Introduction

The purpose of this tutorial is to test the correctness of the code for performing a grid search for a complete moment tensor using the program wvfmtgrd96. Because this program follows Zhu and Ben-Zion (2013) by performing a grid search over five parameters, the derived moment tensor will not be exactly the true moment tensor. This tutorial provides a complete processing environment to duplicate the evaluation given below.

Zhu, L., and Y. Ben-Zion (2013). Paramaterization of general seismic potency and 
   moment tensors for source inversion of seismic waveform data, 
   Geophys. J. Int. 194, 839-843.  doi: 10.1093/gji/ggt137

Processing

The example given here uses Green's functions for the CUS velocity model at a source depth of 1 km. For brevity, the grid search is applied only at one source depth, rather than at a number depths, to focus on the comparison of the true moment tensor to those resulting from wvfmtgrd96. The t.tgz contains the shell scripts and the Green's functions for five epicentral distances and just a source depth of 1.0 km. It is assumed that Computer Programs in Seismology and ImageMagick have been installed.

To install this tutorial, download t.tgz, and then

gunzip -c t.tgz | tar xf - 
cd TESTMGRD
DOALL
Note that the grid search will take computational time.

The results of the test run will be in subdirectories such as TEST01. The scripts in TEST01/MTGRD.REG are the current scripts for processing. Of interest will be

Discussion

For each of the tests show below, the first row displays the predicted P, SV, SH amplitudes and S-wave polarization on the lower hemisphere of the focal sphere. A red circle displays the lune position of the moment tensor. The second row presents the mt.msg generated by the call to mtinfo. In addition hte Mw and moment tensor are presented. The final row compares the observed and predicted waveforms in red and blue, respectively. As expected the comparison is excellent, as expected.

These plots were made since it was not obvious that the inversion gave the correct results when the moment tensors were compared. This is especially seen in the case of Test 05, which is dominated by Mxz. For the most part, there is agreement in the amplitudes. Since these computations are made with synthetics, the difference can be traced to the granularity of the five parameters used for the grid search.

TEST

The evaluation consists of making observed waveforms for a given moment tensor and then inverting these. The presentation below provides the comparison.