Introduction

In this exercise we will make some synthetics for the case of waves incident to the boundary of two halfspaces. In the region with the source we would expect to see the direct wnad reflected waves, and in the other region transmitted waves. The waveforms will be complicated because the medium is elastic and we have to worry about conversions between P and SV waves.

Example

The model used is the simple crustal model of Exercise 1. We will use the wavenumber integration technique to make the synthetics. As usual everything is placed into a shell script, DOIT, with comments. 

#!/bin/sh

#####
#   clean up
#####
rm -f *.png
rm -f *.PLT

cat > SCM.mod << EOF       create the velocity model 
MODEL.01
Simple crustal model
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    
    40.0000     6.0000     3.5500     2.8000   0.00       0.00       0.00       0.00       1.00       1.00    
     0.0000     8.0000     4.7000     3.3000   0.00       0.00       0.00       0.00       1.00       1.00    
EOF

cat > dfile << EOF       create the file that  
 10.0 0.25 256 0 0       gives distance, dt, npts, t0 vred
 20.0 0.25 256 0 0
 30.0 0.25 256 0 0
 40.0 0.25 256 0 0
 50.0 0.25 256 0 0
 60.0 0.25 256 0 0
 70.0 0.25 256 0 0
 80.0 0.25 256 0 0
 90.0 0.25 256 0 0
100.0 0.25 256 0 0
110.0 0.25 256 0 0
120.0 0.25 256 0 0
130.0 0.25 256 0 0
140.0 0.25 256 0 0
150.0 0.25 256 0 0
160.0 0.25 256 0 0
170.0 0.25 256 0 0
180.0 0.25 256 0 0
190.0 0.25 256 0 0
200.0 0.25 256 0 0
EOF

#####
#    we will make synthetics for the receiver above and below the interface
#####

mkdir INTERFACE_ALL_TOP
hprep96 -M SCM.mod -d dfile -ALL -HS 21 -HR 20 -TH -BH  Create the control for the program hspec96. Since the 
                                                        model file has a reference layer of 40 km, the source is placed 19 km above the 
                                                        interfce, and the receiver is 20 km above the interface. 
hspec96  -SD

                                                        Only consider waves leaving the source in a downward direction.  
                                                        Because of the source position, the synthetics will not have a direct wave  
                                                        Now put in the source time function, convert to Sac files and place in a subdirectory  
hpulse96 -V -p -l 1  | \
 (cd INTERFACE_ALL_TOP ;  f96tosac -G )
# make plots
gsac << EOF
r INTERFACE_ALL_TOP/*TSS
title on location top size small text "TSS HS=21 HR=20 Interfase z=40"
bg plt
prs amp 0.25 color 2 shd neg
                                                        shade the negative amplitudes of the trace in the color red  
mv PRS001.PLT TOP_TSS.PLT

r INTERFACE_ALL_TOP/*ZEX
title on location top size small text "ZEX HS=21 HR=20 Interfase z=40"
bg plt
color red
prs amp 0.25 
mv PRS002.PLT TOP_ZEX.PLT

r INTERFACE_ALL_TOP/*REX
title on location top size small text "REX HS=21 HR=20 Interfase z=40"
bg plt
color blue
prs amp 0.25 
mv PRS003.PLT TOP_REX.PLT
q
EOF

mkdir INTERFACE_ALL_BOT
hprep96 -M SCM.mod -d dfile -ALL -HS 21 -HR 60 -TH -BH
hspec96  -SD
hpulse96 -V -p -l 1  | \
 (cd INTERFACE_ALL_BOT ;  f96tosac -G )
gsac << EOF
r INTERFACE_ALL_BOT/*TSS
title on location top size small text "TSS HS=21 HR=60 Interfase z=40"
bg plt
prs amp 0.25 color 2 shd neg
mv PRS001.PLT BOT_TSS.PLT

r INTERFACE_ALL_BOT/*ZEX
title on location top size small text "ZEX HS=21 HR=60 Interfase z=40"
bg plt
color red
prs amp 0.25 
mv PRS002.PLT BOT_ZEX.PLT

r INTERFACE_ALL_BOT/*REX
title on location top size small text "REX HS=21 HR=60 Interfase z=40"
bg plt
color blue
prs amp 0.25 
mv PRS003.PLT BOT_REX.PLT
q
EOF
                                                        Each external plot in a gsac execution has a unique identifier. Thus three PRS calls create PRS001.PLT PRS002.PLT PRS003.PLT  

#####
# some representative traces
#####
gsac << EOF
color list red blue
fileid name
r INTERFACE_ALL_BOT/0160*[ZR]EX
title on location top size small text "Z (red) R(blue) 160 km HS=21 HR=60 Interfase z=40"
bg plt
p overly on

r INTERFACE_ALL_TOP/0160*[ZR]EX
title on location TOP size small text "Z (red) R(blue) 160 km HS=21 HR=20 Interfase z=40"
p overly on

q
EOF
                                                        Here the plot calls create P001.PLT and P002.PLT  

mv P001.PLT BOT_160.PLT
mv P002.PLT TOP_160.PLT


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


#####
#    clean up
#####
rm -f hspec96.???
rm -f PRS*.CTL
rm -f t.eps
rm -f dfile
rm -f *.PLT

Results

Running DOIT creates eight PNG graphics files:

TOP_TSS.png Transverse component reflections from strike slip source
TOP_REX.png Radial component (away from source) from expansion source
TOP_ZEX.png Vertical component (away from source) from expansion source
TOP_160.png Overlay of vertical (up) and radial (away) components from EX source at 160 km
BOT_TSS.png Transverse component reflections from strike slip source
BOT_REX.png Radial component (away from source) from expansion source
BOT_ZEX.png Vertical component (away from source) from expansion source
BOT_160.png Overlay of vertical (up) and radial (away) components from EX source at 160 km

Here are the plots:

TOP_TSS.png

TOP_REX.png

TOP_ZEX.png

BOT_TSS.png

BOT_REX.png

BOT_ZEX.png

It is interesting to overlay the traces to look at particle motion to determine the nature of the wave.
TOP_160.png

BOT_160.png

Exercise

  1. For the plots TOP_160.png and BOT_160.png identify the phase in terms of particle motion. For TOP_160.png, the ray is in the upward direction at the receiver. For BOT_160.png the ray is in the downward direction. Note some arrivals be be due to numerical noise.
  2. In the plot TOP_TSS.png, what are the arrivals at 180 km - there are two.
  3. In the plot TOP_TSS.png, What is the signal before the reflected S - you can easily compute the time of the reflected S.
  4. What arrivals do you see in TOP_ZEX.png? Why don't you see a refraced SV?
  5. For this model, make and plot synthetics for the case that the epicentral distance is 100 km, the source is at a depth of 20 km, and an array of receivers are at 0, 2, 4, ..., 38, 40, 42, ..., 58, 60 km. In gsac you would use the prs stel portrait command.