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# W-phase documentation

## Installation

### Getting the code

Currently, the W-phase package is hosted as a github repository. To check out the W-phase repository:

git clone https://github.com/eost/wphase.git wphase_package

To update your W-phase repository (pull changes)

cd /to/the/wphase/directory/
git pull origin master

### Dependencies

The w-phase package have only been tested on Unix and Linux computers. You will need the following:

1. csh shell
2. gcc and gfortran
3. python2.7 (or later)
4. You have to install numpy, matplotlib, basemap and netCDF4 to run some python scripts which make figures.
5. rdseed

To install these dependencies on MacOs, you can refer to this page.

### Building the code

To install the code, we must first setup a few environment variables. If you use csh or tcsh:

setenv RDSEED       /path/to/rdseed/executable
setenv GF_PATH      /path/to/greens/functions/database
setenv WPHASE_HOME  /path/to/wphase

If you use bash:

export RDSEED=/path/to/rdseed/executable
export GF_PATH=/path/to/greens/functions/database
export WPHASE_HOME=/path/to/wphase/package

These variables are necessary both at installation time and at run time. In addition to these variables, it is handy to include the wphase “bin” directory into the PATH environment variable:

setenv PATH         ${PATH}:$WPHASE_HOME/bin

or in bash:

export PATH=${PATH}:$WPHASE_HOME/bin

All theses variable assignment can be included in your .tcshrc or your .bashrc file.

Once you have downloaded the last version of the W-phase package and that the above environment variables are properly defined. Then you can proceed as follows to compile the package:

cd ${WPHASE_HOME}/src make -B ## How to run W-phase You should also have a look to the W-phase tutorial page. ### Preparing directories, i_master and CMTSOLUTION Before each inversion, it is necessary to create a “run” directory containing two input ascii files: • CMTSOLUTION: a file containing the PDE, the event centroid location and timing and optionally a “reference” moment tensor solution. • i_master: a file containing other parameters such as the band-pass filter parameters, minimum and maximum distances, etc. The format of these files are described in the file formats section. Path to SEED file(s) must be correctly specified after the keyword 'SEED:' in the i_master file. If multiple SEED files are used for the same inversion, each of them must be referenced properly in i_master using one 'SEED:' line per file. ### Extracting data from SEED Once the i_master and CMTSOLUTION files are created, we can extract waveforms and instrument response parameters and perform a rough screening by epicentral distance. This can be done using: ${WPHASE_HOME}/bin/extract.csh

which will extract Z, N, E, 1, 2 channels in SEED file(s).

Data is extracted from SEED volumes and written in SAC format in the subdirectory 'DATA'. PZ files containing instrument responses are also located in this directory. After running an extract*.csh script, screened and windowed data files are listed in 'scr_dat_fil_list' while 'coeffs_rec_lut' contains the coefficients for the time domain deconvolution of the instrument response.

### Calculating Synthetics, deconvolution and filtering

The next step is to calculate the kernel functions associated with the 6 elements of the seismic moment tensor for the stations listed in 'scr_dat_fil_list' and to convolve them with the moment rate function (MRF) specified in the CMTSOLUTION file (time shift and half duration). We must then deconvolve the instrument response from the data and band pass filter each waveform in the frequency pass band specified in i_master. This is performed using:

${WPHASE_HOME}/bin/prepare_wp.csh for Z, N, E, 1, 2 channels or ${WPHASE_HOME}/bin/prepare_wp.csh Z

for Z channel only

The scripts listed above will generates i_wpinversion which is a list of sac files to be used in the inversion. This original input file usually includes lots of noisy channels which should be removed further. Output kernel functions will be found generally in ./GF

### Inversion

The inversion can then be performed using the Kernels functions in ./GF and data files listed in i_wpinversion.

For more details on options run

${WPHASE_HOME}/bin/wpinversion -h By default, this program assumes a zero trace moment tensor (i.e. deviatoric moment tensor). This constraint can be disabled by adding the option “-nont”. Another interesting option is “-dc” which enable the inversion for a pure double couple. The options “-stike”, “-dip”, “-rake” and “-mom” provide the possibility to run double couple inversions at fixed strike, dip, rake and/or scalar moment. Several output files are created after running the inversion: • WCMTSOLUTION (ASCII) is the solution obtained after inversion. • p_wpinversion (postscript) which can be visualized with gv (or gs, evince …) and printed with lp or lpr. • o_wpinversion (ASCII) is the output list of stations. The 1st column is the list of sac files, the 2nd column is the azimuth (degrees), the 3rd column is the epicentral distance (degrees), the 4th column is the index of the first sample of each channel in the concatenated data vector, the 5th column is the index of the first sample of the next channel, the 8th column is the rms misfit • fort.15* (ASCII) is a comparison between observed and predicted concatenated W-phase traces. The first column is the data vector, the second column is the predicted data vector after inversion and the (optional) third column is the data predicted from the (optional) reference solution in the CMTSOLUTION file. • fort.15_LH? files (ASCII) where '?' is Z, N, E, 1 or 2 are the same concatenated traces but separated by channels. • *.synth.sac (SAC files) which are the predicted data after inversion. Since i_wpinversion includes a lot of noisy traces, the result is usually uncertain. To improve the solution, we must remove noisy data. This can be done as follows: 1. A first screening can be performed using the option -med : this will reject data with an anomalously small or large interval between maximum and minimum amplitudes. 2. After a first run of the inversion, it is possible to perform another inversion throwing out the stations with a relative mismatch exceeding 3.0 (i.e. really bad data). The file o_wpinversion which was created by the first inversion will be used an input. After inversion with the better dataset, a new o_wpinversion file will be created. For example using a threshold of 3.0 : $WPHASE_HOME/bin/wpinversion -ifil o_wpinversion -ofil o_wpinv.th3.0 -th 3.0

(in this example, the new o_wpinversion file is named o_wpinv.th3.0). This step can be repeated two or more times with different thresholds using the option -th (e.g 1.3, 0.9, etc.):

$WPHASE_HOME/bin/wpinversion -ifil o_wpinv.th3.0 -ofil o_wpinv.th1.3 -th 1.3$WPHASE_HOME/bin/wpinversion -ifil o_wpinv.th1.3 -ofil o_wpinv.th0.9 -th 0.9 
3. Finally, it is possible to remove the channels showing a large rms ratios (observed/predicted and predicted/observed) using the option –nr (e.g. –nr 2.0):
$WPHASE_HOME/bin/wpinversion -ifil o_wpinv.th0.9 -ofil o_wpinv.th1.3 -nr 2.0 At the end of the screening process, it is necessary to clean up the run directory so that o_wpinversion correspond to the optimum dataset which can be used later by grid-search and plot routines : mv o_wpinversion o_wpinv.noth cp o_wpinv.th0.9 o_wpinversion ### RUNA scripts Data extraction, screening and inversion described above can be performed by running one of the RUNA3*csh scripts (usually in bin). These scripts perform data extraction/screening and calculate a moment tensor solution after median data screening and after rejecting traces associated with large misfit using the threshold 5.0 3.0 0.9 (i.e. -th, see 2. in section 4): ${WPHASE_HOME}/bin/RUNA3.csh

will perform median and rms misfit screening for Z, N, E, 1 and 2 channels,

${WPHASE_HOME}/bin/RUNA3_only_Z.csh  will perform median and rms misfit screening for Z channels only. These two scripts don’t perform the “ratio screening” (i.e. 3. above). To run the same routines with an additional screening based on the amplitude ratio (observed/predicted and predicted/observed), the following script can be used: ${WPHASE_HOME}/bin/RUNA3r.csh

will perform median, rms misfit and rms ratio for channels Z, N, E, 1, 2 channels,

Remark: RUNAr.csh is not yet fully tested.

Several optional parameters can be used when running RUNA3*csh scripts. These parameters will apply to the wpinversion program. They are described when running wpinversion -h. e.g.: RUNA3.csh -wz 1.0 -wn 0.3 -we 0.5 will give a weights of 1.0, 0.3 and 0.5 for Z, N, E components respectively.

To perform data screening and inversion only, using previously extracted SAC data, it is possible to use:

${WPHASE_HOME}/bin/RUNA3_lite.csh that is designed for Z, N ,Z ,1, 2 channels ### Grid searches In the grid-search scheme, there is a first global rough exploration which is followed by finer samplings around minimal points. If the optimum is found near a bound, the explored space is extended. Grid searches can be performed using the script ${WPHASE_HOME}/bin/wp_grid_search.py

. A detailed help can be found by using

${WPHASE_HOME}/bin/wp_grid_search.py -h . The grid-search computation is parallelized using openMP (if available, it takes advantage of muliple cores). This script run a time-shift (ts) grid search followed by a centroid position grid-search : • By default, the ts grid-search only shift the Green's functions to find an optimum centroid timing. At the end of the grid-search, a new inversion is performed by fixing the source half duration (hd) to the optimal value of ts. Using the option -s, the grid-search is preformed while considering ts=hd which is more time consuming. Grid-search results can be found in grid_search_ts_out (see note 3). A postscript file (ts_p_wpinversion) as well as a CMTSOLUTION file (ts_WCMTSOLUTION) corresponding to the optimum ts will also be generated automatically. In gereneral all the output files containing the prefix ts_are associated to the time-shift grid search. • Then, using the optimum value of ts, it perform a 2D centroid position grid-search (lat/lon). The centroid position grid-search generates a text file named grid_search_xy_out with a structure similar to grid_search_ts_out (see note 3). As for time-shift grid-search, you will also find the usual output files with the prefix xy_. • It is also possible to perform a 3D grid-search using the option –z. ### Plot routines All the plotting scripts are coded using python and the module pylab which have to be installed before using them. The module basemap is also needed for plotting maps but it is optional (even if we recommend to install it). There are 3 script which can be used to plot the W phase inversion results: • The first script is ${WPHASE_HOME}/bin/make_grids.py

which be used to display grid-searches results. Use

${WPHASE_HOME}/bin/make_grids.py -h to have more details on available options and arguments. The 2 other scripts plot observed and synthetic seismograms after W phase inversion. • In order to plot complete seismograms individually and place station on a map: ${WPHASE_HOME}/bin/traces.py

which draw complete seismograms and show station location on a map (if basemap is available). Please use

${WPHASE_HOME}/bin/traces.py -h for more details on available options. • To plot concatenated waveforms: ${WPHASE_HOME}/bin/make_cwp.py

For more details on available options and arguments see

## Data formats

You can also have a look to the W-phase tutorial page.

#### CMTSOLUTION FILE

example:

 PDE 2003  9 25 19 50  6.40  41.8100  143.9100  27.0 6.9 8.1 HOKKAIDO, JP
event name:     092503C
time shift:     19.8100
half duration:  33.5000
latitude:       42.2100
longitude:     143.8400
depth:          28.2400
Mrr:       7.770000e+27
Mtt:      -4.110000e+27
Mpp:      -3.660000e+27
Mrt:       1.320000e+28
Mrp:       2.590000e+28
Mtp:      -6.620000e+27

The first line of this file is the PDE.

• The first 4 characters of this line (including the first white space in the example above) generaly indicates the agency which provide the origin time, the hypocenter location and preliminary magnitude estimates.
• Characters from 6 to 27 correspond to the PDE origin time
• Characters from 29 to 52 are the PDE latitude, longitude and depth. This hypocenter location will be used to define the time window in order to select the part of the waveform which will be inverted
• Characters from 54 to 60 are PDE magnitude estimates The rest of the line provides some details on epicenter location (region, country, …)

The second line, 'event name' correspond to the event id

Lines 3 and 4 are the parameters of the STF.

Lines 5, 6 and 7 are the 'latitude', 'longitude' and 'depth' of the centroïd wich will be used for the rotation of horizontal components and for the computation of synthetic kernel functions.

The last 6 lines are optional, they correspond to a moment tensor solution (e.g. a reference GCMT for comparision with the W phase inversion).

#### i_master file

This file is composed of several fields (some of them are optional):

• EVNAME: Arbitrary event name
• SEED: path to SEED file. This field must be used several times if there are multiple SEED files.
• DMAX: Maximum distance to be used.
• DMIN: Minimum distance to be used (optional). If omitted, it is defaulted to 0.
• CMTFILE: Path to the CMTSOLUTION file
• filt_order: order of the butterworth filter.
• filt_cf1: low-frequency cut –off.
• filt_cf2: high-frequency cut –off.
• filt_pass: unused parameter (let it to 1).
• IDEC_2: the second number is the number of seconds just before P wave over which the baseline is defined (let the other parameters to 2 and 0.1) .
• IDEC_3: Instrument response fit parameters for the deconvolution. The two first parameters define the frequency band in which the fit is measured. The third parameter is the number of samples used in this frequency range and the last parameter is a maximum misfit above which the channel is rejected.
• WP_WIN: time window definition.
• If one value $B$ (eg. WP_WIN: 15) is used, then the window is defined by $[P_{tt},P_{tt}+B\times\Delta]$ where $P_{tt}$ is the P-wave travel-time.
• If two values $A$ $B$ are specified (e.g., WP_WIN: 0. 15.), then the window is $[P_{tt}+A\times\Delta,P_{tt}+B\times\Delta]$.
• If three values $A$, $B$ and $C$ are used (e.g., WP_WIN: 0. 15. 12.) the time window is defined as:
• $[P_{tt}+A\times\Delta,P_{tt}+B\times\Delta]$ if $\Delta>C$
• $[P_{tt}+A\times C,P_{tt}+B\times C]$ if $\Delta<C$
• If Four values, $A$, $B$, $C$ and $D$ are given (e.g., WP_WIN: 0. 15. 12. 50.) then the window is:
• $[P_{tt}+A\times \Delta,P_{tt}+B\times\Delta]$ if $C<\Delta<D$
• $[P_{tt}+A\times C,P_{tt}+B\times C]$ if $\Delta<C$
• $[P_{tt}+A\times D,P_{tt}+B\times D]$ if $\Delta>D$
• GFDIR: Name of the Green's function directory (optional)

example:

EVNAME:   Tokachi-Oki_2003
SEED:    ../../WP6/SEEDS/2003_tokachi_oki_LH.SEED
DMAX:    90.
DMIN:    0.
CMTFILE: CMTSOLUTION

# data deconvolution
filt_order: 4
filt_cf1  : 0.001
filt_cf2  : 0.005
filt_pass : 1
IDEC_2:  2  280   0.1
IDEC_3:  0.001   0.1  100  0.03

#inversion
WP_WIN: 15.
GFDIR: ./GF 

#### Grid-search output files: grid_search_ts_out and grid_search_xy_out

grid_search_ts_out corresponds to the time-shift grid-search.

Example:

   60.0000   0.20140377
81.7621   0.32070120
000 000     1.0000    81.7621   -35.8500   -72.7100    44.8000   0.60186830   1.83279165
001 000     5.0000    81.7621   -35.8500   -72.7100    44.8000   0.58186860   1.60449952
002 000     9.0000    81.7621   -35.8500   -72.7100    44.8000   0.55865993   1.40553383
003 000    13.0000    81.7621   -35.8500   -72.7100    44.8000   0.53241366   1.23245105
004 000    17.0000    81.7621   -35.8500   -72.7100    44.8000   0.50339138   1.08142045
(…)
014 000    57.0000    81.7621   -35.8500   -72.7100    44.8000   0.20380139   0.31131967
015 000    61.0000    81.7621   -35.8500   -72.7100    44.8000   0.20198340   0.30827735
016 000    65.0000    81.7621   -35.8500   -72.7100    44.8000   0.21088280   0.32324637
017 000    69.0000    81.7621   -35.8500   -72.7100    44.8000   0.22888998   0.35415847
018 000    73.0000    81.7621   -35.8500   -72.7100    44.8000   0.25358477   0.39808714
(…)
039 000   157.0000    81.7621   -35.8500   -72.7100    44.8000   0.65903444   3.48513694
040 000   161.0000    81.7621   -35.8500   -72.7100    44.8000   0.65708573   3.35654281
041 000   165.0000    81.7621   -35.8500   -72.7100    44.8000   0.65410621   3.18301823
042 001    59.0000    81.7621   -35.8500   -72.7100    44.8000   0.20151331   0.30749196
043 001    63.0000    81.7621   -35.8500   -72.7100    44.8000   0.20516181   0.31360143
044 001    67.0000    81.7621   -35.8500   -72.7100    44.8000   0.21889318   0.33689015
045 002    58.0000    81.7621   -35.8500   -72.7100    44.8000   0.20231439   0.30883067
046 002    60.0000    81.7621   -35.8500   -72.7100    44.8000   0.20140377   0.30730901
047 002    62.0000    81.7621   -35.8500   -72.7100    44.8000   0.20324196   0.31038266
048 002    64.0000    81.7621   -35.8500   -72.7100    44.8000   0.20771868   0.31790207

The two first lines correspond respectively to the optimum and to the initial centroid time-shifts, the first column being the time-shift itself and the second column being the associated rms misfit.

The following lines provide some details on the grid-search : 1st col. : index for this time-shift value, 2nd col. : iteration number, 3rd col. : time-shift 4rd col. : centroid latitude 5th col. : centroid longitude 6th col. : centroid depth 7th col. : rms 8th col. : normalized rms

In the example above you can see that a global grid-search is performed from 1 to 165 sec (until computation 41) at the 0th iteration with a time step of 4sec. The 1st iteration corresponds to computations 42-44 which extend the grid-search to unexplored time-shift between 57sec and 69sec with a sampling interval of 2sec. The 2nd iteration perform an even finer sampling to guarantee a 1sec grid-search between 57sec and 65sec. Once this file is available to us (after running the time-shift grid-search), we can run

${WPHASE_HOME}/bin/make_grids.py –t  to create the file grid_search_ts.pdf containing Fig. 1 which corresponds to the above example. The output centroid position grid-search file grid_search_xy_out as a quite similar same structure replacing the time-shit in the 2 first lines by optimum and initial latitudes, longitudes and depth.  -35.4500 -72.8325 25.5000 0.19118874 -35.2500 -72.7100 25.5000 0.19314386 000 000 60.0000 60.0000 -36.4500 -74.1794 25.5000 0.24214954 0.37750789 001 000 60.0000 60.0000 -36.4500 -73.6896 25.5000 0.22150727 0.34137918 002 000 60.0000 60.0000 -36.4500 -73.1998 25.5000 0.20980594 0.32142471 003 000 60.0000 60.0000 -36.4500 -72.7100 25.5000 0.20938393 0.32071163 (…) 067 001 60.0000 60.0000 -35.6500 -72.4651 25.5000 0.19798867 0.30161961 068 001 60.0000 60.0000 -35.8500 -72.4651 25.5000 0.19830051 0.30213800 069 001 60.0000 60.0000 -35.8500 -72.7100 25.5000 0.19640545 0.29899114 070 001 60.0000 60.0000 -34.6500 -72.9549 25.5000 0.19787217 0.30142600 (…) 104 002 60.0000 60.0000 -35.3500 -72.5875 25.5000 0.19326491 0.29379393 105 002 60.0000 60.0000 -35.3500 -72.7100 25.5000 0.19296721 0.29330241 106 002 60.0000 60.0000 -35.5500 -72.7100 25.5000 0.19360157 0.29435001 The first line corresponds to the optimum centroid location and the second line indicates the a priori location specified in the CMTSOLUTION file. In these two lines, the 1st, 2nd and 3rd column correspond respectively to the centroid latitute, longitude and depth. The 4th column presents the associated rms misfits. The following lines provide some details on the grid-search : 1st col. : index of the explorated centroid position, 2nd col. : iteration number, 3rd col. : time-shift 4th col. : half duration 5th col. : centroid latitude 6th col. : centroid longitude 7th col. : centroid depth 8th col. : rms 9th col. : normalized rms Once the grid-search is performed, the grid_search_xy_out is available to us (after running the time-shift grid-search), we can run ${WPHASE_HOME}/bin/make_grids.py –p -b

to create the file grid_search_xy.pdf containing Fig. 1 which corresponds to the above example. The option –b is optional: it allows to use the basemap module in order to plot coastlines and topography.