Table of Contents
W-phase tutorial
You may also refer to the W-phase documentation page, where scripts and executables are described in this section, input and output file-formats are described here.
This tutorial page only provides a typical example of W phase inversion run.
Example of run for the 2010 Maule earthquake
We consider here an example of run for the Mw8.8 2010 Maule earthquake.
Input files
The first thing to do is to create i_master and CMTSOLUTION files. We can use as input the following CMTSOLUTION file
PDEW2010 2 27 6 34 15.60 -35.8500 -72.7100 44.8 8.9 8.9 NEAR COAST OF CENTRAL CH event name: 201002270634A time shift: 81.7621 half duration: 81.7621 latitude: -35.8500 longitude: -72.7100 depth: 44.8000 Mrr: 1.040000e+29 Mtt: -3.920000e+27 Mpp: -1.000000e+29 Mrt: 3.040000e+28 Mrp: -1.520000e+29 Mtp: -1.190000e+28
This file correspond to the Global CMT solution except that we fixed the centroid latitute, longitude and depth to the PDE preliminary hypocenter values and that the time-shift and half duration have been fixed a priori using some initial magnitude estimate (for more detailed information about file formats, please refer to the "File formats" section of the W-phase documentation page).
The i_master file is the following :
EVNAME: NEAR_COAST_OF_CENTRAL_CH SEED: ../SEEDS/201002270634A_eqdat.seed DMIN: 5.00 DMAX: 55.00 CMTFILE: CMTSOLUTION filt_order: 4 filt_cf1: 0.00100 filt_cf2: 0.00500 filt_pass: 1 IDEC_2: 2 280 0.1 IDEC_3: 0.001 0.1 100 0.03 GFDIR: GF WP_WIN: 15.0
According to the i_master file above, data is included in the seed file ../SEEDS/201002270634A_eqdat.seed (in this case the seed volume was obtained using the request tools of the IRIS DMC). It contains a large dataset of LH channels from 0 to 180 degrees of epicentral distances for a distribution of stations corresponding to FDSN, GSN_BROADBAND and STS1 virtual networks. For the purpose of this example, we decided to restrict the our dataset to the stations having epicentral distances within 5.0 to 55.0 degrees. Of course it is possible to consider more stations by increasing DMAX since the green function database allow us to perform the W phase inversion for stations within 90 degrees of epicentral distances. The filter pass band is 1mHz-5mHz and the time window extent is from the P wave until $15\times\Delta$.
Preliminary inversion with a fixed centroid location
Once these files are ready, we can proceed with a moment tensor inversion at the centroid location specified in CMTSOLUTION (i.e. the PDE location in this example):
${WPHASE_HOME}/bin/RUNA3.csh
This command will extract the data from seed volume, calculate the kernel functions corresponding to each moment tensor element, filter the waveforms, screens the data and perform inversion. The solution is displayed on the terminal and is given in the WCMTSOLUTION file:
PDEW2010 2 27 6 34 15.60 -35.8500 -72.7100 44.8 8.9 8.9 NEAR COAST OF CENTRAL CH event name: 201002270634A time shift: 81.7621 half duration: 81.7621 latitude: -35.8500 longitude: -72.7100 depth: 44.8000 Mrr: 9.106371e+28 Mtt: 5.055543e+27 Mpp: -9.611925e+28 Mrt: -8.117296e+28 Mrp: -1.862157e+29 Mtp: -1.167994e+28
Other output files are provided, such as p_wpinversion and fort.15 as detailed in previous sections. The ASCII beach ball can be drawn using the cmtascii routine:
${WPHASE_HOME}/bin/cmtascii WCMTSOLUTION
Moment mag. : 8.83
PDE location : Lat= 35.85S; Lon= 72.71W; Dep= 44.8 km
Centroid loc.: Lat= 35.85S; Lon= 72.71W; Dep= 44.8 km
Origin time : 2010/02/27 06:34:15.60
Time delay : 81.8 sec
Half duration: 81.8 sec
(…)
Best Double Couple: M0=2.24E+29 dyn.cm
NP1: Strike=351 ; Dip=14 ; Slip= 60
NP2: Strike=202 ; Dip=78 ; Slip= 97
#########
-----------------
----------------####---
----------------########---
----------------##########---
----------------############---
---- ---------##############---
----- P --------################---
----- --------################---
---------------#################---
--------------######## #######---
-------------######### T #######---
------------######### #######--
----------###################--
---------##################--
--------################---
-----################--
--#############--
######---
Final inversion after centroid grid-search
The previous solution was computed with a fixed location (PDE). It is also possible to determine an optimum centroid position and timing by running the wp_grid_search.py script:
${WPHASE_HOME}/bin/wp_grid_search.py –z
Without the '-z' flag, this command performs a 2D grid search with a fixed depth. If the option –z is given, depth is also explored. This command will perform the time-shift grid-search as well as the centroid position grid-search.
The grid-search is first performed with a large sampling interval and refined around the parameters corresponding to minimal rms misfits. The solution after time-shift grid-search is given in ts_WCMTSOLUTION and the final optimum solution after centroid position grid-search is given in xy_WCMTSOLUTION:
PDEW2010 2 27 6 34 15.60 -35.8500 -72.7100 44.8 8.9 8.9 NEAR COAST OF CENTRAL CH event name: 201002270634A time shift: 60.0000 half duration: 60.0000 latitude: -35.4500 longitude: -72.8325 depth: 25.5000 Mrr: 9.393492e+28 Mtt: 2.707494e+26 Mpp: -9.420567e+28 Mrt: 1.669174e+28 Mrp: -1.567680e+29 Mtp: -1.197536e+28
Again, this solution can be drawn using cmtascii :
${WPHASE_HOME}/bin/cmtascii WCMTSOLUTION
Moment mag. : 8.78
PDE location : Lat= 35.85S; Lon= 72.71W; Dep= 44.8 km
Centroid loc.: Lat= 35.45S; Lon= 72.83W; Dep= 25.5 km
Origin time : 2010/02/27 06:34:15.60
Time delay : 60.0 sec
Half duration: 60.0 sec
(…)
Best Double Couple: M0=1.84E+29 dyn.cm
NP1: Strike= 18 ; Dip=16 ; Slip=111
NP2: Strike=176 ; Dip=75 ; Slip= 84
----###--
-------########--
---------############--
-----------##############--
-----------################--
------------#################--
-------------#################---
--------------######## #######---
---- -------######## T #######---
---- P -------######## #######---
---- -------##################---
---------------################----
--------------################---
-------------###############---
-------------#############---
------------###########----
-----------########----
----------##-----
#####----
Wphase solution after grid search
Each spatial and temporal location explored during the grid-search is detailed in grid_search_ts_out (time-shift grid search) grid_search_xyz_out (lat, lon, dep grid-search) and grid_search_xy_out (finer lat, lon grid-search which is performed at the optimum depth found during the lat, lon, dep global exploration).
Plotting the results
The grid-search exploration result can be displayed using the python script make_grids.py :
${WPHASE_HOME}/bin/make_grids.py –b
The optional parameter –b activates the use of the cartopy toolkit in order to draw the topography and coastlines. The resulting figures shown here in Fig. 1 and Fig. 2 are written in the pdf files grid_search_ts.pdf and grid_search_xy.pdf.
There are two script which allows to compare predicted and observed waveforms. The first one shows the comparison between concatenated W phase traces using fort.15 files:
${WPHASE_HOME}/bin/make_cwp.py
The resulting figures are given in files CWP_R.pdf CWP_W.pdf where the predicted waveforms in CWP_R.pdf are computed from the reference solution (e.g. CMTSOLUTION) and the predicted waveforms in CWP_W.pdf are calculated from the W phase solution (either in WCMTSOLUTION, ts_WCMTSOLUTION or xy_WCMTSOLUTION). The LHZ traces contained in CWP_W.pdf are drawn in Fig. 3. The second script plot the waveform fit:
${WPHASE_HOME}/bin/traces.py
The resulting figure is given in file wp_pages.pdf which is shown here in Fig. 4. If the cartopy python module is available, a map is drawn showing the station location with respect to the centroid location. Otherwise, a simple polar representation is used to display the station location.
