,/head>

Introduction

We are now going to run some surface wave codes, specifically we will determine the dispersion for a simple crustal model at a period of 20.0 seconds. This output will give the eigenfunctions as a funciton of depth and also the partial derivatives.

The basic shell script is

#!/bin/sh

#####
#    create a model
#####
cat > SCM.mod << EOF
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    
    10.0000     6.0000     3.5500     2.8000   0.00       0.00       0.00       0.00       1.00       1.00    
    10.0000     6.0000     3.5500     2.8000   0.00       0.00       0.00       0.00       1.00       1.00    
    10.0000     6.0000     3.5500     2.8000   0.00       0.00       0.00       0.00       1.00       1.00    
    10.0000     6.0000     3.5500     2.8000   0.00       0.00       0.00       0.00       1.00       1.00    
    10.0000     8.0000     4.7000     3.3000   0.00       0.00       0.00       0.00       1.00       1.00    
    10.0000     8.0000     4.7000     3.3000   0.00       0.00       0.00       0.00       1.00       1.00    
    10.0000     8.0000     4.7000     3.3000   0.00       0.00       0.00       0.00       1.00       1.00    
    10.0000     8.0000     4.7000     3.3000   0.00       0.00       0.00       0.00       1.00       1.00    
EOF

#####
#    do surface waves
#####
sprep96 -L -M SCM.mod -PER 20.0
sdisp96
slegn96 
sdpegn96 -L -C -TXT
slegn96 -DER
sdpder96 -L -C -TXT

The -L flag indicates that we are looking Love wave propagation. The model is a single layer over a halfspace, but with layers finely divided. We want to look at the value of the eigenfunctions at the layer interfaces and also the partial derivatives in the layers. After running this script we have two files:

SLEGN.TXT



                     LOVE WAVE        MODE #  0

    N     T          F            C            U           ARE        GAMMA
    1  20.00     0.5000E-01   3.8012       3.4220      0.53573E-03  0.00000E+00
which gives the phase and group velocity for the model at a period of 20.0s econds. ARE = 1/2cUIo and GAMMA relates to anelastic attenuation.

SLDER.TXT

  
 Model:
  LAYER     H(km)     Vp(km/s)     Vs(km/s)  Density     QA(inv)     QB(inv)
    1    10.00000     6.00000     3.55000     2.80000     0.00000     0.00000
    2    10.00000     6.00000     3.55000     2.80000     0.00000     0.00000
    3    10.00000     6.00000     3.55000     2.80000     0.00000     0.00000
    4    10.00000     6.00000     3.55000     2.80000     0.00000     0.00000
    5    10.00000     8.00000     4.70000     3.30000     0.00000     0.00000
    6    10.00000     8.00000     4.70000     3.30000     0.00000     0.00000
    7    10.00000     8.00000     4.70000     3.30000     0.00000     0.00000
    8    10.00000     8.00000     4.70000     3.30000     0.00000     0.00000


                   LOVE WAVE        MODE #  0
        T = 0.2000E+02 C =    0.3801E+01 U   = 0.3422E+01
        AL= 0.5357E-03 GAMMA= 0.0000E+00 ZREF= 0.0000E+00
    M       UT         TT       DC/DH      DC/DB      DC/DR
    1   0.100E+01  0.000E+00 -0.105E-01  0.394E+00 -0.352E-01
    2   0.950E+00 -0.347E+00 -0.105E-01  0.331E+00 -0.215E-01
    3   0.806E+00 -0.660E+00 -0.105E-01  0.230E+00  0.412E-03
    4   0.582E+00 -0.908E+00 -0.105E-01  0.130E+00  0.222E-01
    5   0.301E+00 -0.106E+01  0.000E+00  0.491E-01  0.180E-01
    6   0.185E+00 -0.655E+00  0.000E+00  0.186E-01  0.680E-02
    7   0.114E+00 -0.403E+00  0.000E+00  0.703E-02  0.257E-02
    8   0.699E-01 -0.248E+00  0.000E+00  0.428E-02  0.156E-02

This gives the UT and TT at the layer boundary and the partial derivatives of the phase velocity with respect to layer thickness, S velocity and density.

Assignment

If the S-velocity in layer 2 is changes from 3.55 km/s to 3.65 km/s, then the phase velocity for the new model should be
3.801 + [0.331] * [ 0.1 ] = 3.834 km/s

Change the model, get the new phase velocity and verify that the partial derivatives are correct.