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======= W-phase tutorial =======

You may also refer to [[wphase:documentation|the W-phase documentation page]], where scripts and executables are described in [[wphase:documentation#How to run W-phase|this section]], input and output file-formats are described [[wphase:documentation#Data formats|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
<code>
 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
</code>

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 [[wphase:documentation#Data formats|the "File formats" section of the W-phase documentation page]]).

The i_master file is the following :
<code>
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
</code>

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):
<code>${WPHASE_HOME}/bin/RUNA3.csh </code>
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:
<code>
 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
</code>

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:

<code>
${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 #######---
 ------------#########   #######-- 
  ----------###################--  
   ---------##################--   
    --------################---    
      -----################--      
         --#############--         
             ######---
</code>

==== 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:
<code>
${WPHASE_HOME}/bin/wp_grid_search.py –z
</code>
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:

<code>
 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
</code>
Again, this solution can be drawn using cmtascii :

<code>
${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 -------########   #######---
----   -------##################---
---------------################----
 --------------################--- 
  -------------###############---  
   -------------#############---   
    ------------###########----    
      -----------########----      
         ----------##-----         
             #####----
</code>

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 :
<code>
${WPHASE_HOME}/bin/make_grids.py –b
</code>

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:
<code>
${WPHASE_HOME}/bin/make_cwp.py
</code>

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:
<code>
${WPHASE_HOME}/bin/traces.py
</code>

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.
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