SEISMIC FIRST BREAK PICKING ALGORITHM WITH
CASE STUDIES FOR FULL WAVE ELASTIC PHYSICAL MODELING
IN THE LAB
______________________________________
A Thesis
Presented to
the Department of Earth and Atmospheric Sciences
University of Houston
______________________________________
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
______________________________________
By
Heng Yao
May 2012
SEISMIC FIRST BREAK PICKING ALGORITHM WITH
CASE STUDIES FOR FULL WAVE ELASTIC PHYSICAL MODELING
IN THE LAB
_____________________________________________
Heng Yao
APPROVED:
_____________________________________________
Dr. Christopher Liner (Chairman)
_____________________________________________
Dr. Bernhard Bodmann (Member)
_____________________________________________
Dr. Robert Wiley (Member)
_____________________________________________
Dr. Jolante Van Wijk (Member)
_____________________________________________
Mark A. Smith (Dean)
ii
Acknowledgments
First and foremost, I would like to express my appreciation to my advisor, Dr.
Christopher Liner, for his support, guidance and wisdom during my MS study and
research in the Geophysics area. Dr. Liner introduced me to a brand new field since I
had no Geophysics background. He always gives me encouragement, assistance, and
inspiration in many aspects and helps me build up my research ability. Without his
support, I wouldn’t have been so happy to be in this field and learn so much. I would
also give my appreciation to Dr. Bernhard Bodmann, who brought me many thoughts
that are very helpful throughout the research. Dr. Robert Wiley, and Anoop Willam,
both helped me with the experiments in the Allied Geophysical Lab and processing the
data. I would also like to thank Dr. Jolante Van Wijk for serving on my committee.
Their insightful thoughts provided valuable inputs to my thesis.
I would also give my sincerely gratitude to our GK/AGL group members and
my friends and colleagues at UH. They give me a lot of spiritual support.
Many thanks to my financial support sources, without which my MS study and
research would not have been so smooth. They are Allied Geophysical Lab,
GeoKinetics company, and UH Department of Earth and Atmospheric Science.
In the end, I would like to give my thanks to my parents for all the support they
gave me.
iii
SEISMIC FIRST BREAK PICKING ALGORITHM WITH
CASE STUDIES FOR FULL WAVE ELASTIC PHYSICAL MODELING
IN THE LAB
______________________________________
An Abstract of a Thesis
Presented to
the Department of Earth and Atmospheric Sciences
University of Houston
______________________________________
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
______________________________________
By
Heng Yao
May 2012
iv
Abstract
This thesis presents several experiments of physical modeling in the Allied
Geophysical Lab (AGL) at the University of Houston. The purpose of our physical
models is to simulate the shallow water seismic acquisition using aluminum to represent
a hard seafloor. The calibration of the model requires characterization of our particular
aluminum, so several experiments were conducted to estimate its P-wave and S-wave
velocity. The experiments cover a range of frequencies from 100 kHz to 5 MHz,
allowing me to analyze the relation between velocity and frequency (velocity
dispersion).
In these measurements, travel time picking is critical for estimating the velocity
accurately. Therefore, a fast and reliable picking algorithm was developed (named
suaglpickr) and implemented in the C programming language as a program in the
Seismic Unix (SU) processing package. The new picking program was validated and
proved to be accurate and reliable. Picking details are made flexible through user inputs
for choices of threshold level, or noise and signal window extent. The user can also
adjust parameters to fine-tune the probability of false positive picks, for example, to
control event-picking reliability. The picking algorithm is applied to seismic data from
laboratory experiments to estimate seismic velocity in aluminum.
v
Table of Contents
Acknowledgments .................................................................................................................. iii
Abstract ...................................................................................................................................... v
List of Figures: ....................................................................................................................... vii
List of Tables:........................................................................................................................ viii
List of Abbreviations:............................................................................................................. ix
Chapter 1 .................................................................................................................................... 1
Introduction ............................................................................................................................... 1
1.1 Background and Motivation..................................................................................................... 1
1.2 General Concepts ........................................................................................................................ 1
1.2.1 Physical model and AGL ................................................................................................................ 1
1.2.2 Transducers ......................................................................................................................................... 4
1.2.3 Aluminum block ................................................................................................................................ 7
Chapter 2 .................................................................................................................................... 8
Models and Experiments ........................................................................................................ 8
2.1 Experiment Design...................................................................................................................... 8
2.2 Experimental Procedures and Measurements ..................................................................... 8
2.3 Rescale .........................................................................................................................................11
Chapter 3 ................................................................................................................................. 11
Results and Error Estimates ............................................................................................... 11
3.1 Frequency Band Limits ...........................................................................................................11
3.1.1 Decibel method for frequency band ..........................................................................................11
3.1.2 Statistical method for frequency band ......................................................................................14
3.2 Error for Velocity .....................................................................................................................14
Chapter 4 ................................................................................................................................. 16
Picking Algorithm ................................................................................................................. 16
4.1 First Arrival Time Picking Methods ....................................................................................16
4.1.1 Method 1: Manual picking ...........................................................................................................16
4.1.2 Method 2: Picking sample number by amplitude in SU .....................................................17
4.1.3 Method 3 An automatic picking algorithm .............................................................................19
4.2 Velocity Picking Algorithm Case Study ..............................................................................32
4.2.1 Case study 1 ......................................................................................................................................32
4.2.2 Case study 2 ......................................................................................................................................34
4.3 Dispersion in Alloy Aluminum Block ...................................................................................39
Chapter 5 ................................................................................................................................. 42
Discussions and Conclusion ................................................................................................ 42
vi
Chapter 6 ................................................................................................................................. 43
References ............................................................................................................................... 43
Appendix A ............................................................................................................................. 48
Appendix B Source Code for “suaglpickr” ..................................................................... 49
List of Figures:
Figure 1. Allied Geophysical Lab (AGL) Elastic, Acoustic and Ultrasonic Measurement
System (a) Numerically controlled system 1 (b) Water tank 1(c) Numerically
controlled system 2 (d) Water tank 2 ..................................................................................... 3
Figure 2. Allied Geophysical Lab transducers: (a) Spherical transducer with central
frequency of 600 kHz (b) Pin transducers with central frequency of 300 kHz (c) 3C transducer with central frequency of 500 kHz (d) Contact transducers ................... 5
Figure 3. Transducers with different frequencies and sizes ..................................................... 6
Figure 4. Aluminum block used for transmission experiments and as a proxy for a hard
seafloor in shallow water seismic experiments. .................................................................. 7
Figure 5. P- and S-wave first arrivals through aluminum block in Figure 4. This
experiment used 500 kHz S-wave transducers and was repeated 20 times (one trace
per experiment) .......................................................................................................................... 10
Figure 6. (a) Waveform for direct contact measurement on aluminum block using 100
kHz shear wave transducers (b) Fourier transform and normalize dB to 0 of
waveforms for direct contact measurement using 100 kHz shear wave transducers
........................................................................................................................................................ 13
Figure 7. Waveform of direct contact measurement on the aluminum block by using 500
kHz shear wave transducers ................................................................................................... 17
Figure 8. Tap plot for the first trace using 500 kHz shear wave transducers on aluminum
block, first column: sample number; second column: amplitude; third column: tap
plot of the amplitude (a) First arrival for P-wave picking (b) First arrival for Swave picking............................................................................................................................... 19
Figure 9. Waveform with defined noise window and signal window ................................. 20
Figure 10. "suaglpickr" description in SU with required parameters and optional
parameters ................................................................................................................................... 23
Figure 11. Input traces: (a) Trace 1 (red) and trace 2 (green), both have peaks at sample
number of 50, 51 and 55, 56 (b) SU script to generate these two traces shown in (a)
........................................................................................................................................................ 24
Figure 12. (a) Y-t plot for trace 1 (see detail for Y in text) (b) Y-t plot for trace 2 (c)
Output traces using the picking algorithm (d) Details of the time window with the
peaks of output traces .............................................................................................................. 26
Figure 13. (a) Script for the input traces (b) Output traces: amplitude vs. time sample
number.......................................................................................................................................... 27
vii
Figure 14. (a) SU output for trace 1, first arrival time pick: 0.192s; first arrival sample
number pick: 49 (b) SU output for trace 2, first arrival time pick: 0.212s; first
arrival sample number pick: 54............................................................................................. 28
Figure 15. SU result for all traces including mean first pick time, variance, and standard
deviation ...................................................................................................................................... 29
Figure 16. (a) Output traces using the script in Figure 13 (a) with Signal to Noise ratio
of 6 (b) Output picking results .............................................................................................. 30
Figure 17. (a) Picking result of two traces with Signal/noise=5 of input traces (b)
Picking result of two traces with Signal/noise=4 of input traces (c) Picking
result of two traces with Signal/noise=3 of input traces ........................................ 31
Figure 18. (a) Picking result of two traces with Signal/noise=2 of input traces,
default threshold level beta=2.25 (b) Picking result of two traces with
Signal/noise=2 of input traces, threshold level beta=2.15 ..................................... 32
Figure 19. (a) Shot record (20 traces) for AGL 'KONG' sample in AGL system (b)
Results of first break picking time for AGL sample from direct contact
measurements with 1 MHz 3-C transducers ..................................................................... 34
Figure 20. Result of first break picking time from direct contact measurements with 1
MHz 3-C transducers (data now shown) ............................................................................ 36
Figure 21. Result of first break picking time for RPL sample first break time with 1
MHz 3-C transducers (data not shown) .............................................................................. 37
Figure 22. (a) P-wave velocity vs. log scale frequency with error range for both velocity
and frequency using P-wave transducers (b) S wave velocity vs. log scale
frequency with error range for both velocity and frequency using S wave
transducers (c) P-wave velocity vs. log scale frequency with error range for both
velocity and frequency using S-wave transducers ........................................................... 41
Figure 23. (a) dB picking for 500 kHz shear wave transducers (b) dB picking for 2.25
MHz shear wave transducers (c) dB picking for 5 MHz shear wave transducers .. 48
Figure 24. (a) dB picking for 500 kHz P wave transducers (b) dB picking for 1 MHz P
wave transducers (c) dB picking for 5 MHz P wave transducers ............................... 48
List of Tables:
Table 1. Transducer diameter (D) and wavelength (L) calculations assume a P-wave
velocity of 6140m/s and S-wave velocity of 3070m/s ...................................................... 6
Table 2. Frequency range by dB picking method ..................................................................... 13
Table 3. Frequency range by statistical method ........................................................................ 14
Table 4. Measurements for P wave velocity of RPL Sample and AGL sample 'KONG'
by using both AGL system and 1 MHz 3-C transducers ............................................... 38
Table 5. Measurements for P wave velocity of RPL Sample and AGL sample 'KONG'
by using both RPL system and 1 MHz 3-C transducers ................................................ 38
viii
Table 6. Measurements for P wave velocity of RPL Sample and AGL sample 'KONG'
by using both AGL system and RPL transducers ............................................................ 39
Table 7. Comparison for P wave velocities with different measurement parameters .... 39
Table 8. Velocities with error bar vs. frequency range............................................................ 40
List of Abbreviations:
AGL
Allied Geophysical Laboratories
CMP
Common-Mid Point
RPL
Rock Physics Lab
3-C transducer
3-component
Al
Aluminum
𝒎𝒕
Travel time through the medium
𝒅𝒕
Travel time by direct contact measurement
𝒓𝒕
Real travel time by subtracting dt from mt
𝒍
Length of the medium
∆𝒕
The error of the real travel time
∆𝒎𝒕
The error of the travel time through the medium
∆𝒅𝒕
The error of the travel time by direct contact measurement
ix
Chapter 1
Introduction
1.1 Background and Motivation
Seismic surveys can be used for non-invasively detecting the structure and
nature of the Earth’s subsurface. In the oil and gas industry, there are two main
categories of seismic acquisition: onshore and offshore. Shallow water with a hard
seafloor presents many data complications not found in deep-water data. For shallow
water, the water depth is less than the seismic wavelength. Shallow water exploration is
very complex, yet vast areas of the world have prospective petroleum provinces in
shallow water. Therefore, high quality shallow water marine seismic data is important
to seismic applications and research.
In order to understand shallow water seismic data better, 1:10000 scale models
are used in the Allied Geophysical Lab (AGL) at the University of Houston. The basic
physical model for shallow water has a tank filled with water, representing seawater, a
block of aluminum (Figure 1), serving as a hard seafloor, and piezoelectric transducers
used as sources and receivers. The objective of this paper is to analyze the properties of
the aluminum seafloor material.
1.2 General Concepts
1.2.1 Physical model and AGL
1
A physical model is a smaller or larger physical copy of an object, used to
simulate an event in order to get effect analogous to full-scale results. The geometry of
the model and the object it represents are often similar in the sense that one is rescaling
of the other. In such cases the scale is an important characteristic. The earliest seismic
physical model involved modeling elastic waves for earth studies for protection of
structures and equipment from damage (Terada and Tsuboi, 1927). Another early
physical model was by Rieber (1936) who used a new type of equipment and technique
to present a series of figures, showing wave patterns in various types of structures,
ranging from simple to complex. Physical models have been used for a long period of
time to study elastic wave propagation in the laboratory (White, 1965, and McDonald et
al. 1983). Physical modeling has also been applied to many aspects of seismic
acquisition processing and interpretation, including anisotropic media (Urosevic and
McDonald, 1985; Stewart, 2011), shear waves (Ebrom et al, 1990), bore hole sonic data
(Zlatev, Poeter and Higgins, 1987), multicomponent data (Ebrom et. al., 1998),
tomography (Schneider and Balch, 1991), elastic converted waves (Purnell, 1992), the
classic thin bed (Cooper, 2010), and many others.
The University of Houston Allied Geophysical Laboratories (AGL) includes a
center for seismic physical modeling research (Figure 1). It has the capability for elastic,
acoustic and ultrasonic measurements. A number of physical models have been built in
AGL for data acquisition and analysis projects directed at improved imaging and
analysis of subsurface reservoirs.
2
Figure 1. Allied Geophysical Lab (AGL) Elastic, Acoustic and Ultrasonic Measurement
System (a) Numerically controlled system 1 (b) Water tank 1(c) Numerically controlled
system 2 (d) Water tank 2
The goals of physical modeling research include: (1) improved seismic data
acquisition, processing and interpretation and (2) understanding the propagation of
elastic waves in complex media. The physical model is often made of synthetic
materials, such as Lucite, silicon rubbers, aluminum alloy, etc., immersed into the water
tank and connected to piezoelectric transducers. Source and receiver transducers range
over several hundred kilohertz central frequency and a range of several centimeters in
diameter. Since physical modeling is repeatable and inexpensive, it has been widely
used and is considered as an important tool for seismic exploration research.
3
There are two physical modeling systems used in the AGL: (1) the water tank
system, typically used for marine 3D surveys (2) the solid modeling system, mainly
used for elastic wave propagation studies. Operation of the systems is controlled by
computer systems.
In this paper, a set of experiments is conducted using the solid modeling system
and analyzed for the acoustic properties of the aluminuml.
1.2.2 Transducers
The transducers used in physical modeling, are piezoelectric devices that can
convert electrical signals to acoustic energy. In the elastic modeling system, the source
and receiver have direct contact with the medium and both P-waves and S-waves are
generated.
A broadband wavelet can be generated by the source, and amplified by a digital
oscilloscope connected to a computer to control the experiment. Multiple traces can be
output into a data file, typically in the SEG-Y format.
AGL has a variety of transducers to generate P-wave and S-wave energy. Pwave transducers can generate mostly P-waves, with some small amount of S-wave
energy. Conversely, S-wave transducers can generate mostly S-waves with a small
amount of P-wave energy. Unlike P-waves, S-waves can be polarized with the
polarization set by the orientation of the source transducer. The P-wave transducer has
sensitivity normal to the contact surface while the S-wave transducer excites/records
motion parallel to the contact surface.
4
The transducers have various shapes (Figure 2), including spherical transducers,
pin transducers, and 3 Component transducers. They all have a frequency range from
100khz to 5mhz.
Figure 2. Allied Geophysical Lab transducers: (a) Spherical transducer with central
frequency of 600 kHz (b) Pin transducers with central frequency of 300 kHz (c) 3-C
transducer with central frequency of 500 kHz (d) Contact transducers
Several pairs of piezoelectric P-wave and S-wave contact transducers shown in
Figure 2 (c) and Figure 2 (d) were used as sources and receivers in the physical
modeling. They are flat-faced and cylindrical-shaped. Figure 3 shows a set of
transducers with different central frequencies. We used a scientific caliper to measure
the diameter of each transducer in Table 1. One of the limitations for physical models is
5
the scaling of the size of the transducer with respect to wavelength. Table 1 gives the
comparison of transducer diameter and wavelength.
Figure 3. Transducers with different frequencies and sizes
Table 1. Transducer diameter (D) and wavelength (L) calculations assume a P-wave
velocity of 6140m/s and S-wave velocity of 3070m/s
Frequency (MHz)
LP (mm)
LS (mm)
D (mm)
D/LP
D/LS
0.1
61.40
30.70
31.80
0.52
1.06
0.25
24.56
12.28
13.03
0.53
1.06
0.5
12.28
6.14
31.94
2.58
5.15
1
6.14
3.07
16.68
2.72
5.43
2.25
2.73
1.36
16.68
6.11
12.26
5
1.23
0.61
8.98
7.30
14.72
In field land seismic data, near surface P wavelength might be 100 m and the
source size 2 m (vibroseis baseplate), yielding D/LP = 0.02 which is significantly
smaller than in any of our physical modeling experiments.
6
1.2.3 Aluminum block
Shallow water seismic noise can be generated by the high impedance contrast
between the seawater and seafloor. Aluminum alloy has high velocity and density,
leading to a large acoustic impedance (velocity times density). Therefore, in order to
study shallow water seismic data, we use a block of aluminum alloy to act as an elastic
physical model of the seafloor. Figure 4 shows the dimension of the aluminum block.
Figure 4. Aluminum block used for transmission experiments and as a proxy for a hard
seafloor in shallow water seismic experiments.
The block is composed predominantly of aluminum with unknown quantities of
alloying elements: copper, magnesium, manganese, silicon and zinc. It has a density of
2.63𝑔/𝑐𝑚3 and an approximate of P-wave velocity of 6300m/s. Dimensions of the
block were measured with a scientific caliper. To characterize elastic properties of the
7
aluminum block, several transmission experiments were conducted at a variety of
frequencies.
Chapter 2
Models and Experiments
2.1 Experiment Design
In our experiment, the model consists of an aluminum block (304.55x100.13x
101.98 mm), a pair of transducers acting as source and receiver, a caliper and a
connected numerically computer controlled system to record the data. The dimensions
are measured by a scientific caliper with an accuracy of 0.01mm. To avoid complicated
first-arrival waveforms, the source transducer should be relatively small compared to
the contact surface area. To accomplish this, we decided to use the 101.98mm
dimension as the wave propagation distance and Face A (Figure 4) as the source contact
surface.
To analyze the relationship between the frequency of the transducers and the
velocity through the medium, we use the following transducers: 100 kHz S, 500 kHz S,
500 kHz P, 1 MHz P, 2.25 MHz S, 5 MHz S, 5 MHz P. In each case, direct contact
measurements are taken before measuring travel time of waves propagating through the
aluminum block.
2.2 Experimental Procedures and Measurements
Procedures of the experiments include the following two steps:
8
Step1: Measurement for direct contact travel time.
Direct contact travel time means that source and receiver transducers are placed
face-to-face without an intervening medium. Travel time was measured from one
transducer to the other and used as a calibration time for the transducer pair.
Step2: Measurement of travel time through the medium.
This step is to measure the travel time for wave propagating through the sample
medium across a fixed distance. The source transducer is placed in contact with one
side of the sample and the receiver transducer is on the other side. The travel time from
source through the medium to the receiver is the sample travel time. To improve
accuracy, the experiment is repeated 20 times.
The real travel time needs to be corrected by subtracting the direct-contact
calibration time from the sample travel time. Since the travel distance is known and P𝑠
waves are the fastest wave-type, the P wave velocity can be calculated by 𝑣𝑃 = , where t
𝑡
is the measured travel time and s is the distance through the. Figure 5 shows the first
arrivals for P and S wave plotted using Seismic Unix (SU) with 20 traces.
9
Figure 5. P- and S-wave first arrivals through aluminum block in Figure 4. This
experiment used 500 kHz S-wave transducers and was repeated 20 times (one trace per
experiment)
From the procedures above, several parameters are measured by the experiments
to calculate the velocities: travel time by direct contact measurement (𝑑𝑡), travel time
through the medium (𝑚𝑡), real travel time (sample travel time subtracting direct contact
time)(𝑟𝑡), and the length of the medium (l). We also do error estimates for frequency
and velocity to study velocity dispersion.
10
2.3 Rescale
Physical modeling is used to simulate real world seismic exploration in a
laboratory environment. This requires rescaling of parameters to get results that can be
compared with real data. Typically, 1km in the real world represents 10 cm in the lab
and 1 second in real time is 0.0001 second in the lab. Therefore laboratory length and
time are scaled by a factor of 10,000 for comparison with real data.
Chapter 3
Results and Error Estimates
3.1 Frequency Band Limits
For dispersion work, it is important to estimate the actual frequency band
emitted by transducers during the experiment, rather than simply trusting the
manufacture’s labeled frequency. We used two methods to analyze the frequency band,
using data is from the direct contact measurements. A total of seven transducer pairs
were tested and processed in SU to generate amplitude spectra with linear and decibel
scales.
3.1.1 Decibel method for frequency band
The decibel (dB) is a logarithmic unit representing the ratio of a physical
quantity relative to a specified or implied reference level. Since we measured the
amplitude versus frequency, dB is calculated as the ratio of the squares of the measured
amplitude 𝐴1 and reference amplitude 𝐴0 , in a formula as:
11
𝐿𝑑𝐵
𝐴12
𝐴1
= 10𝐿𝑜𝑔10 ( 2 ) = 20𝐿𝑜𝑔10 ( )
𝐴0
𝐴0
Based on visual inspection of spectra, we decided that -15 dB seemed a
reasonable threshold for choosing high and low signal frequency limits.
Figure 6 (a) illustrates an amplitude spectrum generated by SU using a pair of 100kHz
shear wave transduces in direct contact. We transform the amplitude to dB normalize to
0, as shown in Figure 6 (b), and add a horizontal line at -15 dB. The intersection of the 15 dB line with the spectrum curve gives our definition of the lowest and highest
frequency radiated from this transducer. For the case in Figure 6 (b), these limits are 70150 kHz.
12
Figure 6. (a) Waveform for direct contact measurement on aluminum block using 100
kHz shear wave transducers (b) Fourier transform and normalize dB to 0 of waveforms
for direct contact measurement using 100 kHz shear wave transducers
Using the same method, we get a data set (Table 2) of all the frequencies’ range,
dominant frequencies and peak frequencies for seven pairs of transducers, as compared
with central frequencies.
Table 2. Frequency range by dB picking method
Central Frequency
Frequency range
Dominant Frequency
Peak Frequency
(kHz)
(kHz)
(kHz)
(kHz)
100 S
70-150
110
105
500 S
190-660
425
440
500 P
205-705
455
375
1000 P
630-1100
865
750
2250 S
1300-3800
2550
2200
5000 S
1100-5500
3300
4800
13
5000 P
2800-6500
4650
4700
(More frequency picking results are included in the Appendix A section)
3.1.2 Statistical method for frequency band
Another method to determine the frequency band is to calculate all the sample
values in each trace using Matlab to get the mean and standard deviation of the whole
data set. Table 3 demonstrates the results by using the statistical method.
Table 3. Frequency range by statistical method
Central Frequency
Frequency range
Mean Frequency
Error Frequency
(kHz)
(kHz)
(kHz)
(kHz)
100 S
91.8-134
112.9
21.1
500 S
366.5-485.5
411.0
74.5
500 P
322.8-506
414.4
91.6
1000 P
762.7-916.3
839.5
76.8
2250 S
2065.8-2824
2444.9
379.1
5000 S
3177.4-4071
3624.2
446.8
5000 P
3994.5-5121.3
4557.9
563.4
Frequency range obtained from statistical method is used as a reference to
estimate the velocity error.
3.2 Error for Velocity
Error estimate for the velocity brings more precise and reliable data and a range
of values that can be referenced for the velocity model. In our experiment, P-wave
velocity is determined by two parameters: propagating distance through the medium
and the associated real travel time. The approximated velocity error can be calculated in
the formula below.
14
𝑣 ± ∆𝑣 =
𝑥
∆𝑥 ∆𝑡
(1 ±
± )
𝑡
𝑥
𝑡
𝑟𝑡 = 𝑚𝑡 − 𝑑𝑡
The relative error for velocity is determined by the sum of the relative distance
error and travel time error. The real travel time (𝑟𝑡) is calculated by travel time through
medium (𝑚𝑡) subtracting the travel time in direct contact (𝑑𝑡). Hence the error of 𝑟𝑡 is a
summation of the errors of 𝑚𝑡 and 𝑑𝑡.
∆𝑡 = ∆𝑚𝑡 + ∆𝑑𝑡
The Vernier Calli scientific caliper accuracy is 0.01 mm, which is the ∆𝑥 in the
equation. It is a fixed value for the distance error in the experiment. Thus the error of
the velocity depends mostly on the travel time error ∆𝑡 .
The first break picking
accuracy for 𝑚𝑡 and 𝑑𝑡 makes considerable difference for the velocity error estimates.
For example, one dataset is gathered as: travel distance is 101.33 mm, and the
mean travel time 𝑡 is 0.159 s, ∆𝑡 is the standard deviation of the 𝑟𝑡, 0.001203 s. We can
use the above parameters to calculate the error of the velocity as:
𝑑𝑡 = 0.012𝑠, 𝑚𝑡 = 0.0171𝑠, 𝑟𝑡 = 𝑚𝑡 − 𝑑𝑡 = 0.159𝑠,
∆𝑚𝑡 = 0.000707𝑠, ∆𝑑𝑡 = 0.000496𝑠, ∆𝑡 = ∆𝑚𝑡 + ∆𝑑𝑡 = 0.001203𝑠
𝑥 = 0.10133𝑚, ∆𝑥 = 0.00001𝑚
𝑣 + ∆𝑣 = 6373 (1 +
0.001203
0.159
0.00001
+ 0.10133) = 6373 ± 49𝑚/𝑠 (1)
Another data set is obtained with the same travel distance but smaller, ∆𝑡 as
0.000812 s, the error of the velocity is calculated using the same equation above as:
𝑟𝑡 = 0.159𝑠
∆𝑡 = 0.000812𝑠
15
𝑥 = 0.10133𝑚, ∆𝑥 = 0.00001𝑚
𝑣 + ∆𝑣 = 6373 (1 +
0.000812
0.159
0.00001
+ 0.10133) = 6373 ± 33𝑚/𝑠 (2)
The velocity errors calculated in (1) and (2) represent that the travel time error
can make big difference for the velocity error. Therefore, first break picking can affect
the accuracy of the velocity calculation.
Chapter 4
Picking Algorithm
4.1 First Arrival Time Picking Methods
The P-wave and S-wave amplitudes are quite small and could not be
distinguished from signal and noise, so it is often difficult to determine a distinct first
arrival time. Several methods were attempted to identify the first arrivals.
4.1.1 Method 1: manual picking
Figure 7 shows the waveform generated by a pair of 500 kHz shear wave
transducers with direct contact measurement. The data is populated in SU and repeated
twenty times (20 traces). In this case, first arrival travel time needs to be read from the
figure for all the traces. This method takes time and the manual picking error can be
relatively large. Therefore, this method is inefficient and not reliable.
16
0
5
Trace
10
15
20
0.01
Time (s)
0.02
0.03
0.04
0.05
AGL/AL 500 kHz S DC
Figure 7. Waveform of direct contact measurement on the aluminum block by using 500
kHz shear wave transducers
4.1.2 Method 2: Picking sample number by amplitude in SU
The data recorded with SEG-Y format was used as input and processed in SU,
we use the SU command suedit to analyze each sample for every trace in the data
record. When the amplitude is changing dramatically, we consider the corresponding
sample number as the first break. The first arrival time equals the sample number
multiplied with the sample rate.
17
From Figure 8, we consider the sample number 188 as the first break sample for
P wave, because it is the starting point that the amplitude changed from 0 to negative.
Meanwhile, sample number of 346 is considered as the first break sample for S wave
because the amplitude is changing dramatically from 2 positive units to 4 positive units.
The sample rate for this seismic record is 1ms, therefore, the first arrival time of P-wave
(0.188s) and S wave (0.346s) for trace one are obtained as their corrresting sample
numbers multiplied by the sample rate (1ms).
With the same method, the rest of 20 traces also need to be picked by analyzing
sample’s amplitudes. This requires a lot of time, and the standard for the picking is not
easily fixed to guarantee reproducibility.
18
Figure 8. Tap plot for the first trace using 500 kHz shear wave transducers on aluminum
block, first column: sample number; second column: amplitude; third column: tap plot
of the amplitude (a) First arrival for P-wave picking (b) First arrival for S-wave picking
4.1.3 Method 3 An automatic picking algorithm
4.1.3.1 Statistical method
This method aims to pick the first arrival time automatically for multiple traces.
It can reduce the picking error by adjusting a probability of false positive everywhere in
the statistical method, and create a text report showing picking results and calculate the
mean value picking time and standard deviation for all the traces.
The proposed method uses the standard deviation of the noise (before signal
arrival) in order to quantify the amount of amplitude standout that will be considered as
a signal arrival, and deduces P-wave first arrival time. Due to its statistical nature, the
estimation of arrival times comes with a probability of a false positive/arrival, which
can be adjusted by the user to trade off sensitivity against specificity.
The method has the following steps:
1. Choose the noise window and the signal window (Figure 9). These windows are
assumed to contain with certainty, only noise, or noise with a possible
superposed signal arrival, respectively.
2. Choose the threshold level 𝛽, a quintile for the noise distribution, which controls
the probability of the algorithm that may generate false positives in the presence
of pure noise.
3. Compute the noise mean.
4. Compute the noise standard deviation.
19
5. Divide the entire trace amplitude by noise standard deviation, and call this X.
6. Adjust the mean to be zero.
7. Assign a new value Y using the following criteria.
a. If |X| < 𝛽, then Y = 0
b. If 𝛽 ≤ |X|, then Y = 1
8. Find the first m consecutive occurrences where Y  0, and this is our first Pwave arrival.
9. Correlate this specific Y with its sample number and obtain the arrival time.
Figure 9. Waveform with defined noise window and signal window
4.1.3.2 Parameters and constraints
20
There are several constraints for the algorithm:
1. The definition of the noise window and signal window is based on the
assumption that the noise window contains no signal while the signal window is
allowed to have some noise.
2. The consecutive number m is an integer, while the standard deviation threshold
level 𝛽, can be any positive floating number.
Based on the method described above, a program called ‘suaglpickr’ is developed as
a Seismic Unix (SU) command written in C language. This code is designed to pick the
first arrival time for multiple traces and calculate both the mean time and standard
deviation for the time.
In the code, several default parameters are defined as:
𝑡𝑛1 =0
starting time (s) of the noise window
𝑡𝑛2 =0.15
end time (s) of the noise window
𝑡𝑠1 =0.15
begin time (s) of the signal window
𝑡𝑠2 =0.3
end time (s) of the signal window
𝑚=2
consecutive samples over threshold to be considered as signal
𝑏𝑒𝑡𝑎=2.2
standard deviation threshold level 𝛽
𝑓𝑖𝑙𝑒𝑛𝑎𝑚𝑒= 𝑜𝑢𝑡𝑝𝑢𝑡. 𝑡𝑥𝑡
output txt file
𝑜𝑢𝑡=1
output SU data is origAmp/noiseStdDev with zero before
1st break pick while out=2 output zero trace except the
1st break pick has unit amplitude
We assume that 𝑧 represents the standard deviation normal variable. 𝑃 is the
probability.
21
If: 𝑃(|𝑧| ≥ 𝛽) = 𝑃
Then: 𝑃(|𝑧1 | ≥ 𝛽, |𝑧2 | ≥ 𝛽, … |𝑧𝑚 | ≥ 𝛽) = 𝑃𝑚
Therefore: 𝛽 = (signal window length in sample number – 𝑚 + 1) 𝑃𝑚
The user needs to give input data with .su format and output filename to save the
result. The algorithm also includes a probability calculation to give the false positive
probability within the signal window of the trace, for the given threshold level and the
number of consecutive values above the threshold. Users can adjust the m, 𝛽
parameters, or the length of noise window or signal window to get a feasible false
positive probability for the trace.
The output SU data is calculated by dividing the input amplitude by the noise
standard deviation. The final result is saved in a text file, which gives the noise window,
signal window length in seconds, signal window length in sample number, 𝛽 , m,
probability of error, first arrival time sample number, first arrival time in seconds, and
probability of false positive anywhere per trace. In addition, trace number, picking time
per trace, mean of the first pick time in seconds, variance, and standard deviation for the
first pick in seconds are calculated as well.
4.1.3.3 Validation
The algorithm is developed in SU as a command using C program, called
“suaglpickr”. Figure 10 shows the description for this command in SU. There’s no
required parameter, but some optional parameters. If user doesn’t give any value to any
of the parameters, the command will be operated using the default values of the
parameters.
22
Figure 10. "suaglpickr" description in SU with required parameters and optional
parameters
The next step is to validate the algorithm. As shown in Figure 11(a), I created
two seismic traces, red and green, using a SU command “suspike” shown in Figure
11(b). Red trace has a peak with two consecutive numbers at sample number 50 and 51,
while green trace has a peak at sample number 55 and 56. For validation, we want to
apply the picking algorithm-“suaglpickr” to the input trace and find out if the results
match the input peak that we created.
23
Figure 11. Input traces: (a) Trace 1 (red) and trace 2 (green), both have peaks at sample
number of 50, 51 and 55, 56 (b) SU script to generate these two traces shown in (a)
I applied “suaglpickr” to the input traces, and redefined the parameters as shown
in Figure 13 (a): tn1=0.0 tn2=0.17, which means the noise window is redefined as from
0 to 0.17 second, and ts1=0.17 ts2=0.3 means the signal window is redefined as from
0.17 to 0.3 second. The threshold level 𝛽 is assigned as 2.25 and m =2, which means
that when no less than 2 consecutive numbers of samples occur on the condition that the
amplitude over the standard deviation of noise window is equal to or greater than 2.25,
then it’s considered as the first break starting from the first consecutive number minus
1.
The output shown in Figure 12 (a) (b) gives the Y-t plot for trace 1 (red trace)
and trace 2 (green trace). The Y is has the same definition as in Section 4.1.3.1:
24
Divide the entire trace amplitude by noise standard deviation, and call this X.
Adjust the mean.
Assign a new value Y using the following criteria.
a. If |X| < 𝛽, then Y = 0
b. If 𝛽 ≤ |X|, then Y = 1
The plot shows that there are several time samples, which satisfy the condition
that the ratio of amplitude over the standard of noise window is greater than or equal to
the threshold level 𝛽 (2.25), which triggers Y’s value gives value to be 1.
The output shown in Figure 12 (c) is amplitude versus time based on the
parameter of “output =1”, which makes the output amplitude as 0 before the first break
and keeps the original amplitude after the first break. Figure 12 (d) shows the traces by
zooming in the time range from 0.18s to 0.24s. The first break time for trace 1 (red
trace) is approximated at 0.19s, the first break time for trace 2 (green trace) is
approximated at 0.21s.
25
Figure 12. (a) Y-t plot for trace 1 (see detail for Y in text) (b) Y-t plot for trace 2 (c)
Output traces using the picking algorithm (d) Details of the time window with the peaks
of output traces
To validate the data, the output traces were converted to time sample number
versus amplitude. Figure 13 (b) shows the output traces; the first time arrival sample
number for trace 1 is read as 49, and the first arrival sample number for trace 2 is 54.
Both of the two sample numbers match the input value exactly, therefore the picking
result is proved to be correct.
26
Figure 13. (a) Script for the input traces (b) Output traces: amplitude vs. time sample
number
The algorithm creates a text file including the picking results. Figure 14 (a)
shows the output results for trace 1 (red trace). The first time arrival sample number is
49, and the first break time is 0.192s. Figure 14 (b) shows the output results for trace 2
(green trace). The first time arrival sample number is 54, and the first break time is
0.212s. Those results are perfectly in good agreement with the input data. Therefore, the
picking algorithm is validated. Meanwhile, it also gives the probability of false positive
anywhere as 0.020125. It is a relative small value, which means that the parameters for
the threshold 𝛽 and m are chosen reasonably and the picking is highly reliable.
27
Figure 14. (a) SU output for trace 1, first arrival time pick: 0.192s; first arrival sample
number pick: 49 (b) SU output for trace 2, first arrival time pick: 0.212s; first arrival
sample number pick: 54
The purpose of the picking is to calculate the first arrival time for each trace
with reliability, therefore, the algorithm creates a summary for all the traces, including
the average first picking time and standard deviation for the picking time at the end of
the text report shown in Figure 15. It shows that there are a total of 2 traces from the
input data, each trace has the first break time as 0.192s and 0.212s, the mean first pick
time is 0.202s, variance of the two picking time is 0.0002s, and the standard deviation
for the two picking time is 0.014142s.
28
Figure 15. SU result for all traces including mean first pick time, variance, and standard
deviation
The case above shows that the algorithm can pick the first arrivals for the
seismic traces with a signal to noise ratio of 7. In order to complete the validation of the
algorithm, a range of signal to nose ratio was tested from 6 to 2.
Figure 16 (a) shows the two traces generated by the script in Figure 13 (a), set
the peaks for the traces the same, but the signal to noise ratio is changed from 7 to 6 in
order to find if the picking algorithm is still applicable for more noisy trace. Figure 16
(b) shows the picking results from the text report generated by the algorithm. That
means the picking algorithm is validated for a signal to noise ratio of 6. In order to find
out how noisy of the signal can be picked with the algorithm, the ratio is changed from
6, 5, 4, and 3, and the picking is still available with the algorithm with the no false
positive probability of 0.020125. That means the picking for a signal to noise ratio of 3
is still quite reliable using this algorithm. (Figure 17)
29
Figure 16. (a) Output traces using the script in Figure 13 (a) with Signal to Noise ratio
of 6 (b) Output picking results
30
Figure 17. (a) Picking result of two traces with Signal/noise=5 of input traces (b)
Picking result of two traces with Signal/noise=4 of input traces (c) Picking result of two
traces with Signal/noise=3 of input traces
When the input signal to noise ratio decreases to 2, as shown in Figure 18 (a),
the picking algorithm is not working for the two traces, and can not pick the first
arrivals any more. In order to pick the first arrival, the threshold level beta is
compromised and decreased from 2.25 to 2.15, which will cause a higher probability of
no false positive everywhere from 0.020125 to 0.03305. This higher probability shows
the reliability of the picking is decreased but still acceptable in Figure 18 (b).
31
Figure 18. (a) Picking result of two traces with Signal/noise=2 of input traces, default
threshold level beta=2.25 (b) Picking result of two traces with Signal/noise=2 of input
traces, threshold level beta=2.15
The algorithm is fully validated and proved to be accurate. With this algorithm,
the first arrival time can be picked automatically for multiple traces, and the mean and
standard deviation of the picking time are also provided in the text report. The first
arrival time in a higher noise trace can be picked with this algorithm
by decreasing the threshold level beta or consecutive number m.
4.2 Velocity Picking Algorithm Case Study
4.2.1 Case study 1
32
Datasets were recorded in Allied Geophysical Lab (AGL) using 3-component
transducers. Figure 19 (a) shows the image results after processing the data. The figure
shows that the signals at the beginning have large amplitude, which can be considered
as machine noise. Therefore, user can use ‘suaglpickr” to pick the first arrival time by
avoiding the machine noise, to set the noise window after the machine noise. From the
figure, we can estimate that the first arrival time is at around 0.16 seconds, and the
machine noise disappears after 0.05 seconds. Thus, the noise window can range from
0.05 to 0.15 seconds, and the signal window from 0.15 to 0.2 seconds. Using
‘suaglpickr” with the signal window and noise window redefined, we can get the result
as in Figure 19 (b) that the mean first pick time is 0.1657 seconds. This result matches
our estimates in the beginning by looking at the figure but it gives a more accurate and
reliable picking.
33
Figure 19. (a) Shot record (20 traces) for AGL 'KONG' sample in AGL system (b)
Results of first break picking time for AGL sample from direct contact measurements
with 1 MHz 3-C transducers
4.2.2 Case study 2
Another experiment was conducted in the Allied Geophysical Lab (AGL) and
Rock Physics Lab (RPL). Two aluminum samples with different dimensions were used
in the experiment for comparison. Two different transducers (AGL 3-component
transducer and RPL transducer) were tested as source and receiver. Both of the
transducers have a central frequency of 1 MHz. The experiments measured acoustic
response through test samples to determine first arrival time, and acoustic response with
the transducers in direct contact to establish zero-time.
Figure 20 shows the results of direct contact first break picking time for 1 MHz
3-C transducers from processing the data from AGL using ‘suaglpickr’. The data has 20
34
traces with mean first break time as 0.0067 seconds, variance of 0.000004 and standard
deviation of 0.00047 seconds. The data for RPL sample shown in Figure 21 has 24
traces; the mean first break time is 0.126917 seconds, with a variance of 0.000002 and
standard deviation of 0.000282 seconds for the first break time. P wave velocity was
measured in two acquisition systems (RPL and AGL) with two transducers. Two
calibration records were tested through two different samples: AGL sample (named as
‘KONG’) and RPL sample. Table 4 shows the test results of the two samples for P wave
velocity in AGL system, using 3-C transducers of 1MHz. Table 5 shows the test results
of the two samples for P wave velocity in RPL system using 3-C transducers of 1MHz.
Table 6 shows the test results of the two samples for P wave velocity in RPL system
using RPL transducers of 1 MHz. Table 7 shows the comparison for all the velocities
with different components. The data with 3-C transducer in RPL system is chosen to be
the reference data for future use.
35
Figure 20. Result of first break picking time from direct contact measurements with 1
MHz 3-C transducers (data now shown)
36
Figure 21. Result of first break picking time for RPL sample first break time with 1
MHz 3-C transducers (data not shown)
37
Table 4. Measurements for P wave velocity of RPL Sample and AGL sample 'KONG'
by using both AGL system and 1 MHz 3-C transducers
Table 5. Measurements for P wave velocity of RPL Sample and AGL sample 'KONG'
by using both RPL system and 1 MHz 3-C transducers
38
Table 6. Measurements for P wave velocity of RPL Sample and AGL sample 'KONG'
by using both AGL system and RPL transducers
Table 7. Comparison for P wave velocities with different measurement parameters
4.3 Dispersion in Alloy Aluminum Block
From the above method, calculated velocities versus frequencies for the
aluminum block are listed in the Table 8. Based on the P and S velocities from the
39
Table 8, curve with frequency versus velocity is plotted as shown in Figure 22 (a) (b)
(c). It shows that dispersion occurs in the aluminum block.
Table 8. Velocities with error bar vs. frequency range
40
Figure 22. (a) P-wave velocity vs. log scale frequency with error range for both velocity
and frequency using P-wave transducers (b) S wave velocity vs. log scale frequency
with error range for both velocity and frequency using S wave transducers (c) P-wave
velocity vs. log scale frequency with error range for both velocity and frequency using
S-wave transducers
41
Chapter 5
Discussions and Conclusion
In conclusion, this thesis describes several physical models to study the property
of an aluminum block in order to understand seismic properties of the seafloor better.
The purpose is to get the P and S wave velocities using transducers with different
frequencies. In order to deliver a more precise first arrival time automatically, a picking
algorithm, “suaglpickr” was developed and implemented, both included as a C program
and a command in Seismic Unix. This algorithm was validated, and also proved to be
flexible by changing the threshold levels and no false positive probability. When
applied to the real seismic data, the results show that the algorithm delivers a precise
data set with high reliability.
Some dispersion was found in the aluminum, which means that the velocities
vary with the frequencies of the transducers. The dispersion should not occur in the pure
aluminum based on the theory of a previous reference. However, this ‘dispersion’ can
be caused by the calibration of the lab system, the lab system shows the error ranges
about 1%, therefore, in Figure 22, the velocity for P-wave and S-wave can be connected
by a straight horizontal line correlated with the lab system error. The error can also
caused by the composition of the aluminum alloy. In order to analyze this abnormal
phenomenon, the aluminum block needs to be further studied and also compared with
the lab system.
42
For future work, the picking algorithm can be applied to pick the S-wave first
arrival time. Since the S-wave has a smaller velocity than P-wave, P-wave first arrival
occurs earlier than the S-wave first arrival, user can set the noise window after the Pwave signal to catch the S-wave first arrival time.
Chapter 6
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White, J. E. and Sengbush, R. L., 1953, Velocity measurements in near surface
formations: Geophysics, v. 18, p. 54-69.
White, J. E., 1965, Seismic waves: Radiation, transmission and attenuation: McGrawHill Book Co.
Wuenschel, P. C., 1965, Dispersive Body Waves- An experimental Study: Geophysics,
v. 30, p, 539-551
W. S. Jardetzy and F. Press, Crustal Structure and Surface Wave Dispersion (Part 3),
Bull. Seism, Soc. Am., 43: 137-144 (1953)
Yilmaz, O. 2001. Seismic Data Analysis, Processing, Inversion and Interpretation of
Seismic Data. Stephen, M. Doherty, editor. Society of Exploration Geophysics.
Zlatev P., Poeter E. and Higgins J. (1987), “Physical Modeling of the Full Acoustic
Waveform in a Fractured Fluid-filled Borehole”, Geophysics, vol.53, p.1219-1224.
47
Appendix A
Figure 23. (a) dB picking for 500 kHz shear wave transducers (b) dB picking for 2.25
MHz shear wave transducers (c) dB picking for 5 MHz shear wave transducers
Figure 24. (a) dB picking for 500 kHz P wave transducers (b) dB picking for 1 MHz P
wave transducers (c) dB picking for 5 MHz P wave transducers
48
Appendix B Source Code for “suaglpickr”
/* Copyright (c) Colorado School of Mines, 2005.*/
/* All rights reserved.
*/
/* SUOP: $Revision: 1.17 $ ; $Date: 2006/12/05 07:35:34 $
*/
#include "su.h"
#include "segy.h"
#include <stdio.h>
#include <math.h>
/*********************** self documentation **********************/
char *sdoc[] = {
"
",
" SUAGLPICKR - First arrival picking based on standard devition of noise",
"
",
" suaglpickr <stdin > amp_over_stddev [optional params]
",
"
",
" Required parameters:
",
" none
",
"
",
" Optional parameter:
",
" tn1=0
begin time (s) of the noise window
",
" tn2=0.15
end time (s) of the noise window
",
" ts1=0.15
begin time (s) of the signal window
",
" ts2=0.3
end time (s) of the signal window
",
" m=2
consecutive samples over threshold
",
"
to be considered as signal
",
" beta=2.2
standard deviation threshold level
",
" filename=output.txt
output txt file
",
" out=1
output su data is origAmp/noiseStdDev with zero before 1st break pick
",
"
=2 output zero trace except 1st break pick has unit ampitude
",
"
",
" Note:
",
" 1. output su data is input amp divided by noise std deviation
",
NULL};
/* Credits:
*
* Chris clone of suop.c 7/31/2011
*
Heather Yao: add a and m for the threshold level for false probability calculation
49
8/28/2011
* Heather: Add pickr for first time arrival time and sample number
*
* Notes:
*/
/**************** end self doc ***********************************/
/* segy data */
segy *trp;
/* SEGY trace array */
segy tr; /*SEGY trace */
int main(int argc, char **argv) {
int nt;
/* number of samples on input trace
*/
float dt;
/* time sampling interval */
float twobydt;
/* 2*dt */
float *tmp;
/* temp trace for some calcs */
float *tmp1;
/* temp trace for some calcs */
int j;
float val;
float mean;
int i;
float tn1, tn2;
/* min and max time of noise window */
int itn1, itn2; /* min and max time samples of noise window */
int nw;
/* length of the noise window in samples */
float ts1, ts2;
/* min and max time of signal window */
int its1, its2; /* min and max time samples of signal window */
int sw;
/* length of the signal window in samples */
float sdev;
/* standard dev of noise */
int m;
/* consecutive variable for the sample over threshold */
float beta;
/* threshold level tao=a*sdev */
float prob_false_pos_x;
/* Probility of false positive of position x */
float prob_no_false_pos_x;
/* Probility of no false positive of position x */
float prob_false_anywhere;
/* Probility of false positive of anywhere */
float prob_no_false_anywhere;
/* Probility of no false positive anywhere */
float prob_f;
/* error function probility based on a */
int pickN;
/* the number picked as the first time arrival */
float picktime;
/* the time picked as the first time arrival */
int icnts;
/* initial number */
cwp_String filename;
/* filename for output txtfile */
int out;
/* output su data is origAmp/noiseStdDev with zero before 1st break
pick when out=1; zero trace except 1st break when =2 */
float SumTime;
/* summation of first pick time */
int tr_num;
/* trace number */
float mean_pick;
/* mean of the pick time */
float picktime_array[100];
float val_pick;
float sdev_pick;
/* standard dev of pick time */
FILE *fp;
50
/* Initialize */
initargs(argc, argv);
requestdoc(1);
/* Get information from first trace */
if (!gettr(&tr)) err("can't get first trace");
nt = tr.ns;
dt = tr.dt/1000000.0;
twobydt=2*dt;
/* allocate temp trace */
tmp = alloc1float(nt);
tmp1 = alloc1float(nt);
/* get user preferences */
/* noise */
if (!getparfloat("tn1", &tn1)) tn1 = 0.0;
if (!getparfloat("tn2", &tn2)) tn2 = 0.15;
/* signal */
if (!getparfloat("ts1", &ts1)) ts1 = 0.15;
if (!getparfloat("ts2", &ts2)) ts2 = 0.3;
/* algorithm params */
if (!getparint("m",&m)) m = 2;
if (!getparfloat("beta", &beta)) beta = 2.2;
/* output text file */
if (!getparstring("filename", &filename)) filename ="output.txt";
/* output su amplitude */
if (!getparint("out",&out)) out = 1;
/* find time samples associated with top and
bottom of noise window */
itn1 = tn1/dt;
itn2 = tn2/dt;
/* find length of noise window in samples */
nw = itn2 - itn1 + 1;
/* find time samples associated with top and
bottom of signal window */
its1 = ts1/dt;
its2 = ts2/dt;
/* find length of signal window in samples */
sw = its2 - its1 + 1;
/* find the probility of of false positive at position time sample */
prob_f=1-erf(beta/sqrt(2));
/* prob of false positive at random sample */
prob_false_pos_x=pow(prob_f,m);
51
/* prob of no false positive at random sample */
prob_no_false_pos_x=1-prob_false_pos_x;
/* prob of no false positive for all samples */
prob_no_false_anywhere=pow(prob_no_false_pos_x,sw);
/* prob of false positive for all samples */
prob_false_anywhere=1-prob_no_false_anywhere;
/* open output text file and echos success */
fp = fopen(filename, "w");
if (fp){
warn("Text file open");
}
else {
err("Error opening output file");
}
/* Main loop over traces */
SumTime=0;
tr_num=0;
do {
/* copy trace into temp array */
for (i = 0; i < nt; ++i) {
tmp[i] = tr.data[i];
}
/* calc mean of noise */
val = 0.0;
for (j = itn1; j <= itn2; ++j) {
val += tmp[j];
}
mean = val/nw;
/* calc std dev of noise (with mean correction) */
val = 0.0;
for (j = itn1; j <= itn2; ++j) {
val += (tmp[j] - mean)*(tmp[j] - mean);
}
sdev = sqrt(val/ (float)(nw-1) );
/* divide data amps by std dev of noise */
for (i = 0; i < nt; ++i) {
tr.data[i] = tr.data[i] / sdev;
}
/* find the first time arrival sample number */
pickN=0;
picktime=0;
52
icnts=0;
/* need to add positive and negative amplitude options */
for (i=its1; i<its2; ++i){
if (fabs(tr.data[i])>=beta){
icnts++;
if (icnts==m) {
pickN=i-m+1;
picktime=(i-m)*dt;
goto next;
}
}
else {
icnts=0;
}
}
next:
/* need to add positive and negative amplitude options
for (i=0; i<nt; ++i){
if (fabs(tr.data[i])>=beta){
icnts++;
if (icnts==m) {
pickN=i-m+1;
picktime=(i-m)*dt;
goto next;
}
}
else {
icnts=0;
}
}
next:
*/
/* Output amp/noise_std_dev after the first arrival, before the first pick value=0 */
if (out==1) {
for (i=0; i<pickN; ++i) {
tr.data[i]=0;
}
}
else {
for (i=0; i<nt; ++i) {
if (i==pickN-1) {
tr.data[i]=1;
}
else {
53
tr.data[i]=0;
}
}
}
puttr(&tr);
/* Output the result */
fprintf(fp, "Noise window(s) : %f %f \n", tn1, tn2 );
fprintf(fp, "Signal window(s) : %f %f \n", ts1, ts2 );
fprintf(fp, "Signal window length : %d \n",sw );
fprintf(fp, "beta : %f \n",beta );
fprintf(fp, "m : %d \n",m );
fprintf(fp, "i : %d \n",i );
fprintf(fp, "dt : %f \n",dt );
fprintf(fp, "Probability of error : %f \n",prob_f );
fprintf(fp, "First time arrival sample number : %d \n",pickN );
fprintf(fp, "First time arrival time(s) : %f \n",picktime );
fprintf(fp, "Probability of false positive anywhere : %f \n",prob_false_anywhere );
for (i=0; i<sw; ++i){
fprintf(fp, "%f %f \n", ts1+i*dt, tr.data[i]);
}
/* add value to trace number and summation of pick time to calculate the mean value of
pick time */
SumTime=SumTime+picktime;
picktime_array[tr_num]=picktime;
tr_num++;
} while (gettr(&tr));
/* calculate mean of the pick time */
mean_pick=SumTime/tr_num;
fprintf(fp, "trace number : %d \n",tr_num );
/* calculate the standard deviation of the pick time */
val_pick = 0.0;
for (j =0; j < tr_num; ++j) {
val_pick += pow((picktime_array[j] - mean_pick),2);
fprintf(fp, "trace_number : %d pick_time(s) : %f\n", j, picktime_array[j]);
}
fprintf(fp, "mean first pick time(s) : %f \n",mean_pick );
sdev_pick = sqrt(val_pick/ (float)(tr_num-1) );
fprintf(fp, "val : %f \n",val_pick );
fprintf(fp, "standard deviation for first pick time(s) : %f \n",sdev_pick );
54
/* close text file */
fclose(fp);
return(CWP_Exit());
/* return 1 */
}
55