
17.7594
18.0063
18.3073
18.6597
19.0613
19.51
20.0029
20.5366
21.1071
1.00
21.5284
21.1606
20.9078
20.7535
20.6662
20.6095
20.5517
20.4703
20.352
20.1923
19.9944
19.7695
19.5346
19.3099
19.1138
18.9572
18.8392
18.7484
18.6689
18.5884
18.5026
18.4146
18.3315
18.2579
18.1919
18.1247
18.0455
17.9477
17.8342
17.7198
17.6279
17.5824
17.5993
17.684
17.8344
18.0465
18.3169
18.6437
19.0252
19.4591
19.9424
20.4707
21.039
1.50
21.9994
21.6653
21.4439
21.3169
21.2508
21.2083
21.1577
21.0781
20.9588
20.7979
20.601
20.3804
20.1533
19.9388
19.7534
19.6053
19.4916
19.3994
19.3127
19.2194
19.1167
19.0104
18.9101
18.8224
18.745
18.667
18.5736
18.454
18.3078
18.1494
18.0051
17.9035
17.8645
17.8958
17.9964
18.1632
18.3938
18.6873
19.0426
19.4577
19.9284
20.4491
21.0136
2.00
22.5993
22.3036
22.1124
22.0057
21.9501
21.9089
21.8524
21.7627
21.633
21.4653
21.2677
21.0532
20.8382
20.6392
20.4693
20.3336
20.2267
20.1349
20.0419
19.9365
19.8179
19.6944
19.5781
19.4771
19.3895
19.3028
19.1995
19.0641
18.8918
18.6946
18.4996
18.3391
18.2372
18.2054
18.2456
18.3568
18.5386
18.7916
19.1154
19.5076
19.9631
20.4743
21.0332
2.50
23.2959
23.0397
22.8761
22.7836
22.7297
22.6797
22.6069
22.4977
22.3503
22.1711
21.9709
21.7628
21.5612
21.3795
21.227
21.1053
21.0071
20.9176
20.8204
20.7054
20.5733
20.4351
20.3049
20.1919
20.0948
20.001
19.8909
19.7454
19.5546
19.3262
19.0863
18.8685
18.7014
18.6011
18.5739
18.6226
18.7493
18.9564
19.2447
19.6113
20.0493
20.5491
21.1006
3.00
24.0474
23.8275
23.6868
23.6029
23.5445
23.4795
23.385
23.252
23.084
22.8916
22.6877
22.485
22.2954
22.1291
21.9918
21.8826
21.7924
21.7056
21.6059
21.4838
21.3418
21.1925
21.0512
20.928
20.8221
20.7215
20.6058
20.4534
20.2502
19.9992
19.7233
19.456
19.2284
19.0614
18.9667
18.9514
19.0212
19.1807
19.4318
19.7711
20.19
20.6763
21.2178
3.50
24.8124
24.6214
24.4965
24.4148
24.347
24.2644
24.1482
23.9936
23.8079
23.6046
23.3974
23.1984
23.0175
22.8619
22.7347
22.633
22.5467
22.4603
22.358
22.231
22.0828
21.9268
21.7783
21.6473
21.5333
21.4251
21.303
21.1443
20.9327
20.6673
20.3668
20.0622
19.7853
19.5608
19.4057
19.3317
19.3483
19.4627
19.6777
19.9896
20.3876
20.8577
21.3861
4.00
25.5567
25.3838
25.2651
25.1784
25.097
24.9967
24.8629
24.6939
24.4984
24.2899
24.0818
23.8855
23.7093
23.5586
23.4346
23.3333
23.2447
23.1541
23.0472
22.9166
22.766
22.6079
22.4565
22.3205
22.1997
22.0835
21.9535
21.7883
21.571
21.2985
20.9847
20.6566
20.3448
20.0764
19.8728
19.7505
19.7226
19.7983
19.981
20.2661
20.6416
21.0924
21.6043
4.50
26.2564
26.0892
25.9664
25.8671
25.7687
25.6523
25.5073
25.3332
25.1374
24.9311
24.726
24.5323
24.3578
24.2069
24.0799
23.9723
23.8749
23.7751
23.6612
23.5272
23.3768
23.2204
23.0697
22.9318
22.8059
22.6823
22.5446
22.3736
22.1537
21.8799
21.5621
21.2224
20.8891
20.5905
20.3517
20.1933
20.1317
20.1773
20.3331
20.5933
20.9454
21.3747
21.8675
5.00
26.8999
26.726
26.5893
26.4716
26.3547
26.2247
26.0744
25.9031
25.7151
25.5177
25.3196
25.1301
24.9561
24.8019
24.6676
24.5491
24.4386
24.3261
24.2029
24.0651
23.9157
23.7629
23.6153
23.4779
23.3491
23.2202
23.0768
22.9023
22.6827
22.4122
22.0966
21.7536
21.4088
21.091
20.8281
20.6442
20.5582
20.5816
20.7161
20.9547
21.285
21.6933
22.1675
5.50
27.4877
27.2971
27.1391
26.9994
26.8644
26.7239
26.5725
26.4084
26.2324
26.0477
25.8599
25.6763
25.5035
25.3452
25.2019
25.0705
24.9451
24.8185
24.6849
24.5422
24.3932
24.2439
24.1002
23.9648
23.8352
23.7034
23.557
23.3818
23.1652
22.9007
22.591
22.2498
21.9003
21.571
21.2916
21.0889
20.9842
20.9899
21.1077
21.3297
21.6433
22.0356
22.4952
6.00
28.0314
27.8179
27.6349
27.4725
27.3208
27.1721
27.021
26.8645
26.7005
26.5289
26.3524
26.176
26.0051
25.8433
25.6915
25.5475
25.4076
25.2671
25.1227
24.9742
24.8242
24.6772
24.5369
24.4041
24.2751
24.1424
23.995
23.8209
23.6087
23.3515
23.0496
22.7135
22.3642
22.0293
21.7388
21.5212
21.4
21.39
21.4942
21.7051
22.0095
22.3937
22.8454
6.50
28.549
28.3114
28.1037
27.9199
27.753
27.5964
27.4445
27.2929
27.1376
26.9763
26.8093
26.6396
26.4711
26.3067
26.1475
25.9926
25.8398
25.6868
25.5323
25.3773
25.2249
25.0787
24.9407
24.8099
24.6818
24.5489
24.4014
24.2288
24.021
23.771
23.4779
23.1501
22.806
22.4715
22.1757
21.9475
21.8124
21.7883
21.8814
22.0859
22.3875
22.7702
23.22
7.00
29.0584
28.7995
28.5703
28.3676
28.1865
28.021
27.8653
27.7141
27.5624
27.4067
27.2457
27.0805
26.9135
26.7469
26.5818
26.4181
26.2548
26.0913
25.9279
25.7667
25.6111
25.4641
25.3268
25.1969
25.069
24.9355
24.7875
24.6158
24.4116
24.1685
23.8854
23.5692
23.2361
22.9093
22.6162
22.3849
22.242
22.208
22.2931
22.4934
22.7942
23.1774
23.6268
7.50
29.5723
29.2967
29.0504
28.8317
28.6369
28.4609
28.298
28.1425
27.9892
27.834
27.6748
27.5112
27.3443
27.1755
27.0057
26.8352
26.6639
26.4924
26.322
26.1555
25.9965
25.8479
25.7097
25.5789
25.4497
25.3145
25.1652
24.9937
24.7925
24.5565
24.285
23.9842
23.6682
23.3574
23.0767
22.8527
22.7116
22.6753
22.756
22.9519
23.2493
23.6298
24.076
8.00
30.0973
29.8093
29.5497
29.3174
29.1096
28.9219
28.7491
28.5858
28.4268
28.2681
28.1068
27.9419
27.7735
27.6021
27.4284
27.253
27.0762
26.8993
26.7242
26.554
26.3922
26.2412
26.1007
25.9674
25.8352
25.6972
25.5459
25.3743
25.1765
24.9486
24.6909
24.4093
24.1159
23.8287
23.5698
23.3637
23.2348
23.2042
23.2843
23.475
23.7648
24.1368
24.5743
199
TEC generated using eighteen well distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.0184
22.6114
25.5695
27.1661
25.0206
23.7978
26.7565
26.8593
25.1356
21.7607
21.8465
22.7426
22.3161
22.0154
23.5924
27.2451
26.2382
24.1332
25.0181
27.2647
26.2983
23.8542
20.9504
22.4191
22.6626
22.0691
22.4018
25.0402
27.4025
25.302
23.6158
26.3664
26.9858
25.4581
22.2661
21.626
22.7124
22.4043
21.9825
23.2436
26.7994
26.5287
24.3963
0.50
22.3214
21.5215
21.3907
23.8436
23.9351
24.395
26.2558
26.9885
25.9094
23.8862
22.6856
22.4295
22.4452
22.025
21.1842
22.6435
24.0193
23.934
25.1653
26.8148
26.7139
25.0531
23.1916
22.5158
22.4232
22.3774
21.6408
21.2001
23.6844
23.9602
24.2242
26.0229
27.0045
26.1367
24.1448
22.7685
22.4406
22.4431
22.1305
21.2721
22.2102
24.0054
23.9135
1.00
21.2518
21.062
20.0344
20.5782
21.9248
23.562
25.3662
26.5844
26.4794
25.0046
22.9191
21.2907
21.0218
21.2827
20.6154
20.0447
21.1336
22.5913
24.3575
26.0196
26.7249
25.9779
24.114
22.0927
20.9872
21.21
21.1483
20.1259
20.4238
21.7326
23.3251
25.1403
26.4878
26.5805
25.2576
23.1934
21.4417
20.9777
21.2896
20.7741
19.9923
20.958
22.3804
1.50
19.6726
19.1674
18.7805
18.6595
19.1912
20.3871
21.7745
22.9227
23.4217
23.0344
22.0481
20.9385
20.0453
19.4361
18.9839
18.6748
18.7911
19.6536
20.9927
22.3252
23.2425
23.357
22.651
21.5574
20.5133
19.7526
19.2273
18.8231
18.6466
19.0746
20.2066
21.5956
22.7985
23.4063
23.1309
22.1957
21.0784
20.1458
19.505
19.0381
18.7007
18.7352
19.5003
2.00
25.4099
26.6014
26.3124
24.4791
21.9755
20.0726
20.009
21.0586
20.7995
20.1578
20.9084
22.4427
24.3683
26.0646
26.6875
25.6701
23.4085
20.9874
19.8062
20.4168
21.3579
20.3224
20.3547
21.5002
23.2579
25.1799
26.515
26.45
24.7855
22.3045
20.235
19.9179
20.9088
20.9803
20.1489
20.754
22.2072
24.109
25.8825
26.6946
25.896
23.7443
21.2712
2.50
26.4709
26.8431
25.6623
23.8441
22.6524
22.2634
22.4379
21.5444
19.652
21.6851
23.2407
23.9923
25.6045
26.8399
26.4919
24.8642
23.2165
22.3945
22.3123
22.2425
20.8341
19.5583
22.6607
23.5083
24.6025
26.3001
26.8912
25.8861
24.068
22.7601
22.2734
22.424
21.7328
19.9474
21.249
23.1445
23.8503
25.3664
26.7598
26.6294
25.1147
23.3904
22.4587
3.00
27.122
26.6854
24.5517
21.7724
22.236
22.6117
22.2534
22.2326
24.1209
27.8626
25.3911
23.5245
25.8977
27.1936
25.9567
23.206
21.7269
22.5234
22.4948
22.1197
22.7143
26.013
26.6819
24.5214
24.1257
26.9497
26.8496
24.9251
21.992
22.1175
22.6196
22.3096
22.1623
23.6931
28.0525
25.6723
23.7199
25.4956
27.2308
26.2117
23.6298
21.6559
22.4545
3.50
25.7471
25.7636
24.5189
22.366
23.1376
23.4335
21.9879
21.7322
24.1064
25.7857
25.5943
24.4566
25.1013
25.8955
25.4215
23.4901
22.4672
23.5162
22.7167
21.6217
22.7888
24.9498
25.997
25.0268
24.4851
25.6362
25.8223
24.7816
22.5254
22.9823
23.5383
22.0932
21.5005
23.8172
25.6297
25.7401
24.5418
24.9239
25.8796
25.5541
23.8242
22.3564
23.4277
4.00
22.3261
23.9612
25.8956
25.2228
24.922
24.8225
23.9144
23.8402
24.8654
26.3271
25.3127
23.6933
22.4162
22.8046
24.9737
25.7194
24.9949
24.9442
24.4477
23.7139
24.21
25.4759
26.0532
24.6243
23.0428
22.2784
23.6592
25.7867
25.3254
24.9222
24.8861
24.0189
23.7696
24.7025
26.2412
25.507
23.9076
22.529
22.6086
24.667
25.8277
25.0466
24.9381
4.50
22.267
22.8035
23.664
24.2369
24.4924
24.5847
24.6297
24.7005
24.7512
24.5625
23.9622
23.0963
22.3734
22.4022
23.1873
23.9596
24.3772
24.5447
24.6044
24.6559
24.7346
24.7146
24.3517
23.6007
22.7318
22.2636
22.6939
23.5597
24.1824
24.4709
24.5773
24.6231
24.6894
24.7523
24.6103
24.0634
23.2143
22.4395
22.3415
23.0682
23.8768
24.3399
24.5312
5.00
24.7306
24.8892
25.0779
24.8111
23.8555
22.5664
21.5516
22.1082
23.5468
24.4095
24.6806
24.7261
24.7107
24.7798
24.9889
25.0501
24.4662
23.3114
22.0314
21.5506
22.7459
24.0183
24.5732
24.7156
24.7191
24.7219
24.8599
25.0661
24.8895
24.0111
22.7403
21.6264
21.9355
23.3739
24.3385
24.663
24.7262
24.7112
24.7612
24.9589
25.0711
24.5852
23.4825
5.50
23.3952
23.7095
24.711
25.8167
24.9608
23.5353
22.8578
23.8072
25.4808
25.2109
24.7307
24.8914
23.9058
23.3241
24.195
25.0878
25.6472
24.3161
23.0921
23.0539
24.5868
25.6515
24.8788
24.7895
24.6716
23.476
23.5793
24.6155
25.75
25.1471
23.7027
22.8682
23.5915
25.3142
25.3349
24.7372
24.8825
24.0822
23.3118
24.0447
24.9213
25.7469
24.5149
6.00
21.745
22.4456
24.9318
26.2636
25.2269
24.4012
25.847
26.1438
25.0147
22.3301
22.4564
23.3339
22.2297
21.5559
23.5307
25.8125
26.001
24.6218
24.88
26.2409
25.826
24.0031
21.7299
23.0296
23.041
21.8449
22.1398
24.6163
26.2464
25.4279
24.3632
25.6313
26.2017
25.254
22.7176
22.2511
23.3233
22.3995
21.5672
23.1932
25.5772
26.1254
24.7874
6.50
22.2075
22.3654
24.8039
26.6997
24.6814
23.8962
26.5674
27.0341
25.4343
22.704
22.1084
22.563
22.4035
22.1347
22.9901
27.0054
25.7387
23.9842
25.0551
27.1429
26.5379
24.2849
22.025
22.3677
22.5557
22.2499
22.2637
24.2535
27.0238
24.9154
23.7115
26.2635
27.1218
25.7376
23.0428
22.0366
22.5384
22.4479
22.1419
22.7434
26.3133
26.015
24.1824
7.00
22.3715
20.9508
18.6204
21.7747
23.1144
24.2807
25.9674
26.8572
26.2174
24.531
22.9729
22.1874
22.3028
21.8727
20.0057
20.0281
22.5193
23.5386
25.0077
26.5273
26.7631
25.5504
23.7788
22.5272
22.1286
22.4313
21.1924
18.836
21.4549
22.9907
24.0824
25.7569
26.8255
26.3835
24.7732
23.1399
22.2411
22.2424
22.0526
20.3234
19.4888
22.3316
23.4005
7.50
19.6347
21.0371
20.3248
19.9973
20.8845
22.5713
24.5887
26.2451
26.618
25.153
22.5295
19.9221
19.1053
20.2344
21.0081
20.0114
20.2576
21.5416
23.44
25.4015
26.6204
26.194
24.0914
21.3165
19.2328
19.4757
20.8745
20.4696
19.9622
20.7119
22.3163
24.324
26.0777
26.6742
25.4385
22.9041
20.2131
19.0594
20.0411
21.1233
20.0794
20.1557
21.3264
8.00
23.5276
25.3192
25.7476
24.0052
21.6921
19.6634
18.8866
18.8622
18.7248
18.5894
19.0746
20.4522
22.3799
24.3666
25.8047
25.1447
23.0188
20.7198
19.1513
18.8571
18.8307
18.6312
18.6916
19.5727
21.2506
23.2613
25.1184
25.8466
24.2927
22.0016
19.8778
18.9174
18.8634
18.7542
18.585
18.9574
20.2266
22.1106
24.1163
25.6916
25.3651
23.3264
21.0083
200
TEC generated using eighteen well distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.1964
22.0959
22.1638
22.3477
22.515
22.5667
22.4806
22.2875
22.0484
21.8242
21.6125
21.3112
20.7987
20.0989
19.5081
19.4039
19.7691
20.2452
20.5701
20.6803
20.6175
20.4699
20.3413
20.2999
20.3362
20.3849
20.3838
20.3061
20.1635
20.0013
19.8873
19.8761
19.9729
20.1392
20.3277
20.5063
20.6605
20.788
20.8925
20.9795
21.0544
21.1211
21.182
0.50
21.8903
21.7002
21.8226
22.1798
22.5021
22.6202
22.5148
22.2361
21.888
21.6211
21.487
21.2855
20.7361
19.8003
18.9326
18.8267
19.4393
20.1333
20.5458
20.6356
20.4749
20.1933
19.9725
19.947
20.0806
20.2255
20.2679
20.1707
19.9512
19.6781
19.4789
19.468
19.6424
19.909
20.1812
20.4159
20.6026
20.7464
20.858
20.9481
21.0249
21.0937
21.1573
1.00
21.6632
21.3457
21.5222
22.0913
22.581
22.7552
22.6121
22.201
21.6413
21.246
21.2599
21.3167
20.9123
19.988
19.0674
18.9453
19.5887
20.2919
20.668
20.6719
20.3588
19.868
19.4943
19.5062
19.8085
20.0981
20.1993
20.0806
19.7594
19.3087
18.9573
18.961
19.2788
19.6944
20.0685
20.3594
20.571
20.7219
20.833
20.921
20.9972
21.0674
21.1339
1.50
21.7791
21.4262
21.6426
22.3052
22.8449
23.0198
22.8377
22.3122
21.5049
20.8818
21.0499
21.4187
21.2813
20.6595
20.0098
19.8742
20.2643
20.7285
20.9487
20.833
20.3692
19.663
19.1178
19.1734
19.65
20.0658
20.2105
20.0823
19.6835
19.0175
18.4343
18.4819
19.0016
19.575
20.0329
20.3567
20.5722
20.7137
20.813
20.8933
20.9675
21.0399
21.1108
2.00
22.3605
22.1546
22.3815
22.9085
23.32
23.4341
23.2438
22.7439
21.96
21.3018
21.4147
21.7711
21.7581
21.414
21.0381
20.9162
21.0726
21.2924
21.3638
21.1692
20.6483
19.8867
19.3052
19.3423
19.7969
20.187
20.3173
20.2129
19.8693
19.1487
18.3927
18.45
19.044
19.6512
20.1111
20.4168
20.6021
20.7113
20.7862
20.8553
20.9296
21.0084
21.0874
2.50
23.175
23.1434
23.3398
23.6611
23.8999
23.9469
23.7774
23.4163
22.9461
22.5372
22.4133
22.4276
22.3181
22.0666
21.8101
21.6883
21.7277
21.8329
21.8582
21.6671
21.1899
20.5386
20.0488
19.9847
20.214
20.4292
20.4849
20.423
20.2886
19.8729
19.2398
19.131
19.4894
19.9357
20.2943
20.5233
20.64
20.6915
20.7313
20.7923
20.8768
20.9718
21.0651
3.00
23.9519
24.009
24.1437
24.2989
24.4077
24.4229
24.2758
24.0064
23.7863
23.6161
23.3785
23.1327
22.8812
22.6067
22.3561
22.1975
22.164
22.2313
22.2922
22.1609
21.7567
21.2296
20.8195
20.6559
20.6689
20.696
20.6462
20.5651
20.5471
20.4374
20.1034
19.9405
20.0672
20.3116
20.5242
20.6382
20.6523
20.6195
20.6186
20.689
20.8072
20.934
21.049
3.50
24.6112
24.7028
24.766
24.7556
24.6901
24.6588
24.583
24.3512
24.1532
24.0977
23.942
23.6664
23.3568
23.043
22.7561
22.5356
22.4156
22.4131
22.4713
22.4017
22.1061
21.7128
21.3791
21.1717
21.0575
20.9549
20.81
20.6508
20.5731
20.5689
20.5204
20.4929
20.5574
20.6683
20.7458
20.7331
20.6182
20.4678
20.424
20.5448
20.7355
20.9106
21.0496
4.00
25.1781
25.3158
25.3572
25.2058
24.8893
24.6983
24.7334
24.606
24.2766
24.1623
24.2029
24.0285
23.7292
23.3952
23.074
22.7981
22.5944
22.4868
22.463
22.4186
22.259
22.0183
21.7752
21.5722
21.4042
21.2402
21.0581
20.8788
20.7765
20.7984
20.8722
20.9301
20.9693
20.9856
20.9509
20.8261
20.5837
20.2843
20.1895
20.4207
20.7141
20.9311
21.0815
4.50
25.6712
25.8998
26.0432
25.9078
25.4711
25.1529
25.1013
25.0638
24.924
24.7303
24.5912
24.3582
24.0383
23.6888
23.3502
23.0494
22.8064
22.6381
22.5476
22.4955
22.4168
22.2847
22.1148
21.9316
21.7491
21.5719
21.4075
21.28
21.2315
21.2808
21.366
21.4024
21.3705
21.2894
21.165
20.9772
20.6928
20.3301
20.2013
20.5152
20.829
21.0248
21.1538
5.00
26.0655
26.3725
26.6612
26.6586
26.1787
25.7991
25.6638
25.6402
25.8021
25.5965
25.1013
24.6847
24.3035
23.9376
23.5988
23.3042
23.068
22.8996
22.7996
22.7489
22.7043
22.6221
22.4854
22.3063
22.1127
21.9351
21.8043
21.7516
21.7992
21.9193
22.0033
21.9551
21.7959
21.5985
21.4021
21.2078
21.0089
20.8416
20.8366
20.9734
21.0887
21.1812
21.2591
5.50
26.3474
26.6525
26.8522
26.8598
26.566
26.3294
26.3027
26.0654
25.9687
25.824
25.3663
24.911
24.5055
24.1395
23.8167
23.5496
23.35
23.224
23.1677
23.1596
23.1533
23.0919
22.9462
22.7335
22.5014
22.3031
22.1863
22.1927
22.3437
22.5799
22.702
22.5517
22.2274
21.8991
21.6411
21.4592
21.3455
21.3188
21.3733
21.3569
21.3305
21.3444
21.376
6.00
26.5568
26.9399
27.291
27.2847
26.8694
26.7292
27.0409
26.682
26.0504
25.7542
25.4072
25.0136
24.6342
24.2912
23.9986
23.7722
23.6273
23.5742
23.6106
23.7047
23.7785
23.7352
23.5366
23.2333
22.9137
22.6544
22.5116
22.5301
22.7361
23.0621
23.2405
23.0275
22.5729
22.1439
21.847
21.6817
21.6061
21.5363
21.4356
21.4566
21.4826
21.4845
21.4891
6.50
26.6693
27.1599
27.7685
27.8173
27.0979
26.8244
27.0449
26.7826
26.1771
25.7477
25.3953
25.0442
24.7043
24.3972
24.1432
23.964
23.883
23.9227
24.0927
24.3541
24.5712
24.5573
24.2564
23.7954
23.3351
22.9757
22.767
22.7395
22.9047
23.1916
23.3553
23.1588
22.715
22.2855
21.9977
21.8682
21.8697
21.9225
21.8374
21.7079
21.6544
21.6174
21.5951
7.00
26.6186
27.0277
27.4033
27.3953
26.9689
26.6883
26.6393
26.4485
26.0719
25.6955
25.3571
25.0367
24.7345
24.466
24.2524
24.1199
24.1005
24.2317
24.5423
24.9961
25.3934
25.42
24.9895
24.34
23.7229
23.2538
22.9635
22.8555
22.9138
23.0648
23.1414
22.9933
22.6667
22.3274
22.0911
22.0011
22.0678
22.257
22.2858
22.0219
21.8339
21.7391
21.6896
7.50
26.4424
26.7153
26.903
26.8823
26.675
26.4711
26.329
26.1462
25.8816
25.5833
25.287
25.0022
24.7366
24.5051
24.3285
24.235
24.2608
24.4513
24.845
25.4076
25.9075
25.9616
25.4632
24.7104
24.0041
23.4661
23.1135
22.9297
22.8812
22.9031
22.8951
22.7763
22.5573
22.3195
22.1422
22.0706
22.1159
22.2266
22.2364
22.0851
21.9272
21.8247
21.7651
8.00
26.2201
26.3954
26.4969
26.4836
26.372
26.2268
26.0782
25.9048
25.6903
25.4474
25.1954
24.9482
24.7179
24.5198
24.3739
24.3066
24.3517
24.549
24.9259
25.4377
25.8746
25.919
25.4788
24.7921
24.1225
23.5906
23.2179
22.9873
22.8651
22.8018
22.7378
22.6286
22.4722
22.3045
22.1708
22.1018
22.1011
22.1312
22.1218
22.047
21.9517
21.8738
21.8207
201
TEC generated using eighteen random distributed reference points with multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
22.2311
21.7362
21.3186
20.9844
20.7316
20.5507
20.4277
20.3473
20.2956
20.2605
20.2326
20.2042
20.1692
20.1231
20.0623
19.9842
19.887
19.7697
19.6318
19.4733
19.2947
19.0969
18.8815
18.651
18.4095
18.1622
17.9155
17.6755
17.4466
17.2297
17.022
16.818
16.6114
16.3967
16.1709
15.935
15.6952
15.4634
15.2578
15.1016
15.0191
15.0306
15.147
0.50
22.241
21.7429
21.328
21.004
20.7687
20.6107
20.5133
20.4592
20.4329
20.4216
20.4155
20.4067
20.389
20.3579
20.3096
20.2418
20.1529
20.0419
19.9086
19.7532
19.5763
19.3786
19.1616
18.9276
18.6806
18.4266
18.1733
17.9291
17.6999
17.4871
17.2871
17.0925
16.8943
16.6848
16.4592
16.2173
15.9645
15.713
15.482
15.2964
15.1835
15.1661
15.2574
1.00
22.3362
21.839
21.4293
21.1159
20.8963
20.7577
20.6817
20.6491
20.6438
20.6524
20.6646
20.6725
20.6697
20.6514
20.614
20.5551
20.4732
20.3677
20.2388
20.0869
19.9128
19.7172
19.5011
19.2664
19.0168
18.7583
18.5002
18.2531
18.025
17.8187
17.6295
17.448
17.263
17.0643
16.8454
16.6044
16.346
16.0824
15.8332
15.6242
15.4838
15.4367
15.4979
1.50
22.5259
22.0359
21.6349
21.332
21.1249
21.0002
20.9388
20.9213
20.9309
20.9542
20.9805
21.0015
21.0107
21.0028
20.9742
20.9223
20.8459
20.7448
20.6196
20.4714
20.3012
20.1099
19.8982
19.667
19.4192
19.1604
18.9006
18.6524
18.4267
18.2275
18.0501
17.8836
17.7146
17.531
17.324
17.0903
16.8336
16.5655
16.3055
16.0796
15.9159
15.8396
15.8677
2.00
22.8121
22.3358
21.9472
21.6548
21.4562
21.3389
21.2848
21.275
21.2931
21.3255
21.3613
21.3917
21.4096
21.4096
21.3873
21.3404
21.2675
21.1692
21.0466
20.9018
20.7364
20.5516
20.3478
20.1252
19.8852
19.6321
19.3754
19.1289
18.906
18.7128
18.5454
18.3926
18.2401
18.0736
17.8824
17.661
17.4116
17.1452
16.8808
16.6434
16.4604
16.3568
16.351
2.50
23.1874
22.7302
22.3569
22.0747
21.8813
21.7661
21.7128
21.7044
21.7251
21.7614
21.8024
21.8386
21.8623
21.8674
21.8491
21.8046
21.733
21.6352
21.5136
21.3711
21.2105
21.0337
20.8409
20.6317
20.4056
20.1649
19.9173
19.6761
19.4562
19.2661
19.1044
18.9612
18.8225
18.673
18.4994
18.2936
18.0557
17.7953
17.5307
17.2858
17.087
16.9589
16.9208
3.00
23.6382
23.203
22.8465
22.574
22.384
22.2674
22.2108
22.1991
22.2178
22.2542
22.2967
22.3357
22.3626
22.3703
22.3535
22.309
22.2359
22.136
22.0128
21.8708
21.714
21.5452
21.3648
21.1717
20.9638
20.7408
20.5075
20.2752
20.0585
19.8683
19.7065
19.5669
19.4372
19.3021
19.146
18.9574
18.7338
18.4828
18.2213
17.9721
17.7607
17.6113
17.5439
3.50
24.1483
23.7358
23.396
23.133
22.9453
22.8259
22.7638
22.7462
22.7602
22.7936
22.8352
22.8745
22.9023
22.9106
22.893
22.8458
22.7684
22.6635
22.5358
22.3916
22.2364
22.0738
21.9048
21.7276
21.5386
21.3351
21.1187
20.8975
20.6846
20.4919
20.325
20.1821
20.0547
19.9291
19.7881
19.6171
19.4099
19.1714
18.9164
18.6663
18.4458
18.2793
18.1873
4.00
24.7023
24.3115
23.9874
23.7332
23.5476
23.425
23.3567
23.3321
23.3398
23.3685
23.4071
23.445
23.472
23.4788
23.4583
23.406
23.3217
23.2087
23.0737
22.9243
22.7676
22.6082
22.4474
22.283
22.1101
21.9242
21.7239
21.5142
21.3055
21.1093
20.9335
20.7808
20.6478
20.5242
20.3935
20.2387
20.0494
19.8265
19.5819
19.335
19.11
18.9319
18.8219
4.50
25.2871
24.9161
24.6063
24.36
24.1762
24.0505
23.9759
23.9438
23.9442
23.9669
24.0012
24.036
24.0606
24.0644
24.0391
23.9796
23.8859
23.7627
23.6179
23.4607
23.2995
23.1397
22.9828
22.8261
22.6643
22.4913
22.3041
22.1047
21.9002
21.7002
21.5136
21.3465
21.2003
21.0698
20.9421
20.7993
20.6271
20.4215
20.1901
19.9505
19.7266
19.5441
19.4247
5.00
25.8921
25.5387
25.2415
25.002
24.8194
24.6905
24.6096
24.5696
24.562
24.5774
24.6057
24.6359
24.6563
24.6555
24.6237
24.5555
24.4512
24.3164
24.1607
23.9943
23.8263
23.6628
23.5053
23.3511
23.1944
23.029
22.8505
22.6589
22.458
22.255
22.0582
21.8753
21.7114
21.5667
21.433
21.2943
21.1337
20.9424
20.724
20.4944
20.2775
20.099
19.9804
5.50
26.5095
26.1713
25.8845
25.6504
25.4684
25.3359
25.2483
25.1998
25.1831
25.1896
25.2099
25.233
25.2471
25.2396
25.2
25.1223
25.0072
24.8613
24.6951
24.5196
24.3441
24.1746
24.013
23.8565
23.6997
23.5365
23.3622
23.1751
22.9768
22.772
22.5677
22.3716
22.1905
22.0277
21.8798
21.734
21.5739
21.3882
21.1783
20.9594
20.7549
20.5895
20.4827
6.00
27.133
26.8075
26.5292
26.2991
26.1166
25.9796
25.8847
25.8267
25.7992
25.7948
25.8044
25.8175
25.8221
25.8055
25.7567
25.6694
25.5446
25.3896
25.2151
25.0321
24.8496
24.6735
24.5055
24.3434
24.1824
24.017
23.8426
23.6568
23.4595
23.2539
23.0452
22.8399
22.6445
22.4629
22.2944
22.1304
21.9574
21.7659
21.558
21.3493
21.1623
21.0188
20.9344
6.50
27.7579
27.4429
27.1711
26.9432
26.759
26.6167
26.5133
26.4445
26.4047
26.3869
26.3828
26.3824
26.374
26.3454
26.2859
26.1895
26.0572
25.8961
25.7164
25.5284
25.3405
25.1582
24.9831
24.8135
24.6457
24.475
24.2972
24.1096
23.9116
23.705
23.4932
23.2811
23.0732
22.8728
22.6797
22.4892
22.2931
22.0869
21.8764
21.6787
21.5144
21.4006
21.3473
7.00
28.3807
28.0739
27.8067
27.5797
27.3926
27.2438
27.1309
27.05
26.9961
26.9627
26.9421
26.9249
26.9003
26.8572
26.7858
26.6809
26.5432
26.379
26.1971
26.0068
25.8156
25.6281
25.4462
25.2689
25.0932
24.9154
24.732
24.5404
24.3397
24.1304
23.9148
23.6956
23.4753
23.2556
23.0368
22.817
22.594
22.3703
22.1571
21.9731
21.8361
21.7573
21.7402
7.50
28.9988
28.6982
28.434
28.2065
28.0153
27.8592
27.7358
27.6417
27.5723
27.5216
27.4824
27.4463
27.4034
27.3442
27.2604
27.1475
27.0058
26.8405
26.6587
26.4682
26.2752
26.0841
25.8965
25.712
25.5285
25.3431
25.153
24.9559
24.7506
24.537
24.3158
24.0883
23.8552
23.6173
23.3749
23.1292
22.8831
22.6459
22.4342
22.2674
22.1599
22.1166
22.1355
8.00
29.6104
29.3144
29.0517
28.8224
28.6263
28.4621
28.3277
28.2197
28.134
28.0651
28.0065
27.9505
27.8887
27.813
27.7167
27.596
27.451
27.2854
27.1048
26.9151
26.7218
26.5282
26.3362
26.1456
25.9551
25.7626
25.5658
25.3626
25.1518
24.9327
24.7051
24.4691
24.2246
23.972
23.7124
23.4493
23.1901
22.9487
22.7447
22.5973
22.5172
22.5049
22.5544
202
TEC generated using eighteen random distributed reference points with sphere multiquadric method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
24.6777
25.4758
24.1588
20.3778
18.4139
17.7078
18.129
19.6782
23.4128
24.4214
25.0101
24.7534
24.3699
25.0362
25.6975
22.3132
19.3314
17.9741
17.7477
18.6647
21.2999
23.8732
24.7624
25.0026
24.489
24.5791
25.3811
24.7384
20.772
18.5912
17.7386
18.0064
19.4018
23.2498
24.3001
24.9768
24.8302
24.3569
24.9246
25.6555
22.8547
19.6152
18.0868
0.50
22.6479
22.4778
19.6438
15.8897
14.983
14.3342
14.8623
17.0309
19.8801
22.1095
23.6388
23.4363
22.1917
22.7968
21.6602
17.5764
15.4838
14.619
14.3722
15.6062
18.3322
20.8454
22.9569
23.775
22.8172
22.5534
22.6181
20.2101
16.0896
15.1029
14.3721
14.6992
16.6575
19.5524
21.8144
23.5287
23.5669
22.1787
22.7809
21.9742
18.2182
15.5959
14.7225
1.00
21.094
20.4117
18.9336
16.1896
13.1728
10.8744
10.763
13.1317
16.7876
20.3004
22.4526
22.6934
21.6326
20.7991
19.9499
17.834
14.881
11.992
10.5012
11.5292
14.658
18.3874
21.4758
22.7592
22.3281
21.2015
20.5154
19.2186
16.584
13.5651
11.0792
10.624
12.7069
16.2872
19.8811
22.284
22.7477
21.7882
20.8831
20.1157
18.1935
15.2844
12.3318
1.50
18.2163
17.0584
19.0944
18.6258
14.3254
9.89767
9.90811
14.9373
21.6055
26.7335
28.452
26.0997
20.9077
17.0593
17.893
19.4347
17.0848
12.1208
9.18615
11.6355
17.8459
24.1553
27.9662
27.9182
24.0209
18.7531
16.9187
18.8602
18.9476
15.0118
10.3093
9.57076
14.0912
20.7541
26.2203
28.4577
26.6296
21.6384
17.3072
17.5957
19.411
17.6276
12.7741
2.00
9.91655
13.2316
17.6135
21.1498
22.5635
21.9107
20.5507
20.0545
19.9497
18.1712
14.3268
10.564
9.21938
11.092
15.1218
19.3469
22.0569
22.4788
21.2909
20.1977
20.0748
19.4828
16.6661
12.5265
9.59121
9.66153
12.6852
17.0432
20.7852
22.5118
22.0787
20.7015
20.0619
20.0158
18.5515
14.8915
10.9641
9.20956
10.6809
14.5322
18.8421
21.8269
22.5429
2.50
14.2284
16.7578
19.4029
22.0434
23.402
22.9131
22.1937
22.0115
19.9056
15.1822
14.4759
13.4948
13.4739
15.1806
18.0073
20.4933
22.8721
23.3931
22.3984
22.2298
21.4376
18.0421
14.8885
14.0228
13.2974
13.9991
16.3694
19.1037
21.72
23.3341
23.0637
22.1891
22.1067
20.355
15.7219
14.599
13.5986
13.3824
14.8586
17.6349
20.1158
22.6568
23.4323
3.00
17.6683
20.2482
23.0911
24.2243
24.7188
24.1215
23.9017
24.6715
24.0137
20.122
17.8158
16.8817
17.0235
18.4755
22.171
23.6042
24.5663
24.5773
23.7848
24.2693
24.7624
22.3604
18.8727
17.289
16.7964
17.4782
19.7144
22.9307
24.0911
24.7171
24.2446
23.815
24.5979
24.3479
20.5962
18.0194
16.9485
16.9338
18.195
21.6696
23.4478
24.4794
24.6439
3.50
20.2389
21.8924
24.2876
25.1435
25.3985
25.1964
25.1892
25.6791
25.5006
23.0115
20.8739
19.7966
19.7866
20.7932
23.107
24.7633
25.3233
25.3409
25.1247
25.3665
25.8495
24.5395
21.9608
20.275
19.662
20.1049
21.5774
24.0807
25.0697
25.3977
25.2302
25.1557
25.6056
25.6797
23.3631
21.0978
19.878
19.7272
20.6041
22.7302
24.6424
25.2788
25.367
4.00
21.712
23.2325
24.0776
24.2364
24.6675
24.3924
24.0924
23.9642
23.7366
23.1643
22.1762
21.4249
21.3811
22.2215
24.0743
23.7395
24.575
24.5816
24.2436
24.0214
23.9045
23.5222
22.8017
21.7712
21.3144
21.6068
22.973
24.2585
24.0929
24.6728
24.4397
24.1219
23.977
23.7876
23.2544
22.3195
21.486
21.3434
22.0356
23.8323
23.7535
24.4986
24.6164
4.50
21.4128
21.5548
21.7058
21.9332
21.9424
21.5916
21.0008
20.582
20.8101
20.9885
21.1288
21.2248
21.3337
21.4765
21.6123
21.8038
21.9837
21.8288
21.3559
20.7324
20.664
20.9003
21.0535
21.1734
21.2671
21.3935
21.5372
21.6804
21.9067
21.9634
21.6551
21.0869
20.5833
20.7777
20.9692
21.1131
21.2127
21.3168
21.4571
21.5943
21.7718
21.9751
21.8705
5.00
21.2404
21.021
21.2254
21.337
21.3526
21.3662
21.4867
21.6874
21.7998
22.1936
22.509
22.2087
21.6096
21.0421
21.1083
21.2887
21.3526
21.3505
21.4027
21.573
21.7484
21.9005
22.4165
22.4331
21.9721
21.3219
21.0052
21.2009
21.3286
21.3537
21.3597
21.4635
21.6628
21.7856
22.1149
22.5093
22.2712
21.698
21.0877
21.0787
21.272
21.3496
21.3504
5.50
24.3836
24.3293
23.9064
22.9782
21.8115
21.192
21.3921
22.6561
24.3022
24.2839
24.8559
24.7334
24.4575
24.3662
24.2211
23.5482
22.4562
21.4488
21.1718
21.7844
23.506
24.2074
24.6065
24.8617
24.6018
24.3944
24.3448
23.998
23.1232
21.9483
21.2291
21.3135
22.418
24.207
24.208
24.8247
24.7712
24.4858
24.3698
24.2653
23.6659
22.6205
21.5453
6.00
25.2687
25.9037
24.9612
22.0135
20.0899
19.3157
19.6215
20.8872
23.7094
24.9387
25.3654
25.2281
25.0711
25.5352
25.979
23.6253
21.0296
19.6193
19.3187
20.0615
21.9742
24.4233
25.1923
25.3643
25.104
25.2034
25.8261
25.3238
22.3609
20.2763
19.3555
19.5214
20.6619
23.3829
24.8407
25.3424
25.2682
25.0587
25.4474
26.0034
24.039
21.3059
19.7411
6.50
23.8112
24.3026
22.273
18.5891
16.9198
16.3002
16.8205
18.8678
22.1965
23.6066
24.4896
24.1589
23.3635
24.1579
23.9417
20.4765
17.6839
16.5363
16.3639
17.4844
20.4921
22.8483
24.1041
24.5097
23.6842
23.6863
24.3134
22.7823
18.9539
17.0697
16.3254
16.6733
18.4765
21.9331
23.4345
24.4332
24.2762
23.3515
24.0669
24.1199
21.0212
17.9218
16.6365
7.00
22.0238
21.3319
18.5151
14.8927
13.8433
12.8128
13.176
15.343
18.2079
20.96
23.0095
23.1188
22.1951
21.878
20.4531
16.488
14.5138
13.304
12.7436
13.922
16.6152
19.2265
22.0949
23.2767
22.7063
22.0508
21.5118
19.0528
15.0336
14.0129
12.8936
13.0186
14.9752
17.8579
20.5441
22.8537
23.202
22.2816
21.9386
20.7739
17.1357
14.6403
13.4616
7.50
19.6644
19.7999
20.2535
17.9396
13.1476
9.26339
8.67569
11.5854
16.3011
20.5168
22.5286
22.0241
20.3273
19.5279
20.1437
19.7022
15.9767
11.1661
8.539
9.57515
13.5462
18.3141
21.7174
22.5752
21.3096
19.7745
19.703
20.2951
18.4505
13.8052
9.6204
8.53366
11.0457
15.6559
20.0582
22.4171
22.2029
20.5425
19.5333
20.0441
19.9444
16.6146
11.7365
8.00
7.51291
13.058
19.6506
24.1009
24.6347
21.3997
17.0911
16.068
19.5559
20.6183
14.5313
8.29979
6.20088
9.54809
16.0013
21.9853
24.8559
23.6003
19.4111
16.0283
17.2079
21.0567
18.3891
11.5468
6.71448
7.05372
12.1806
18.8416
23.7141
24.8073
21.9774
17.565
15.903
18.9793
21.0246
15.4681
8.96018
6.15321
8.84767
15.0984
21.3275
24.7095
23.9886
203
TEC generated using eighteen random distributed reference points with IDW method
Coor.
99.00
99.50
100.00
100.50
101.00
101.50
102.00
102.50
103.00
103.50
104.00
104.50
105.00
105.50
106.00
106.50
107.00
107.50
108.00
108.50
109.00
109.50
110.00
110.50
111.00
111.50
112.00
112.50
113.00
113.50
114.00
114.50
115.00
115.50
116.00
116.50
117.00
117.50
118.00
118.50
119.00
119.50
120.00
0.00
21.9829
21.8744
21.8195
21.8349
21.9206
22.057
22.2133
22.3609
22.4822
22.5703
22.6256
22.6514
22.6514
22.6284
22.5841
22.5197
22.4356
22.3328
22.2131
22.0787
21.9329
21.7793
21.6216
21.4638
21.3107
21.1686
21.0455
20.9487
20.879
20.8254
20.7667
20.679
20.5408
20.3319
20.0304
19.609
19.0363
18.2887
17.3879
16.4769
15.8817
15.9129
16.3726
0.50
21.878
21.7299
21.6499
21.6657
21.78
21.9643
22.1732
22.3669
22.523
22.6355
22.7075
22.7449
22.753
22.7357
22.6947
22.6305
22.5432
22.433
22.3017
22.152
21.9877
21.8128
21.6313
21.4471
21.2649
21.0919
20.9417
20.8336
20.779
20.7636
20.7514
20.7061
20.6016
20.4182
20.1341
19.7181
19.1279
18.3178
17.2791
16.1436
15.3389
15.4372
16.1416
1.00
21.8105
21.6214
21.5145
21.5297
21.673
21.9054
22.1651
22.4007
22.5871
22.7202
22.8062
22.8536
22.8698
22.8589
22.8227
22.7604
22.6708
22.5533
22.4094
22.2425
22.0572
21.8581
21.6492
21.4335
21.213
20.992
20.7875
20.6438
20.6071
20.6571
20.7199
20.7359
20.6777
20.5325
20.2851
19.9081
19.3585
18.5869
17.5782
16.4646
15.6787
15.7586
16.2567
1.50
21.822
21.6026
21.4764
21.4927
21.6585
21.9253
22.2187
22.4803
22.6843
22.8291
22.9237
22.9786
23.0019
22.9984
22.969
22.9114
22.8217
22.6975
22.5402
22.3546
22.1466
21.9215
21.6834
21.4341
21.1713
20.8867
20.5802
20.3355
20.3202
20.4969
20.6791
20.7744
20.7693
20.669
20.4717
20.1597
19.7
19.0555
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16.7135
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2.00
21.952
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21.5956
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22.061
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22.617
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2.50
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22.579
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20.7066
20.4568
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18.6488
18.13
17.6313
3.00
22.6279
22.4476
22.349
22.3626
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22.8664
23.0458
23.1906
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23.3799
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3.50
23.1523
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23.5574
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4.00
23.7764
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4.50
24.4906
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5.00
25.2917
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25.0119
24.7951
24.5714
24.371
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24.0678
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5.50
26.1706
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21.086
6.00
27.0918
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26.7308
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25.7682
25.282
24.8842
24.6024
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6.50
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27.6
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26.3592
25.719
25.1934
24.816
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24.5122
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24.777
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7.00
28.6866
28.6892
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27.6626
26.8625
26.0926
25.4571
24.9945
24.7048
24.5735
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21.861
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7.50
29.0974
29.128
28.761
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27.1928
26.3501
25.6462
25.1242
24.7817
24.5984
24.5499
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8.00
29.1396
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28.821
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27.2938
26.4538
25.7384
25.1936
24.8192
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22.2839
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22.4256
22.5483
22.4651
22.2554
22.0586
21.8883
204