Instruction- Analysis of SPAC Method April. 05, 2021
IISEE, BRI, Japan
By T. Yokoi

1

Revision from SPAC2020 to SPAC2021 is minor.

Acknowledgments:
The revision for the 2021 version was partly supported by Japan Science andTechnology Agency (JST) and Japan International Cooperation Agency (JICA) underthe “Science and Technology Research Partnership for Sustainable Development(SATREPS): Integrated Research on Great Earthquakes and Disaster Mitigation in
Nepal Himalaya (FY2016-2021)”.
2

Procedures of analysis
Field Work

Estimation of Shear Wave Velocity Structure
velocity (km /sec)
0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.000
0.020
0.040

Depth (km)

0.060
0.080
0.100
0.120
0.140

Microtremor Array Measurement(Vertical Component)

0.160
0.180

Multi-channel Records

Velo.profile

4. Heuristic Search of Vs Structure
0.200

1. (Multiplexing &) Resampling

Inversion or
Heuristic Search

0.4
0.2
0
-0.2

Average over azimuth

-0.4
0

0.5

1

1.5

SPAC Coefficient

0.6

0.8
0.6
0.4
0.2
0
-0.2
-0.4

2

0

0.5

Frequency
1.2
1
0.8
0.6
0.4
0.2
0
-0.2

Average over azimuth

-0.4
0

0.5

1

Frequency

1

1.5

2

Frequency

1.5

2

1
0.8
0.6

Phase Velocity

1

1
0.8

Least Square Fitting to Jo(kr)Calculation of the phase velocity

SPAC Coefficient

Complex Coherence Function

Complex Coherence Function

Calculation of SPAC Coefficient

0.4
0.2
0
-0.2

Frequency

-0.4
0

0.5

1

1.5

2

Frequency

2. Calculation of SPAC coefficient

3. Determination of Dispersion Curve
3

Note: This version was developed on Linux: Ubuntu 19.10 (Eoan Ermine) on VirtualBox
version 6.1.0 r135406on Windows10 Home 64bit (Build 14393) for 64bit PC, using
gfortran compiler.
Operation on other OS may require additional revision or modification by users
themselves.
Execution of commands is conducted as./bin/executable_file_name.exeorsh shell_script_file_name.sh
If it is necessary to leave log file of execution, for example,./bin/executable_file_name.exe 2>&1 | tee ./spacwkf/log/log_file_name.log
orsh shell_script_file_name.sh 2>&1 | tee ./spacwkf/data/log/log_file_name.log
4Folder Structure
Every necessary programs and files are stored
under the folder “SPAC2021”. The command
operation must be conducted in the same folder,
where shell script files are stored.
The source codes of the programs are stored in
the subfolder “source”, document files including
this instruction manual in “doc”, executable ones in“bin”.

The subfolder of work space “spacwkf” contains
the subfolder “prm” for parameter files that includes
script files of GNUPLOT and the subfolder “data”
for data files including graphic ones.
The compressed file “spacwkf.tar.gz” keeps
subfolder structure of “spacwkf” and all parameter
files in “spacwkf/prm”.
5Note: GNUPLOT scripts files
Some files of GNUPLOT scripts are stored under the subfolder“./spacwkf/prm/gnuplt_scripts”

These can be loaded on GNUPLOT as load ‘????’
Some programs create the scripts of GNUPLOT that include the command‘set terminal x11’ ,This works on the GNUPLOT on Ubuntu and may be that on Windows.
If any problem on Windows, it is worth to try to replace it with‘set terminal wxt’ .

6Note: Executable files
The folder “SPAC2021” includes a sub-folder “bin” where several executable files
are stored. Their source code files are stored in the subfolder “./source”. Then, thefollowing command is required to re-compile them if necessary. In the folder
SPAC2021, type in the following command.
gfortran ./source/???.for –o ./bin/???.exeOr,make allto compile all necessary source codes at once as shown below.

7Note: Shell script files
The folder “SPAC2021” includes several shell script files.
They are composed of few executing commands to reduce the typing tasks in dataprocessing.
The following command can execute the shell script files.
sh shell_script_file_name.sh
As the contents of the shell script files contained in this program package aresimple, they can work as batch files. However, it is necessary to activate batch files
using the following.
chmod u+x shell_script_file_name.shFor execution as a batch file,shell_script_file_name.sh8

Note: Cleaning up the subfolders• Use
sh clean_all.shin the folder “SPAC2021” to delete all files of input data,interim outputs and results for a new processing task.
• Use
sh clean_sg2.shin the folder “SPAC2021” to delete all input files of sg2
format under “./spacwkf/data/sg2_files”.
• Use
sh clean_ls.shin the folder “SPAC2021” to delete all input files of win
format under “./spacwkf/data/ls_files”, but subfolder
9
structure is kept.

Note: Format of Data Files• Basically, users themselves are responsible to convert theformat of the input data files to one of those acceptableformats by this program package.
• The acceptable format is “*.cdm” described in the section “1.
Resampling”.
• The following two format converters are provided:• sg2 (seg2 standard of IEEE)➔./spacwkf/multiplexed_files/*.dat• ls (Win format of Hakusan-Kogyo)➔./spacwkf/cdm_files/*.cdm10Build SPAC2021
makefile:
FC = gfortranstore= 2>&1 | tee -a ./spacwkf/log/make_all.log
all:clean_log${FC} ./source/cf_panel1.for-o ./bin/cf_panel1.exe ${store}${FC} ./source/comparison_plt.for -o ./bin/comparison_plt.exe${store}${FC} ./source/disp_err1.for-o ./bin/disp_err1.exe ${store}${FC} ./source/disp_sma1_2.for-o ./bin/disp_sma1_2.exe ${store}${FC} ./source/distazi.for-o ./bin/distazi.exe ${store}${FC} ./source/fourier_plt.for-o ./bin/fourier_plt.exe ${store}${FC} ./source/geometry.for-o ./bin/geometry.exe ${store}${FC} ./source/interim_plt.for-o ./bin/interim_plt.exe ${store}${FC} ./source/lstocdm2.for-o ./bin/lstocdm2.exe ${store}${FC} ./source/mk_title.for-o ./bin/mk_title.exe ${store}${FC} ./source/multi_pre.for-o ./bin/multi_pre.exe ${store}${FC} ./source/multipx6.for-o ./bin/multipx6.exe ${store}${FC} ./source/prm_maker.for-o ./bin/prm_maker.exe ${store}${FC} ./source/resample5.for-o ./bin/resample5.exe ${store}${FC} ./source/resample6.for-o ./bin/resample6.exe ${store}${FC} ./source/resample_pre.for-o ./bin/resample_pre.exe ${store}${FC} ./source/results_plt.for-o ./bin/results_plt.exe ${store}${FC} ./source/seeblk1.for-o ./bin/seeblk1.exe ${store}${FC} ./source/seewav7.for-o ./bin/seewav7.exe ${store}${FC} ./source/seg2read.for-o ./bin/seg2read.exe ${store}${FC} ./source/vel_model_plt.for -o ./bin/vel_model_plt.exe ${store}${FC} ./source/zcorrel5_3.for-o ./bin/zcorrel5_3.exe${store}clean:
cd ./bin/; rm *.exe; cd ..
clean_log:
rm –f ./spacwkf/log/make_all.log 2>/dev/null

110. Format conversion
0.1. seg2 standard format
Shell Script used:
sh seg2read.shProgram and parameter file used:
seg2read.exe +./spacwkf/prm/seg2read.prm
seg2read.exe is prepared for the field data files of seg2 standard
format.

Terminology
Multiplexing:
To sort the data individually stored in single channel files
into a multi-channel file of the time-sequential format.

12Here, seg2 standard (multiplexed binary) format (IEEE) is
explained.
The expected input files of seg2 format are, for example, thoseobtained in the field using multi-channel data logger designed forthe exploration geophysics.
seg2read.exe+ Convert data format from seg2 standard format (binary & multichannel) in the sub-folder “spacwkf/data/sg2_files" to cdm format(ascii text, multi-channel),+ Channel pivoting and extraction+ Store the output files into “spacwkf/data/multiplexed_files”

13First: Copy all the seg2 format
files to be converted into the subfolder “spacwkf/data/sg2_files".
Example:14

seg2read.sh:#!/bin/sh -x
cd spacwkf/data/sg2_files
ls *.sg2 > sg2file.lst
cd ../../..
./bin/seg2read.exe | tee spacwkf/log/seg2read.log
cd spacwkf/data/multiplexed_files
rename 's/^....../ss/' *.dat
ls *.dat > mltfile.lst
cd ../../..
./bin/mk_title.exe

Shell script executes "ls *.sg2 > sg2file.lst" in this sub-folder and existingsg2 files are listed in the newly created file "sg2file.lst".
All the files listed in it that have the extension specified in the 3rd line of theparameter file “seg2read.prm”.
Finally, the first line of “seg2read.prm” is copied to “graph_title.txt” in the
subfolder “./spacwkf/prm”.
15

Example: seg2read.prm
All the files listed in "sg2file.lst" that have the extension specified in the 3rd line
are converted to the output files that have the extension given in the 4th line.
Edit the file "sg2file.lst" using “gedit” or other text editor if necessary.
seg2read.prm
Iwaki City Hall, radius=25m, McSeis/SW, L22 X 7 points
Dec.23 2012 :comment(a70)
0.055:(A12) scaling factor (for output files in mkine(1.e-3cm/s)/gal(1.e cm/s^2))
sg2: extension of input seg2 format files(a3)dat: extension of output ascii text files(a3)0 3 0.1 1.0 1.5 :nfilter(=1:apply),nchara=3:bandpass),fl,fh,fs
pvlist 7 6 5 4 3 2 1

16

Explanation: seg2read.prm
All the files listed in "sg2file.lst" that have the extension specified in the 3rd line
are converted to the output files that have the extension given in the 4th line.
Edit the file "sg2file.lst" using “gedit” or other text editor if necessary.
seg2read.prm
1st line : comment (a70)
2nd line : scaling factor (use the value that makes the unit of the output files"mkine" (1.e-3 cm/s))
3rd line : extension of input seg2 format files(a3)
4th line : extension of output ascii text files(a3)➔Fix it “.dat”
5th line : nfilter(=0:pass, =1:apply, =2:DC & Trend removal),ncharacter(=2:lowpass,=3:bandpass),fl,fh,fs
6th line : Channel Pivoting'normal' : no pivoting, all channel used
'rev_al' : all channel used but in reversed order'rev_fh' : all channel used but former half in reversed order'rev_lh' : all channel used but latter half in reversed order‘pvlist 2 1 3 4 6 23 24’ : Pivoting list.

17

Examples of the 6th line of seg2read.prm

Use all channels without pivoting:normal: Channel Pivoting
Use all channels but reversed order:
reverse: Channel Pivoting
Use the first 7 channels of the input files without changing order:
pvlist 1 2 3 4 5 6 7 : Channel Pivoting
The same as above but 7th channel moved to the first:
pvlist 7 1 2 3 4 5 6 : Channel Pivoting
Use only odd numbered channels among 24 without changing order:
pvlist 1 3 5 7 9 11 13 15 17 19 21 23 : Channel Pivoting
If a channel number in pvlist is negative, the polarity of thatchannel is reversed.

Note: Be sure to put ‘ ‘(blank) before ‘:’(colon), otherwise the program canhave an error in detecting the end of line.

18

Execution

Input files are copied in ‘./spacwkf/data/sg2_files’.
Multiplexed outputs are stored &./spacwkf/data/multiplexed_files”.
Log file is stored in ‘spacwkf/log/seg2read.log’

19

The converted files are stored in “./spacwkf/data/multiplexed_files”

Note: The converted files are already multiplexed and stored in the
subfolder “./spacwkf/data/multiplexed_files” with the extension“.dat”. For these files, the next step is resampling.

20

Format of output files
in ./spacwkf/data/multiplexed _files:
Users who use single channel recorders or data loggers must multiplex
the record files in the following format by themselves.
7 0.0020
0.5500E-01
16384 mkine
Iwaki City Hall, radius=25m, McSeis/SW, L22 X 7 points
Dec.23 2012
0.000000 -0.3943280E-05 0.9517429E-05 -0.2661598E-06 -0.7497172E-05
0.002000 -0.4349669E-05 0.9327264E-05 0.5046593E-06 -0.8176097E-05
0.004000 -0.4659054E-05 0.9203497E-05 0.5160243E-06 -0.8879738E-05
0.006000 -0.4855397E-05 0.9563433E-05 -0.1432124E-06 -0.9843301E-05
0.008000 -0.6745830E-05 0.1001426E-04 -0.5579629E-06 -0.1409490E-04

0.34044
0.352410.35992
0.37105
0.37764

1st line: Number of channels, Dt(sec), scale, number of samples,unit (mkine or gal)
2nd line: Comment (less than 50 characters)
3rd line: Time, 1st-ch sample, 2nd-ch sample, 3rd-ch sample, ….

In the next step (resamplec.for reads this file as follows)read(1,*)nch00,dt00,scale00,ndata00,cunit…
read(1,'(a50)')comment…
read(1,*,end=10) xdum,(x(i,j),j=1,nch)21

Warning!
seg2read.exe can handle less than or equal to 25 channels andless than or equal to 500,000 samples in every channel.
Exceedance may result in a significant error.
It is recommendable to split the input data file if too long, forexample, into several files of 1 hour or 30 minutes data.
Ref:
500,000 samples correspond to 1.38 hours for 100 Hz sampling,
1.11 hours for 125 Hz sampling,
41.6 minutes for 200 Hz sampling,33.3 minutes for 250 Hz sampling
16.6 minutes for 500 Hz sampling.
22

Output files is stored in“./spacwkf/data/multiplexed _files”

Jump to “1.2. Plot Waveform”.

230. Format conversion
0.2. win format for LS8800
This is the example of individually recorded data using a tri-axial
sensor and three channel data logger at each observation point.
Format conversion & Multiplexing must be done by the users prior
to the analysis for the case of individual recording at each site.
Here win format is explained. The win format data files are created,e.g., LS8800 of Hakusan Kogyo.
The converted files must be written in a format that is readable in thenext step: multiplexing.
As it is impossible to cover all existing formats in the world, it isstrongly recommended for users to make their own program forformat conversion.
24Format conversion is conducted using
sh lstocdm2.shin the folder “SPAC2019”.
Note: Usage of 4 seismographs in a site is assumed.
Preparation:1) Edit the parameter file “prm_maker.prm”
Sitename_: site name (a9)3 3: numbers of obs_ponts and channels
１0: duration of each connected file in min.(integer)
17091511.45 : first file name (yymmddhh.mm)
20: number of output connected files (integer)2) Copy the data files (binary) of LS8800 into the subfolders of“spacwkf/data/ls_files” as follows:“no1” files from seismograph No.1
“no2” files from seismograph No.2
“no3” files from seismograph No.3
“no4” files from seismograph No.4

25

lstocdm2.sh#!/bin/sh -x./bin/prm_maker.exe | tee spacwkf/log/prm_maker.log./bin/lstocdm2.exe | tee spacwkf/log/lstocdm2.log
cd ./spacwkf/data/cdm_files
rm *.cdm 2>/dev/null
cd ../../..
mv ./spacwkf/data/ls_files/Combined_Data/*.cdm ./spacwkf/data/cdm_files

Execution:./bin/prm_maker.exe➔ “lstocdm2.prm” is created in “spacwkf/prm”.
./bin/lstocdm2.exe➔ All converted and separated files are stored in“./spacwkf/data/ls_files/Combined_Data”.
All converted and separated files are automatically stored in“spacwkf/data/ls_files/Combined_Data”.
Then, the subfolder “./spacwkf/data/cdm_files” is cleaned.
Finally, by the command “mv” at the last line all of the cdm files are moved from“./spacwkf/data/ls_files/Combined_Data” to “./spacwkf/data/cdm_files”.
26

Example:lstocdm2.prm: automatically created by lstocdm2.sh

27

This error message means theclipping of data. Check thetime and eliminate thecorresponding part.
28

File name (E1151145.cdm) includes the following information:
1st letter: component
2nd letter: numbering of seismograph (=numbering of station)
3rd & 4th: Date in (i2)5th & 6th: hour in (i2)7th & 8th; minutes in (i2)29

Example of a converted file

3 lines for header

Data lines:

Numbering,
(A8)

time,
(A13)

data
(e16.7)30

The created single channel file by this format conversion program will be read in
the next step using “multipx6.exe” as follows.
“multipx6.for”
character cline(3)*80,cdum*13,cdummy*8! Declare three! character strings………………………………………………………..
do i=1,3
read(1,'(a80)')cline(i)! Read 3 lines header
enddo
do i=1,nst0-1
read(1,*)cdummy! Skip first nst0 sec data
enddo
do i=1,ndur0c read input dataread(1,*,end=10)cdummy,cdum,xdum
x(i,j)=xdum/scaleenddo
10 ndur0=i-1! Adjust number of samples………………………………………………………..
Character strings cline(3) are not used further. Neither cdummy nor cdum.

31Preparation for Multiplexing• In the next step, multipx6.sh is used with the parameter file
“multipx6.prm”.
• For automatic editing of multipx6.prm, multi_pre.sh is prepared.
• Edit the following “multi_pre.prm” in “spacwkf/prm” and run“sh multi_pre.sh”.
CityHall 3P-Array l=35m 2017/09/11:45-2H20M:comment(A50)10: duration of each connected file in min.(integer)
V1151145: first file name (yymmddhh.mm)
cdm: extention (A3)
1 2 3 0: station pivot (0=4th_ch_not_used)
20: number of output connected files(integer)

•
•
•
•
•
•

1st line: Comment but later used as the title of all graphs showing the results of analysis.
2nd line: Duration of connected files same as the 3rd line of “prm_maker.prm”.
3rd line: The eariest file name for the 1st position (A8)
4th line: Extension of the name of files in the folder “cdm_files”, i.e., cdm.
5th line: Station pivoting list.
32
6th line: Number of connected files same as the 5th line of “prm_maker.prm”.

Execution

Automatically created multipx6.prm which will be used in the next step.

Edit it in an appropriate way if necessary.

33

Note: Example for the instruction below
An example that consists of three arrays of different sizes is shown below.
+ SS-1 Array: 7 points equilateral triangle array with the center+ MM-1 Array: 4 points equilateral triangle array with the center+ LL-1 Array: 4 points equilateral triangle array with the center
Note: these are different from the examples of the data format conversion
shown in the previous slides.
For SS-1 Array

For MM-1 Array

For LL-1 Array

1.Multiplexing& Resampling

1.Multiplexing& Resampling

1.Multiplexing& Resampling

2.Calculation of
SPAC coefficient

2.Calculation of
SPAC coefficient

2.Calculation of
SPAC coefficient

3.Determinationof dispersion curve
4. Heuristic Searchof Vs Structure34

1. (Multiplexing &) Resampling35

Flow of the data processing for the conventional SPAC
5

Multiplexing
Resampling &Screening

4

6
7
1

3

2

Field.data

Field measurement
Single channel files
Individual Recording

Multi-channel files

Multi-channel &multi-measurement
file

SPAC Coeff.

System Correction
Multiplexing
Resampling &Screening

6 57
1 43
2

Huddle test
Single channel files
Multi-channel files

Huddle.Test.
data
Multi-channel &multi-measurement
file

36

1. Multiplexing & Resampling
1.1. Multiplexing (Optional)
Single channel files are combined into a multi-channel file
(This step is not necessary for the multi-channel recording cases)
multipx6.sh + ./spacwkf/prm/multipx6.prm
First step is to edit the parameter file multipx6.prm.
However, it is recommendable for users to make own conversion
program from her/his original format files directly to multiplexed
files of the format explained below.
37

Terminology
Multiplexing:
To sort the data individually stored in single channel files into a multichannel file of the time-sequential format.
Huddle test:
Common input motion recording to determine the difference of the systemcharacteristics among the recording system and/or channels.
The seismometers used in field measurement are put close each other like a
huddle and simultaneous recording is conducted.

Re-sampling:
It can be done to thin the data out in order to reduce the size of data files andthe load to PC for processing. This can cause the aliazing effect. Then, it Is
necessary to apply the digital anti-alias filter that has high cut characteristics
before thinning out.
System correction:
The difference of the characteristics among the recording system can becorrected using the data obtained by huddle tests.

38

Multiplexing the single channel files
5
7 stations
4

6
7
1

2

3

Simultaneously &individually
recorded data

S11
S21
S31 S41S51 S61 S71

S12S22
S32 L42S52 S62 S72

S13
S23
S33 S43S53 S63 S73

Multipx6.forMultiplexing

Multiplexing

Multiplexing

SS01.dat

SS02.dat

SS03.dat

multipx6.prm

Multi-channel files

39Warning:

The program multipx6.sh does not have the functionality to adjust
the time difference among the single channel files. The input files
must have the same timing.
Confirm the following:+ All input files have the same sampling interval.
+ All input files have their first datum that are sampled at the same
time.

40

multipx6.prm
3

1st case

2nd case

3rd case:Number of cases:This blank is necessary
4 0.01:Number of Channels,dt
0.0
163.83:tst,tdur
1.e11 mkine:scale(input data is divided by this scale),unit(a5)0 3 0.005 1.0 1.5:nfilter(=1:apply), ncharacter(=2:lowpass,=3:bandpass),fl,fh,fs
4.cdm:nattach, cattach
2 MM:n_out(A12),cout("**.dat" is attached)
MM-1, Iwaki City Hall, Dec.22, 2012
:comment(A50)
21 8:number of measurement in the same array configuration,n_charactersxm21001 sxm21002 sxm21003 sxm21004...
sxm23601 sxm23602 sxm23603 sxm23604:This blank is necessary
7 0.002:Number of Channels,dt
0.0
32.766:tst,tdur
3.16e2 mkine:scale(input data is divided by this scale)0 3 0.005 1.0 1.5:nfilter(=1:apply), ncharacter(=2:lowpass,=3:bandpass),fl,fh,fs
4.cdm:nattach, cattach
2 SS:n_out(A12),cout("**.dat" is attached)
SS-1, Iwaki City Hall, Dec.22, 2012
:comment(A50)
30 8:number of measurement in the same array configuration,n_charactersxs10101 sxs10102 sxs10103 sxs10104 sxs10105 sxs10106 sxs10107…
sxs13001 sxs13002 sxs13003 sxs13004 sxs13005 sxs13006 sxs13007:This blank is necessary
4 0.01:Number of Channels,dt
0.0
163.83:tst,tdur
3.16e10 mkine:scale(input data is divided by this scale)0 3 0.005 1.0 1.5:nfilter(=1:apply), ncharacter(=2:lowpass,=3:bandpass),fl,fh,fs
4.cdm:nattach, cattach
2 LL:n_out(A12),cout("**.dat" is attached)
LL-1, Iwaki City Hall, Dec.22, 2012
:comment(A50)
28 8:number of measurement in the same array configuration,n_charactersxl21001 sxl21003 sxl21005 sxl21007
41…
sxl24601 sxl24603 sxl24605 sxl24607

multipx6.prm
3:Number of cases:This blank is necessary
4 0.01:Number of Channels,dt
0.0
163.83:tst,tdur
1.e11 mkine:scale(input data is divided by this scale),unit(a5)0 3 0.1 1.0 1.5 :nfilter(=1:apply),ncharacter(=2:lowpass,=3:bandpass),fl,fh,fs
4.cdm:nattach, cattach ➔ Input single channel file name2 MM
:n_out(A12),cout ("**.dat" is attached)
MM-1, Iwaki City Hall, Dec.22, 2012
:comment(A50)
21 8:number of measurement in the same array configuration,n_charactersxm21001 sxm21002 sxm21003 sxm21004
1st...
sxm23601 sxm23602 sxm23603 sxm23604
21th measurement

1ch

2ch

3ch

4ch

Input file names : sxm2??0?.cdm
consist of the character string ‘sxm2??0?’ of 8 characters plus anothercharacter string ‘.cdm’ of 4 characters. These character strings and their
number of characters are indicated in the 7th line for the latter and the 11th line
and below for the former. Program ‘multipx6.exe’ automatically combinesthem and read the data from the files.
42

multipx6.prm

Output file name: SS01.dat for the 1st measurement. ’01’ shows thenumbering of measurement.
…
SS30.dat for the 30th measurement. ’30’ shows thenumbering of measurement.
These output file names consist of the character string ‘MM’ of 2characters as indicated in the 8th line. The following two integers show
the numbering of measurement. ‘.dat’ is attached to all automatically.
The data from tst to tst+tdur are processed in every files.
Values read from the input files are divided by the scale factor given in
the 5th line. This value must be selected to make the unit of data in the
output file is ‘mkine’, i.e., 1.0E-5 M/sec for ground velocity. For groundacceleration ‘gal’, i.e., 1.0E-2 M/sec2 should be used. Otherwise theamplitudes of the data will be erroneously shown in the output figures.

43

sxm21001.cdm:
Example: format of input file (dt=0.01 sec) of single channel datain ./spacwkf/data/cdm_files
File=01001.cdm
ch. 1
unit
V
0 00:00:00.000 -0.1396391E+11
1 00:00:00.010 -0.1513392E+11
2 00:00:00.020 -0.1472600E+11
3 00:00:00.030 -0.1314799E+11
4 00:00:00.040 -0.7706377E+10
5 00:00:00.050 -0.3947473E+10

3 lines for header

Data lines:

16383 00:02:43.830 -0.7844215E+10
Numbering,
(A8)

time,
(A13)

data
(e16.7)44

Example of execution (from the folder SPAC2021):~$sh multipx6.sh

Working Folder=./spacwkf/prm/
Nch=
4 dt= 9.99999978E-03
Scale Factor= 9.99999980E+10
Does this scale convert the unit of data mkine ?
Please change the value if not.
0
3 4.99999989E-03 1.00000000
MM-1, Iwaki City Hall, Dec.22, 2012:
1 -th measurement:
4
sxm21001 sxm21002 sxm21003 sxm21004
16383

1.50000000./spacwkf/data/multiplexed_files/MM01.dat
2 -th measurement:
4…
Normal End

45

Example of output file (stored in the subfolder ./spacwkf/data/multiplexed_files

7 0.0020
0.3160E+03
16382 mkine
SS-1, Iwaki City Hall, Dec.22, 2012:
0.000000 -0.0000000E+00 -0.0000000E+00 -0.0000000E+00
0.002000 -0.8961562E-04 0.5361709E-05 -0.2044998E-04
0.004000 -0.1640327E-03 0.8138977E-04 -0.1974745E-04…

0.0000000E+00 -0.0000000E+00
0.1081865E-03 -0.1978091E-05
0.1997052E-03 0.2068763E-04

0.0000000E+00 -0.0000000E+00
0.2530022E-04 -0.4171700E-04
0.4874512E-04 -0.9626019E-04

1st line: channel number, dt, scale factor, number of samples, unit
2nd line & below: time, 1ch,2ch,3ch,…, 7ch.

46

Warning!
• The declared array size for input data in
multipx6.for is 1,200,000. This gives theconstraint:
tdur/dt < or =1,200,000• Similarlynch< or =1547

For much longer data file:“multipx6.for” can handle 1200,000 samples of 15 channels at once. If you
have data of longer recording time, it is recommendable to separate them
beforehand.
An alternative may be the following way of using “tst” and “tdur”
in ”multipx5.prm” can let you utilize the data fully.
For the 1st operation:
0.0
3600.0:tst(start time)),tdur(duration) in sec.

For the 2nd operation:
3600.01 3600.0:tst(start time)),tdur(duration) in sec.

For the 3rd operation:
7200.01 3600.0…

:tst(start time)),tdur(duration) in sec.

Namely, “multipx6.for”skips int(tst/dt) data and thenstarts reading the next data.
48

Example Data files: These are already multiplexed.
multi_SS.tar.gz
multi_MM.tar.gz
multi_LL.tar.gz
Copy these three compressed files into the subfolder“./spacwkf/data/multiplexed_files” for exercise with these example Data
files.

49

1.2. Plot Waveformseewav7.sh+ ./spacwkf/prm/seewav7.prm

50

Flow of the data processing for the conventional SPAC
5

Multiplexing
Resampling &Screening

4

6
7
1

2

3

Field.data

Field measurement
Single channel files
Individual Recording

Multi-channel files

Multi-channel &multi-measurement
file

SPAC Coeff.

seewav7.forseewav7.prm

Post Script files

Paste-up of Waveform
51

Multi-channel file: SS01.dat
7 0.0020
0.3160E+03
16382 mkine
SS-1, Iwaki City Hall, Dec.22, 2012:
0.000000 -0.0000000E+00 -0.0000000E+00 -0.0000000E+00
0.002000 -0.8961562E-04 0.5361709E-05 -0.2044998E-04
0.004000 -0.1640327E-03 0.8138977E-04 -0.1974745E-04…

0.0000000E+00 -0.0000000E+00
0.1081865E-03 -0.1978091E-05
0.1997052E-03 0.2068763E-04

0.0000000E+00 -0.0000000E+00
0.2530022E-04 -0.4171700E-04
0.4874512E-04 -0.9626019E-04

seewav7.forseewav7.prm
SS01.ps

Figures in Multi-page Post Script
file. Post Script file can be opened,for example, by “gv &”, where “gv
and “&” stand for “ghost view” andbackground operation.
If “ghost view” is not installed yet:sudo apt-get install gv

52

seewav7.prm
1

1.0 10.0 12.5 3
1.5

dtl denotes the time duration that corresponds
to 1cm along the time axis.
In one page, 28*dtl/dt time step can be plotted. If
the file has more, new pages are automatically
added as much as necessary and multi-page PS
file is created.

:nfilter,fl,fh,fs,nchara(=2:lowpass, =3:bandpass):dtl(sec/cm),25,50==>10,20 min/page

Band Pass Filter
Amplification
1.0

nfilter=0: no effectnfilter=1: bandpass filter is applied
Frequency (Hz)fh
fsflThis BPF does not affect to the data files. 53

If the records have significant DC-offset(base line shift due to DC component)

seewav7.prm
1

0.1 50. 60.0
1.0

:nfilter,,fl,fh,fs:dtl(sec/cm)

Set nbandpass = 1 andfs>Nyquist frequency

Waveform plots with DC-offset
correction, but without applying
bandpass filter, are given.
This program plots at once all data files listed in./spacwkf/data/multiplexed_files/mltfile.lst .
Number of channels is read from the first line of the data files.
54

Example of execution:

Output files:
PostScript files are stored in the folder:./spacwkf/data/results/fig_wave
with extension “ps”. Use “gv &” to draw it.

55

1.3. Re-sampling & Screening
Re-sampling & Screening
resample_pre.shresample5.sh + ./spacwkf/prm/resample5.prm
orresample6.sh + ./spacwkf/prm/resample6.prm

Then, check the selected time blocks using
seeblk1.sh + seeblk1.prm
56

Note: Modify the file “./spacwkf/prm/graph_title.txt”, if you have not started
the processing from “sh seg2read.sh”. This means that your original data
files are not seg2 format.
The contents of the file “./spacwkf/prm/graph_title.txt” is used for the titleof various graphs produced in further processing. It is recommendable togive an appropriate title to the figures to prevent potential confusion.

57

Re-sampling & Screening
Multi-channel data files from the same array configuration
SS01.dat
Anti-alias filter for resampling is applied
automatically.

SS02.dat

Two steps for screening areapplied.

SS03.dat

resample_pre.forresample5.forresample6.forresample5.prm

resample6.prm

IWSS-1.dat
Resampled & screened multi-channel& multi-measurement data file58

Screening: Step-1
Parameter: ajudge
Time Block

If the maximum amplitude in a time block exceeds the product of the“ajudge” parameter to RMS amplitude of the same time block, this time
block is not used in analysis.
This is a countermeasure against impulsive noise due to traffic, i. e.,vehicles passing near by seismometers.
The bigger value of “ajudge” means looser screening. The smaller valuemeans fewer available time blocks.

59Screening: Step-2
Parameter: a_sgm
If the RMS amplitude in a time block deviates more than the “a_sgm”
parameter multiplied to the standard deviation from the average, this time
block is not used in analysis, where the average and the standard
deviation are calculated over the all time blocks that survived in thescreening Step-1.

This is a countermeasure against outliers.
The bigger value of “a_sgm” means looser screening. The smaller valuemeans fewer available time blocks.

60Warning:
Be sure to use the same resampling interval and the same block size, incase of the combination of arrays of various sizes. Otherwise, a heavy
problem will take place in the further step of analysis, namely, thedetermination of dispersion curves.
The declared array size for input data in resample5.for and resample6.foris 750,000.
This gives the constraint: tdur/dt < or =750,000
Similarlynch< or =11
and number of data in one time block < or = 8192
It is recommendable to make a multiplexed data file for every 30 minutesor shorter duration, in order to avoid the problem due to the exceedance of
input data quantity.
61

resample5.prm or resample6.prm
7 0.002 10
7.0 1.5
0.0 32.766
IWSS-1.dat
1024
30
SS01.dat
SS02.dat
SS03.dat…
SS30.dat:nch,dt,number of Channels,dt,nskip:ajudge,a_sgm:tst,tdur:output file name:number of data in one time block after resampling:number of measurement in the same array configuration

sh resample_pre.sh
activates pre-processor to modify resample5.prm
and/or resample6.prm easier.

1st line: Channel number, sampling interval, skip data number
2nd line: ajudge, a_sgm: parameters for two step screening
3rd line: start time and duration for processing
4th line: Output file name
5th line: number of data in one time block after resampling.
resample5.for divides all the data into the time blocks that havethis number of data allowing overlapping of 50 % between
neighboring blocks.
6th line: number of measurement in the same array configuration.
Example1 is the single measurement case.
7th line: Input file name62

Example of execution: Output file isstored in ‘./spacwkf/data/resampled_files’

63Resampled & screened multi-channel & multi-measurement data file

2nd block 1st block

1st line:file parameters
7
1
2
…
1024
1
…
1024
1
…

27

1024 (i8,f16.4, 7e15.7) mkine
0.0000 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
0.0200 -0.6542959E-10 0.6730985E-10 0.8688813E-11 -0.9121746E-10 0.3278066E-10 0.3681669E-10 -0.2157925E-10
20.4600 0.6798404E-01 0.8341893E-01 0.7360612E-01 -0.3876965E-01 0.1080229E+00 -0.9545929E-01 -0.1346539E+00
10.2400 -0.1701506E+00 0.9676924E-01 0.3960467E-01 -0.3436972E+00 0.1931517E+00 0.1742720E-01 0.8249036E-01
30.7000 -0.4059438E-01 0.2059561E-02 0.2788787E-01 -0.1173913E+00 0.2213649E-01 -0.1785946E-01 -0.9963673E-01
0.0000 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00

The file includes mmblk=27 time blocks of nch=7 channel data.
Each time block is composed of nblk=1024 data.
Each line corresponds to a time step. The format used to store each line iscform3=‘(i8,f16.4, 7e15.7)’.
The unit for these data is “mkine”.
These file parameters are stored in the 1st line.
As all of the data are delimited by space, this file can be read using free format.

64For MM-1 array: resample6.prm
4 0.01 2
4.0 2.0
0.0 163.83
IWMM-1.dat
1024
21
MM01.dat…
MM21.dat:nch,dt,number of Channels,dt,nskip:ajudge,a_sgm:tst,tdur:output file name:number of data in one time block after resampling:number of measurement in the same array configuration

Execution:~SPAC2021$ sh resample6.sh./spacwkf/prm/resample6.prm
Working Folder=./spacwkf/prm//
Band-Pass:fl= 0.100000001 fh= 20.2500000 fs= 22.5000000
Nch=
4
Nskip=
2 f(Nyquist)= 25.0000000
fh= 20.2500000
ajudge= 4.00000000
a_sgm= 2.00000000
0.00000000
163.830002
First screening (peak/rms< 4.00000000 ):1 -th measurement:./spacwkf/data/multiplexed_files/MM01.dat
Band-Pass:fl1= 5.00000007E-02 fh1= 1.00000000 fs1= 1.50000000
14 blocks remained among
14 blocks…
21 -th measurement:./spacwkf/data/multiplexed_files/MM21.dat
Band-Pass:fl1= 5.00000007E-02 fh1= 1.00000000 fs1= 1.50000000
14 blocks remained among
14 blocks
Data stored in the temporary file./spacwkf/data/resampled_files/IWMM-1.dat
Second screening ({rms-average(rms)}/sigma< 2.00000000 ):280 blocks remained among
294 blocks~SPAC2021$

65

What’s special of resample6.exe incomparison with resample5.exe./bin/resample5.exe./bin/resample6.exe

Input file

Input fileAnti-alias filter

Anti-alias filter

Resampling

Resampling

Judge
Screening
Output file

Band Pass Filter
Long Period (>1.0s) Comp.
Judge

Screening
Output file

For short period observation

For long period observation

66

Output files:
IWSS-1.dat  resample5.exe
IWMM-1.dat  resample6.exe
IWLL-1.dat  resample6.exe
Resample6.prm is edited after obtaining IWMM-1.dat67

Check the selected time blocks
Parameter file:./spacwkf/prm/seeblk1.prm
0 0.005 1.0 1.5 3
1 10
IWSS-1.dat:nfilter,fl,fh,fs,nchara(=2:lowpass, =3:bandpass):n_mea,n_character

Example of execution: Output file is storedin ./spacwkf/data/results/fig_wave’~SPAC2021$ .sh seeblk1.sh./spacwkf/prm/seeblk1.prm./spacwkf/data/resampled_files/IWSS-1.dat
28
10
28
20
4.42062318E-03 4.99999989E-03./spacwkf/data/results/fig_wave/IWSS-1.ps~SPAC2021$
Multi-page postscript files are created in ./spacwkf/data/results/fig_wave

68

69

1.2 Calculation of Inter station
Distance and Azimuth & Plot
Geometry of array
Programs used:distazi.shthat controls:
distazi.exe + ./spacwkf/prm/distazi.prm
geometry.exe + ./spacwkf/prm/distazi.prm
A temporary file is used: temp0.dat
70

5Coordinates
distazi.for

6
1

4

7
2

distazi.prm

3

dist_azi.dat(Inter-station distances & azimuths)

distazi.sh#!/bin/sh
rm ./spacwkf/data/results/temp0.dat# rm ./spacwkf/data/results/distazi.dat# rm ./spacwkf/prm/./bin/distazi.exe./bin/geometry.exe
gnuplot -e "load 'geometry.plt' ;
pause -1"

gnuplot is used for plotting.
If not yet installed,
sudo apt-get install gnuplot –x11

71

Example：SS-1 Array

distazi.prm
Iwaki City Hall, SS-1
:Explanation (a45)2:Type X-Y(=0), Lat-Long(=1),Dist-Angle(=2)
7SS-1:Number of stations, Title of figure
25.0
90.0
1
12.50
30.0
2
25.0
-30.0 312.50 -90.0 4
25.00 -150.0 5
12.50 150.0
6
0.0
0.0
7

dist_azi.dat
Iwaki City Hall, SS-1
7
:number of station
id st1 st2 distance azimuth
1
2
7
12.500 -150.000
24712.50090.0003
6
712.500 -30.000
41221.651 -60.000
51
621.651 -120.000
62321.651 -60.000
72421.651 -120.000
82621.651 180.000
93421.651 180.000
104521.651 -180.000
114621.651 120.000
125621.65160.00013
1
725.000 -90.000
143725.000 150.000
155725.00030.00016
1
437.500 -90.000
172537.500 -150.000
183637.500 150.000
191343.301 -60.000
20
1543.301 -120.000
213543.301 -180.000

The same image is saved simultaneously in a PostScript file inthe subfolder “./spacwkf/data/results/fig_geometry/”.

72

distazi.prm
Iwaki City Hall, SS-1
:Explanation (a45)2:Type X-Y(=0), Lat-Long(=1),Dist-Angle(=2)
7SS-1:Number of stations, Title of figure
25.0
90.0
1
12.50 30.0 2
25.0
-30.0
3
12.50 -90.0
425.00 -150.0
512.50 150.0
6
0.0
0.0
7

The 1st line & the 2nd parameter of the 3rd line are read and used later.

For Lat-Long (=1):
The statement for reading in distazi.for is:read(1,*)xla(ista),ylo(ista),id(ista)

73

Example of execution:~SPAC2021$ sh distazi.shDist-Azimuth coordinates are selected
X-axis toward East, Y-axis toward North.
1 25.0 -0.0
2 6.2 10.8
3 -12.5 21.7
4 -12.5 -0.0
5 -12.5 -21.7
6 6.3 -10.8
7 0.0 0.0
1
2 21.6506348-59.9999962...
6
7 12.5000010-30.0000038./spacwkf/data/./spacwkf/data/results/distazi.dat
1 2 7 12.500 -150.000...
21 3 5 43.301 -180.000
Iwaki City Hall, SS-1
7 SS-125.0000000-9.99999997E-07
6.25000000
10.8253174-12.5000000
21.6506348-12.5000000-9.99999997E-07-12.5000019-21.6506348
6.25000095-10.8253174
0.00000000
0.00000000

Plot appears in a pop-up window

74~SPAC2021$ gv &Automatically stored in a PS file, too.

Output files./spacwkf/data/results/distazi.dat./spacwkf/data/results/geometry.dat./spacwkf/prm/gnuplt_script/geometry_SS-1.plt
geometry.plt
Contents of ‘geometry.plt’
load './spacwkf/prm/gnuplt_script/geometry_SS-1.plt'./spacwkf/data/results/fig_geometry/geometry_SS-1.ps

75

Example: MM-arraydistazi.prm
Iwaki City Hall, MM-1
:Explanation (a45)2:Type X-Y(=0), Lat-Long(=1),Dist-Angle(=2)
4 MM-1:Number of stations, Title of figure37.5 90.0 1
37.5 -30.0 2
37.5 -150.0 3
0.0 0.0 4
Then run distazi.sh

distazi.dat
Iwaki City Hall, MM-1
4:number of station
IDX
Y
1 37.500000 -0.000002
2 -18.750000 32.475952
3 -18.750002 -32.475952
4 0.000000 0.000000
id st1 st2 distance azimuth
1 1 4 37.500 -90.000
2 2 4 37.500 150.000
3 3 4 37.500 30.000
4 1 2 64.952 -60.000
5 1 3 64.952 -120.000
6 2 3 64.952 -180.000

762. Calculation of SPAC coefficient
Program used:zcorrel.shthat controls./bin/zcorrel5_3.exe + ./spacwkf/prm/zcorrel5_3.prm
and./bin/interim_plt.exe + ./spacwkf/prm/zcorrel5_3.prm
for plotting the results77Calculation of SPAC coefficientsResampling &Screening

Input files are the output from resample5.exe orresample6.exe. They have to be velocity records
in mkine (1.0E-5 M/sec).

Field.data
Multi-channel &multi-measurement
file

Zcorrel5_3.for
Zcorrel5_3.prm

SPAC Coeff.
System Correction
Resampling &Screening
Huddle.Test.
data
Multi-channel &multi-measurement
filezcorrel.sh#!/bin/sh
rm ./spacwkf/data/results/temp*.dat./bin/zcorrel5_3.exe./bininterim_plt.exe
gnuplot -e "load 'interim.plt' ;
pause -1
78"

zcorrel5_3.prm
1st line is used as the title of figures createdIwaki City Hall, SS-1
0.1 10.0 0.02 0.25 0 2 :fmin,fmax,dt,bw(>3.71/Td),n_huddle,nhide
HDSS-1.dat
1 1:Huddle test file name (A12),n_coh_hud,n_pow_hud
IWSS-1.dat
1 1:input file name (A12),n_coh,n_pow
5
3 27 47 67
12.5
9 12 16 23 24 26 34 45 46 56
21.65
3 17 37 57
25.0
3 14 25 36
37.5
3 13 15 35
43.3
SPCSS1.dat:output file name(a10)

For the inter-station distance, 12.5m, 3 pairs namely stations (#2,#7),(#4,#7),(#6,#7)
are averaged.
In the program nn=nn_org*nhide is conducted, where nn_org denotes length of atime block in the input data file. This means the zero padding in order to shorten theinterval of frequency for the calculation of FFT.
79
Time window length including padded zeros is given by Td=nn_org*nhide*dt

1st line
Parameters: fmin, fmax, bw, n_huddle
Selection of frequency range foranalysis

fmin

fmax

Frequency (Hz)bw: bandwidth of Parzen Window that is used for smoothing the
averaged cross- and auto- correlations. The bigger value of “bw”
corresponds to smoother SPAC coefficient. bw=0.0 means exection
without applying Parzen Window.
n_huddle: Flag for executing the system correction using the huddle test
data (0= no effect, =1 conducting system correction). Correction using
the huddle test data is usually not necessary when the array is composedof the seismographs of the same type.
80

2nd line
Parameters: Huddle test file name (A12),n_coh_hud,n_pow_hud

Resampled & screened
Multi-channel &multi-measurement
file of the huddle test
data
Flag for outputing thecoherence file of thehuddle.dat
huddle test data
0= no effect
1= output
huddle_coh.dat

Flag for outputing thepower spectra file ofthe huddle test data
0= no effect
1= output
huddle_psp.dat

This line is read but not used in the analysis if n_huddle in the 1st line is “0”.
81

3rd line
Parameters: input file name (A12),n_coh,n_pow

Resampled & screened
Multi-channel &multi-measurement
file of the huddle test
data
Flag for outputing thecoherence file of the
Input.dat
huddle test data
0= no effect
1= output

Flag for outputing thepower spectra file ofthe huddle test data
0= no effect
1= output
Input_cor_psp.dat

Input_cor_coh.dat

The coherence and the power spectra of the field data without the systemcorrection are output as default.
Input_coh.dat
Input_psp.dat

82interim_plt.exe

zcorrel5_3.exe

Example of execution:~SPAC2021$ sh zcorrel.sh
Program zcorrel5_3.for./spacwkf/prm/zcorrel5_3.prm
Huddle Test Skipped.
nn= 2048
28
10
28
20
power and cross spectra for field data calculated.
Block Averaging has been done.
./spacwkf/data/results/IWSS-1_psp.dat
Output:./spacwkf/data/results/IWSS-1_psp.dat./spacwkf/data/results/IWSS-1_coh.dat./spacwkf/data/results/SPCSS1.dat

Power Spectra
Coherence Output

Look the next page83

interim_plt.exe

Iwaki City Hall, SS-1
Iwaki City Hall, SS-1
Hit return to continue
Hit return to continue
Hit return to continue
Hit return to continue
Hit return to continue
Hit return to continue
Hit return to continue

Power spectra~SPAC2021$

All Coherence functions

SPAC coefficients

These figures are automaticallystored as PS files in./spacwkf/data/results/fig_interim
Individual SPAC function
with error bar

84Procedure for MM-1 Array+ Edit ./spacwkf/prm/resample6.prm for MM-1 Array+ $ sh resample5.sh➔ resampled & screened file IWMM-1.dat+ Edit ./spacwkf/prm/seewav6.prm for MM-1 Array+ $ sh seewav6.sh➔ Waveform plot files MM??.ps+ Edit ./spacwkf/prm/distazi.prm for MM-1 Array+ $ sh distazi.sh ➔geometry plot file geometry_MM-1.ps+ Edit ./spacwkf/prm/zcorrel5_3.prm for MM-1 Array+ $ sh zcorrel.sh ➔ SPAC coefficient file SPCMM1.dat etc.

Power spectra
All Coherence functions

SPAC coefficients

Individual SPAC function
with error bar

These figures are automatically stored as PS files in./spacwkf/data/results/fig_interim85Procedure for LL-1 Array+ Edit ./spacwkf/prm/resample6.prm for LL-1 Array+ $ sh resample6.sh➔ resampled & screened file IWLL-1.dat+ Edit ./spacwkf/prm/seewav6.prm for LL-1 Array+ $ sh seewav6.sh➔ Waveform plot files LL??.ps+ Edit ./spacwkf/prm/distazi.prm for LL-1 Array+ $ sh distazi.sh ➔geometry plot file geometry_LL-1.ps+ Edit ./spacwkf/prm/zcorrel5_3.prm for LL-1 Array+ $ sh zcorrel.sh ➔ SPAC coefficient file SPCLL1.dat etc.

Power spectra

All Coherence functions
SPAC coefficients

Individual SPAC funtion
with error bar

These figures are automatically stored as PS files in./spacwkf/data/results/fig_interim86Power Spectra

10*Log10 (Fourier Coefficient *Td* omg**2) of eachfrequency is plotted in PostScript filespacwkf/data/results/fig_interim/IWMM-1_psp.psin the unit 10*Log10(M**2/Sec**4/Hz)
Also output into
spacwkf/data/results/IWMM-1_psp.dat
that is CSV format file.
IWMM-1_psp.dat# Period
1-ch
2-ch
3-ch
4-ch Power Spc
0.100 -122.523 -121.038 -123.098 -122.525
0.100 -121.617 -120.174 -122.290 -121.659
0.101 -120.964 -119.546 -121.741 -121.039
…

1-ch
2-ch
3-ch
4-ch S.D.
-123.525 -121.061 -123.484 -122.815-122.703 -120.218 -122.836 -122.091-122.073 -119.536 -122.445 -121.599

10*Log10 (Fourier Coefficient * Td * omg**2)
10*LOG10(sqrt(variance of Fourier Coefficient)*Td*omg**2)
where omg=2p/period
When Velocity Fourier Amplitude Spectral Density is required, type
sh fourier.shin the folder SPAC2017. fourier_plt.exe convert the above mentioned psp toFourier Amplitude Spectra.

87

Example: Up to this slide the red part of the below shown diagram has been
performed for SS-1 Array (7 points). The next step is to do the same procedure forMM-1 Array (4 points), i.e., the blue part of the diagram below. Then, the green part.

For SS-1 Array

For MM-1 Array

For MM-1 Array

1.Multiplexing& Resampling

1.Multiplexing& Resampling

1.Multiplexing& Resampling

2.Calculation of
SPAC coefficient

2.Calculation of
SPAC coefficient

2.Calculation of
SPAC coefficient

3.Determinationof dispersion curve

4. Heuristic Searchof Vs Structure
SPCSS1.dat, SPCMM1.dat, SPCLL1.dat are used in the next step of analysis.
88

3. Determination of Dispersion Curve
Programs used:
cf_panel1.shthat controls./bin/cf_panel1.exe + cf_panel1.prm
for fitting to Bessel function, plotting SPAC coefficientand determination of dispersion curve using the imaging
technique.
For plotting
vel_model.shthat controls./bin/vel_model_plt.exe + vel_model_plt.prm
89

All input files must have the same df=1/Td
SPCSS1.dat

SPCMM1.dat SPCLL1.dat

cf_panel1.for

cf_panel1.prm

comparison.dat

vel_model.dat

The same file name is used for every case90Determination of dispersion curve
1st step:+ The fif-th order polynomial that approximates the inverse function of Jo(x)y=-6.0803x5+9.2477x4-3.9322x3+0.1815x2-1.7079x+2.4121
is used to calculate the tentative values of the phase velocity c(r,w), where y=kr=rw/c(r,w),x=r(r,w) .
+ The wave lengths are estimated from the observed SPAC coefficients through thistentative phase velocity.
+ The frequency range for analysis is narrowed below the frequency that corresponds tothe spacial Nyquist wave length, i.e., 2 times the minimum interstation distance.
+ The frequency range for analysis is again narrowed above the frequency of the
maximum value of SAC coefficient curves.

2nd step:+ Imaging technique is applied to determine the phase velocity of eachfrequency. The misfit function is set for the SPAC coefficient curves.
91

Example:
cf_panel1.prm
Iwaki city Hall (test data) 2017 version:graph title(a50)0 1 0 40.96 0.1 :n_message,n_comparison(0=no, 1=yes),nfskip(0=no, 1=yes),Td, aps
0.10 5.0 80.0 1000.0 :fmin,fmax,vmin,vmax that specify the range of analysis
3:file number
SPCSS1.dat:file name (a12)5:Number of Radius
12.5 1.0:Radius(m),Min and Max of the frequency(Hz) for fitting
21.6 1.0
SS-1-array
25.0 1.0
37.5 1.0
43.3 1.0
SPCMM1.dat:file name (a12)MM-1-array
2:Number of Radius
37.5:Radius(m),Min and Max of the frequency(Hz) for fitting
65.0
SPCLL1.dat:file name (a12)
LL-1-array
2:Number of Radius
75.0:Radius(m),Min and Max of the frequency(Hz) for fitting
130.0

The list of inter-station distances must be coincident to the contents of the SPAC coefficient’s file.
The minimum and maximum frequency for fitting can be specified, if not fmin and fmax in the 3rdline will be used in place of them.

92

Example of execution:$ sh cf_panel1.sh
n_message= 0 n_comparison= 1 nfskip= 0 0.200E+00
Range of Analysis: from 0.10(Hz) to 5.00(Hz)and from 50.00(m/s) to 1000.00(m/s)
Number of files= 3 for SPAC Coef. curves.
1 SPCSS1.dat
2 SPCMM1.dat
3 SPCLL1.dat
No. Distance min_fr max_frmHzHz
1 12.50 1.47 3.56
2 21.60 1.42 2.86
3 25.00 1.10 2.32
4 37.50 1.07 2.03
5 43.30 1.05 1.93
6 37.50 1.10 2.34
7 65.00 0.24 1.81
8 75.00 0.34 1.81
9 130.00 0.17 1.51
Range of analysis: fmin= 0.561999977
fmax= 3.56399989./spacwkf/prm/gnuplt_script/SPAC_coef.plt./spacwkf/prm/gnuplt_script/cf_panel1.plt
Hit return to continue

These figures are automatically stored as PS
files in./spacwkf/data/results/fig_results
93

Wave_Length l = Phase_Velocity c / Frequency f
Nyquist_Wavelmax

lmin=2rmin< 7rmax : longer side limit of the critical range< 3rmax : limit between the critical and the acceptable ranges< rmax : limit between the acceptable and the reliable ranges(After Cornou et al., 2006)
lmax = 7rmax
lmax = 5rmax
critical range
acceptable range
lmax = 3rmax

reliable range
lmin=2rmin

94

Example of Output
vel_model.dat for the determined dispersion curve# freq.(Hz) Vel.(km/s)
0.561
0.951
0.586
0.950
0.610
0.941
0.635
0.914
0.659
0.883

0.165
0.158
0.153
0.140
0.130

…
Standard Deviation

Comparison.dat
for checking the glade of fitting…
6 37.500
0.071-0.1800.199
f= 1.953
Hz 160.00=cr SPAC_Coef. Cal_Bessel S.D.
0.000
1.000
1 12.500
0.777
0.783
0.076
2 21.600
0.388
0.423
0.091
3 25.000
0.176
0.272
0.205
4 37.500-0.241-0.2150.186
6 37.500
0.048-0.2150.198
f= 1.977
Hz 157.00=cr SPAC_Coef. Cal_Bessel S.D.
…

Standard deviation of the observed SPAC coefficient
SPAC coefficient calculated using determined phse velocity
Observed SPAC coefficientInter-station distance95Plot the determined dispersion curve:
Execution: After editing ./spacwkf/prm/vel_model_plt.prm
for the graph title, [fmin,fmax] and [vmin, vmax]./spacwkf/prm/vel_model_plt.prm
Iwaki City Hall SS,MM,LL Arrays 2012/09/15
0.5 4.0:fmin,fmax
80. 1000.
:vmin,vmax
1: n_mod:title(a50)+++
1st line: title of phase velocity plot
2nd line: fmin and fmax for plotting
3rd line: vmin and vmax for plotting
4th line: n_mod=1: wavelength/3 – Vs will be plotted in Vs structure plototherwise not plotted.

96File: vel_model.dat••••[fmin, fmax] described in vel_model_plt.prm and used by vel_model_plt.exe andcf_panel.exe are not reflected to the contents of the file vel_model.dat.
It is recommendable to edit vel_model.dat manually to select the frequency range
used in the next step.
Don’t leave a blank line at the end of the file vel_model.dat after editing.
Run vel_model_plt.exe after editing it.➔ sh .vel_model.sh~SPAC2021$ sh vel_model.sh./spacwkf/prm/gnuplt_script/vel_model.plt

Vmax

This figure is automatically stored as PS
files in./spacwkf/data/results/fig_results
Vmin
fmin

fmax
97

Plot the SPAC coefficient curve fitting:Execution:$ sh comparison.sh…
Type in the frequency that you want to select.
…
./spacwkf/prm/gnuplt_script/comparison.plt

Simultaneously the same imge is saved in a PostScript file:./spacwkf/data/results/fig_results/comparison.ps98

4. Heuristic Search of Vs Structure
Programs used:

inversion.shthat controls./bin/disp_sma1_2.exe + ./spacwkf/prm/disp_sma1_2.prm./bin/disp_err1.exe
results.shthat controls./bin/results_plt.exe

99Observed Dispersion Curve

Search Range Filevel_model.dat

str_range.dat

disp_sma1_2.for
disp_sma1_2.prm
Curve fitting by Heulistic Search

Optimum Velocity Structure
vel_cal.dat

Comparison of Cal. To Obs.
disp_cal.dat

disp_err1.for
Optimum Velocity Structurewith error estimate
vel_cal_err.dat
100

inversion.sh#!/bin/sh -x
rm ./spacwkf/data/results/temp*.dat 2>/dev/null./bin/disp_sma1_2.exe | tee spacwkf/log/disp_sma1_2.log./bin/disp_err1.exe | tee spacwkf/log/disp_err1.log
rm ./spacwkf/data/results/temp*.dat

results.sh#!/bin/sh -x./bin/results_plt.exe
gnuplot -e "load 'results.plt’ ; pause -1"

101disp_sma1_2.forCombination of the Down Hill Simplex Method (Nelder & Mead (1965)) andthe Very Fast Simulated Annealing method (Ingber, 1989).
DHSM: Down Hill Simplex Method (Nelder & Mead (1965))
An efficient algorithm to find “local minimum”.
Faster than Geiger’s method. Partial derivatives are not necessary.
Result is controlled by given initial values and easily captured by
local minimum.
Example of application to the microtremor array: Ohori et al(2002)
VFSA: Very Fast Simulated Annealing method (Ingber, 1989)
One of the heuristic search methods.
Analogy of cooling and crystallization process of metals.
Results can escape from local minimum and can get global minimum
with some probability.
Time consuming due to the probabilistic search for each parameter.
Example of application to the microtremor array &appropriate values of parameters for this purpose: Yamanaka (2004)
102

Example: disp_sma1_2.prm
1 1. 0.6 1.3 10000 5 :idum,t0,a,c,ntemp,j0
0.0025:eps0
1 1:n_roh,n_vp
1 0 1:ini_flg,ndsp_flg,n_err
0 1:kflg,jflg
0 0:n_vs,n_th
str_range.dat:File name for the initial velocity model (a25).
vel_model.dat:File name for the obseved dispersion relation (a25).
vel_cal.dat:File name for the estimated velocity structure (a25)disp_cal.dat:File name for the calculated dispersion relation (a25)Control parameter for the simulated annealing method
idum :Random seed (integer): As the result may depend on the initial velocity model given by random number, it is strongly recommended forusers to apply this program several times with various values of random seed and to grasp the scatter of result.
t0, a,c :Initial Temperature, Coefficients for T=T0*exp(-c*k**a), where k is iteration number. T0=1.0, a=0.6 & c=1.3 are of the fastest schedule
ntemp :Maximum number of temparature changej0:Number of iteration for each temperaturethreshold for conversion
eps0 : threshold of misfit function
flags for roh and vp
n_vp : 1=by Ludwig et al(1970): vp=1.11*vs+1.29; 0=fixed to the initial values
n_roh : 1=by Kitzunezaki et al(1990): roh=1.2475+0.399*vp-0.026*vp**2; 0=fixed to the initial values
flags for output to Display
ini_flg : Initial Velocity Structure Model. 1=yes
ndsp_flg : Observed Dispersion Relation . 1=yes
n_err : Error at each iteration, 1=yes
kflg: Missfit at each temp. change, 1=yes
jflg: Missfit at each itration with the same temp. 1=yes
n_vs : Vs value(n_vs=layer number, 0=no output)n_th: Thickness value (n_th=layer number, 0=no output)
n_err :

103

Example: str_range.dat  Initial Search Range
Iwaki City, S-M-L 22/12/2012 :Model(a30)
6:IL(I5),Layer Number
1.9
1.5
0.005 0.030 0.10 0.12 :density,Vp,hmin,hmax,vmin,vmax
1.9
1.50.005 0.030 0.10 0.20 :density,Vp,hmin,hmax,vmin,vmax
1.9
1.50.005 0.030 0.20 0.40 :density,Vp,hmin,hmax,vmin,vmax
1.9
1.50.005 0.300 0.40 0.70 :density,Vp,hmin,hmax,vmin,vmax
1.9
1.50.005 0.300 0.70 1.00 :density,Vp,hmin,hmax,vmin,vmax
2.0
1.70
998.0 999.0
1.00 3.20(hmin, hmax) : Search range for layer thickness.
(vmin, vmax) : Search range for Vs (Shear Wave Velocity)104

Example of execution(1): inversion.sh$ sh inversion.shOpening+---------------------------------------------------++++
Disp_sma1++++ Program to obtain the optimum undeground velocity ++ structure for the given dispersion relation of++ Rayleigh wave.
++++ The used method is a combination of the down hill ++ simplex method (Nelder & Mead (1965)) and the++ very fast simulated annealing method (Ingber++ (1989)).
++++ The subroutine DSPRAY and DSPMRX published in++ "Seismological Algorithm" are used directly.
++ AMOEBA and AMOTRY published in "Numerical Recipe" ++ are also used, but with significant modification ++ for the adaptation with the very fast simulated++ annealing method.
++++ By the combination with the down hill simplex++ method, the very fast simulated annealing method ++ is gotten much faster.
++++
July 6, 2005++
CopyRight by Toshiaki Yokoi, IISEE, BRI, Japan.++---------------------------------------------------+./spacwkf/data/results/progress.dat
Interim output./spacwkf/prm/disp_sma1_2.prm
Input files./spacwkf/prm/str_range.dat
Initial values randomly produced

105

Example of execution(2):Range of random fluctuation
Thicknes Density
Vp
Vs
Thickness
Vs
Initial model selected
0.018
1.756
1.403
0.102
0.005
0.030
0.100
0.120
0.026
1.770
1.445
0.139
0.005
0.030
0.100
0.200
using random number
0.023
1.849
1.696
0.365
0.005
0.030
0.200
0.400
with in the given initial
0.120
1.952
2.036
0.672
0.005
0.300
0.400
0.700
0.275
1.993
2.176
0.798
0.005
0.300
0.700
1.000
search range
999.000
2.356
3.645
2.121 998.000 999.000
1.000
3.200
./spacwkf/data/results/vel_model.dat
Input file (Dispersion Curve)
5
0.0092043458
100.0059573189
Iterations
15
0.0059573189...
(Number , Misfit func.)
810
0.0024932232./spacwkf/data/results/vel_cal.dat
Output file
Thicknes(Km) Density(g/cm^3)
Vp(Km/sec)
Vs(Km/sec)
1
0.021996
1.755735
1.401826
0.100744
20.006866
1.784393
1.490328
0.180476
30.006150
1.850516
1.699537
0.368953
40.146807
1.861471
1.734910
0.400820 Optimum Solution
5
0.027075
2.031596
2.3141060.9226186999.000000
2.101820
2.572326
1.155249./spacwkf/data/results/disp_cal.dat./spacwkf/data/results/err_estm.dat
Output files

Output-1
progress.dat: Structure Models of every j0 iterations are stored.
err_estm.dat: Data for error estimation (Next Step) are stored.

106

Example of execution(3): inversion.sh
Error estimate by disp_err1.exe./spacwkf/prm/disp_sma1_2.prm./spacwkf/prm/str_range.dat
Input files./spacwkf/data/results/vel_model.dat./spacwkf/data/results/err_estm.dat
IL= 6 MP=13 NP=12
minimum = 1th vertex
Sensitivity calculated by finite diference& stored in the output file sensitivity.dat
Output files./spacwkf/data/results/Vel_cal_err.dat
Thicknes(Km) SD
Roh(g/cm^3) SD
Vp(Km/sec)SD
Vs(Km/sec)
SD
1
0.022
0.000
1.756
0.000
1.402
0.000
0.101
0.000
2
0.007
0.000
1.784
0.002
1.490
0.005
0.180
0.004
3
0.006
0.006
1.851
0.013
1.700
0.043
0.369
0.039
4
0.147
0.011
1.861
0.003
1.735
0.010
0.401
0.009
5
0.027
0.131
2.032
0.222
2.314
0.795
0.923
0.717
6 999.000
0.000
2.102
0.041
2.572
0.154
1.155
0.139

107

Output-1
vel_cal.dat: Optimum Solution
Thicknes(Km) Density(g/cm^3)
Vp(Km/sec)
Vs(Km/sec)
1
0.021996
1.755735
1.401826
0.100744
20.006866
1.784393
1.490328
0.180476
30.006150
1.850516
1.699537
0.368953
40.146807
1.861471
1.734910
0.400820
50.027075
2.031596
2.3141060.9226186999.000000
2.101820
2.572326
1.155249

disp_cal.dat: Observed & Calculated Dispersion Curves#

Frequency(Hz)
0.561
0.586
0.610
0.635
0.659
0.684
0.708
0.732
0.757
0.781
0.806
...

Observed Velocity Calculated Velocity
0.951
0.957
0.950
0.942
0.941
0.925
0.914
0.903
0.883
0.880
0.846
0.853
0.804
0.827
0.767
0.801
0.731
0.775
0.709
0.750
0.686
0.726

0.165
0.158
0.153
0.140
0.130
0.117
0.107
0.098
0.090
0.084
0.079

108

Output-2
vel_cal_err.dat: Optimum Solution with estimated error (SD).
Thicknes(Km) SD
Roh(g/cm^3)
1
0.022
0.000
1.756
2
0.007
0.000
1.784
3
0.006
0.006
1.851
4
0.147
0.011
1.861
5
0.027
0.131
2.032
6 999.000
0.000
2.102

SD
Vp(Km/sec)
0.000
1.402
0.002
1.490
0.013
1.700
0.003
1.735
0.222
2.314
0.041
2.572

SD
Vs(Km/sec)
0.000
0.101
0.005
0.180
0.043
0.369
0.010
0.401
0.795
0.923
0.154
1.155

SD
0.000
0.004
0.039
0.009
0.717
0.139

sensitivity.dat: results of sensitivity analysis of structural parameters (h & vs) to Vs.
Frequency
h=1
h=2
h=3
h=4
h=5
v=1
v=2
v=3
v=4
v=5
v=6
0.561E+00 0.596E+01 0.398E+01 0.171E+01 0.124E+01 0.258E+00 0.511E+00 0.120E+00 0.679E-01 0.804E+00 0.375E-01 0.610E+00
0.586E+00 0.711E+01 0.440E+01 0.176E+01 0.134E+01 0.227E+00 0.664E+00 0.141E+00 0.746E-01 0.116E+01 0.340E-01 0.548E+00
0.610E+00 0.912E+01 0.515E+01 0.196E+01 0.156E+01 0.216E+00 0.869E+00 0.175E+00 0.877E-01 0.155E+01 0.334E-01 0.459E+00
0.635E+00 0.119E+02 0.682E+01 0.244E+01 0.182E+01 0.231E+00 0.122E+01 0.248E+00 0.117E+00 0.195E+01 0.371E -01 0.355E+00
0.659E+00 0.143E+02 0.794E+01 0.267E+01 0.195E+01 0.218E+00 0.157E+01 0.305E+00 0.137E+00 0.228E+01 0.368E -01 0.260E+00
0.684E+00 0.166E+02 0.894E+01 0.280E+01 0.200E+01 0.200E+00 0.191E+01 0.363E+00 0.156E+00 0.250E+01 0.353E -01 0.179E+00

...

109

Graphical Output: sh results.sh./spacwkf/prm/gnuplt_script/disp_cal.plt./spacwkf/prm/gnuplt_script/cal_cf_panel.plt./spacwkf/prm/gnuplt_script/vs_structure.plt
Hit return to continue
Hit return to continue

Set n_mod=0 in ‘vel_model_plt.prm’to eliminate green circles.
These figures are automatically stored as PS files in./spacwkf/data/results/fig_results

110

A way to find the optimum solution- Explanation using another example -111

S_ & L_ Tsukb

In the highest frequency range, thephase velocity is about 0.3 (Km/sec).

1.2

Phase Velocity

1
0.8
0.6
0.4
0.2
0
0

1

2

3

4

5

At the lowest frequency 0.664 (Hz)the phase velocity estimated is0.695(Km/sec).
Then,thecorresponding wave length is about
1 (Km) and the expected explored
depth very roughly estimated may
be about 250 (m).

Hz

112

Examples of Search Range
str_range.dat (4 layer model for exploration from surface to the seismic bedrock)
Yamanaka (2001)
4
1.8 1.956 0.001 0.05 0.4
2.0 2.400 0.001 0.30 0.7
2.3 2.955 0.010 0.30 1.2
2.5 4.842 998.0 999.0 2.6:Model(a30):IL(I5),Layer Number
0.9 :density,Vp,hmin,hmax,vmin,vmax
1.3
1.8
3.6

str_range.dat(4 layer model for exploration from surface to the engineering bedrock)
Engineering Bedrock:Model(a30)
6:IL(I5),Layer Number
1.5 1.5 0.0
0.03 0.08 0.15 :density,Vp,hmin,hmax,vmin,vmax
1.5 1.5 0.001 0.03 0.10 0.15
1.5 1.5 0.001 0.03 0.08 0.15
1.6 1.5 0.001 0.03 0.15 0.25
1.7 1.6 0.001 0.03 0.25 0.35
1.8 1.8 998.0 999.0 0.35 0.8

1131st Search Range
S_ & L_ Tsukb
5
1.5
1.6
0.001 0.2
0.2
1.8
1.956 0.01 1.0
0.4
2.0
2.4
0.1
1.0
0.7
2.3
2.955 0.1
1.0
1.2
2.5
3.2
998.0 999.0 2.6:Model(a30):IL(I5),Layer Number
0.5 :density,Vp,hmin,hmax,vmin,vmax
0.9
1.3
eps=0.01
1.8
3.6

S_ & L_ Tsukb (1st Search Range)
0

1

2

3

0
0.2

250m

Depth

0.4
0.6
0.8

Density(g/cm^3)
Vp(Km/sec)
Vs(Km/sec)

1
1.2
1.4

114

2nd Search Range
S_ & L_ Tsukb
5
1.5
1.6
0.001 0.2
0.2
1.5
1.6
0.001 0.2
0.3
1.5
1.6
0.001 0.2
0.3
1.5
1.6
0.001 0.2
0.4
1.8
1.956 998.0 999.0 0.5
S_ & L_ Tsukb
0
0

Depth

0.1

1

2

3

:Model(a30):IL(I5),Layer Number
0.4 :density,Vp,hmin,hmax,vmin,vmax
0.5
0.5
eps=0.0065
0.6
0.9
Density(g/cm^3)
Vp(Km/sec)
Vs(Km/sec)

250m

0.2
0.3
0.4
0.5

115

3rd Search Range
S_ & L_ Tsukb
4
1.5
1.6
0.001 0.2
0.2
1.5
1.6
0.001 0.2
0.3
1.5
1.6
0.001 0.2
0.4
1.8
1.956 998.0 999.0 0.5:Model(a30):IL(I5),Layer Number
0.4 :density,Vp,hmin,hmax,vmin,vmax
0.5
0.6
0.9
eps=0.0065

S_ & L_ Tsukb
0
0

1

2

3

Density(g/cm^3)
Vp(Km/sec)
Vs(Km/sec)

Depth

0.1

0.2

0.3

116

disp_sma1_2.prm
1 1. 0.6 1.3 500
0.0065
1
1
1
0
1
0
1
0
0
str_range.dat
vel_model.dat
vel_cal.dat
disp_cal.dat
c idum
c t0
c a,c

5

:idum,t0,a,c,ntemp,j0:eps0:n_roh,n_vp:ini_flg,ndsp_flg,n_err:kflg,jflg:n_vs,n_th:File name for the initial velocity model (a25).
:File name for the obseved dispersion relation (a25).
:File name for the estimated velocity structure (a25):File name for the calculated dispersion relation (a25):Random seed (integer):Initial Temperature:Coefficients for T=T0*exp(-c*k**a), where k is iteration number<The optimum schedule is given t0=1.0, a=0.6, c=1.3 (Yokoi(2006)).>c ntemp:Maximum number of temparature change
c j0:Number of iteration for each temperaturec threshold for conversion
c eps0: averaged deviation117

disp_sma1_2.prm (continuation)c flags for roh and vp
c n_vp: 1=by Kitzunezaki et al(1990), vp=1.11*vs+1.29
c0=fixed to the initial values
c n_roh: 1=by Ludwig et al(1970), roh=1.2475+0.399*vp-0.026*vp**2
c0=fixed to the initial valuesc flags for output to Display
c ini_flg : Initial Velocity Structure Model
1=yesc ndsp_flg : Observed Dispersion Relation
1=yes
c n_err: Error at each iteration
1=yes
c kflg: Missfit at each temp. change
1=yes
c jflg: Missfit at each itration with the same temp. 1=yes
c n_vs: Vs value(n_vs=layer number, 0=no output)
c n_th: Thickness value (n_th=layer number, 0=no output)118

S_ & L_ Tsukb
4
1.5
1.6
0.001 0.2
0.2
1.5
1.6
0.001 0.2
0.3
1.5
1.6
0.001 0.2
0.4
1.8
1.956 998.0 999.0 0.5

1
2
3
4

:Model(a30):IL(I5),Layer Number
0.4 :density,Vp,hmin,hmax,vmin,vmax
0.5
0.6
0.9

Thicknes(Km) Density(g/cm^3)
0.057347
1.820632
0.074116
1.878893
0.147796
1.882880
999.000000
2.021464

Vp(Km/sec)
1.604092
1.791601
1.804653
2.277869

Vs(Km/sec)
0.282966
0.451893
0.463651
0.889972

119

Comparison of Cal. to Obs.
disp_cal.dat
Observed Velocity Calculated Velocity
0.694
0.698
0.636
0.618
0.545
0.543
0.507
0.496
0.460
0.467
0.449
0.449
0.440
0.436
0.426
0.427
0.434
0.419
0.408
0.413
0.411
1.2 0.407
0.405
0.401
0.394
0.396
1
0.382
0.390
0.376
0.383
0.375
0.8 0.376
0.372
0.369
0.367
0.361
0.6
0.350
0.353
0.341
0.345
0.337
0.4 0.337
0.338
0.330
0.334
0.323
0.2 0.317
0.331
0.312
0.312
0.309
0 0.308
0.306
0.304
0
0.303
0.300
0.297
0.297
0.293
0.294
0.291
0.292

Phase Velocity (Km/sec)

Frequency(Hz)
0.664
0.742
0.820
0.898
0.977
1.055
1.133
1.211
1.289
1.367
1.445
1.523
1.602
1.680
1.758
1.836
1.914
1.992
2.070
2.148
2.227
2.305
2.383
2.461
2.539
2.617
2.695
2.773
2.852
2.930
3.008

1

0.281
0.118
0.085
0.061
0.074
0.058
0.051
0.068
S_&L_Tsukb
0.066
0.151
0.132
0.110 Calculated Velocity
0.096
Observed Velocity
0.085
0.074
0.066
0.061
0.058
0.037
0.050
0.045
0.045
0.041
0.039
0.071
0.070
0.068
2
3
4
0.063
Hz
0.055
0.037
0.033

5

120

Determined Velocity Structure
vel_cal.dat

1
2
3
4

Thicknes(Km) Density(g/cm^3)
0.057347
1.820632
0.074116
1.878893
0.147796
1.882880
999.000000
2.021464

S_ & L_ Tsukb
0
0

1

2

3

Vp(Km/sec)
1.604092
1.791601
1.804653
2.277869

Vs(Km/sec)
0.282966
0.451893
0.463651
0.889972

Comparison with PS-logging Data

Density(g/cm^3)
Vp(Km/sec)
Vs(Km/sec)

0500

Depth(m)1000 1500 2000 2500

0

Depth

0.1

0.2

Velocity(m/sec)

50
100
150
200
250

0.3

Vp(SPAC)
Vs(SPAC)
Vp(PS logging)Vs(PS logging)

300

121