HIGH PRECISION GLOBAL POSITIONING SYSTEM DATA PROCESSINGVELOCITY VECTOR DETERMINATION FOR GEODYNAMIC APPLICATION
RABIEAHTUL ABU BAKAR
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Masters of Science (Geomatic Engineering)
Faculty of Engineering and Science Geoinformation
Universiti Teknologi Malaysia
OCTOBER 2006
ii
I declare that this thesis entitled “High Precision Global Positioning System Data
Processing - Velocity Vector Determination For Geodynamic Application “is the result
of my own research except as cited in the references. The thesis has not been accepted
for any degree and is not concurrently submitted in candidature of any other degree.
Signature
: ....................................................
Name
: Rabieahtul Abu Bakar
Date
: 12th October 2006
iii
To my lovely family and my beloved husband.
"Scientists still do not appear to understand sufficiently that all earth sciences must
contribute evidence toward unveiling the state of our planet in earlier times, and that
the truth of the matter can only be reached by combing all this evidence. . . It is only
by combing the information furnished by all the earth sciences that we can hope to
determine 'truth' here, that is to say, to find the picture that sets out all the known
facts in the best arrangement and that therefore has the highest degree of
probability. Further, we have to be prepared always for the possibility that each new
discovery, no matter what science furnishes it, may modify the conclusions we draw."
Alfred Wegener. The Origins of Continents and Oceans (4th edition)
iv
ACKNOWLEDGEMENT
In preparing this thesis, I was in contact with many people, researchers,
academicians, and practitioners. They have contributed towards my understanding and
thoughts. In particular, I wish to express my sincere appreciation to my supervisor,
Professor Dr. Shahrum Ses, for his encouragement, patience and of all the funding
throughout this study.
I am also very thankful to my friend as well as teacher Mr Soeb Nordin for his
guidance to understanding the Bernese software from the setting up right to the
processing end of it. I am also indebt to Mr Peirre Fredez from AIUB, though via the emails, for his prompt reply to my cry of help to out put problems encountered during the
processing stages.
My sincere appreciation also extends to Prof. Madya Kamaludin Omar, and my
external panel Drs Sokba for their comments and ideas contribution to this study. A huge
gratitude to all my colleagues in FKSG and others who have provided assistance at
various occasions. Their views and tips are useful indeed. I am grateful to all my family
members, my Dad, Abu Bakar Omar, Mom, Maimunah Abdul Gani, my sisters, and
brother. Last but not least, my beloved husband Khamarrul Azahari Razak for his help
and emotional support has made this journey possible.
v
ABSTRACT
Geodynamic studies involving Malaysia have been ventured upon in the
South-East Asia region since the first GeodySEA project was carried out in 1996.
For the fact that both East and West Malaysia lies on the same plate, we can assume
that there will be no linear distortion for any two points joined relative to one
another. In other words, for GPS observations over MASS stations, the baselines
formed relative to any other MASS station can be roughly assumed to be constant
without any significant changes. Though presumably Malaysia is out danger, but we
take it for granted that it lies within the buffer of the ‘Ring of Fire’. We are situated
near several active faults lines. This study will only look upon three years of MASS
data from which most of the data were available simultaneously processed with 3
consecutive years of selected IGS. Since this movement is not evident for short
observation or even observation of 1-year time span, therefore, a longer period of
observation is needed to identify this movement. In this research the author will
output the relative MASS stations coordinates and velocity estimates in ITRF2000.
At present the measures of quality for GPS derived coordinates given by commercial
software packages tend to be unrealistic because unmodelled errors remain
unaccounted for (Brown et al., 2002). In addition, commercial software packages are
either over-optimistic, or conversely, are overly conservative and therefore have low
fidelity (Keenan and Cross, 2001, Barnes et. al., 1998, Wang, 1999). However, in
this study Bernese high precision GPS processing software version 4.2 is utilised to
determine the final solution for the relative MASS station coordinates. Screening
cycle slips, using linear combination of phase observables to estimate the site
specific atmospheric parameters, and resolving ambiguities give a reliable coordinate
of lesser than 10mm in horizontal and 15mm in vertical in predefined ITRF2000
frame.
vi
ABSTRAK
Kajian tentang pergerakkan kerak bumi melibatkan Malaysia telah diterokai
di rantau Asia Tenggara bermula dengan GeodySEA pada tahun 1996. Timur dan
Barat Malaysia terletak di atas kerak bumi yang sama maka, boleh dianggap bahawa
tiada herotan garis dasar antara dua stesen cerapan yang relatif antara satu sama lain.
Walaupun Malaysia tidak berada di dalam bahaya yang nyata, namun, ia berada di
sekitar lingkungan Gegelang Api (“Ring of Fire”) dan berhampiran kawasan gempa.
Maka, pergerakkan kerak bumi haruslah sentiasa diawasi agar perubahan ini dapat
dijangka. Dalam kajian ini, data MASS sepanjang 3 tahun bermula dari tahun 2000
hinggalah ke 2002 telah diproses bersama dengan 3 tahun data dari 15 stesen IGS
pada jangka masa yang sama. Disebabkan perubahan pada kerak bumi tidak ketara
untuk cerapan jangka masa pendek walaupun data dalam setahun lamanya, maka,
data jangka masa yang lebih panjang diperlukan untuk mengenalpasti perubahan ini.
Pada masa ini, hasil kordinat dari GPS yang diproses menggunakan perisian komersil
tidak memuaskan kerana banyak ralat yang tidak dapat dikenalpasti (Brown et al.,
2002). Tambahan lagi, perisian komersil terlalu optimistik atau terlalu kurang
optimistik maka tidak dapat dipercayai. (Keenan dan Cross, 2001, Barnes et. al.,
1998, Wang, 1999). Dalam kajian ini perisian berkejituan tinggi Bernese versi 4.2
dipasangkan pada komputer Linux untuk pemprosesan data. Data ini kemudiannya
diskrin, parameter atmosfera dianggarkan dengan linear combination dan peleraian
ambiguity menghasilkan koordinat yang boleh dipercayai dengan rms horizontal
kurang dari 10mm dan rms vertical kurang dari 15mm dalam ruang ITRF2000.
Dalam kajian ini penulis dapat menghasilkan koordinat terakhir untuk pemprosesan
data MASS kepada “a posteriori unit weight” 0.0023m dan anggaran halaju
pergerakkan kerak bumi kepada 2cm setahun pada ITRF2000.
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
LISTS OF TABLES
xii
LISTS OF FIGURES
xiii
LISTS OF ABBREVIATION
xviii
INTRODUCTION
1.1
General Background
1.2
GPS and Its Ability to Predict the Plate
1
Deformation
4
1.3
Problem Statement
6
1.4
Research Objective
8
1.5
Research Scope
8
1.6
Research Contribution
9
1.7
Research Methodology
10
1.7.1
Hardware and Software Setup
11
1.7.2
Data Preparation
13
viii
1.8
2
Literature Review
13
GLOBAL POSITIONING SYSTEM
2.1
2.2
2.3
2.4
Background of Global Positioning System
(GPS)
16
GPS Satellite Signals and its Application
19
2.2.1
Pseudo-Random Codes
20
2.2.2
The Navigation Message
21
2.2.3
Signal Processing
22
GPS Continuous Observation Centers
23
2.3.1
International GPS Service (IGS)
23
2.3.2
MASS
25
2.3.2.1 The MASS System
27
The GPS Observables
28
2.4.1
Pseudoranges
28
2.4.2
Pseudorange Observation Equation 29
2.4.2.1 Code Pseudorange
Observation Equation
29
2.4.2.2 Phase Pseudorange
2.4.2
2.4.3
Observation Equations
30
GPS Differencing Techniques
31
2.4.2.1 Single Difference
32
2.4.2.2 Double Differencing
32
2.4.2.3 Triple Differncing
33
Linear Phase Combination
34
2.4.3.1 Ionosphere-free
35
2.4.3.2 Geometry-free
36
2.4.3.3 Wide-Lane
36
2.4.3.4 Melbourne Wubenna
37
ix
2.5
2.6
GPS Errors Elimination and Biases
Reduction
38
2.5.1
Satellite Orbit
38
2.5.2
Keplerian Orbit
41
2.5.3
Earth Rotation Parameters (EOP)
43
2.5.4
Antenna Phase Center
Variations (PCV)
44
2.5.5
Receiver Clock
45
2.5.6
Ionosphere
46
2.5.7
Troposhere
47
2.5.8
Tide and Loading
50
2.5.8.1 Ocean Loading
50
2.5.8.2 Ocean Tide
51
2.5.8.3 Atmosphere Loading
52
Ambiguity Resolution
52
2.6.1 Directly Resolving
Ambiguities on
Short Baselines
54
2.6.2 The Quasi-Ionosphere-Free
(QIF) Ambiguity Resolution
Strategy
3
54
2.7
ITRF
55
2.8
Summary
57
GPS for Geodynamic Studies
3.1
Introduction to Geodynamic
58
3.2
Evolution of the Plate Tectonic Theory
58
3.2.1
59
3.3
3.4
Pangea
Continental Drift
60
3.3.1
61
Sea-Floor Spreading
Plate Boundary Zones
64
x
3.4.1
Divergent Boundaries
65
3.4.2
Convergent Boundaries
65
3.4.2.1 Oceanic-oceanic
convergence
66
3.4.2.2 Oceanic-continental
convergence
66
3.4.2.3 Continental-continental
3.4.3
67
Transform Boundaries
67
3.5
The “Ring of Fire”
67
3.6
Plate Tectonic and GPS
69
3.7
Malaysia
70
3.8
Site Description
71
3.9
Previous Regional Campaigns
72
3.9.1
Geodyssea
72
3.9.2
APRGP
73
3.9.3
GDM2000
73
3.10
3.11
4
convergence
Velocity
74
3.10.1 Velocity Frame
74
3.10.2 Absolute
74
3.10.3 Relative
74
3.10.4 Absolute-Free Velocities
75
3.10.5 Absolute-Fix Velocities
75
3.10.6 Relative-Free Velocities
75
3.10.7 Relative-Fix Velocities
75
Summary
76
DATA ACQUISITION AND PROCESSING
4.1
Introduction
77
4.2
Data Acquisition
77
4.3
Data Preparation
78
xi
4.3.1
4.4
4.5
4.6
4.7
5
TEQC
78
Bernese Version 4.2
79
4.4.1
RINEX Files
79
4.4.2
Ocean Loading Files
80
4.4.3
Velocity Files
80
Data Processing
81
4.5.1
RXOBV3 (Transfer Part)
82
4.5.2
PRETAB & ORBGEN
83
4.5.3
CODSPP
86
4.5.4
SNGDIF
88
4.5.5
MAUPRP
88
Adjustment- Parameter Estimation
90
4.6.1
Parameter Estimation GPSEST1
90
4.6.2
RESRMS
92
4.6.3
SEROBVS
92
4.6.4
GPSEST II
92
4.6.5. GPSEST III
93
4.6.6
GPSEST IV
94
4.6.7
Troposphere Estimation
95
4.6.8
Ionosphere Modelling
96
4.6.9
Ocean Loading Parameters
96
4.6.10 Ambiguity Resolution
96
4.6.11 Weekly Solution
96
4.6.12 Helmert Transformation
97
4.6.13 Generating Velocity
98
Summary
98
RESULTS AND ASSESSMENT
5.1
Outcome and Reliability
99
5.2
Helmert Transformation
104
5.3
Final Coordinates
105
xii
6
5.4
Station Velocity
106
5.5
Residual Graphs
107
CONCLUSIONS AND RECOMMENDATIONS
6.1
Summary
6.2
Other Method of Detecting Earth
6.3
References
109
Deformation
109
Recommendations
110
111
xiii
LISTS OF TABLES
TABLE NO.
TITLE
2.1
Components of the satellite signal
2.2
Linear combinations (LCs) of the L1 and L2
PAGE
19
observables used in Bernese
38
2.3
Errors in baseline components due to orbit errors
40
2.4
Estimated quality orbits in 2000
41
2.5
Pertubing accelerations acting on a GPS satellite
43
5.1
Final Coordinate Difference
105
xiv
LISTS OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Earth’s Core
1
1.2
Continental Plates of the Earth
2
1.3
The Ring of Fire
3
1.4
Fault lines in the South-East Asian Region
4
1.5
IGS Sites selected to tie the MASS to ITRF
5
1.6
MASS sites in East and West Malaysia
6
1.7
GPS Processing Diagram
10
1.8
Process Control Script flow chart
12
2.1
GPS orbits (Earth and orbital planes)
17
2.2
GPS Block II satellite and satellite-fixed
coordinate System
19
2.3
Biphase modulation of the GPS signal
20
2.4
The Distribution of the IGS stations
24
2.5
Distribution of the MASS locations in Malaysia
26
2.6
Geodesy Data Processing Centre Configuration
in Kuala Lumpur
26
2.7
Remote Base Station set-up
27
2.8
The set of orbital elements
42
2.9
GPS Signals with Ionospheric Delays
46
2.10
Tilting of the ‘Tropospheric’ Zenith by the Angle β
50
2.11
The ocean tides for harmonics M2
51
2.12
The IGS stations are distributed all around the globe
57
3.1
PANGAEA
59
3.2
Holmes’ model of convection currents
60
3.3
Earth’s Interior
61
xv
3.4
Sea Floor Spreading
62
3.5
The Tectonic Plate Boundaries
63
3.6
The ‘Ring of Fire’
68
3.7
Malaysia and Its Plate Location
69
3.8
Malaysia
71
4.1
Bernese Concise Processing Diagram
81
4.2
Transfer Menu
82
4.3
Orbit Menu
83
4.4
Standard Orbit Generation Menu
84
4.5
Results for ORBGEN Program
85
4.6
Results for ORBGEN Program
85
4.7
Input Menu for CODSPP
86
4.8
Determining the Atmosphere Models
86
4.9
Result from CODSPP Program
87
4.10
SNGDIFF program Menu 4.3
88
4.11
MAUPRP Program Menu 4.4.2
89
4.12
MAUPRP Input Menu 4.4.2-1
89
4.13
Diagram of the Daily Adjustment of the
Bernese Processing
90
4.14
GPSEST I Menu 4.5
91
4.15
Output files for GPSEST I
91
4.16
Menu 4.5-2.4 GPSEST IV Program
94
4.17
Menu 4.5-2.4B
95
5.1
Ambiguity Resolution Percentage of the
first day of year 2001
100
5.2
RMS of Residuals of Observation
101
5.3
Daily RMS
102
5.4
Weekly Residual RMS GPS Week 1046
102
5.5
Formal Accuracy of the Coordinate week 1046
103
5.6
Overall Weekly Residual RMS
104
5.7
Velocity for the year 2000-2002 for the first months
106
5.8
Residual Weekly Graph
107
xvi
LISTS OF ABBREVIATION
AIUB
-
Astronomical Institute of the University of Bern
AR
-
Ambiguity Resolution
ARP
-
Antenna Reference Point
AS
-
Anti-Spoofing
BKG
-
Federal Agency of Cartography and Geodesy
CBIS
-
Centre Bureau Information System
CGGS
-
Centre for Geodynamics and Geodetic Study
CIO
-
Conventional International Origin
CODE
-
Centre for Orbit Determination in Europe
CPC
-
Central Processing Center
DS
-
Data Screening
DSMM
-
Department of Survey and Mapping, Malaysian
ERP
-
Earth Rotation Parameter
EUREF
-
European Reference Frame
GDPC
-
Geodesy Data Processing Center
GIPSY
-
GPS-Inferred Positioning System
GLOSS
-
Global Sea Level Observing System
GMT
-
Graphical Mapping Tools
GPS
-
Global Positioning System
GPSEST
-
Program used in Bernese for Parameter Estimation
IAG
-
International Association of Geodesy
IAU
-
International Astronomical Union
IERS
-
International Earth Rotation Service
IGN
-
Institute Geographical National
IGS
-
International GPS Service
ITRF
-
International Terrestrial Reference Frame
ITRS
-
International Terrestrial Reference System
xvii
IUGG
-
International Union of Geodesy and Geophysics
JPL
-
Jet Propulsion Laboratory
JUPEM
-
Malaysia Language for DSMM
LLR
Long Laser Ranging
LOD
-
Length Of Day
MASS
-
Malaysian Active GPS System
MAUPRP
-
Program used in Bernese for Phase Check
MSRF
-
Malaysian Spatial Reference Frame
N
-
Number for independent baseline
NASA
-
National Aeronautic and Space Administration
NAVSTAR GPS
-
NAVigation Satellite Timing and Ranging GPS
NGS
-
National Geodetic Survey
PRN
-
Pseudo-Range Number
RINEX
-
Receiver Independent Exchange
RTK
-
Real Time Kinematic
RMS
-
Root Mean Square
SA
-
Selective Availability
SINEX
-
Solution Independent Exchange
SIO
-
Scripps Institution of Oceanography
SLR
-
Satellite Laser Ranging
SNGDIF
-
Program used in Bernese for Single Differences
SVN
-
Satellite Vehicle Number
UTM
-
Universiti Teknologi Malaysia
VLBI
-
Very Long Baseline Interferometry
CHAPTER 1
INTRODUCTION
1.1
General Background
Sun, Moon and Planets are continuously in motion, each on its own orbit in a
continuous manner, of which, theoretically started from the birth of the universe
between 10 to 20 billion years ago during the primeval fireball also known as the Big
Bang (Hawkings, 1993). They influence each other through their very existence,
exerting gravitational forces between two bodies according to Newton’s law of
gravitation. Focusing on the moving bodies that co-exist on earth such as; the ocean
tides, earth tides, plate tectonics, and dynamics of the earth mantle are some of the
movements that we take for granted in our daily lives until nature takes it toll.
Figure 1.1: Earth’s Core
2
According to the theory of plate tectonics derived during the 1960’s evolved
from the theory of continental drift by Alfred Wegener in 1912, said that the Earth'
s
outer layer, or crust, consists of a series of plates made up of lithospheric material,
which floats on the denser upper fluid asthenosphere mantle within the Earth'
s
interior. These movements may cause the plates to convergent, divergent forming
trenches and ridges or even having lateral movements that cause an earthquake. The
earth consists of 12 major plates, the Eurasian plate, Indian plate, Philippine plate,
Pacific plate, Nazca plate, Caribbean plate, North American plate, South American
plate, African plate, Arabian plate, Australian plate and the Antarctic plate. The
edges of these plates form the (plate margin) fault lines to where the occurrences of
earthquakes and volcanic activities are profound.
Eurasian plate where
Malaysia is situated
Figure 1.2: Continental Plates of the Earth
In Malaysia, these movements are taken for granted since geographically
the peninsular is located on one command plate, the Eurasian plate. The fault lines
however, meanders not very far from the edges of the peninsular and passes through
the Indonesian Javanese Island. Krakatau is situated between Sumatra and Java in
3
Indonesia, and forms part of the volcanic arc of a subduction zone in the IndoAustralian Plate, moves towards the northeast (Forde, 1994).
Malaysia
Figure 1.3: The Ring of Fire
The Sunda Islands allocated in the western part of Indonesia consists of
Sumatra, Java, Kalimantan and Sulawesi. They also form a string of volcanic islands
extending from the Bay of Bengal forming an arc facing the Indian Ocean toward
Australia curving back to the north and west, constituting what is called an island arc
in geology. The Philippine Plate is located on the northeast from the edge of the
Eurasian plate. Another string of islands extends from the Mollucas to the north into
the Philippine islands. This island arc, often called the Sunda arc, encloses to the
north the Malay Peninsula, the great island of Kalimantan (Borneo) and four armed
islands of Sulawesi (Celebes), with a string of small volcanic islands extending from
the north eastern arm of Sulawesi to the Philippines. The above description all falls
into an area also known as the "Ring of Fire" which is an arc stretching from New
Zealand, along the eastern edge of Asia, north across the Aleutian Islands of Alaska,
and south along the coast of North and South America. It is composed over 75% of
the world'
s active and dormant volcanoes located at the borders of the Pacific Plate
and other tectonic plates.
4
Fault lines
Malaysia
Figure 1.4: Fault lines in the South-East Asian Region.
Earthquakes occurrences along these lines do influences and disrupt the
stability of buildings and structures in Malaysia. For instance, a powerful earthquake
rocked the Indonesian island of Sumatra according to the United States Geological
Survey (USGS) on the 4th of June 2000 recorded the quake at 7.9 on the Richter scale
and it was felt throughout KL, though no massive destruction occurred. The latest
occurrence is the oceanic earthquake on December 2004 carrying a magnitude of 8.9
on the Richter scale and brought with it the Tsunami one of the biggest in the
century. The seawater displacement result from the plate subduction killed over
hundreds of thousands across Asia.
1.2
GPS and Its Ability to Predict the Plate Deformation
A fiducial network incorporates VLBI, SLR, and GPS systems which are
operated on a permanent, continuous basis, and which will provide reference
geodetic data to which regional studies occupying many sites on a short-term,
temporary basis can anchor. GPS, VLBI, SLR, and LLR technology can be
integrated to monitor plate motion and deformation, to monitor Earth rotation, and to
5
define and maintain a terrestrial reference frame. Permanent regional and local
monitoring networks deployed across tectonically active regions to measure and
analyze the motion and deformation over a broad range of spatial and temporal
scales.
Figure1.5: IGS Sites selected to tie the MASS to ITRF
The DoD of America adopted global Positioning System (GPS) and had
launched their first satellite for the purpose of military was on the 18th February
1978. To date, GPS is known to many civilian users for many different purposes, one
of which mentioned above, for instance, scientist utilize it for monitoring plate
motion. In general, static relative positioning GPS are able to provide users with high
accuracy of ±1ppm or 1mm for 1km baseline with good sky view and over 10minute
of observation (Wellenhof et al, 1994). If a GPS observation is done over a long
session of over several hours continuously even for long baselines, it can promise
accuracy of 1ppm with proper scientific software and reliable strategy, and this will
be explained further in the other chapters.
6
Figure1.6: MASS sites in East and West Malaysia
Currently, there are 18 permanent GPS stations around Malaysia as shown in
figure 1.6, operating on a 24 hours basis called the MASS. The reconnaissances of
the stations were carried out in the late 1997 as proposed after the GEODYSSEA
second campaign by the DSSM (Majid et al., 1998). Moreover, with the realization
of the ITRF, Malaysia can now be mapped onto the globe more accurately. Basically,
the ITRF frame is a conventional frame created under international sponsorship in
order to satisfy the accuracy requirements of various modern space techniques.
Furthermore, the origin, coordinate axes orientation, and scale of the ITRF frame are
implicitly defined by the coordinates adopted for the worldwide tracking GPS sites
involved in each IERS yearly global solution (Soler et al., 1999). Thus, the IGS sites
in ITRF frame will be very useful for those scientifically advancing countries to fix
their region onto the same frame as the rest of the world.
1.3
Problem Statement
Since both East and West Malaysia lies on one plate, which is the Indo-
Australian plate we can assume that there will be no linear distortion for any two
points joined relatively to one another. In other words, for a GPS observation
between MASS stations, the baselines formed from one MASS station to another, for
example GETI, in Kelantan to BINT, in Bintulu, over a long period of time or
7
between epochs of different time line can be roughly assumed to be relatively
constant without any significant differences.
Presumably Malaysia is out danger, but we take it for granted though
realizing that it lies within the buffer of the ‘Ring of Fire’. It is fortunate, that
Malaysia do not lie on a fault line, however, Malaysia is situated near several active
faults lines. Therefore, monitoring of the plate motion is essential for predicting the
changing plate motion.
The world changes in more then one way i.e. the eccentricity of the earth
increases over time making the earth more elliptical (Pine, 1989). Monitoring the
trend of the unpredictability might help us take some precautionary actions before
the occurrence of natural disaster, to identify changing fault lines or new born faults.
Moreover, since crustal movements but could be patterned if monitored over several
of years. A long time series of measurements, of several years or more, are required
in order to obtain accurate site velocity estimates (Mao et al. 1999).
Learning from the 2004 Tsunami that hit Aceh, India and reflected to a small
area in the Upper West Coast of Malaysia proofs that geodynamic exploration should
be escalated and this study is a form of realization to this vulnerability.
This study will only look upon three years of MASS data from which most of
the data were available simultaneously processed with 3 consecutive years of
selected IGS. Since this movement is not evident for short observation or even
observation of 1-year time span, therefore, a longer period of observation is needed
to identify this movement. In this research the author will output the relative MASS
stations coordinates and velocity estimates in ITRF2000.
At present the measures of quality for GPS derived coordinates given by
commercial software packages tend to be unrealistic because unmodelled errors
remain unaccounted for (Brown et al., 2002). In addition, commercial software
packages are either over-optimistic, or conversely, are overly conservative and
therefore have low fidelity (Keenan and Cross, 2001, Barneset al., 1998, Wang,
1999).
8
However, in this study Bernese high precision GPS processing software
version 4.2 was utilised to determine the final solution for the relative MASS station
coordinates, hence to estimate the relative velocity of each station to the global
velocity (NUVEL1A). Screening cycle slips, using linear combination of phase
observables to estimate the site specific atmospheric parameters, and resolving
ambiguities will give a reliable coordinate of lesser than 10mm in horizontal and
15mm in vertical in predefined ITRF2000 frame.
1.4
Research Objectives
Referring to the applicability of GPS to geodetic and geodynamic studies the
objectives of this study are as follows:
1. To produce a high precision GPS solution of the Malaysian Network.
2. To derive accurate position Time Series leading to accurate velocity
determination.
3. To make a geodynamic interpretation from the GPS analysis using the
derived velocity.
1.5
Research Scope
The continuous GPS data for over three years were acquired from DSMM for
all the available 18 MASS stations with another 15 IGS stations so that the MASS
will be tied to the global network. These data were processed via Highbred GPS
Processing Software known as Bernese version 4.2. The processes were carried out
on a day-by-day basis to form network solutions. Whilst after weekly solutions were
formed comprising of 7 days of the GPS week for the available stations.
9
These weekly solutions were tied with reference to the mid of each respective
week. Final coordinates for each MASS stations were acquired and their residuals
plotted. These residual plots were over a period of three consecutive years, thus,
resulting in a time series. From these time series, graphs plotted were analysed to
determine the accuracy of the relative velocity of each station.
The weekly solutions were stacked together to produce the velocity
estimation of each station. The mean from this stations velocity is the result of the
overall movement of the peninsular and East Malaysia with respect to the IndoEurasian Plate. Thus, geodynamic interpretation can be analysed from the derived
velocity.
1.6
Research Contribution
Generally, this study will be of benefit for DSMM towards a dissertation of
handling of the Bernese GPS software version 4.2 and the processing strategy to
achieve accurate MASS final coordinate. Conversely, generating relative velocity
estimates for the MASS stations and give a geophysical study of the crustal motion
achieved from the GPS measurements.
MASS station coordinates are refined which was previously computed with
reference to ITRF 97 over a period of 1 and a half year are process over an even
longer period to derive to an up to date coordinate with reference to the ITRF 2000
frame towards 1ppm in precision. 5mm level of accuracy within a 95% confidence
interval for the horizontal components and vertical component of no more than three
times the ratio to the horizontal component of the MASS absolute coordinate is to be
achievable.
Data qualities of the MASS stations are analysed for the three years
processing and one can identify the station that profoundly contributes to the biases
and the errors due to low data quality.
10
Estimating the velocity of each MASS station and determine the accuracy of
this velocity generated. These velocity can later be use to interpret geodynamic
movements of the plates.
1.7
Research Methodology
There are 4 major phases in processing, before we can achieve the end
products of both the estimated relative velocity and the time series of each MASS
station coordinates. The 4 phases are as followings:
•
Pre-processing
•
Daily Adjustment
•
Weekly Solutions
•
Velocity Generation and Time Series Plotting
PreProcessing
GPS data input
AR, DS, Iono/ Tropo
Modelling
Daily
Solution
Residual plotted and
weekly solution stacked
Daily Solution Stacked and
tied to the Mid-Week
Weekly
Solution
Generate
Velocity
Figure 1.7: GPS Processing Diagram
11
Methodology of this study consist mainly preparation and processing before
the final output can be achieved. Each of these steps are crucial and it is essential for
them to be carried out well before proceeding to the next phase, since they are
interrelated and the accuracy of the results very much depends on the reliability of
the former stages. However, chapter four will explain this process in greater length.
1.7.1 Hardware and Software Set-up
GPS data will be processed using the Bernese version 4.2. Specification of
the hardware compatible for mounting the Bernese environment and to manage the 3
years of data will be rather immense. A large hard disk space is recommended eg. the
power station that is utilized in this study have two 80GByte hard disk one as the
processing platform and the other for backing up the data and results. Anyway, a
large space will be needed to store the GPS data.
Most importantly, a large space hard disk will make it possible to process the
GPS data efficiently and at ease especially with the ability of the BPE. Then, even
months of continuous data can be processed within a short time span compared to
other lower graded workstation. However, minimal computer is not stated regardless
utilizing 48MB of RAM and old Intel 386 processor the Bernese software is still
capable to run. For safety purposes and maintenance of hardware a UPS system will
be very useful and overnight processing.
Red Hat Linux 8.0 is mounted as the operating system since it complies well
with the Bernese Processing Engine (BPE) and its virus free system is an advantage
for the processing. Networking has to be set-up and user specified for ability to ftp to
other computers and important download sites. An IP address and host name of the
PC has to be stipulated for BPE to be able to communicate with the hardware and run
each bernese program and script automatedly.
12
Only then can one set up the bernese environment on root later then on the
main user home utilising bernese. More then one user in a group specified to use the
bernese environment could use bernese simultaneously. However, it is preferable that
only the main user has all the unrestricted access and managers all the files, folders
of bernese as well as the RHL8.0 system. Fortran compiler G77 and source F77 are
use for these and BPE demo will be install automatically then after editing the
remote hosts and remote bash profile is needed for bernese to run properly. It is
mandatory to recompile the software after installation for it to link the directories and
folders.
For BPE to run the processing control script (PCS) are edited. Each program
to be run for the GPS processing edited to the preference of the user. Strategy setting
for GPS processing starts here. Then each program run tested. BPE is well suited to
process data from permanent GPS arrays in a completely automatic and efficient
way.
START
Can a script be run ?
Is there a CPU to run?
Are all scripts done ?
Find a temp directory
Sleep
Run the script
FINISH
Figure 1.8: Process Control Script flow chart. Basically how the BPE works.
13
Bernese GPS software itself is created to cater for rapid processing of smallsize single and dual frequency surveys and permanent network processing. It can
resolve ambiguity on long baselines of up to 2000km using final orbits and taking
into accounts of other parameters to be modelled or estimated.
1.7.2 Data Preparation
The hourly MASS data was acquired from DSMM headquarters for 1st
January 2000 up to 31st December 2002. Most of the data was already archived in a
24hours daily compact rinex zip form. These data were then scanned through teqc for
quality and checking for errors in the header. Essentially, the monument name, dome
number, antenna and receiver pair type, and the antenna height. Data were decimated
to 30seconds interval and kept in the RAW folder in the campaign directory. Data
with too many missing observation can be predicted to cause inaccuracy in the
processing later.
IGS stations scattered around the Malaysian parameters were selected to its
availability and to the period of establishment of the station which will determine the
stability of the data collected. These data are usually readily ‘teqc’ed. However, this
does not mean that they are free from causing problems to the results later on. Thus,
the data quantity has to be checked before processing can even take place. Low
quality and inadequate data quantity of lesser than 12 hours observation should be
identified and listed out.
1.8
Literature Review
The Bernese GPS Software version 4.2 is a tool meeting highest accuracy
standards. Users of this software are typically scientists for research purposes,
academician for education, survey agencies responsible for high accuracy GPS
surveys or to maintain arrays of permanent GPS receivers and commercial
14
applications for demanding high accuracy, reliability and high productivity
(Hugentobler et. al., 2001). It is also suitable for permanent GPS stations processing
on long baseline (2000km) ambiguity resolution for post-processing (Beutler et al,
1996).
Ambiguity resolutions are recommended in baseline mode, whereby each
baseline are processed separately then introducing the resolved ambiguities as known
quantities into the subsequent session processing (Hugentobler et. al., 2001). Over
long baselines of over thousands of kilometres the processing strategy (proposed are
as follows:
•
Use of IGS precise orbit and ERP parameters
•
Processing using 24 hours sessions of 15/30 second data
•
Elevation cut-off angle 15 degrees and with dependent satellite
elevation-weighting COS Z.
•
Phase center offset are referenced to antenna phase center variations
(PCV) Phasigs-01. table
•
Single difference using OBMAX / SHORTEST test for the better
dependent on station location and data availability
•
Zenith delay parameters at least once every two hours and residual
markings.
•
Estimated troposphere parameters
•
L3 linear combination of ionosphere-free float solution
•
Quasi-Ionosphere Free (QIF) ambiguity resolution strategy
•
Daily solutions computed for normal equations and analysis of
precision
•
Weekly solutions formed by combining the daily normal equations
(can skip this step if its a small campaign)
15
•
Final solution staking of all (weekly/daily) normal equations and
constrained to the fudicial stations final coordinates in the respective
ITRF reference frame
Usually, the achievable precision for the final coordinates will fall within 2 to
8mm in horizontal position and 10 to 20 mm in vertical position, and about 1-2x10-8
(or 1 to 2 cm in thousand kilometer baseline). The absolute coordinate accuracy in
the ITRF frame could be approximate or at least better than 3cm (Becker et al., 1998;
Alves Costa et al., 2001; Li and Cheng et al., 2001; Rozsa, 2002)
According to Borkowski et al. (2002) the EPN time series analysis station are
located more than 700km from the local LGN network. Few of the European
network station selected to tie to the local network are located close to the research
area thus possesses significantly worse quality parameters. Selections of the
reference stations were made from the mean trend congruency analysis of the EPN
stations coordinate time series. Relative velocities between selected EPN stations
evaluated using different approaches (time series analysis, ITRF2000 velocities,
NUVEL1A-NNR velocities)
In China, Fu et al. (2002) the regional crustal deformation was taken relative
to ITRF97 kinematic plate model. Data of the ‘Investigation on Present Crustal
Motion and Geodynamics in China’ (CMMN), which consist of four campaigns, with
1000km, average in baseline length and situated in each geological tectonic block in
China. Horizontal velocity accuracy of site produced better than 1.5mm/year. Then
China setup its fudicial network reconnaissance since mid of 1998, and was
operational in 1999 known as the CMONC, ‘Crustal Movement Observation
Network of China’. With that China produced its sub-plate Euler vector from
incorporating the global ITRF97 velocity field plate model to the 45 regional GPS
sites in the same ITRF frame.
Chapter 2
GLOBAL POSITIONING SYSTEM
2.1
Background of Global Positioning System (GPS)
Leick (1994) and Hofmann-Wellenhof et al., (1994) are few of the numerous
writers, depicted here, for their comprehensive description of the nature of GPS in
their publications. In 1973 the U.S. Department of Defence decided to establish,
develop, test, acquire, and deploy a space borne Global Positioning System (GPS).
The result of this decision is the present NAVSTAR GPS (NAVigation Satellite
Timing And Ranging Global Positioning System).
According to [Wooden, 1985], “The NAVSTAR Global Positioning System
(GPS) is an all-weather, space-based navigation system under development by the
U.S. Department of Defence to satisfy the requirements for the military forces to
accurately determine their position, velocity, and time in a common reference
system, anywhere on or near the Earth on a continuous basis. ”
From this definition it is clear that the primary goals for developing the GPS
were of a military nature. But the U.S. Congress has allowed civilians to use this
system with some restrictions. The civilian usage of the NAVSTAR GPS has
developed enormously within the last two decades. With the elimination of SA
(Selective Availability) on 2nd of May 2000, the usefulness of the system for civilian
users was even more pronounced. One of the most important events for the highaccuracy civilian applications of GPS was the establishment of the International GPS
Service (IGS) [Mueller and Beutler, 1992] [Beutler, 1992]. There are several other
global positioning systems either operational or under development like the
17
GLONASS and GALILEO. However, NAVSTAR GPS has undoubtedly the greatest
impact on the scientific community at present. Therefore, the term GPS is used as a
synonym for NAVSTAR GPS.
The constellation of the GPS was subject to several changes due to budgetary
considerations (Butler et al, 1999). The present full constellation provides global
coverage with four to eight simultaneously observable satellites above 15˚ elevation.
These are accomplished with the existents of 24 satellites orbiting the earth (in
January 2001, 28 satellites were active). The satellites are located in six orbital
planes on almost circular orbits with an altitude of about 20, 200 km above the
surface of the Earth, inclined 55˚ with respect to the equator and with orbital periods
of approximately 11 hours 58 minutes (half a sidereal day).
Consequently, almost identical Earth-satellite configurations are repeated 4
minutes earlier on consecutive days. The distributions of the satellites were over six
orbital planes. The first GPS satellite PRN 4 (Pseudo-Random Number) was
launched on February 22, 1978. PRN 4 was the first in a series of 11 so-called Block
I satellites. The Block I satellites had an inclination of about 63˚ with respect to the
Earth’s equator. The test configuration was optimized for the North American region
in the sense that four or more satellites could be observed there for a considerable
fraction of the day. The test configuration was not optimal in other parts of the world.
Today, all Block I satellites are deactivated and replaced with the Block II satellites.
(a) Viewed from a latitude of ø = 35˚. (b) Viewed from a latitude of ø = 90˚.
Figure 2.1: GPS orbits (Earth and orbital planes).
18
It was on July 17, 1995 that the system achieved its full operational
capability. Since it has been opened for used for civilians, to date, it has been widely
used in several fields especially in the daily engineering fields. These include
geodetic control surveys, engineering surveying, hydrography, vehicle tracking, dam
monitoring, subsidence, sea-level and crustal dynamics monitoring. In short, GPS
has already revolutionised almost all positioning applications, within and outside the
surveying community. Its application in land surveying is widespread, primarily
through the speed of measurement, lack of requirement for intervisibility between
stations, and from the high precision and accuracy of the results from data processing
achieved.
Each GPS satellite broadcast a navigation message to enable GPS receivers to
determine the coordinates of the satellite at the time of transmission of the signal.
The receiver then determines the time of travel of the signal using the ranging codes
within the signal. The time is used with the satellite coordinates to derive the range
between the satellite and the receiver. Normally, four satellites and hence four ranges
are used to compute the three-dimensional position of the GPS antenna and the
receiver clock offset.
The GPS satellites provide a platform for radio transmitter, atomic clocks,
computers, and various equipments used for positioning and for a series of other
military projects (e.g., atomic flash detection). The electronic equipment of the
satellites allows the user to operate a receiver to measure quasi-simultaneously
topocentric distances to more than three satellites. Each satellite broadcasts message
that allows the user to recognize the satellite and to determine its position in space
for arbitrary time epochs. The satellites are equipped with solar panels for power
supply, reaction wheels for attitude control, and a propulsion system for orbit
adjustments. The operational constellation is realized through the Block II, Block
IIA, and Block IIR satellites. The first Block II satellite was launched in February
1989. Today, a full constellation of at least 24 satellites is available
19
Figure 2.2: GPS Block II satellite and satellite-fixed coordinate system.
2.2
GPS Satellite Signals & It’s Application
All signals transmitted by the satellite are derived from the fundamental
frequency f0 of the satellite oscillator.
Table 2.1: Components of the satellite signal.
Component
Fundamental frequency
Carrier L1
Carrier L2
P-code P (t)
C/A-code C (t)
Navigation message D (t)
Frequency [MHz]
f0 = 10.23
f1 = 154 f0 = 1575.42 (_1. = 19.0 cm)
f2 = 120 f0 = 1227.60 (_2. = 24.4 cm)
f0 = 10.23
f0/10 = 1.023
f0/204600 = (50)(10-6)
The two sinusoidal carrier frequencies f1 and f2, which corresponds to
wavelengths L1 19 cm and L2 24 cm respectively, are modulated with the codes
and the navigation message to transmit information such as the readings of the
satellite clocks, the orbital parameters, etc. The so-called biphase modulation is used
as shown in figure 2.3.
20
Figure 2.3: Biphase modulation of the GPS signal.
According to [Baueršíma, 1982] the resulting signals may be described as
L1 (t) = ap P(t) D(t) cos 2 (f1 t) + ac C(t) D(t) sin 2
L2 (t) = bp P(t) D(t) cos 2
(f2 t)
(f1 t)
(2.1)
where ap, ac and bp are the amplitudes of the signals.
2.2.1
Pseudo-Random Codes
The two codes P(t), C(t) consist of so-called pseudo-random noise (PRN)
sequences. The generation of these sequences is based on hardware devices called
tapped feedback shift registers. The C/A-code (Coarse-Acquisition or Clear-Access)
is generated by the combination of two 10-bit tapped feedback shift registers where
the outputs of both registers are added again by binary operation to produce the code
sequence. A unique code is assigned to each satellite, the sequence has a length of
1023 bits and because of the basic frequency of 1.023 MHz it repeats itself every
millisecond. The time interval between two subsequent bits (10-6 s) approximately
corresponds to 300 meters. The generation of the P-code (Precise or Protected) is
similar, but the length of the resulting sequence is approximately 2.3547·1014 bits
corresponding to a time span of about 266 days. The total code is partitioned into 37
one-week segments. One segment is assigned to each satellite (which defines the
PRN number of the satellite). The P-code repeats itself every week. The time interval
between subsequent bits is 10 times smaller than in the case of the C/A-code.
21
Therefore the accuracy is approximately 10 times higher than for the C/A-code. The
P-code may be encrypted. This procedure is called Anti-Spoofing (AS) and converts
the P-code to the Y-code which is only usable when a secret conversion algorithm is
accessible to the receiver. Since 1995 the encryption is turned on for all satellites.
2.2.2
The Navigation Message
The navigation message is 1500 bits long and contains information
concerning the satellite clock, the satellite orbit, the satellite health status, and
various other data. The message is subdivided into five subframes. Each subframe
contains 10 words. The first word is the so-called telemetry word (TLM) containing
a synchronization pattern and some diagnostic messages. The second word of each
subframe is the hand-over word (HOW). This word contains among others the socalled Z-count that gives the number of 1.5 s intervals since the beginning of the
current GPS week. This number and the P-code give the reading of the satellite clock
at signal transmission time. The first subframe contains various flags and the
polynomial coefficients, which define the satellite clock correction.
The second and the third subframe contain the broadcast ephemerides of the
satellite. Using the broadcast ephemerides the Earth-fixed geocentric coordinates of
the satellites may be computed according to the formulas given in [Dierendonck et
al., 1978]. The fourth and the fifth subframe contain data for military use,
information on the ionosphere, and so-called almanac data (low-accuracy orbits of all
the GPS satellites). The GPS user may decide whether to use the broadcast
ephemerides or the precise ephemerides (produced by the IGS) for processing. The
broadcast ephemerides are available in real time, but they have an accuracy of “only”
several meters. The precise ephemerides have an accuracy of several centimetres and
they are available with a delay of about two weeks for final products, of below one
day for so-called rapid products.
The satellite clock corrections are required for processing. The accuracy of
this information in the broadcast message was artificially degraded (Selective
Availability, SA) for non privileged users until May 2, 2000, when the degradation
22
was disabled by the U.S. The effect of SA was fully eliminated in geodetic
applications when only relative positions of receivers were estimated. The IGS
precise orbits contain highly accurate satellite clock corrections, too.
2.2.3
Signal Processing.
The receivers contain elements for signal reception and signal processing
(antenna, preamplifier, radio frequency (RF) section, microprocessor, storage device,
control device, and power supply). After signal input from the antenna, the signals
are discriminated, i.e., separated into satellite-specific signals. Usually this is
achieved through the C/A-codes which are unique for each satellite. The basic
elements of the RF section are oscillators to generate a reference frequency, filters to
eliminate undesired frequencies, and mixers. The pseudorange measurements are
achieved as follows: a reference carrier is generated in the receiver and then
modulated with a copy of the known PRN code. This modulated reference signal is
correlated with the received satellite signal. Neglecting the receiver and satellite
clock errors this correlation gives directly the travel time or, multiplied by the
velocity of light c, the so-called pseudorange.
GPS satellites transmit two L-band frequencies, L1 (1575.42 MHz) and L2
(1227.60 MHz). Both are derived from the basic frequency of 10.23 MHz. These
dual frequencies are essential in order to eliminate errors due to atmospheric
refraction. Superimposed onto these L1 and L2 carrier waves are two pseudorandom
noise (PRN) codes. The first, the C/A (Coarse/Acquisition) code is modulated only
on L1 and is designated as the Standard Positioning Service (SPS) for civilian use.
The second, the P (Precise) code is modulated on both L1 and L2 carriers and is
designated as the Precise Positioning Service (PPS). Both L1 and L2 carriers have
data messages such as the satellite ephemeris, ionospheric modelling coefficients,
status information, system time and clock bias and drift information.
General uses of GPS are wide; it can be use globally, regionally, and even
locally. Its efficient contribution to navigation and survey as well as geodynamic
monitoring is verbose to describe. As a powerful geodetic tool, GPS is involved in
23
monitoring global changes over time. This gives a long-term understanding of the
geodynamic phenomena. Applications include measuring crustal deformations,
postglacial rebound, volcanic uplift, plate tectonics and earth rotation. GPS is more
cost effective compared to other techniques that can also be used for these purpose
like VLBI and SLR techniques.
2.3
GPS Continuous Observation Centres
Main role of most GPS continuous observation centres are for the purpose of
detecting deformation from the continuous observation stations deployed on several
or more parts of the globe. Amongst the available GPS continuous observation
centres are the IGS, which are effective globally and the MASS, setup locally to
cater to geodetic positioning and geodynamic studies. There are many others like
EUREF and CODE in Europe, and SIRGAS in France. However, this chapter shall
focus on the former two permanent GPS stations network, the IGS and MASS.
2.3.1
The International GPS Service (IGS)
Within the last decade, GPS has come to play a major role in earth sciences.
In the face of continued growth and diversification of GPS applications, the
international scientific community has made an effort to promote international
standards for GPS data acquisition and analysis, and to deploy and operate a
common, comprehensive global GPS tracking network. As a result of this effort, the
International GPS Service (IGS) was established by the International Association of
Geodesy (IAG) in 1993 and began its official operation on 1 January 1994 (Beutler
et al., 1994, 1995b; Neilan, 1995). The IGS, with a multinational membership of
organizations, agencies, and universities, makes available based on the contributions
of seven analysis centres:
•
Highly accurate ephemeredes of all active GPS satellites,
24
distinguishing between a final, a rapid, and a 2-day predicted orbit
products,
•
Earth rotation parameters (ERPs), as X- and Y-component of polar
wobble and length of day (LOD),
•
IGS tracking station coordinates and velocities in SINEX (Solution–
INdependent EXchange) format (Kouba et al., 1996),
•
Satellite and station clock information, and
•
Since 26 January 1997 also station-specific troposphere zenith path
delay estimates (Gendt, 1998).
Figure 2.4: The Distribution of the IGS stations
The mentioned products refer to the IERS Terrestrial Reference System
(ITRS) realized by the IERS Terrestrial Reference Frame (ITRF), at present ITRF97
(Boucher et al., 1998). The IGS final products are available within about two weeks
of observations. Both IGS member institutions and the interested public can access
them on the Internet through the information system (CBIS) maintained by the IGS
central bureau (CB), which is sponsored by the National Aeronautic and Space
Administration (NASA) and managed by the Jet Propulsion Laboratory (JPL) of the
California Institute of Technology.
25
The raw data of the global IGS tracking network is a very valuable IGS
product as well. It is collected, archived, and distributed using RINEX (Receiver
INdependent EXchange) format (Gurtner, 1994). The IGS consist of components like
network stations, global and regional data centres, analysis centres, analysis center
coordinator, central bureau, governing board, and users to mention the most
important ones (Neilan, 1995; IGS, 1998). At present seven contribute to the IGS
service:
•
COD, Center for Orbit Determination in Europe, AIUB, Berne,
Switzerland,
•
EMR, Energy, Mines and Resources, NRCan, Ottawa, Canada,
•
ESA, European Space Agency, ESOC, Darmstadt, Germany,
•
GFZ, GeoForschungsZentrum Potsdam, Germany,
•
JPL, Jet Propulsion Laboratory, Pasadena, California, USA,
•
NGS, National Geodetic Survey, NOAA, Silver Spring, Maryland,
USA, and
•
SIO, Scripps Institution of Oceanography, San Diego, California,
USA.
Note that the 3-character acronyms at the beginning of each analysis centres
are used to identify the individual products.
2.3.2
MASS
The
Malaysian
Active
GPS
System (MASS)
were
setup
before
GEODESSYA 96 for the purpose of geodetic positioning across the peninsular and
the venture of Department of Survey and Mapping Malaysia (DSMM) in providing
24 hours GPS data for GPS users in Malaysia. The system consists of 18 permanent
GPS tracking stations with 10 stations in Peninsular and the rest in Sabah and
Sarawak (Figure 3.1). All MASS stations are equipped with a dual frequency GPS
receiver, a geodetic or choke ring antenna, computers and modems. The stations
track GPS data 24 hours a day, continuously. The data are stored and formatted at an
26
hourly interval in the site computers. These data are downloaded every day to the
Geodesy Data Processing Centre in Kuala Lumpur (GDPC) (Figure 3.2) (Abdul
Majid, 1999).
Figure 2.5: Distribution of MASS locations in Malaysia
Figure 2.6: Geodesy Data Processing Centre configuration in Kuala Lumpur
The objective of establishing the system is to derive products such as the
highly accurate GPS ephemeris, earth rotation parameters, coordinates and velocities
27
of the stations, GPS satellite and tracking clock information, and also the ionospheric
and tropospheric information. With the derived products, the realization and
continuous improvement of the ITRF is possible and consequently a National Spatial
Reference Frame can be realized (Samad Abu and Azhari Mohd., 1998).
2.3.2.1 The MASS System
All MASS stations are connected to the processing centre in Kuala Lumpur.
Its function is to monitor the 18 remote stations and to download the data on a daily
basis and provide all the information to GPS users. The composition of the remote
permanent GPS reference station includes GPS TRIMBLE 4000SSE/SSI CORS with
24 channels, Choke Ring Antenna, RF Connector, Computer, Uninterrupted Power
Supply (UPS), Power Block/TR and Lightning Arrester. The computer is connected
to the GPS receiver locally, which stores the GPS data. The data is then sent to a
central processing centre (CPC) by a high-speed modem via telephone line.
Lightning
Antenna
Electricity
Supply
Remote Station
Telephone
Line
Choke Ring
Receiver
Figure 2.7: Remote Base station set-up
28
The acquired GPS data will be handled and managed by the CPC at the
DSMM headquarters in Kuala Lumpur. The data will then be made available for
distribution through this centre. Data acquisition and management will be as follows:
•
Converted to RINEX format;
•
Acquisition of data by DSMM for 24 hrs/day, 365/366 days/year
except for maintenance periods;
2.4
•
Recorded on a 15-second or shorter interval (in future);
•
Will be stored on-line at central data facility for 16 days;
•
Will be backed-up using storage media with a 14 day recycle period;
•
Will be backed-up using CD-ROM media.
The GPS Observables
GPS observables refer to the measurable parameters of the GPS system.
There are basically two types of measurement that a user'
s receiver can make on a
GPS satellite signal those are code pseudorange and carrier phase pseudorange.
These measurements are used to estimate geodetic parameters such as station
coordinates and orbital elements.
2.4.1
Pseudoranges
Code pseudorange or pseudo-random code is the true distance between the
satellite and the user'
s receiver plus an offset due to the receiver clock bias. This
offset arises from time synchronization errors due to the signal emission at an instant
as defined by the satellite clock and the reception at an instant measured by the
receiver clock. This is why signals from four, rather than three satellites are required
to determine a three-dimensional position. The receiver generates a replica of the
code, correlates it with the incoming signal and adjusts in time to obtain a perfect
match between the two. Rothacher (1992) reported that measurement accuracies of
29
about 1 metre for P code and 3 to 5 metres for C/A code pseudoranges can be
obtained.
Phase pseudorange or carrier phase measurement is a range measurement to
the satellite in terms of the number (integer and fractional part) of the carrier
wavelengths. It is carried out by differencing the phase of the carrier signal of the
satellite with the reconstructed carrier phase of the receiver. The carrier phase of, for
example L2 can be reconstructed by squaring the signal. However, the effect of this
are loss of satellite clock and orbit information (therefore have to be obtained from
an alternate source such as IGS) and since the noise is also squared, the signal to
noise ratio is substantially reduced. The accuracy of these phase measurements is
about 1 - 3 mm.
2.4.2
Pseudorange Observation Equation
The general equation gives a measure of the absolute range between receiver
and satellite, biased by the receiver and satellite clock errors (Blewitt, 1995)
Rφ
t*
= c t* − T
(2.2)
*
where Rφ (t *) is the observed pseudorange, c is the speed of light, t* is the
actual reception time as kept by station clock (a.k.a. receiver clock) and T* is the
actual transmission time as kept by satellite clock.
2.4.2.1 Code Pseudorange Observation Equation
Code Pseudorange, p=
+ c (dt – dT) + dion + dtrop +
where by
p
(2.3)
is the geometric range to the satellite
c
is the speed of light
( dt – dT ) is the difference between satellite and receiver
30
clock offset with respect to GPS time.
dion
is the ionospheric delay
dtrop
is the tropospheric delay
p
the bias due to multipath and receiver noise
For high precision GPS work, code pseudorange observables are not used on
their own but are used to determine receiver clock errors and to assist ambiguity
resolution. Instead, carrier phase observables are used for the determination of
precise baselines.
2.4.2.2 Phase Pseudorange Observation Equations
Carrier phase pseudorange is more precise observable than the code
pseudorange. It refers to the received carrier with respect to that of the reconstructed
carrier of the receiver. So, the carrier phase observable is the total number of full
carrier cycles and fractional cycles between the satellite and the receiver at any
instant. The following is a generalised equation for the observed carrier (beat) phase
(modified from Blewitt, 1995)
φ obs t * =
where
f
R φ t * + B sat
c
, rec
(2.4)
t*
Rφ (t *)
is the measurement epoch,
is the pseudorange (except ionospheric delay has opposite
f
Bsat, sta
sign),
is the nominal frequency and
is the carrier phase bias (in unit of cycles).
In a simpler form
Carrierphase,
Φ = ρ + c(dt − dT ) + λ ( N ) − αion + αtrop + ε
where by
is the geometric range to the satellite
(2.5)
31
is the speed of light (299 792 458 ms-1)
c
( dt – dT ) is the difference between satellite and receiver clock offset with respect to
GPS time.
wave length
N
is the integer ambiguity
(-) αion
is the ionospheric delay, slows down much of the signal modulations
αtrop
is the tropospheric delay
ε
the bias due to multipath and receiver noise
There are several techniques that can be used to eliminate the biases
introduced; amongst them the common ones are by differencing and forming linear
combinations of the equation.
2.4.2
GPS Differencing Techniques
From the generalized equation for the phase carrier or observed carrier (beat)
phase is (modified from Blewitt, 1995):
φ obs t * = cf R φ t * + Φ
sat
−Φ
rec
where
Φsat
is the satellite ambiguity,
Φrec
is the receiver ambiguity and
Nsat
is the integer ambiguity (at lock-on).
+ N rec , sat
(2.6)
32
2.4.2.1 Single Difference
Single Difference involves differencing simultaneously the carrier phases of
signals (or the pseudoranges) from a satellite at each of two stations, m and n and
i
satellite i. Hence by definition the single difference phase observable φ mn
(t *) is:
(2.7)
φ mni t * = φ ni t * − φ mi t *
Substituting Equation 2.8, the following expression is obtained,
φ mni t * =
f
R i (t * ) − Φ
c mn
nm
+ N mn
(2.8)
where
i
(t *) = Rni (t *) − Rmi (t *) , Φ nm = Φ m − Φ n is the receiver's ambiguity and
Rmn
is the integer ambiguity
N mn = N m − N n
Thus, by performing single difference, the effects of bias or instabilities in the
satellite clock can be eliminated.
2.4.2.2 Double Differencing
ij
Double difference phase observable φ mn
(t *) is obtained by differencing two
single differences to two satellites i and j .
φ mnij t * = φ mnj t * − φ mni t *
(2.9)
Substituting Equation 2.10 for satellites i and j gives
φ mnij t * =
f
R mnij t * − N mnij
c
ij
(t *) = Rmni (t *) − Rmni (t *) and N mnij = N mnj − N mni
where, Rmn
(2.10)
33
Double differencing technique in essence removes all frequency-independent
errors (non-dispersive delays) such as effects of non-synchronised satellite and
receiver clocks, geometric delay, inaccurate satellite ephemerides and tropospheric
propagation delay. It is a popular technique and was used to process MASS and field
data sets in this study with the Bernese software. Most GPS software systems
providing the highest accuracies, including the Bernese version 4.2 as used in this
study process double differenced data as its observables so that the double difference
phase biases are integer numbers.
2.4.2.3 Triple Differencing
ij
(t*,t * *)
Triple difference φ mn
*
**
between two epochs t and t .
refers to differencing double-differences
φ mnij t * , t * * = φ mnij t * * − φ mnij t *
(2.11)
Substituting Equation 2.11 for epochs t* and t** gives
φ mnij t * , t * * =
f
R mnij t * , t * *
c
(2.12)
ij
(t*, t * *) = Rmnij (t * *) − Rmnij (t *)
where Rmn
Triple differencing eliminates cycle ambiguities and is useful for quick
solution and as a filter for cycle slips. However it is not a good observable due to
large '
noise level'due to the fact that the number of observations had been reduced to
a third.
34
2.4.3
Linear Phase Combinations
Linear combinations of the original L1 and L2 carrier phase can be formed in
an infinite number of ways. The general form of such a linear combination of two
phases ϕ1 and ϕ2 is given by (modified from Hofmann-Wellenhof et al., 1994):
ϕ n n = n1ϕ1 + n2ϕ 2
1 2
(2.13)
where n1 and n2 are the coefficients of the linear combinations. The corresponding
frequency and wavelength are:
f n1n 2 = n1 f1 + n2 f 2
(2.14)
and
λn n =
1 2
c
(2.15)
f n1n2
where f1 and f2 are frequencies of L1 and L2 respectively.
The ambiguity of the linear combination is given by:
N n1n2 = n1 N1 + n2 N 2
(2.16)
where N1 and N2 are the integer ambiguities. For example, the ionosphere-free
linear phase combination has the values of n1 and n2 as 2.5457 and 1.5457
respectively. Beutler et al., (1989) underlined the purpose of differencing and
forming linear combination of observations on different carriers as follows:
•
the elimination of satellite clock errors, receiver clock errors and
initial phase ambiguities in single, double and triple differences
•
the reduction of ionospheric refraction to avoid biased solutions
•
the difficulty in ambiguity resolution on longer baselines when using
L1 and/or
It is often useful to form particular linear combinations of the basic carrier
phase and/or code measurements. The linear combinations are forms by using either
35
zero- or double-difference measurements. L1, L2 represent the phase observables
(zero- or double-differences). However, in the following linear combination
equations only phase observables will be laid forth.
2.4.3.1 Ionosphere-free
The linear combination
L3 =
(
1
f 12 L1 − f 22 L2
2
f − f2
2
1
)
(2.17)
is often called “ionosphere-free” because the ionospheric path delay is virtually
eliminated. The same is true for the corresponding combination of code
measurements. Taking into account the double-difference phase measurements and
neglecting tropospheric refraction ∆α klij , where i and j are the two satellites and k
and l are two stations on the ground.
The ionosphere-free linear combination has the form
Lijkl = α klij − ε 3ijkl
(2.18)
where, ε 3ijkl is the L3 bias or also known as the ionosphere-free bias is as below
ε 3ijkl =
(
1
f12 λ1 n1ijkl − f 22 λ 2 n2ijkl
2
f − f2
2
1
)
(2.19)
where,
f12 , f 22 are frequency of LI and L2 respectively
λ1 , λ 2 are the wavelength of L1 and L2
n1ijkl , n1ijkl are the unknown ambiguity of the two wave length L1 and L2 between the
observations of two satellites i,j and two stations k,l.
36
This bias cannot be expressed in the form λ3 n3ijkl , where n3ijkl is an integer
ambiguity. The difference between the ambiguity of L1 and L2, n3ijkl = n1ijkl − n2ijkl
which is also known as wide-lane, the ionosphere-free bias equation can be as below
f2
1
n ij +
n1ijkl
2 3 kl
f − f2
f1 + f 2
cf
c
= 2 2 2 n3ijkl +
n1ijkl
f1 − f 2
f1 + f 2
ε 3ijkl = c(
ε 3ijkl
2
1
)
(2.20)
λ3
where, c is the speed of light and the formal wavelength of λ3 is approximately
11cm. Therefore, the unknown ambiguity n1ijkl above is often called narrow-lane
ambiguity.
2.4.3.2 Geometry-free
The linear combination
L4 = L1 - L2
(2.21)
is independent of receiver clocks and geometry (orbits, station coordinates). It
contains the ionospheric delay and the initial phase ambiguities. It may be used for
the estimation of ionosphere models. The same linear combination may be formed
using the code observations.
2.4.3.3 Wide Lane
The linear combination
L5 =
1
( f1 L1 − f 2 L2 )
f1 − f 2
(2.22)
is used in the Bernese GPS Software on the double-difference level for phase
observations for the purpose of cycle slip fixing and ambiguity resolution. For this
37
ij
equation both, the ionospheric refraction α ion = α ion
and the tropospheric refraction
ij
are neglected
α trop = α trop
The formal wavelength for L5 is about 86 cm and is roughly four times
longer than that of L1 or L2. Therefore, this linear combination is called wide-lane
combination and the ambiguity in equation (2.19) n3ijkl = n1ijkl − n2ijkl is called wide-lane
ambiguity.
2.4.3.4 Melbourne Wubenna
The Melbourne-Wübbena combination is a linear combination of both, carrier
phase (L1 and L2) and P-code (P1 and P2) observables as described by [Wübbena,
1985] and [Melbourne, 1985]. This combination eliminates the effect of the
ionosphere, the geometry, the clocks, and the troposphere. The combination is given
by
L6 =
1
( f1 L1 − f 2 L2 ) − 1 ( f1 P1 + f 2 P2 )
f1 − f 2
f1 + f 2
(2.23)
where, P1 , P2 are the code pseudorange on L1 and L2
For double-difference observations, the following equation was obtain
Lij6 kl = λ5 n5ijkl
With “good” P-code data (rms
(2.24)
1 m) this linear combination may be used for
the resolution of the wide-lane ambiguities n5ijkl .On the zero-difference level, the
same linear combination gives Li6 k = λ5 n5i k which means that this linear combination
may be used to check zero-difference observations for cycle-slips. However, only the
difference n1ik − n2i k can be checked in this way.
38
Table 2.2: Linear combinations (LCs) of the L1 and L2 observables used in Bernese
LC
Description
L1
L2
L3
L4
L5
L6
Basic carrier
Basic carrier
Ionosphere-free LC
Geometry-free LC
Wide-lane LC
Melbourne-Wüebbena
LC
Wavelength
in cm
19
24
0
∞
86
86
Noise
rel to L1
1.0
1.0
3.0
1.4
5.7
0.7
Ionosphere
rel to L1
1.0
1.6
0.0
0.6
1.3
0.0
The most important linear combinations and their characteristics are
summarized in above table 2.2. The specifications with respect to “noise” and
“ionosphere” are based on units of meters. L1 and L2 (expressed in meters) are
assumed to be equally accurate and uncorrelated. It is to be noted that the noise of
“L6” is given relative to that of P1 and P2, respectively, since this noise level is predetermined exclusively by the quality of the P-code data considered.
2.5
GPS Errors Elimination and Biases Reduction
2.5.1
Satellite Orbit
∆x ( m ) ≈
1
1(km)
.∆X (m) ≈
∆X (m)
d
25,000(km)
(2.25)
Prior to 1992, the orbit quality was considered as one of the primary accuracy
limiting factors in the applications of the GPS for geodesy and geodynamics. Since
the IGS started its operations on June 21, 1992, this statement is no longer true.
Orbits of an unprecedented accuracy are available today for all active GPS satellites
with a delay of less than 12 days after the observations. Since January 1, 1996, socalled IGS preliminary orbits were made available only 36 hours after the
observation; since June 30 (beginning of GPS week 860) this preliminary orbit is
39
called IGS Rapid Orbit and is ready to be used only 24 hours after the observations,
and the former Rapid Orbit is called IGS Final Orbit and it is made available 13 days
after the observations. A new IGS product, the IGS Ultra Rapid Orbit, is generated
since March 2000. The orbits are delivered twice a day at 3 UT and 15 UT with an
average delay of only 9 hours. The first 24 hours in the files are based on the about
40 IGS stations delivering hourly data, the following 24 hours are extrapolated and
may be used for real-time applications.
The effect of unmodeled orbit errors on the estimated station coordinates.
There is a crude, but handy rule of thumb which was derived by [Baueršíma, 1983],
giving the error x in a component of a baseline of length l as a function of an orbit
error of size where d= 250000 km is the approximate distance between the satellite
system and the survey area. [Zielinski, 1988] is more optimistic (by a factor of 4–10)
using statistical methods.
For sessions of about 1–2 hours (and shorter) equation 2.25 gives satisfactory
results [Beutler, 1992], for permanent site occupations the formulae given by
[Zielinski, 1988] (based on statistics) seem to be more appropriate. Table 2.3 gives
the actual baseline errors in meters and in parts per million (ppm) for different
baseline lengths and different orbit qualities according to the equation 2.25
40
Table 2.3: Errors in baseline components due to orbital errors.
Baseline Error
in ppm
Baseline Error
in mm
Orbit Error
Baseline Length
2.5 m
1 km
.1 ppm
- mm
2.5 m
10 km
.1 ppm
1 mm
2.5 m
100 km
.1 ppm
10 mm
2.5 m
1000 km
.1 ppm
100 mm
.05 m
1 km
.002 ppm
- mm
.05 m
10 km
.002 ppm
- mm
.05 m
100 km
.002 ppm
.2 mm
.05 m
1000 km
.002 ppm
2 mm
There are namely six types of orbits as follows:-
•
Broadcast Orbits
•
CODE Predicted Orbits
•
CODE Rapid Orbits
•
IGS Ultra Rapid Orbits
•
IGS Rapid Orbits
•
IGS Final Orbits
The estimated accuracies, based on analyses performed by the IGS Analysis
Centre Coordinator, are given in Table below.
41
Table 2.4: Estimated quality of orbits in 2000.
Orbit Type
3.00 m
Delay
Availability
Real Time
CODE
Predicted Orbits
CODE
Rapid Orbits
0.20 m
Real Time
0.10 m
After 16 Hours
CODE
Final Orbits
0.05 m
After 5–11 Days
CODE,
IGS Data Centres
IGS Ultra
Rapid Orbit
0.20 m
After 3 Hours
IGS Data
Centres and CBIS
IGS Rapid
0.10 m
After 19 Hours
IGS Data
Centres and CBIS
IGS
0.05 m
After 13 Days
IGS Data
Centres and CBIS
Orbits
Orbit
Orbit
(m)
Broadcast
Final
Quality
of
at
Available
Broadcast
Message
CODE
through FTP
CODE
through FTP
Keplerian orbit, osculating elements, orbit parameterization, variational
equations, and numerical integration are some of the elements involved in orbital
movements.
2.5.2
Keplerian Orbit
The mathematical description of a satellite orbit would be very simple if the
gravity field of the Earth were spherically symmetric, if the Earth were the only
celestial body acting on the satellite, and if; moreover, non-gravitational forces like
air-drag and radiation pressure would not exist. Maybe life on Earth would be
problematic in this case, however. Under these circumstances the geocentric orbit
r(t) of a satellite in inertial space is described by a simple differential equation
system of second order in time, the so-called equations of motion for the case of the
two-body problem like follows.
42
r .. = −GM
r
r3
(2.26)
where
G
is the product of the constant of gravity
M
is the mass of the Earth,
r
is the length of the geocentric radius vector r of the satellite.
It is well known that the solution of the equations of motion is either an
ellipse, a parabola, or a hyperbola. Here, only the first type of solutions shall be look
upon which is similar to that of the satellite and earth orbit. The set of six parameters
describing the orbit in figure 2.8 below is exactly the set used for orbit
characterization in the Bernese GPS Software.
Figure 2.8: The set of orbital elements
where,
a
is the semimajor axis of the orbit, defining the size of the orbit.
e
is the numerical eccentricity or simply eccentricity of the orbit, describing the
shape of the orbit, i.e., the deviation from circularity.
i
is the inclination of the orbital plane with respect to the equatorial plane.
is the right ascension of the ascending node, i.e., the angle between the
direction to the vernal equinox and the intersection line of the satellite’s
orbital plane with the equatorial plane (in the direction of the satellite
crossing the equatorial plane from the southern to the northern hemisphere). i
43
and
are the Eulerian angles defining the orientation of the orbital plane in
the equatorial system.
is called the argument of perigee, the angle (in the orbital plane) between the
ascending node and the perigee (measured in the direction of the motion of
the satellite).
u0
is called the argument of latitude, the angle between the ascending node and
the position of the satellite at the (initial) time t0. u0 =
+ v(t0), i.e., the
argument of latitude is equal to the sum of the argument of perigee and the
true anomaly at time t0.
Basic astronomy knows that the vernal equinox, defined as the intersection
line of the equatorial and the ecliptic planes is not fixed in space due to precession
and nutation. Therefore, the reference epoch for equator and equinox has to be
specified to make the inertial frame unique. At the CODE Analysis Centre system
J2000.0 is use.
Table 2.5: Perturbing accelerations acting on a GPS satellite.
Perturbation
m/s2
Two-Body Term of Earth’s
Gravity Field
Oblateness of the Earth
Lunar Gravitational Attraction
Solar Gravitational Attraction
Other
Terms
of
Earth’s
Gravitational Field
Radiation Pressure(direct)
Y-Bias
Solid Earth Tides
2.5.3
Acceleration
0.59
5.10-5
5.10-6
2.10-6
3.10-7
9.10-8
5.10-10
1.10-9
Orbit
Error
after one
Day(m)
∞
10,000
3000
800
200
200
2
0.3
Earth Orientation Parameters (EOP)
EOP is required to perform the transformation from the celestial to the Earth-
fixed system or vice versa. Satellite positions in the inertial Earth-fixed frame,
44
namely ITRF2000 from the available precise orbit information are computated.
Therefore, the EOP file corresponding to the orbits used has to be specified in Pole
Information or Pole file. If IGS precise orbits are used the corresponding EOP files
here where it is available at the IGS site and the file is the ERP (Earth rotation
parameters) files are computed using a weighted average of all available centerspecific ERP files. Earth rotation parameters are used for a 3-parameter subset of the
EOP which comprises the polar motion (Xp, Yp) and UT1.
2.5.4
Antenna Phase Centre Variations (PCV)
The antenna phase centre is the electrical centre of the antenna. All GPS
observations need to be reduced from this point to the station marker. Antenna phase
centre tends to move in accordance to the elevation of the GPS satellite. A correction
must then be applied for this motion by using the IGS_01 phase centre model,
differencing observations from identical antennae and to a certain extent, by pointing
the antenna to a common direction.
Satellite and receiver antenna phase centre variationThe receiver antenna
phase center offsets and variations may stem either from chamber measurements or
from estimations using GPS data. The chamber measurements are performed in
anechoic test chambers, where one specific antenna is mounted on a position that
may rotate the antenna around two independent axes and shift it in three directions.
The transmitting antenna is kept fixed while the receiving antenna (to be tested) is
rotated through zenith angles from -90 to +90 degrees for various azimuth values. To
rotate the test antenna as precisely as possible around the “mean” phase center for the
actual measurements, the antenna is first shifted with respect to the center of rotation,
until the phase center variations with elevation are minimal and as symmetrical as
possible for zenith angles corresponding to -z and +z degrees. Apart from recording
the antenna phase values using a strip-chart recorder, the signal amplitude and axial
ratio pattern are common measurements in chamber tests. These recordings have to
be performed for both GPS carrier frequencies. Finally, the location of the center of
45
rotation with respect to a physical point on the test antenna, e.g. the antenna
reference points (ARP) as defined by the IGS, has to be determined.
2.5.5
Receiver Clock
Forming differences of the measurements to two satellites the receiver clock
error could be corrected. This does not mean, however, that the receiver clock error
is completely eliminated in the differences. In order to compute the geometric
distance between the satellite and the receiver at time t (in GPS time scale) the
receiver clock error ∆ rec has to be known to correct the reading of the receiver clock
trec
µ ki (t ) = µ ki (t rec − ∆ rec )
(2.27)
By taking the time derivative of this equation or by differentiating the
equation to with respect to time a new equation is obtained as follows
dµ ki = − µ ki d∆ rec
(2.28)
where
µ ki
radial velocity of the satellite at time t, with respect to the receiver. This
velocity is zero if the satellite is at the point of closest approach and may
reach values up to 900 m·s-1 for zenith distances z _ 80o.
dµ ki
could be interpreted as the error in the distance µ ki made, when assuming an
error
− d∆ rec is the receiver clock synchronization with GPS time. It is concluded that the
error | dµ ki | in the geometric distance µ ki induced by a receiver clock error
| d∆ rec | will be smaller than 1 mm if the receiver clock error | d∆ rec | is smaller
than 1 µs.
46
2.5.6
Ionosphere
On March 25, 1990, the US Department of Defence has adopted a policy of
accuracy denial in order to limit GPS full potential among civil users and would-be
enemies. This policy was enforced with the introduction of the so-called Selective
Availability (SA). SA has been the dominant source of error in single GPS receiver
positioning. The instantaneous accuracies at 95% confidence level are reported as
100 and 156 metres in the horizontal and vertical components respectively. However,
since May 1, 2000, the US administration had decided to turn off SA. This decision
to stop degrading intentionally the GPS accuracy is expected to have a significant
impact on a wide of users worldwide.
GPS is essentially a 3-dimensional positioning system. However, the height
components of GPS solutions tend to be weaker than the horizontal component. It is
the least precise component since measurements are made upward to the satellites.
The GPS signals are delayed when they pass through the atmosphere. The
ionosphere, which extends from 60 to 1000 km, is composed of free electrons and
ions and causes refraction in the GPS signals. Typical absolute range error can be as
much as 2cm over very long baselines. The signals produced are corrupted, where
the distance measured is increased and bended while passing through the ionosphere.
Frequency (f) of the wave going through the ionosphere is as such:
ion
= 1.35 10-7 Ne / f2
where
ion
is the ionospheric delay
t
Figure 2.9: GPS Signals with Ionospheric Delays
t+
ion
47
By forming ionospheric free observables during the processing of dualfrequency GPS observations, most of the effects can be removed.
[
ion 1 =
1.35 10-7 Ne / f 12
ion 2 =
1.35 10-7 Ne / f 22
ion 2 -
ion 1
= 1.35 10-7 Ne (1 / f 22 – 1 / f 12)
ion 2 -
ion 1
] / [1.35 10-7 (1 / f 22 – 1 / f 12)] = Ne
Ne = [
ion 2 -
ion 1]
/ [1.35 10-7 (1 / f 22 – 1 / f 12)]
(2.29)
The ionosphere delay is quantify by using two frequencies L1 and L2
2.5.7
Troposphere
Propagation delays of the GPS code and phase signals due to the neutral
atmosphere, here it’s the troposphere, which is the ultimate accuracy-limiting factor
for geodetic applications of the GPS. On the other hand, tropospheric delay cannot be
eliminated using dual-frequency observations. Unmodelled differential tropospheric
delays can contribute several cm errors in the height difference.
The zenith path delay due to tropospheric refraction is of the order of 2.3 m
for a station at sea level and for standard atmospheric conditions.
Two kinds of troposphere biases can be distinguished as follows:
48
• Relative troposphere biases caused by errors of (mismodeled)
tropospheric refraction at one of the endpoints of a baseline relative to the
other endpoint.
• Absolute troposphere biases caused by errors of (mismodeled)
tropospheric refraction common to both endpoints of a baseline.
Both error sources are dealt with in detail in [Beutler et al., 1988]. It is
remarkable that relative troposphere biases invoke primarily biased station heights
whereas absolute troposphere biases produce scale biases of the estimated baseline
lengths.
For local and smaller regional campaigns, relative troposphere errors are
much more important and more difficult to model. The station height bias due to a
relative troposphere error may be computed as
∆h =
sat
∆α rec
cos z max
where
(2.30)
is the induced station height bias,
∆h
sat
∆α rec
is the relative tropospheric zenith delay error, and
z max
is the maximum zenith angle of the observation scenario.
In the above order of magnitude formula, it is assumed that the satellites are
uniformly distributed over the sky above the observing sites. Due to the fact that the
GPS orbits all have inclinations of 55o with respect to the Earth’s equator, this
assumption is not true, actually. [Santerre, 1991] studies this effect in particular.
A bias of only 1 cm in the relative troposphere leads to an error of
approximately 3 cm in the estimated relative station height, according to [Beutler et
al., 1988] and the corresponding formula for the impact of an absolute troposphere
error reads as
sat
∆α rec
∆l
=
l
Re cos z max
(2.31)
49
where
∆l, l
∆α
Re
sat
rec
are the baseline length and the associated bias,
is the absolute troposphere bias in zenith direction (common to both
endpoints of the baseline), and
is the Earth’s radius.
The equation above shows that an absolute troposphere bias of 10 cm induces
a scale bias of 0.05 ppm, a relatively small effect compared to the height error caused
by a relative troposphere bias. Nevertheless, the effect should be taken into account
for baselines longer than about 20 km. Again, a uniform satellite distribution in a
spherical shell centered above the stations down to a maximum zenith distance of
zmax was assumed when deriving the above.
The consequences of a non-uniform distribution were studied by [Santerre,
1991]. In a certain sense, an absolute troposphere error is very similar to an error
caused by the ionosphere. The main difference between the two effects is due to the
circumstance that tropospheric refraction is produced in the lowest levels of the
atmosphere (99% below 10 km) whereas the ionospheric shell height is about 400
km. Tropospheric refraction tends to be much more site-specific than ionospheric
refraction for that reason.
Moreover, troposphere biases are orders of magnitude above the noise level
of the phase observable. Their influence thus must be reduced to make full use of the
accuracy of the observable by either of the following two methods:
• Model tropospheric refraction without using the GPS observable (e.g., by
using ground met measurements or water vapor radiometers).
• Estimate tropospheric zenith delays in the general GPS parameter
estimation process.
50
Figure 2.10: Tilting of the “tropospheric” zenith by the angle .
2.5.8
Tides & Loading
Earth body tides refer to as the elastic deformation of the earth due to the tidal
forces of the sun, moon and planets, causing time-dependent variation in station
heights.
2.5.8.1 Ocean Loading
Ocean tide loading is the periodic change in water mass distribution as a
result of the tidal rise and fall of sea level due to the gravitational attraction of the
moon, sun and planets. This forcing effect of the ocean tides causes the earth crust to
move vertically with magnitude that reaches tens of millimetres (Baker et al., 1995;
Dodson, 1995). Applying ocean tide loading models can eliminate the effect. On the
other hand, the errors tend to cancel or average out over 24-hour GPS observations.
Ocean tide loading is the deformation of the Earth due to the weight of the ocean
tides. The water in the ocean tides moves back and forth and these mass
redistributions cause periodic loading of the ocean bottom. Since the Earth is not
completely rigid, it deforms under this load and this is called ocean tide loading. One
51
can observe it as variations at your station in vertical and horizontal displacement, in
gravity, tilt and in strain.
2.5.8.2 Ocean Tide
The ocean tides are produced by the gravitational pull of the Moon and Sun,
since, their orbits have more than one periodicities due to the eccentricity, evection
and the ocean tides can be described as a sum of several ocean tides with each having
their own period. The 11 periods, also called harmonics, with the largest amplitude
are mostly used to compute the ocean tide loading. An example of a tidal map is
given in Figure 2.11. The colours represent the amplitude and the contour lines
indicate the phase lag of the tides with a spacing of 60 degrees.
Figure 2.11: The ocean tides for harmonic M2 (period of 12 hours and 25 minutes)
Problem areas are mostly shallow seas with large tidal amplitude and fast
varying phase lag. These include among others: the North Sea, seas around
Indonesia, Pantagonian Shelf, Hudson Bay and the Chinese Sea.
52
To compute the ocean tide loading or the ocean tides are integrated with a
weighting function G:
a (r ) = ρZ (r ')G r − r 'dA
(2.32)
A
Here a is the loading phenomenon (displacement, gravity, tilt or strain) at the
station located at r. The ocean tide at r’ is given in its complex form
Z=Amplitude*exp (i phase).
is the mean density of sea water and G is the Green'
s
function for the distance |r-r’|. The integral is taken over all global water masses A.
The Green'
s function determines how much the Earth deforms due to the point load
of 1kg.
2.5.8.3 Atmosphere Loading
Atmospheric loading is caused by the time-varying atmospheric pressure
distribution over the earth’s surface and analogous to ocean-tide loading. This elastic
response of the earth crust can has a magnitude of several millimetres in vertical
station displacements. The effect can be eliminated by employing a campaign-styled
GPS measurement from 3-5 days to two weeks, using GPS continuous observations
or applying suitable atmospheric loading models.
Of all the error sources listed as above, antenna phase centre variation and
ocean tide loading effects are the most significant. The former will be significant
over long baselines and in GPS observations involving mixed antenna types whilst
the latter is highly localised in nature, especially in coastal areas.
2.6 Ambiguity Resolution
The problem of the resolution of the initial phase ambiguities is by itself a
field of research. Examples of Ph.D. theses dealing with ambiguity resolution are
53
(Frei, 1991) and (Mervart, 1995). Ambiguity resolution always relies on statistical
hypotheses and may be seriously affected by biases not taken into account in the
observation equations. Ionospheric biases play the crucial role in this context, unless
the ionosphere-free LC is used. For that reason, the standard ambiguity resolution
techniques shall be reviewed.
The changing “geometry” of the GPS satellites, makes it possible to separate
double-difference carrier phase ambiguity parameters, initially treated as real-valued
parameters, from the other parameters, like station coordinates. The motivation to fix
phase ambiguities to integers becomes plausible when comparing the code
observation equation (2.2),(2.3) with the corresponding phase observation equation
(2.4),(2.5), assuming the term λ (N ) or could also be written as λN ijkl as known:
L*ijkl = ρ ij'kl
Pijkl = ρ ij'kl
(2.33)
The “ambiguity-fixed” double-difference phase observations, indicated by an
asterisk, are essentially millimeter-accurate code observations. Frei (1991) showed
that in the case of rapid static GPS positioning the formal accuracy of the ambiguity
parameters (and station coordinates) is primarily a function of the baseline
occupation time t. These accuracies are proportional t −1 or t −3 / 2 , assuming the
number of epochs or the data-sampling rate to be constant, respectively. This result
tells us also that ambiguity resolution is increasingly important and more difficult for
shorter occupation time t. It is under such conditions that sophisticated ambiguity
resolution strategies like that of Frei (1991) or Teunissen (1995) are of vital
importance.
But even when processing 24-hour sessions, ambiguity resolution clearly
improves the estimates of the remaining, non-ambiguity parameters, which are
strengthened due to the reduction of unknown parameters and the corresponding
increase of the degree of freedom. Mervart (1995) showed, on the basis of variancecovariance analysis and experimental studies, that the most prominent improvement
concerns the east-west component of station coordinates where one may gain a factor
54
of about two compared to “ambiguity-float” solutions (for 24-hour sessions). Note
that for shorter sessions the gain is more significant. To obtain best possible results,
one is therefore obliged to perform ambiguity resolution even if long sessions are
processed.
2.6.1
Directly Resolving Ambiguities on Short Baselines
For short baselines with lengths up to several kilometers, one may try to
neglect the ionospheric refraction. This leads to the following, simplified phase
observation equations:
Lklij,1 = ρ ij'kl + λ1 N ijkl,1
Lklij, 2 = ρ ij'kl + λ 2 N ijkl, 2
(2.34)
In the case of a static observation scenario with an occupation time longer
than about one hour, it is usually no problem to fix the ambiguity parameters N ijkl,1
and N ijkl, 2 to the correct integers because the corresponding confidence intervals
deduced from the variance-covariance information normally contain exactly one
integer which is then considered to be the correct one. This approach also works for
single-band data, because the ambiguity parameters N ijkl,1 and N ijkl, 2 are treated
independently.
2.6.2
The Quasi-Ionosphere-Free (QIF) Ambiguity Resolution Strategy
The QIF strategy allows to directly resolve the basic phase ambiguities N 1
and N 2 on long baselines without making use of P-code measurements. It was
developed by Schaer (1994) and Mervart (1995). The “quasi-ionosphere-free”
ambiguity resolution strategy can cope with larger ionospheric errors than the
55
traditional phase-based wide-lane method, namely errors up to two L5 -cycles minus
a given search width. Unlike the two-step ambiguity resolution procedure via widelane and narrow-lane LCs, the QIF strategy requires only one operation, where the
dual-band phase observation L1 and L2 are processed together according to
observation equations (2.18) and (2.19) and where ionosphere free biases ε 3ijkl are set
up, slightly constrained, and pre-eliminated epoch by epoch. The basic
ambiguities n1ijkl and n1ijkl that meet certain statistical criteria are resolved pair by pair
doing a full inversion of the updated normal equation system after each fixed
ambiguity pair – thus increasing the probability to resolve the remaining ambiguities.
One essential QIF criterion concerns the deviation of the estimated quality N ijkl,3 from
the “true” value N ij*kl,3
∆N ijkl,3 = N ijkl,3 − N ij*kl,3 = ( N ijkl,1 + N ijkl, 2 ) − ( N ij*kl,1 + N ij*kl, 2 )
(2.35)
Where N ij*kl,1 and N ij*kl, 2 denote the true pair of integers. ∆N ijkl,3 is expected to be
zero and may normally be determined with a few-millimetres accuracy. Because the
wavelength internally used by the QIF strategy is approximately half that of the
narrow-lane wavelength, it is of fundamental importance that all-conceivable doubledifference ambiguity parameters are formed and tested. The QIF ambiguity
resolution strategy, designed for large-area permanent networks, is used by CODE
for regional and global ambiguity resolution. To increase the percentage of
ambiguities fixed by QIF, GPS-derived regional and global ionosphere maps are
taken into account.
2.7 ITRF
ITRF stands for International Terrestrial Reference Frame. This system takes
its datum to the centre of the earth. In order to facilitate the exchange of space
geodesy results between analysis centres and research groups, a well documented
and flexible format was necessary. A working group was formed in 1994 by the
56
International GPS Service (IGS), involving International Terrestrial Reference Frame
(ITRF) section, to establish such a format. The SINEX acronym (Software
Independent Exchange) was suggested by Blewitt et al. [1994], and the first versions,
0.04, 0.05, and 1.00 evolved from the work and contributions of the SINEX Working
Group chaired by G. Blewitt. The SINEX format was then born and widely used by
all IGS and IERS analysis centres. SINEX format, by its structure, is designed to
contain estimated parameters such as station positions, velocities, Earth orientation
parameters, and estimated and a priori (constraint) matrices.
From the beginning of the ITRF2000 project, the IERS analysis centres were
encouraged and assisted to provide TRF solutions without any external constraint
that would disturb their results. The rationale behind this goal is to try to assess the
real quality of station positions and velocities provided by space geodesy techniques.
The submitted geodetic solutions incorporated in the ITRF2000 combination are of
three types, according to the initial constraints applied upon all or a subset of
stations:
(1) removable constraints, solutions for which the estimated station
positions/velocities are constrained to external values within an
uncertainty in few meters for positions and few meter per year for
velocities; this type of constraints is easily removable,
(2) loose constraints, solutions where the uncertainty applied to the
constraints is 1 m for positions and 10 cm/yr for velocities; and
(3) minimum constraints used solely to define the TRF using a minimum
amount of required information, in a similar approach.
These solutions are basically station positions and velocities with full
variance matrices provided in SINEX format for a global coverage. Where for each
solution the type of constraints, loose, removable, or minimum, is indicated.
57
Figure 2.12: The IGS stations are distributed all around the globe.
Observations used in these solutions span about 20 years for pioneering space
geodesy techniques (LLR, VLBI, SLR) and approximately 10 years for GPS
techniques.
2.8
Summary
For a whole GPS is a very useful tool in monitoring deformation and globally
it permanent stations have been setup for this purpose. However, there are many
errors and biases that are involved before any results from a GPS observation could
be achieved.
Chapter 3
GPS for Geodynamic Studies
3.1
Introduction to Geodynamic
With the advent of continuously recording networks of GPS receivers, it is
now possible to examine regional deformation patterns with high accuracy and dense
temporal sampling. However, the questions still remain about how best to estimate
crustal deformation from GPS data and about what these data can tell us. In this
chapter, firstly the historical evolution of the plate tectonic theory shall be concisely
explained, the term geodynamic mainly will be discussed and later GPS usage in
geodynamic will be laid forth. A special session at the American Geophysical Union
less than 5 years ago today, at which several organizations indicated a strong feeling
that is with the availability of more continuous GPS stations would be the best way
to vastly improve measurements of crustal deformation.
3.2
Evolution of the Plate Tectonic Theory
The idea of the plate tectonics was initiated from the continental drift theory
proposed by Alfred Wegener, a German meteorologist, in mid 1911. He came across
the presences of identical fossils of both plants and animals on the opposite sides of
the great oceans (Henry, 2000). Moreover, he also noticed the close fit between the
coastlines of West Africa to that South America.
59
Wegener used the fit of the continents, the distribution of fossils, a similar
sequence of rocks at numerous locations, ancient climates, and the apparent
wandering of the Earth's polar regions to support his theory of continental drift.
Wegener used his observations to hypothesize that all of the present-day continents
were once part of a single supercontinent called Pangaea.
3.2.1
Pangaea
Pangaea meaning “all lands” was hypothesized as a single huge mass of land
that was the initial formation of the continents. The continents were believed once
compressed into a single protocontinent, and over time they drifted apart into their
present positions (Henry, 1960). The spreading of the continents across the earth is
known as Wegener’s drift theory and in modern times known as the continental drift
theory. However, it was considered illogical that the centrifugal and the tidal force
caused the continents to drift apart by ploughing through the solid earth’s crust to
their current positions. Thus this theory lacks the geological mechanism. Later in
1929, Arthur Holmes elaborated Wegener’s hypotheses; the idea that the earth’s
mantle undergoes thermal convection.
Figure 3.1: PANGAEA
60
3.3
Continental Drift
Holmes idea were based on fact that the mantle is heated its density decreases
and rises to the surface until it is cooled and sink again resulted in the currents which
moves the continents apart. Implying that the thermal convection is like a conveyor
belt and that the upwelling pressure could break apart a continent and force them into
different directions carried by the convection currents (Henry, 1978). Thus
continental drifts is the movements of continents over the Earth’s surface and in their
change in position relative to each other.
Figure 3.2: Holmes’ model of convection currents.
whereby,
A is the area of up welling
B is the area of down welling & melting
Geologists have known for over a century now that a ridge exists in the
middle of the Atlantic Ocean. The Mid-Atlantic Ridge is 6,500 feet (2,000 m) above
the adjacent sea floor, which is at a depth of about 20,000 feet (6,000 m) below sea
level. In the 1950s, a seismologist, a scientist who specialises in the study of
earthquakes, showed that the global system of mid-ocean ridges was also an active
seismic belt, or zone of earthquakes. An international group of geologists proposed
that the seismic belt corresponded to a trough, or rift, system similar to the trough
known at the crest of the Mid-Atlantic Ridge. The rifts are about 20 miles (30 km)
wide and 6,500 feet (2,000 m) deep. In all, the oceanic ridges and their rifts extend
for more than 37,500 miles (60,000 km) in all the world's oceans.
Further scientific exploration of the ocean floor and the continents helped in
the discovery of features like mid-oceanic ridges, geomagnetic anomalies parallel to
the mid-oceanic ridges, and the association of island arcs and oceanic trenches
61
occurring together and near the continental margins, suggested that convection is
indeed at work. Hence, Harry Hess (1962) and R. Deitz (1961) discovery lead them
to published a similar hypotheses based on mantle convection currents now known as
“sea-floor spreading”.
3.3.1
Sea-Floor Spreading
Figure 3.3: Earth’s Interior
The modern scientist now know that both continents and ocean floor form
solid plates, which “float” on the asthenosphere, the underlying rock that is under
such tremendous heat and pressure that it behaves as an extremely viscous liquid.
Sea-floor spreading is the creation of new oceanic crust at mid-ocean ridges and
movement of the crust away from the mid-ocean ridges. The lithosphere (from the
Greek, lithos, stone) is the rigid outermost layer made of crust and uppermost mantle.
The lithosphere is the "plate" of the plate tectonic theory. The asthenosphere (from
the Greek, asthenos, devoid of force) is part of the mantle that flows, a characteristic
called plastic behavior. It might seem strange that a solid material can flow. A good
example of a solid that flows, or of plastic behavior, is the movement of toothpaste in
62
a tube. The flow of the asthenosphere is part of mantle convection, which plays an
important role in moving lithospheric plates.
The division of the Earth's interior into lithospheric and asthenospheric
components is based on their mechanical differences. The lithosphere is cooler and
more rigid, whilst the asthenosphere is hotter and mechanically weaker. This division
should not be confused with the chemical subdivision of the Earth into (from
innermost to outermost) core, mantle, and crust. The key principle of plate tectonics
is that the lithosphere exists as separate and distinct tectonic plates , which "float" on
the fluid-like asthenosphere. The relative fluidity of the asthenosphere allows the
tectonic plates to undergo motion in different directions.
In 1962, a geologist presented an explanation for the global rift system. Harry
Hess proposed that new ocean floor is formed at the rift of mid-ocean ridges. The
ocean floor, and the rock beneath it, is produced by magma that rises from deeper
levels. Hess suggested that the ocean floor moved laterally away from the ridge and
plunged into an oceanic trench along the continental margin.
Figure 3.4: Sea Floor Spreading
A trench is a steep-walled valley on the sea floor adjacent to a continental
margin. For example, ocean crust formed at the East Pacific Rise, an oceanic ridge in
the east Pacific, plunges into the trench adjacent to the Andes Mountains on the west
side of the South American continent. In Hess' model, convection currents push the
63
ocean floor from the mid-ocean ridge to the trench. As Hess formulated his
hypothesis, Robert Dietz independently proposed a similar model and called it sea
floor spreading. Dietz's model had a significant addition. It assumed the sliding
surface was at the base of the lithosphere, not at the base of the crust.
Continents are no longer thought to plow through oceanic crust but are
considered to be part of plates that move on the soft, plastic asthenosphere. A driving
force, convection currents, moved the plates. Technological advances and detailed
studies of the ocean floor, both unavailable during Wegener's time, allowed Hess and
Dietz to generate the new hypotheses.
Figure 3.5: The Tectonic Plate Boundaries
The theory states that Earth's outermost layer, the lithosphere, is broken into 7
large, rigid pieces called plates: the African, North American, South American,
Eurasian, Australian, Antarctic, and Pacific plates. Several minor plates also exist,
including the Arabian, Nazca, and Philippines plates.
Therefore, plate tectonics could be said as a relatively new theory that has
revolutionized the way geologists think about the Earth. According to the theory, the
surface of the Earth is broken into large plates. The size and position of these plates
64
change over time. The edges of these plates, where they move against each other, are
sites of intense geologic activity, such as earthquakes, volcanoes, and mountain
building. Plate tectonics is a combination of two earlier ideas, continental drift and
sea-floor spreading.
The place where the two plates meet is called a plate boundary. Boundaries
have different names depending on how the two plates are moving in relationship to
each other
3.4
•
Convergent Boundaries,
•
Divergent Boundaries,
•
Transform Boundaries
Plate Boundary Zones
The cracks that are formed on the surface of the earth’s crust and cut as deep
as the lithosphere can be called as the fault lines. Plate boundary zones are the broad
belts in which boundaries are not well defined and the effects of the plate interaction
are unclear.
There are four types of plate boundaries from which could be identify and
differentiated by the motion and movements of the crust. The size of the Earth has
not changed significantly during the past 600 million years, and very likely not since
shortly after its formation 4.6 billion years ago. [Forde, 1994] The Earth unchanging
size implies that the crust must be destroyed at about the same rate as it is being
created. [Harry Hess, 2000] Hence the recycling of crust takes place along the
convergent boundaries where plates are moving towards each other and sometimes
subduct under another. Whilst, sea floor spreading and divergent boundaries causes
the formation of the earth crust. The kinds of collision occur depends greatly on the
lithosphere involved. The propagation of an oceanic rift into a continent is a
fundamental process leading to continental breakup (Courtillot, 1982; Courtillot and
Vink, 1983; Martin, 1984).
65
3.4.1
Divergent Boundaries
A divergent boundary is an occurrence where new crust is generated as the
plates pull away from each other. This phenomenon usually occurs around spreading
centres where plates are moving apart and a new crust is created by magma pushing
up from the mantle. Mid-Atlantic Ridge, a submerged mountain range, is a well
known divergent boundary that extends from the Artic Ocean to beyond the southern
tip of Africa. The rate of spreading along the Mid-Atlantic Ridge averages about 2.5
centimetres per year, or 25km in a million years [USGS, 1999]. Though this rate
seems invisible to the naked human eyes, but since it have occurs for the past 100 to
200 million years, Mid-Atlantic seafloor spreading has caused the Atlantic Ocean to
grow from a tiny inlet of water between the continents of Europe, Africa, North and
South America into the vast ocean that exist today.
The Red Sea was formed this way, where the plate on which Saudi Arabia
lies spreads away from the rest of the African continent. Actively splitting African
plate and the Arabian plate is also known as the triple junction, where the Red Sea
meets the Gulf of Aden. Continental divergent causes crust to stretch beyond its
limits and cracks. Thus magma rises through the open cracks and eruption might
occur, this is where volcanoes could be formed. An example of continental drift that
causes much havoc in the recent years occurring around the Arabian plates is the
Iranian Earthquake in December 2003 taking thousands of lives. [Reuters, 2003]
3.4.2
Convergent Boundaries
Convergent boundaries are where crust is destroyed as one plate dives under
another. There are three types of convergence, oceanic-oceanic convergence,
oceanic-continental convergence, and continental-continental convergence. The
recent tsunami that causes the loss of hundreds of thousands of live across Asia is
categorised under the oceanic-oceanic convergence between the Sunda Plate and the
Indian Plate.
66
3.4.2.1 Oceanic-oceanic convergence
Thousands of kilometres of deep ocean trenches are profound at the base of
the Pacific Ocean. A cut as deep as 8 to 10km pierced through the seabed created by
plate subduction. The fast-moving Pacific Plate converges against the slower moving
Philipine Plate resulted in the formation of the Marianas Trench. The deepest trench
in the world is known as the Challenger Deep located south of the Marianas Trench,
which plunges deeper into the Earth’s interior 11,000 m than the tallest mount in the
world, Mount Everest that rises 8,854 m above the sea level. A submarine volcano
could rise above sea level to form an island volcano; usually they are strung out in
chains called the island arcs. The Marianas and Aleutian islands are formed this way.
3.4.2.2 Oceanic-continental convergence.
When an oceanic crust subducts under the continental crust a trenches and a
volcanic arc could be formed. Andes Mountains are the resultant of the uplifts of the
oceanic-continental convergence of the oceanic Nazca Plate subducting under the
South American Plate. Even though the Nazca Plate as a whole is sinking smoothly
and continuously into the trench, the deepest part of the subducting plate breaks into
smaller pieces that become locked in place for long periods of time before suddenly
moving to generate large earthquakes. For instance, the deepest and largest
subduction earthquakes ever recorded was the La Paz Earthquake with a magnitude
of 8.3 on the Richter scale and with a depth of 636km. Such earthquakes are often
accompanied by uplift of the land by as much as a few meters. Great depth in the
subduction of the converging plates will generate large earthquake and cause major
damaged.
67
3.4.2.3 Continental-continental convergence.
Prominent Himalayan mountainous range is one of the prominent outcomes
of a plate tectonic movement. Two continents of similar denseness collides head-on,
neither is subducted and resist downward motion. Instead, the collided crust
crumples upwards to form mountainous range and high plateau. For instance, the
collision Indian Plate and the Eurasian Plate million of years ago causes the
formation of the Himalayas with Everest being the highest mount and Tibetan
Plateau being the highest plateau and even higher than the mounts in Alps except
two, Mont Blanc and Monte Rosa.
3.4.3
Transform Boundaries
A transform-fault boundary is where crust is neither produced nor destroyed
as the plates slide horizontally past each other. The concept of transform faults
originated from a Canadian geophysicist J. Tuzo Wilson who proposed that these
transform faults are common around the fractures zones where two continents are
spreading and less commonly found where two continents are colliding. Most
transform faults could be found on the ocean floor an offset to the active sea floor
spreading, producing zig-zag plate margins and are generally shallow earthquakes.
However, few of these transform boundaries do occur on land like the San Andreas
fault, about 1,300km long in California connecting between two divergent
boundaries in the south the East Pacific Rise and in the north the Explorer Ridge.
3.5
The “Ring of Fire”
Volcanic arcs and oceanic trenches partly encircling the Pacific Basin form
the so-called Ring of Fire, a zone of frequent earthquakes and volcanic eruptions.
The trenches are shown in blue-green. The volcanic island arcs, although not labeled,
are parallel to, and always landward of, the trenches. For example, the island arc
68
associated with the Aleutian Trench is represented by the long chain of volcanoes
that make up the Aleutian Islands. Circling the Pacific Basin, on the bottom of the
sea bed, lie a dramatic series of volcanic arcs and oceanic trenches. The zone - the
'Ring of Fire' - notorious for frequent earthquakes and volcanic eruptions coincides
with the edges of one of the world's main tectonic plates. (BBC News - January 29,
1999) The final section of the Ring of Fire exists where the Indo-Australian plate
subducts under the Pacific plate and has created volcanoes in the New Guinea and
Micronesian areas. Near New Zealand, the Pacific Plate slides under the IndoAustralian plate. The "Ring of Fire" is an arc stretching from New Zealand, along the
eastern edge of Asia, north across the Aleutian Islands of Alaska, and south along the
coast of North and South America. It is composed over 75% of the world's active and
dormant volcanoes.
Figure 3.6: The “Ring of Fire”
69
Figure 3.7: Malaysia and its plate location
The north-east side of the Australian plate forms a subducting boundary with
the Eurasian plate on the borders of the Indian Ocean from Bangladesh, to Myanmar
(former Burma) to the south-west of Indonesian islands of Sumatra and Borneo
where the Java Trench is formed.
3.6
Plate Tectonic and GPS
The modern theories of plate tectonics have been around for less then thirty
years. The roots of these theories however have their origins at the beginning of the
century (Cruddace, 1995). Plate Tectonics holds that the earth's crust comprises a set
of plates floating on a mobile Mantle. It’s at the margins of these plates that we get
earthquake activity and frequently volcanism or mountains. Oceanic crust emanates
at (usually undersea) spreading ridges and disappears into the Mantle again at deep
ocean trenches, and the continents move about in the process. The cause of plate
movements and volcanism is a complex thermal - chemical gravitational engine, but
some conceptual grasp can be obtained by picturing convection cells within the
earth's mantle.
70
General uses of GPS are wide; it can be use globally, regionally, and even
locally. Its efficient contribution to navigation and survey as well as geodynamic
monitoring is verbose to describe. As a powerful geodetic tool, GPS is involved in
monitoring global changes over time. It is even possible to measure the speed of
continental plates extremely accurately, using satellite technology. This gives a longterm understanding of the geodynamic phenomena. Applications include measuring
crustal deformations, postglacial rebound, volcanic uplift, plate tectonics and earth
rotation. GPS is more cost effective compared to other techniques that can also be
used for these purpose like VLBI and SLR techniques.
Global Positioning system and Geodesy Precision is based on the following:
•
Geometry of GPS constellation
•
Strength of the tracking network
•
Ability to model/correct the error sources
•
Measurement Noise
•
Absolute station coordinate accuracy is 15mm
•
5mm in latitude and longitude
•
10 mm in height
•
Baselines 12000 km - 2mm
This order of geodetic accuracy of GPS enables the measurements of earth’s
surface to describe the dynamics of the earth Global tracking networks and larger
GPS constellation now yield sufficient sensitivity to allow estimation of geocenter
and polar motion.
3.7
Malaysia
Malaysia is located in Southeastern Asia. There are two distinct parts to
Malaysia being Peninsular Malaysia to the west and East Malaysia to the East.
Peninsular Malaysia is located south of Thailand, north of Singapore and east of the
Indonesian island of Sumatra. East Malaysia is located on the island of Borneo and
71
shares borders with Brunei and Indonesia. Its geographic coordinates is about
2°30 N 112°30 E.
Figure 3.8: Malaysia
3.8
Site Description
For the study in this thesis, GPS data were collected continuously over 3
consecutive years, 2000, 2001, and 2002. There were altogether 18 stations called
MASS, with 11 allocated within the peninsular and the others in East Malaysia. They
are allocated not lesser then 300km apart from one another, dispersed around the
West and East Malaysia. They are referred to collectively as ARAU, allocated in
Perils, USMP, allocated in Penang, KUAL, allocated in Kuala Terengganu, GETI,
allocated in Kelantan, IPOH, allocated in the town center of Perak, KUAN, allocated
in Pahang, BAHR, allocated in INSTUN-Perak, KTPK, allocated in Kuala Lumpur
Jupem
Headquaters, SEGA, allocated in Segamat Johor, UTM, allocated in
Universiti Teknologi Malaysia, Johor. Those in East Malaysia are as BINT, allocated
in Bintulu, Sabah, LABU, allocated in Labuan, MIRI, allocated in Miri, Sarawak,
MTAW, allocated in Tawau, Sarawak, SAND, Sandakan and KUCH as in Kuching,
Sarawak.
72
Malaysia lay on one similar plate and the faults line that goes across the
South East Asia goes around the East and West Malaysia along the Andaman Islands
of Sumatra to the Celebes Island of Indonesia, known as the Ring of Fire that faults
all through Japan bending above the Pacific Ocean to Europe and Hawaii.
3.9
Previous Regional Campaigns
The campaigns carried out around this region helps to portray how the
geodynamic activities are around Malaysia and South East Asia. GPS is use to
measure fault motion. Stations near active faults move relative to each other and to
identify this several stations are occupied at the same time, and all stations observe
the same satellites, the relative positions of all the stations can be determined very
precisely. Distances between stations could be determined even over distances up to
several 100 km, to better than 5 millimeters (about a 1/4 of an inch). Reoccupation of
the same stations are carried out, thus, the stations movement could be determined. If
stations are located on different plate zones faults or slips could be identified by
analysis and least square computation.
3.9.1
GEODYSSEA
The participation of 14 countries, 6 from Europe, 7 from South-East Asia
including Australia, defined to address the plate motions and crustal deformations
deduced from space geodetic measurements for the assessments of related natural
hazards in South East Asia conducted the GEODYSSEA projects. The project
generated a large amount of new information on the tectonic processes in the region.
Two consecutive projects for were conducted in 1994 and 1996. This was when the
Malaysian national network was tied onto the global reference frame with the
collaboration of the Department of Survey and Mapping Malaysia and the IfAG. 16.5
months of gap between the campaigns were given to observe the estimated tectonics
motions in the region.
73
GPS was used to provide a stand-alone result during the project analysis. The
triple junction of the Eurasian, Philippines and the Indo-Australian Plates were
investigated for their deformation and determining the current magnitudes, directions
and rates of motion occurring. An important additional benefit to the region is to
derive the precise three-dimensional coordinates of the GPS stations, which have
been provided in a global reference frame. These points are used to connect the
national geodetic networks in the various countries to the global reference frame and
to integrate the results of other geodynamic projects into a common system. 11
permanent stations of the global network of the International GPS Service for
Geodynamics (IGS) were included in the analyses.
3.9.2
APRGP
APRGP stands for ASIA AND PACIFIC REGIONAL GEODETIC
PROJECT (APRGP) its primary is to facilitate the establishment of a single regional
datum through a network of compatible geodetic datums. This project is also carried
forth by DSMM with the first campaign in 1997.
3.9.3
GDM2000
The launch of the new Geocentric Datum of Malaysia (GDM2000) was in
August 2003. It is an effort by the Department of Survey and Mapping (JUPEM) to
fit Malaysia survey and mapping products into the global geodetic framework. The
GDM2000 reference the datum to GRS80 ellipsoid. From this the new datum the
Geocentric RSO and Geocentric Cassini coordinates are generated.
74
3.10
GPS network for Geodynamic Monitoring cum Reference Frame
The coordinate system realization brought forth some solutions as listed
below:
1. To define frame requires origin, orientation and scale
2. Origin can be determined with one fixed site but any error in this site will
translate to other stations
3. Orientation defined by EOP values but errors again will propagate into all
sites
4. Scale may or may not be a problem. GPS should have well defined scale.
5. When minimum constraints used to define frame then baseline lengths
and rates of change of baseline length not affected
6. If system is over constrained (i.e. two or more sites fixed) then baselines
will be affected.
3.11
Velocity
Ideally according to Brockmann 1996, the velocities estimates would utilize
high quality daily solutions spanning multiple years. However, it more practical and
might even be necessary to derive velocity field from two or three campaigns
spanning a time period of less than two years even though, the velocity estimates will
be considered with some degree of scepticism.
3.11.1 Velocity frame
•
Similar arguments apply to velocity
•
Velocity of one site to fix translation rate
•
Rates of change of EOP for orientation rate
•
Scale rate -- Not clear if should exist
75
3.11.2 Absolute.
Absolute velocities in some expression of an ITRF reference frame. This
solution provides velocities in an absolute global reference frame. Deformation
across plate boundary zones and changes in velocities within the region of
observation where the fault lines runs across would be taken to be as absolute
velocity.
3.11.3 Relative.
Estimate velocities relative to one or more stable stations. This can also be
called local or regional velocity estimation. This method is used when the
deformation of interest is contained within a region that is either not well aligned to
the ITRF reference frame, or where the velocity field is small relative to the ITRF
velocity of the region so that estimating absolute velocity fields would yield
solutions that are completely dominated by errors and the ITRF velocity field. For
instance, motion that is completely contained within a tectonic plate is considered as
relative velocity.
3.11.4 Absolute-Free Velocities
Velocities are estimated in the global ITRF reference frame by minimizing
the rotation and translation transformation of at least two or three stations onto the
existing ITRF apriori coordinate system.
3.11.5 Absolute-Fix Velocities
The coordinates or velocities of one or more stations are tightly constrained
or fixed to their input apriori values. This is done when only one or two regular IGS
76
stations are included in the network processing. Velocities are estimated by tightly
constraining the coordinates and velocities of one or two stations onto their
predefined ITRF values. For fixing of coordinates or velocities on more than four
reliable stations are called as over-constrain.
3.11.6 Relative-Free Velocities
Velocities are estimated by minimizing the translation and rotation
transformation of at least two stations onto their apriori coordinates. The velocity of
these stations is considered to be zero.
3.11.7 Relative-Fix Velocities
Velocities are estimate by tightly constraining the apriori coordinates of one
or two stations. The velocity of these stations is considered zero.
3.12 Summary
Geodynamic studies covers many parts from the geology aspect, geophysical
perspective, in other words can also be said from the core of the earth to the
constellations that holds the earth together. However, in this study the geomatic
perspective of the geodynamic study is look upon. Therefore, the movements of the
plates observed from continuous GPS observations will be discussed later in the
following chapter.
Chapter 4
DATA PREPARATION & PROCESSING
4.1
Introduction
Methodology of this study consists mainly of the preparation part and the
processing part. It also describes how the data and the machine were set up before
the consequent processing can be done. The final output and analysis are described in
chapter five. However, there are stages to be considered in the preparation and
phases to be looked into during the processing. Each of this is crucial and is essential
to be carried out well before proceeding to the next stage or phase. The processing
phases are interrelated and the accuracy of the results very much depends on the
reliability of the former level.
4.2
Data Acquisition
Data for this research study was acquired from few different sources. Some of
the data are attained locally, for instance, GPS data for each MASS stations located
around East and West Malaysia were taken from 3 consecutive years from the
Department of Survey and Mapping Malaysia (DSMM), Geodesy section.
Regionally, IGS data of the global stations were retrieved by downloading them via
internet for all 11 permanent stations relative to the local stations. The precise
ephemeris for each GPS days was also downloaded from the IGS ftp site.
78
4.3
Data Preparation
The hourly MASS data was acquired from DSMM headquarters for 1st
January 2000 up to 31st December 2002. Most of the data was already archived in a
24hours daily compact rinex zip form. These data were then scanned through teqc for
quality and checking for errors in the header. Essentially, the monument name, dome
number, antenna and receiver pair type, and the antenna height. Data were decimated
to 30seconds interval and kept in the RAW folder in the campaign directory. Data
with too many missing observation can be predicted to cause inaccuracy in the
processing later.
IGS stations scattered around the Malaysian parameters were selected to its
availability and to the period of establishment of the station which will determine the
stability of the data collected. These data are usually readily ‘teqc’ed. However, this
does not mean that they are free from causing problems to the results later on. Thus,
the data quantity has to be checked before processing can even take place. Low
quality and inadequate data quantity of lesser than 12 hours observation should be
identified and listed out.
4.3.1
TEQC
The preliminary data quality evaluation was performed by using the TEQC
(Translation Edition and Quality Control) software developed and maintained by
UNAVCO (University NAVSTAR Consortium). Initially there were 17 IGS stations
selected to be potentially available scattering around the MASS covering an area
within few thousands of kilometers. We can retrieve the MP1 and MP2 to indicate
the receiver quality on both frequencies. The smaller the value represents that the
performance of the receiver is better and thus less cycle-slips are avail and more
observations could be acquired. ( 2000, et.al. Fazan)
79
4.4 Bernese Version 4.2
Bernese is a high precision GPS processing software. It is utilized to handle
huge amount of GPS data. It is design to process these GPS files in taking into
account many errors to be estimated, corrected, or modelled. It comes with the
capability to improve on the residuals of the processed GPS data in form of baseline
by iteration on the data screening before the daily network can be formed.
Some files are needed before a bernese processing could take place. The files
needed are as following:
GEN sub directory- also known as the general file. This file keeps all the
basic script needed for the processing. Some scripts are static and do not need to be
updated like: However, some need to be updates every time a new project or
research is to be processed, for instance, the C04_*.ERP-the earth rotation
parameters script SAT_*.CRX-the satellite problem script. Both of this information
needs to be downloaded from the AIUB site (ftp.unibe.ch).
Script like, *_.STN, *_. CRD, *_.BLQ needs to be created. *_.STN, station
abbreviation script could be created manually or by using Bernese software, *_.CRD,
station apriori script, the same could either be manually keyed in or generated with
Bernese. *_.BLQ on the other hand, needs to be retrieved by uploading the initial
apriori station coordinate via internet to the ocean loading provider.
4.4.1
RINEX Files
The RINEX (Receiver Independent Exchange ) files carries signals L1, C1,
L2 and P1 which is encrypted. for all the observed satellites at an epoch of time. This
file is in a binary format and comes in two forms, the observation file and the
navigation file. Amongst the most important information in the RINEX file is the
header. The header of a RINEX file carries the station name also known as the
Marker Name, the antenna and receiver used for the observation, the approximate
80
station position in geocentric XYZ, date and time of observation, interval of
observation. The H value is the antenna height measured from mark of measurement
to BOTTOM OF ANTENNA.
In Bernese it is important that the information on the header of this RINEX
files is compatible to the software. It is needed that the “Marker Name” be in only
four character and the character on each line do not exceed 80.
4.4.2
Ocean Loading Files
The ocean loading values for each station can be acquired via Internet on the
Onsala site. Apriori file is needed here from the Bernese computation which carries
the approximate geocentric values, if best the final geocentric values of each station
to be used in the processing. These geocentric values of each station are forwarded to
the Onsala site before the ocean loading files can be computed and used as the ocean
loading correction files in the Bernese processing.
4.4.3
Apriori Files
Apriori file is the coordinate file for all the stations being processed in the
Bernese software. This value can first be estimated and updated to be refined during
the baseline formation. However, during the final network solution this files is best
the generated and reused for the computation. The rms in the apriori files represents
the observations rms not the coordinate rms. The longer the observation of the point
the better is this rms. Final coordinate generated after daily network is form must
carry the most reliable coordinates and this can be make justified by looking at the a
posteriori sigma of the network to be less than 3cm.
81
4.4.4
Velocity Files
When velocity is estimated, the reliability of the results is based on the
computation of reasonable statistics. This requires the ADDNEQ program to be run
multiple times. Some of the factors that need to be highlighted while generating the
velocity are:
1.
Properly weight the input NEQ files
2.
To estimate the velocity of the stations
3.
To compute reasonable statistics of the repeatabilities
4.5 Data Processing
TRANSFER
ORBIT
RNXOBV3
PRETAB
Code Zero
Difference
Phase Zero
Difference
CODSPP
Code Zero
Differences
MAUPRP
Phase Zero
Differences
SNGDIF
Code Single
Differences
ORBGEN
Phase Single
Differences
ADJUSTMENT
NETWORK
Phase Single
Differences
Figure 4.1: Bernese Concise Processing Diagram
Atmospheric
Correction
82
4.5.1
RXOBV3 (Transfer Part)
Generating files from the RINEX format to the Bernese Format using the
program RNXOBV3. The campaign has now been set up and all necessary files are
available. The first part of processing consists of the transfer from the RINEX into
the Bernese (binary) format. In our example only the RINEX observation files have
to be transferred (we do not use the broadcast orbits at all). This is the task of
program RXOBV3 in Menu 2.7.1. When working through the examples, remember
that the online help system describing all options can be invoked by pressing F1 . It
is recommended that we use the AIUB strategy as it is strongly recommended in the
help files and recommended by the creator of the software.
Figure 4.2: Transfer Menu
If the user leaves the option RINEX blank, a selection list of all of the raw
observation files will be displayed after this menu. Type “s” in the first column to
select individual files or “Ctrl-D” to enter the system command level followed by “S
ALL” to select all files at the same time. Thus all the raw observation files will be
selected to be transferred all at the same time. In the two panels above all the options
for RXOBV3 are specified. The program produces an output file RXOBV3.L* in the
directory P:/MASS/OUT. This file may be browsed using the JOB command. After
having run program RXOBV3 the menu system automatically creates the zerodifference
observation
/MASS/DATPAN .
lists
OBSLIST.CDZ
and
OBSLIST.PHZ
in
P:
83
4.5.2
PRETAB & ORBGEN (Orbit Part )
In this processing example we use only two programs of the orbit part of the
Bernese
GPS Software. The first program is called PRETAB and may be accessed
using Menu 3.2. This menu handles two programs: PRETAB and BRDTAB. Which
of the two is actually used depends on the type of orbits (precise or broadcast)
available. We use precise orbits here. AIUB recommend to use the consistent precise
pole files in a high precision work. In this process the file C04_2000.ERP are used
carrying the information of the Earth rotation parameters. The main task of PRETAB
is to create tabular files for both days of the campaign and to transform the precise
orbits from the terrestrial into the celestial reference frame. Run the program
separately for each session, in other word, for each day of the 3 years adapting the
output file names accordingly. The program generates a satellite clock file, too. This
file will be needed in program CODSPP (see below) if no broadcast orbits are used.
Figure 4.3: Orbit Menu
Generate a source-independent orbit representation where the orbits are
tabulated then tabulated for Bernese processing using the PRETAB and ORBGEN
program. Clock files of the satellites are generated. It prepares the so-called standard
84
orbits using the satellite positions in the tabular orbit files as pseudo-observations for
a least squares adjustment.
Figure 4.4: Standard Orbit Generation Menu
The planetary ephemeris file DE200 is located in the directory $X/GEN. It
contains the JPL ephemerides for Moon, Sun, and Planets. It is not part of the
Bernese GPS Software; therefore, it must be downloaded separately from JPL or
from the AIUB ftp site. The program produces an output file ORBGEN.L* (for each
run) which should look like the following:
85
Figure 4.5: Result for ORBGEN Program
The most important information in the output file are the rms errors for each
satellite. These should not be larger than about 10 cm if precise orbits were used
however, the actual rms errors depend on the quality of the precise orbits, on the pole
file used for the transformation between ITRF and ICRF in PRETAB, and on the
orbit model used in ORBGEN. Rms errors between 5 and 10 cm as they occur in our
example are due to small inconsistencies between the precise orbits COD96*.SP3
and the pole information in C04_2000.ERP. The output will be as follows:
Figure 4.6: Result for ORBGEN Program
86
4.5.3
CODSPP
Processing of the code files for each single station where the old apriori form
the ITRF 2000 coordinate files is compared to the new apriori from the observation
of each station is done. Zero- differencing for each individual station. This is the
processing part of the Bernese 4.2 software. Five runs of this program would have to
be done. The first program is called CODSPP. Its main task is to compute the
receiver clock corrections. The orbit information in session-specific files (standard
orbit files), CODSPP have to be run for each session.
Figure 4.7: Input Menu for CODSPP
Figure 4.8: Determinig the Atmosphere Models
87
If a geocentric coordinates of good quality is not available in the first run
specify a coordinate output file in Panel 4.2 to save the coordinates estimated by
CODSPP. This can be use for as the priori. CODSPP produces the following output:
Figure 4.9: Result from the CODSPP program
The most important message in the output file is CLOCK OFFSETS
STORED IN PHASE OBSERVATION FILE. If this message appears in the output
you are sure that the receiver clock corrections computed by CODSPP were actually
stored not only in code observation files but also in the phase observation files. After
this step the code observations files are no longer being used. The a posteriori rms
error (for each zero-difference file processed) should be checked in the output file
from the program CODSPP. Without SA a value of about 3 m could be expected if
88
P-Code measurements are available. However, much worse code measurements
would still be sufficiently accurate to compute the receiver clock corrections with the
necessary (1 µs) accuracy.
4.5.4
SNGDIF
Forming of baselines and single differencing of receiver-to-receiver
difference where the receiver clock errors are eliminated. Observation on the phase
single difference files will be edited and saved. Double differencing is then carried
forth then triple differencing is done to detect the cycle slips on each frequency. The
second processing program is called SNGDIF and may be activated in Menu 4.3.
SNGDIF creates the single differences and stores them in files. Here, the strategy
OBS-MAX and SNGDIF have to be run independently for each session:
Figure 4.10: SNGDIFF program Menu 4.3
4.5.5
MAUPRP
The observables are then marked and cycle slips are fixed. New ambiguity
integer introduced for discontinuity in the observation and the phase single difference
files are edited and saved again. The main task of program MAUPRP, is the cycleslip screening. Separate program runs for each session using the following options:
89
Figure 4.11: MAUPRP Program Menu 4.4.2
Figure 4.12: MAUPRP Input Menu 4.4.2-1
It is not necessary to run program MAUPRP more than once on each
baseline. However, it is mandatory to run MAUPRP again if program SNGDIF is restart which will re-create the baseline(s). The same case here as in SNGDIF, if an
accurate geocentric coordinates for the sites process not available, specify a
coordinate output file in Panel 4.4.2 to save the coordinates estimated by MAUPRP.
In this case not to save the changes done by MAUPRP into the observation files
(option SAVE SCREENED FILES in Panel 4.4.2–1) but to start the program
MAUPRP for a second time using now the a priori coordinates stemming from the
first run.
90
4.6 Adjustment - Parameter Estimation
Weighted least-squares adjustment applied in the GPSEST run. Mathematical
correlated within the entire sub-network are correctly modeled. The elevationdependent observation-weighting model adopted assumes a zero-difference
observation sigma being proportional to 1/cos(z), where z denotes the satellite zenith
distance angle.
GPSEST I
RESULTS
RESRMS
SRVOBS
GPSEST II
NEQ
FILES
GPSEST IV
GPSEST III
Figure 4.13: Diagram of the Daily Adjustment of the Bernese Processing.
4.6.1
Parameter Estimation GPSEST I
This program forms the ambiguity free solutions using L3 linear combination
fixing on the first station. In this run the troposphere biases of the network is
estimated and residual of the network is saved. The least-squares adjustment is the
task of program GPSEST, accessed by Menu4.5. It is a good idea to start GPSEST
first in the session mode and to produce an ambiguity-free L3 solution. Do not expect
any final results from this run but check the quality of data and save the residuals
after the least-squares adjustment.
91
Figure 4.14: GPSEST 1 Menu 4.5
Figure 4.15: Output files for GPSEST1
It is important to check all observations in this run. Consequently the program
run might be time consuming. The ambiguities may not be pre-eliminated if residuals
should be written into the residual output file. An important information in the output
file is the a posteriori rms error. A posteriori rms error of about the range of 1.0 and
1.5 mm is expected. If the rms error is significantly higher this may mean that either
the data stems from low-quality receivers or that the data was collected under
92
extremely bad conditions or that the pre-processing step (MAUPRP, CODSPP) was
not successfully performed.
4.6.2
RESRMS
If the residuals have been stored in the files (Panel 4.5–0) it is possible to
screen the residuals manually using the program REDISP in Menu 5.3.1 or
automatically using the program RESRMS in Menu 5.3.2. Program RESRMS
produces an output file, which may be used, by the program SATMRK to mark
outliers. Process all baselines separately and resolve the ambiguities using the QIF
strategy. The following panels show the GPSEST options used for that purpose.
Admittedly, it is cumbersome to process the baselines “manually” one after the other.
This baseline-processing mode is necessary because of the tremendous number of
parameters. The attempt to resolve the ambiguities in a session solution might require
too much CPU and memory to be feasible. However to ease the processing for the 3
years data the Bernese Processing Engine was used to automate this processing step.
4.6.3
SERVOBS
Plotting of the residual files for each baselines and eliminates residuals more
than 0.0025m on the L3 frequency. Data pieces of lesser than 6 minutes will be
deleted.
4.6.4
GPSEST II
Ionosphere is modelled using L4 geometry-free linear combination. All
stations are fixed on their a priori values for this run.
93
4.6.5
GPSEST III
Ambiguity resolution using the QIF strategy is carried out. Taken into
account all the parameters that was model and estimated on the previous runs.
Ionosphere and ocean loading parameters are introduced. Ambiguity is resolved on
each frequency individually for each baseline. The troposphere estimates from the
previous network solution is introduce. Alternatively, if no tropospheric estimates are
considered, the set up of tropospheric parameters for each QIF ambiguity resolution
run is required. Pre-elimination handling for each parameter type can be controlled
individually.
For ambiguities and differential ionosphere parameters, however, the preelimination can be enforced already in Panel 4.5.1, and Panel 4.5–2.4.7,
respectively. So, for the current GPSEST run, the Panel 4.5–2.4.8 might be
suppressed by setting “NO” for the corresponding option in Panel 4.5–2.4.
In the first part of the output generated by program GPSEST the selected
options are echoed. Then the results of the initial least-squares adjustment
(ambiguities estimated as real values) are given.
First, the individual iteration steps are described. Ambiguity resolution will
influence other parameters. The results of the ambiguity-fixed solution are given in
part 2 of the output. Usually on average if there is no much problem in the data an
output from altogether 110 ambiguities 88 ambiguities could be resolved. This is not
a bad result for the QIF strategy considering the fact that the baseline length about
thousands of km apart.
After the loop over all baselines is completed and the ambiguities are
resolved, use the program GPSEST in the session mode. In Panel 4.5, not including
the troposphere file as in the baseline runs, but will estimate the troposphere
parameters in Panel 4.5–2.4. In Panel 4.5 all the single difference files of the
corresponding session are selected.
94
4.6.6
GPSEST IV
Daily solution is produce here in both coordinate (CRD) and normal equation
(NEQ) form. S store site coordinates and normal equations in a file named
UTM_00XXX.CRD and UTM_00XXX.NEQ respectively (the extensions are
automatically added from the entries in Panel 0.3.4). Note that GPSEST
automatically generates normal equation files with the extension *.NQ0 to be used
with the new ADDNEQ2 program as well. Important changes have to be made in the
following panels.
Figure 4.16: Menu 4.5-2.4 GPSEST IV program
The ionosphere-free (L3) linear combination is processed. No station is kept
fixed. Ambiguities, which have been resolved in the previous runs of program
GPSEST using the QIF strategy, are introduced as known. The unresolved
ambiguities (estimated as real-valued parameters) are pre-eliminated. It is possible to
use a higher sampling rate. No station is fixed on its a priori position in Panel 4.5–1,
thus, the coordinates of all stations will be treated as unknown parameters. This is
very important to retain the flexibility for later changes of the reference frame
(station constraints) using the program ADDNEQ. However, for numerical reasons it
is necessary to constrain the coordinates of one station using the following options
(the constraints may be removed in ADDNEQ again – see below):
95
Figure 4.17: Menu 4.5-2.4.B
For the final definition of the geodetic datum, use ADDNEQ, also in the case
of having one single normal equation file, only. The estimation of troposphere
parameters is mandatory for a campaign of this type. Increase the number of
estimated parameters (here author uses, 24 instead of 12 parameters per station and
session). In order to keep the size of the resulting normal equation file within
reasonable limits, it does make sense to pre-eliminate this parameter type “after
inversion” (see Panel 4.5–2.4.8). The advanced user stores the full normal equation
system and creates a second, reduced normal equation file using ADDNEQ (and preeliminates the tropospheric parameters there). The large NEQs may be used to
retrieve best possible tropospheric parameters by substituting, e.g., weekly
coordinate results; the small, space-saving NEQs may be kept on-line and used for
later long-term coordinate analysis. Compare the coordinates stemming from
sessions using a 6-parameter Helmert transformation (program computing the
Helmert transformation is accessible through Menu 5.4.2).
4.6.7
Troposphere Estimation
Zenith path delay parameters are solved for at 1-hour intervals for each
station. At the end of each week, the 7 daily sets of troposphere estimates are recomputed on the normal equation level by substituting the 7-day combined station
coordinate results. Troposphere gradient parameters are considered solely within the
scope of test solutions making use of low-elevation data.
96
4.6.8
Ionosphere Modeling
Regional TEC maps are derived from the geometry-free linear combination
(L4) double differences. The ambiguity-free maps are used to improve the QIF
ambiguity resolution. The ambiguity-fixed TEC maps are made available in IONEX
format but were not generated here however the ionosphere parameter is modelled to
dry-Neill. Not modeled (ionosphere eliminated by forming the ionosphere-free linear
combination of L1 and L2). Regional ionosphere maps are generated in order to
improve the QIF ambiguity resolution.
4.6.9
Ocean Loading Parameters
Solid earth tidal displacements are modeled according to displacements IERS
conventions 1996. Ocean loading corrections are computed based on Scherneck'
s
amplitudes and phases. No atmospheric loading corrections are taken into account.
4.6.10 Ambiguity Resolution
Ambiguity resolution is performed by using the quasi-ionosphere-free (QIF)
strategy in conjunction with regional TEC information for regions near to the equator
low latitudes.
4.6.11 Weekly Solution
ADDNEQ is done manually, where the daily NEQ files are combined on each
GPSWEEK to form the weekly solution NEQ files. This is the most tedious stage of
the three. Whilst having to analyse on all the output to the ambiguity resolution
summary file the ITRF2000 coordinates are tied to the mid-week of the GPS week
and compared to the combine solution of that particular week. Weekly free solution
97
is compared in Helmert transformation to the ITRF2000 coordinates. IGS stations
with very poor rms values, which are more than several millimetres in horizontal and
vertical component, are not fixed.
This weekly solution is generated again on the fixed IGS station as selected
previously and analysed. The rms value for the residuals for the horizontal
components are preferable to be less then 10mm and rms value of about 10 to 15mm
in the vertical component. Large rms values on any of the station days will contribute
to the inaccuracy and propagate throughout week to the other stations. Those values
that are outliers to the repeatability of the components through the week will be
inserted to the STACRUX file to be left out for the weekly solution. Thus, this is
done iteratively until a solution of satisfactory rms values as described above is
achieved.
4.6.12 Helmert Transformation
From the Helmert transformation the results between the sessions should be
consistent on the millimeter level. The last program to be used is program ADDNEQ.
This program produces the final solution by stacking the *.NEQ files. If there are
two *.NEQ files (each file stemming from one session) and there are no correlations
between the observations from different sessions, ADDNEQ gives exactly the same
results as GPSEST when processing both sessions together. Processing each session
separately with program GPSEST and combining the *.NEQ files with program
ADDNEQ is much more efficient, however.
The coordinates of station Wettzell were kept fixed on their a priori values
(flag “F”). The result obtained from the program ADDNEQ differs up to 4 mm from
the arithmetic mean of the two coordinate sets UTM_00XXX.CRD and
UTM_00XXX.CRD. This is simply due to the fact that ADDNEQ takes the full
covariance information of the daily solutions into account.
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4.6.13 Generating Velocity
Velocity can be generated after the finalized NEQ files are combined in the
GMT software. The NEQ files of the whole year are stacked and compared. Later the
whole NEQ of three years processing are stacked and compared to NUVELL-1A.
Utilising GMT and Grapher software each MASS station time series can be
plotted in all three variable against time.
4.7
Summary
The Bernese processing software is a high precision GPS processing software
which takes into account many parameters before a reliable final coordinate can be
achieved. The errors that contribute to the deviation of the coordinates are either
estimated, or modeled and corrected to the coordinate. The strategy used in the
processing is guided by the recommended strategy provided by the AIUB and also
can be view in its help file menu. The processing is tedious especially during the data
preparation phase. It is very important to note that if the data input to the processing
is bad means the output result will also be bad.
Chapter 5
RESULTS AND ASESSMENT
5.1
Outcome and Reliability
The final result to meet the motivation of this research for all three years
2000, 2001, 2002, will consists of 156 GPS weeks and 32 stations. 17 MASS stations
and 15 IGS stations were used that encompasses an area of latitude 29° 39’ 26”.423N
to 29° 02’ 47”.607S and longitude of 72° 22’ 12”.852W to 144° 52’ 06”.102E. These
preliminary results are taken from observations of the first four weeks of each
respective year from 2000, 2001 and 2002. Processed using software Bernese GPS
Version 4.2 mounted on Red Hat Linux 8.0 workstation was carried out. Two
strategies are adopted to obtain optimum results and to check for outliers for the final
adjustment those are Free Network with introduction of Helmert Transformation and
heavily constrained adjustment. However, in this study the former strategy is adopted
that is commonly used by GPS high precision software user and recommended by
AIUB.
The result below shows the ambiguity resolution for the QIF solution for the
daily processing of DOY 001 which is the first day of the year 2001. This result is
about the same throughout the year with 90% of the baselines having at least 70%
their ambiguity resolved. The least resolved baseline here is GELH0011 with a
baseline of nearly 3000km from station GETI in Kelantan to LHAS in Tibet, China
with 65.5% ambiguity resolved for DOY 001. The BPE generated baseline using
SHORTEST as the strategy as laid in the methodology chapter, LHAS is an end
point in the GPS network thus the where four baseline were form from GETI, thus,
error propagate to GETI –LHAS baseline.
100
Figure 5.1: Ambiguity resolution percentage of first day of year 2001
The main purpose of the free network adjustment with the introduction of
Helmert Transformation was to adjust the weekly normal equation on float and
freely. Then Helmert Transformation of 7 parameters on 15 IGS stations to
determine the internal reliability of the network and detecting the outliers. Only
reliable IGS stations with acceptable RMS residuals are fixed.
Reference velocity was introduced for the fixed stations and all the final
coordinates for all stations were transformed to the middle of the observation week.
For instance 5th January 2000 for the first week of year 2000, thus, the program
RUNGPS COOVEL will reference the other days within the week to the mid-week.
101
Figure 5.2: RMS of Residuals of Observations
Figure 5.2 is plotted from the RMS residuals of the first GPS week from the
year 2000. Where station in Kinabalu was not functioning for the whole week till
middle of the following week and stations in Segamat and Sibu were not yet
operational till the end of year 2001. From the graph, it can be concluded that the
RMS residual of the MASS stations from the free network adjustment is lesser than 1
to 5 mm in horizontal component and 3 to about 9 mm in vertical component for the
first week of the year 2000. Basically, the average RMS residual for the MASS
stations throughout the first four weeks of each observed year falls lesser than 5mm
and 10mm for horizontal and vertical component respectively.
It can be seen that the northing component for ARAU is larger by more than
half of the vertical component. This could be assumed due to the quality of the GPS
observation at ARAU for week 1043 is considered low.
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Figure 5.3: Daily RMS
Figure 5.4: Weekly Residual RMS GPS Week 1046
However, it was found that GPS week 1046 on KUAN gave residual RMS of
more than 10mm in the vertical component. This could be concluded that the
103
troposphere zenith delay (TZD) was high and is major factor influencing this
abnormality. In this case, the hourly-generated troposphere parameter should be
analysed and those with high standard deviation of more than 0.01 and gave a jump
in the TZD value should be eliminated.
The overall daily RMS for unweighted combined GPS solutions for
horizontal component is below 5mm and less than 7mm for vertical component. This
was true for the first few months of all three years however, the trend might change
in the consequent months.
Figure 5.5: Formal Accuracy of the coordinate, week 1046.
Formal accuracy shows the quality of the observation for the X and Z
components are much better than that of the Y component of which on the equatorial
region Y is the up value for ITRF coordinate. However, a KUAN show a peak in the
Y component is reflects in the residual RMS the Up component almost doubled the
other MASS stations. Therefore it is evident that the vertical component of the
observation quality will directly influence the final result to the rms residual of the
same station.
104
UNW EIGHTED W EEKLY SOLUTION RESIDUAL RM S
9
8
7
RMS (mm)
6
N
5
E
4
U
3
2
1
0
1043
1044
1045
1046
1095
1097
1098
1147
1148
1149
GPS W EEK
Figure 5.6: Overall Weekly Residual RMS
The combined overall weekly solutions of the first month of all three years
are plotted as above. The horizontal components falls below 5mm within a range of
3mm in difference and the vertical component falls below 9mm within a range of
4mm in difference. The north component produces a smoother graph and the vertical
component draws a purtabing graph.
5.2
Helmert Transformation
The is the comparison made from one final coordinate against the apriori
coordinate to determine the reliability of the stations. The stations not falling in the
reliable rms accuracy will not be constrained or fixed on. In APPENDIX A shows
that not all the IGS station that have be use in the processing can be fixed on. IISC,
MALD and DAGR have very high residual rms for all the components, thus, the
stations proof to be unreliable.
105
5.3
Final Coordinates
The MASS final coordinate after the 3 years processing is not much different
from the final coordinate from the GDM2000. The difference starts on the third
decimal place. The following table shows ARAU MY that is the final coordinates
from this study and ARAU GDM means the final coordinate from the JUPEMS
GDM 2000. It shows that for station ARAU the difference for both X and Y
components are on the third decimal places whereas, the difference in height is on
the 5th decimal place. For UTMJ, the difference in the final coordinates shows in the
third decimal place ±0.0061, ±0.0043, ±0.0044 respectively.
Table 5.1: Final Coordinate Difference
X(m)
Y(m)
Z(m)
ARAU MY
-1131051.8751
6236311.7337
711748.1600
ARAU GDM
-1131051.8682
6236311.7355
711748.1609
±0.0069
±0.0018
±0.00009
UTMJ MY
-1503510.1031
6196042.4776
173119.9116
UTMJ GDM
-1503510.1092
6196042.4733
173119.9160
±0.0061
±0.0043
±0.0044
DIFFERENCE
DIFFERENCE
APPENDIX B shows the final coordinates for all the stations of which 15
MASS which are the stations that are available from year 2000 till the year 2002 and
15 IGS station.
APPENDIX C shows the a posteriori sigma unit weight to be 0.0023m, this
shows that the processing is reliable since 0.003m is the maximum a posteriori sigma
unit weight recommended.
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5.4
Station Velocity
Figure 5.7: Velocity for year 2000-2002 for the first months
Magnitude of the movement in the preliminary result is 3cm per year based
only to the first month of each year. The movement of both West and East Malaysia
is to the South-East direction. However, the more north it goes from the East
Malaysia, the direction of the motion of the MASS stations rotation to the South
increases compares to West Malaysia which is rather parallel in direction.
Referring to APPENDIX E on the whole velociy on the X component –0.02m
per year, the Y components has an average velocity estimation of –0.01m per year.
Figure 5.7 shows that station KUCH have a large error amongst al the 15 MASS
sites, and UTMJ is the site with the smallest error.
107
5.5
Residual Graphs
Fit Results
Residuals (Meter)
North Component
0.04
0.02
0
-0.02
-0.04
0
4
Weekly Solution
East Component
Figure 5.8: GMT Plot of station ARAU
Residuals (Meter)
Fit 1: Linear
Equation Y = -0.002788484848 * X + 0.01738666667
Number of data points used = 10
Average X = 5.5
Average Y = 0.00205
Residual sum of squares = 0.000112974
0.04
8
Fit Results
Fit 1: Linear
Equation Y = 0.003749090909 * X - 0.02452
Number of data points used = 10
Average X = 5.5
Average Y = -0.0039
Residual sum of squares = 0.000198746
0.02
0
-0.02
-0.04
0
4
Weekly Solution
8
Residuals (Meter)
Height Component
0.04
0.02
0
-0.02
-0.04
0
4
ARAU
Weekly Solution
8
Figure 5.8: Residual Weekly Graph
The residual weekly plot above shows the Northing, Easthing and height
component of Arau. The best fit line is drawn across the graph and intersects the Y
axis at and about the 2 cm mark. These are also true for most of the other stations
plot that could be found in the APPENDIX D. There is no great spikes to be found
on the plots. Difference between the residual components to the best fit line is lesser
than 1cm for all three components.
The Northing gradient has a negative slope that progressively moves
downwards, whereas, the Easthing gradient have a positive slope progressively
moves upwards. However, for most of the height component for the MASS stations
are nearly horizontal and paralell to the X axis.
For some station especially the newly established ones, their Easthing
components to intersect at more than 2cm mark, therefore, it means that the residual
rms is big and not reliable.For instance, GETI and BINT they have the intersection at
108
nearly 3cm for East components and BINT have both North and East components
above 2 cm.
CHAPTER 6
SUMMARY AND CONCLUSION
6.1
Summary
The velocity of the plate where Malaysia is located is moving at an estimated
velocity rate of 2-3cm per year. It is moving in one common direction and the stations
are relative to one another. With an a posteriori sigma weight of 0.0023mm show the
reliability of the processing strategy using the recommended strategy by AIUB. Thus,
with continuous observations on the MASS stations it is possible to derive estimated
velocity, which means the preliminary geodynamic study of Malaysia.
6.2
Other Methods of Detecting Earth Deformation
Field studies of several extensional basins along the northern margin of the Gulf
of Aden in Yemen show that Oligocene–Miocene syn-rift extension trends N20jE on
average, in agreement with the E–W to N120jE strike of main rift-related normal faults,
but oblique to the main trend of the Gulf (N70jE). These faults show a systematic
reactivation under a 160jE extensional stress that we interpret also as syn-rift. The
occurrence of these two successive phases of extension over more than 1000 km along
the continental margin suggests a common origin linked to the rifting process. After
discussing other possible mechanisms such as a change in plate motion, far-field effects
110
of Arabia–Eurasia collision, and stress rotations in transfer zones, we present a working
hypothesis that relates the 160jE extension to the westward propagation since about 20
Ma of the N70jE-trending, obliquely spreading, Gulf of Aden oceanic rift. The late
160jE extension, perpendicular to the direction of rift propagation, could result from
crack-induced extension associated with the strain localization that characterizes the riftto-drift transition.
6.3
Recommendations
With the availability of more up-to-dates technology the possibility of predicting
the movements of the plate might not be far from reach, however, still it is unclear of
how to achieve the accurate real-time movements of this motion. Detecting of the plate
motions is possible with motion sensors located near faults lines.
Integration between positioning system like, the GALILEO, GLONASS, GPS and the
upcoming L2C and L5 frequencies show that there are doors to this possibilities that
some day the plate movements will be able to be monitored on a real-time basis. Thus,
predicting the plate motion would also be made plausible. It is the sudden plate motion
like the occurrences on 26th December 2004 that awaken us to realize the importance of
the plate movements to be predicted for the purpose of the well being of our daily lives.