Wavenumber integration tests

Introduction

This set of tests uses the CPS program sequence hprep96, hspec96, hpulse9 and f96tosac to create complete synthetics.

We consider the the case of a source at a depth of 10km and epicentral distances of 1, 2, 3, 10 and 20 km.

The two models are

Rock model	Soil model
Rock halfspace ISOTROPIC KGS FLAT EARTH 1-D CONSTANT VELOCITY LINE08 LINE09 LINE10 LINE11 H(KM) VP(KM/S) VS(KM/S) RHO(GM/CC) QP QS ETAP ETAS FREFP FREFS 20.0 6.0 3.5 2.7 0.000 0.000 0 0 1 1		MODEL.01 Soil model with Q overlying a halfspace ISOTROPIC KGS FLAT EARTH 1-D CONSTANT VELOCITY LINE08 LINE09 LINE10 LINE11 H(KM) VP(KM/S) VS(KM/S) RHO(GM/CC) QP QS ETAP ETAS FREFP FREFS 0.0100 1.5 0.3 2.0 0.05 0.10 0 0 1 1 0.0100 1.5 0.6 2.0 0.03 0.06 0 0 1 1 0.0200 1.6 0.8 2.0 0.025 0.05 0 0 1 1 0.0200 3.0 1.5 2.2 0.01 0.02 0 0 1 1 0.1000 5.0 2.5 2.5 0.005 0.01 0 0 1 1 0.0 6.0 3.5 2.7 0.000 0.000 0 0 1 1

The processing script for this angle of incidence is DOIT which calls the script DODIST. These3 scripts is annotated with comments that describe the operations. Note that the shell script DOPLTPNG is used to convert the CPS PLT files to a png file using the ImageMagick convert. If ImageMagick is not installed, do something like

plotnps -F7 -W10 -EPS -K < P001.PLT > P001.eps

The DODIST invokes sacampl with the -TXT flag and the angle is defined as the arc tangent of (epicentral distance/source depth). This means that the ASCII file sacsampl_distance.txt will be available. As an aside, if one wishes to compare the synthetics response to the output of sacampl, then use gsac to create a CSV file.

Running the DOIT creates 8 PNG files. Three compare the time domain seismograms as a function of epicentral distance for the R, T and Z components. The remaining five compare the Soil/Rock spectra ratios as a function of distance.

The plots are

DOPLTPNG

The arrival between P and S at 20 km on the rock trace is an artifact of the wavenumebr integration and can be controlled by effectively making the Δk smaller. The waveforms are simpler in appearance since we are3 essentially looking at the direct P and S rays from the source. The traces for the soil model show some reverberations.

The next step was to window the traces on the S wave, take the Fourier transform and then save the amplitude spectra. At each distance a spectral ratio was obtained and the ration for each component were compared to the quarter-wavelength formula. The plots for the five distances are as follow:

Comparison of the radial component traces for the Rock (red) and Soil (blue) traces as a function of epicentral distance.

Comparison of the transverse component traces for the Rock (red) and Soil (blue) traces as a function of epicentral distance.

Comparison of the vertical component traces for the Rock (red) and Soil (blue) traces as a function of epicentral distance.

Site effect ratios at an epicentral distance of 1.0 km.

Site effect ratios at an epicentral distance of 2.0 km.

Site effect ratios at an epicentral distance of 3.0 km.

Site effect ratios at an epicentral distance of 10.0 km.

Site effect ratios at an epicentral distance of 20.0 km.

The spectral ratios at 1, 2 and 3 km look very similar to the plane wave results. The quarter-wavelength formula seems to fit the horizontal R and T components.

At a distance of 10km the amplification on the radial component increases, while at 20 km, this amplification becomes very large, although the rations of the Z and T components seem to behave well.

DOPLTPNG

#!/bin/sh

for i 
do
B=`basename $i .PLT`
plotnps -F7 -W10 -EPS -K < $i > t.eps
convert -trim t.eps -background white -alpha remove -alpha off ${B}.png
rm t.eps
done