Introduction

The following Email was received from Shan Dou on July 5, 2012:

Hi Prof. Herrmann,

I have a couple of questions about spulse96.

(1) For user-specified source time function (specified with the "-F" option), what type of file format should I use? A two-column ascii, a file96 format ascii, or a sac file?

(2) I did a simple set of test with a two layer + half space model, and the output seismograms are compared against finite difference calculation results. I attached a PDF file in this email to show a couple of differences that can be seen in the results. I marked my questions in blue color, would you please take a look at them? It would be great if I can get some suggestions from you about those questions!

      Thank you very much!


Best Wishes,
Shan
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Response

(1) The format for the "-F rfile" option to spulse96 and hpulse96 is found in the respective source code, e.g., PROGRAMS.330/VOLIII/src/spulse96.f and PROGRAMS.330/VOLVI/src/hpulse96.f  in subroutine pulud. The data format in the spulse96.f  has the following code:

        read(4,*)np,dtt
        read(4,*)(d(i),i=1,np)

I have just modified the hspec96.f to use the same list directed IO input. This will be available in hpulse96 with the next update.

(2) The PDF document concerning this question is CPS_E3D_syntheticSeismograms_Comparison-2.pdf .

To respond to the many questions I created a velocity model file and created synthetics using both modal superposition and the wavenumebr integration techniques.

The scripts to run both the wavenumber integration and modal superposition is given in t.tgz.
Unpack and run using the commands:
gunzip -c t.tgz DOALL

Assuming that you have ImageMagick installed on your computer, you will then file the image files Shandou1/WK.png and ShanDou2/SW.png, which are compared in the next figure (note that each traces is scaled differently and that this is not a true amplitude plot):
Wavenumber Integration - WK.png
Modal Superposition -SW.png

Note that the graphics is performed using gsac. Note also that this is slightly different from the CPS-E3D...pdf in that the sample interval is 6.25E-05 instead of 6.20E-05

Before answering the questions in the PDF, I note that Shan Dou actually made synthetics with a source time function with a duration of 4*40*6.20E-05 sec (0.0992 sec).  The small sample interval requires a lot of computation time. To test the program results, I used the "-NDEC 16" flag on hprep96 to effectively change the sample interval to 0.001 sec, and to make the computations a factor fo 256 faster.  To accomplish the same with the surface-wave codes, I change the sample interval to 0.001 sec and decreased the number of data points a factor of 16 to 512. 
I also begtan the synthetic -0.01 sec before the origin time and I also did not make a synthetic at zero distance, since this is very unstable numerically.

Several questions were asked in the PDF:

a. The high frequency “glitches” that are superimposed on the longer period signal: (Q1: What
causes these series of glitches?)

When adding modes, you must be very careful that the dispersion curves are correctly followed and that there is no mode jumping. "This will be a big problem for low-velocity layers.

Your text indicated the use of the "-LOCK" flag in spulse96. Did you modify the lower part of the model to actually make locked modes.

Adding mode will only provide arrival with phase velocities less than the highest S-wave velocity in the model. If you did not add a high velocity layer at depth, you model will only provide arrivals with phase velocities less than 2800 m/a, which means that near vertical reflections will not be modeled correctly.

b. The very long period signal that are present before the first-P arrivals, which make the time
series appear to be acausa; (Q2: What are the causes of these arrivals? Could inadequate
amount of summed modes be the lead cause?)

When adding modes, you will nefver get the complete synthetic because you are actually phase-velocity filtering everything in an acausal manner. By make in the synthetics start before the origin time, and by NOT using a acausal Ricker wavelet, you can see the P-arrival in the WK synthetics.

If you want to use a Ricker wavelet, then in gsac apply the commands dif, mul -1, and then ricker f 80, which will provide something similar to your E3D synthetics

c. Long period signals are also quite strong in later portion of the synthetic seismograms. Would
this be caused by inadequate amount of summed modes as well?

I do not see this problem.  However in your E3D synthetics there is a strange bifurcation (splitting) starting at time 0.12 sec at trace number 40. It is not that extreme in the WK.png synthetic.


Final comment

There will always be a problem with the suface wave modal superposition because I assume that velocity increases with depth. This means that the eigenfunctions corresponding to the evanescent waves decrease with depth.  For a model with a low velocity zone, there will be cases of low pahse velocity in which the eigenfunctions oscillate in the low velocity region but must exponentially decay in both directions away from this zone. In you problem this would require an exponential decay toward the surface, whereas I actually will compute an expoential increase toward the surface. This problem is worse at higher freuqnecies, or as the thickness of the top layer increases.  Beware!!

See Also

Synthetics for seismic exploration