This tutorial will discuss the organization of and the scripts
used to compute the Green's functions for source inversion.
Grab the GREEN.tgz
cd Suitable_Directory gunzip -c GREEN.tgz | tar xvf -
You will see the following directories:
AK135.TEL/ AK135.TELPBBD/ CUS.REG/ Models/ PROTO.REG/ WUS.REG/
In these you will see scripts that I used for my Green's functions. These are examples. The prototypes for your Green's functions are in the directory PROTP.REG. The Models directory contains the models that I use.
The moment tensor inversion scripts require knowledge of the
location of the Green's functions. To make the scripts
independent of the physical disk location of the Green's functions,
the SHELL variable GREENDIR is used in the scripts. Do the
following on your system:
If using the bash shell, place this
in the .bashrc file in your login directory:
export GREENDIR=/path_to_top_level/GREEN
On my system I have
export GREENDIR=/backup/rbh/GREEN
Now execute the command
source ~/.bashrc
And now verify that this variable is in your environment.
rbh@crust:~> echo $GREENDIR
/backup/rbh/GREEN
will verify that this is correctly set. If you execute the command
ls ${GREEDDIR}
you will see the contents of the distribution
AK135.TEL/ AK135.TELPBBD/ CUS.REG/ Models/ PROTO.REG/ WUS.REG/
Of course if you logout and then login, this will be set without the required source command.
First define a name for your velocity model. This is very important for the proper operation of the scripts. For example, assume that we wish to create Green's functions for regional data in Yunnan Province. YUN is a good identifier.
You can read the tutorial on the overview of synthetic seismogram generation, or use the program mkmod96. I use mkmod96 even for models with very many layers, just manually entering the first few layers and then using a editor to create the complete velocity model file.
Assume that we are given the following information for a model:
Average velocity structure model in Yunnan thickness Vp Vs Qa Qb 4.00 4.85 2.80 600.0 300.0 16.00 6.25 3.61 600.0 300.0 22.00 6.40 3.70 600.0 300.0 0.00 7.75 4.47 600.0 300.0 Wu Jian Ping
Using mkmod96 I interactively create the model file
YUN.mod which is just
MODEL.01
Yunnan model from Wu Jian Ping CEA 2003?
ISOTROPIC
KGS
FLAT EARTH
1-D
CONSTANT VELOCITY
LINE08
LINE09
LINE10
LINE11
H(KM) VP(KM/S) VS(KM/S) RHO(GM/CC) QP QS ETAP ETAS FREFP FREFS
4.000 4.8500 2.8000 2.4670 600. 300. 0.00 0.00 1.00 1.00
16.0 6.25 3.61 2.775 600. 300. 0 0 1 1
22.0 6.40 3.70 2.82 600. 300. 0 0 1 1
0.0 7.75 4.47 3.225 600. 300. 0 0 1 1
I derived the density from the p-wave velocity using a Nafe-Drake relation (buried in surf96). The ETAP=ETAS=0 for wavenumber integration and the FREFP and FREFS are the reference frequency for causal Q, which is always 1 Hz.
In this step we create a unique place for the Green's functions, copy the prototype processing scripts into that directory, and then copy the velocity model there as well as the Model directory. First we go to the proper area, and then we perform these steps.
cd ${GREENDIR}
mkdir YUN.REG
cp YUN.mod YUN.REG
mv YUN.mod Models
cp PROTO.REG/* YUN.REG
cd YUN.REG
The scripts that you see here are the following:
DOIT.WK - computes complete waveform integration synthetics
DOIT.SW - computes synthetics by model superposition and also
creates the eigenfunctions versus depth for source inversion
MKW - a script to compute a complete table of contents for each source depth directory. The
waveform inversion code uses this table of contents.
DODCTL - creates a table of contents for source depths.
Now edit DOIT.WK and DOIT.SW to replace the word PROTO by
your model name, which is YUN for this example.
The
changed lines in DOIT.SW and in DOIT.WK will look like
DEST=${GREENDIR}
#####
#
#####
MODEL=YUN.REG
PMIN=4.0
PMAX=100.0
Mname=YUN.mod
If you wish to use the surface-wave spectral amplitude technique,
then you must create another velocity file with many layers to give
the eigenfunctions as a function of depth. This file must be
called dYUN.mod for the scripts. This is what it looks like:
MODEL.01
Yunnan model from Wu Jian Ping CEA 2003?
ISOTROPIC
KGS
FLAT EARTH
1-D
CONSTANT VELOCITY
LINE08
LINE09
LINE10
LINE11
H(KM) VP(KM/S) VS(KM/S) RHO(GM/CC) QP QS ETAP ETAS FREFP FREFS
1.000 4.8500 2.8000 2.4670 600. 300. 0.00 0.00 1.00 1.00
1.000 4.8500 2.8000 2.4670 600. 300. 0.00 0.00 1.00 1.00
1.000 4.8500 2.8000 2.4670 600. 300. 0.00 0.00 1.00 1.00
1.000 4.8500 2.8000 2.4670 600. 300. 0.00 0.00 1.00 1.00
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.25 3.61 2.775 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 6.40 3.70 2.82 600. 300. 0 0 1 1
1.0 7.75 4.47 3.225 600. 300. 0 0 1 1
1.0 7.75 4.47 3.225 600. 300. 0 0 1 1
1.0 7.75 4.47 3.225 600. 300. 0 0 1 1
1.0 7.75 4.47 3.225 600. 300. 0 0 1 1
1.0 7.75 4.47 3.225 600. 300. 0 0 1 1
1.0 7.75 4.47 3.225 600. 300. 0 0 1 1
This is the most time consuming part. First decide if you require all of the distances. If you are only looking at one earthquake, then you only need to compute the synthetics at the required distances. So,
cp DOIT.WK DOIT.WK.save
I will compute some distances to 566 km. I know that the time
interval between the first P arrival and the end of the surface wave
depends on depth somewhat, but on distance a lot. I thus need
to compute a longer time series for the larger distances. In
the DOIT.WK script you will see that there are two loops over source
depth, within each is a loop over distance. The first loop is
for short distance and the second is for larger, and will have a
longer time series. The number of points and sampling interval
are fine for my sudy of earthquakes from broadband stations 10 - 500
km and in the frequency band of 0.02 - 0.10 Hz.
In selecting the
distances, use distances to the nearest km. Do not change the
depth selection.
The DOIT.SW script accomplished two purposes.
First it creates the eigenfunctions as a function of depth. The are
stored in the subdirectory SW. It also creates the Green's functions
for a selection of depths. For regional earthquakes with M <
5, it is difficult to see the P wave at large distances because of
ground noise. The surface wave is usually very easy to
see. So DOIT.SW creates the Green's functions by adding
together surface-wave modes, e.g., creating a seismogram for the
signal following the first S arrival. These synthetics are very
fast to compute and are actully quite good at 200 km. Compute these
if you do not want to fit the initial P-wave form.
After the
computations are complete the GREEN/YUN.REG directory contains
the following:
007000100.RDD 017500100.RDS 020000100.REX 036000100.RSS 046000100.TDS 007000100.RDS 017500100.REX 020000100.RSS 036000100.TDS 046000100.TSS ......................................................................... 011500100.TSS 019000100.ZDD 035000100.ZDS 045000100.ZEX 056500100.ZSS 011500100.ZDD 019000100.ZDS 035000100.ZEX 045000100.ZSS dfile 011500100.ZDS 019000100.ZEX 035000100.ZSS 046000100.RDD hspec96.dat 011500100.ZEX 019000100.ZSS 036000100.RDD 046000100.RDS hspec96.grn 011500100.ZSS 020000100.RDD 036000100.RDS 046000100.REX W.CTL 017500100.RDD 020000100.RDS 036000100.REX 046000100.RSS
The files 011500100.ZEX is the Green function for the ZEX
source at an epicentral distance of 115.0 km and a source depth
of 10.0 km. The file naming convention used is DDDDdHHHh.GRN which
permits us to represent distances from 0 to 9999.9 km in increments
of 0.1 km and source depths from 0 to 999.9 km in 0.1 km
increments.
The dfile, hspec96.dat and
hspec96.grn are from the computational run and can be
removed. The W.CTL file has entries as follow:
70 0.25 512 3.75 0 0100 007000100 115 0.25 512 9.375 0 0100 011500100 175 0.25 512 16.875 0 0100 017500100 190 0.25 512 18.75 0 0100 019000100 200 0.25 1024 20 0 0100 020000100 350 0.25 1024 38.75 0 0100 035000100 360 0.25 1024 40 0 0100 036000100 450 0.25 1024 51.25 0 0100 045000100 460 0.25 1024 52.5 0 0100 046000100 565 0.25 2048 65.625 0 0100 056500100
The columns are the epicentral distacne, the sample rate, the number of points, the time of the first sample, the reduction velocity (a 0 hear means that the time is actually that of the first sample), the directory for this dource depth, and the Green function prototype for this source depth and the distance. Moment tensor inversion uses the epicentral distance of the actual observed waveform to find the Green function appropriate for that distance by searching the first column for the best fit. For example if the actual distance is 116.51 km, then the processing script will use the Green function computed at a distance of 115 km.
The distribution contains several other
directories.
AK135.TEL gives the scripts
and in the location for teleseismic Green's functions from 30 to 95
degrees. These are used for network QC, and for source
inversion. The computation of the complete set of Green's functions
will keep the computer busy for several weeks. The continental AK135
model is used.
AK135.TELPBBD - The program
hudson96 is used to compute high-frequency synthetics for use
in BroadBand Depth determination from the teleseismic P-wave signal
at epicentral distances of 30 to 95 degrees. This computation
is fast because of the assumption that only one ray parameter is
required. This assumption is fine for shallow earthquakes for which
the P, pP and sP have the same ray parameter, but may not be
appropriate for large epicentral distances and 700 km depths.
CUS.REG - Compute the Green's functions for the CUS model
WUS.REG - Compute the Green's functions for the WUS model
Note that I attempt to
distinguish Green's functions by the naming of the directory. If I
wish to use the AK135 model for regional synthetics, I would place
the Green's functions in a directory named AK135.REG, which would
have the synthetics from 0 to 2000 km