HALFSP

The Rayleigh wave solution for a half-space elastic medium is computed by HALFSP. The man page is read by typing man halfsp in a terminal. The output includes the velocity of the Rayleigh wave (stdout) and a file, halfsp.tmp which gives the motion-stress vectors for the frequency and range of depths required. An example log of this interactive program follows. One types from a terminal, halfsp .
    ENTER RHO,VP,VS
1600,800,200
 ENTER FREQ,NZ,Z0,ZEND
15,50,0,30
  PHASE VEL=  190.2245

The units are $kg/m^3$ for RHO (density), $m/s$ for P- and S-wave velocities (VP and VS), $Hz$ for FREQ (frequency), and meters for the top and bottom of the interval computed (Z0 and ZEND). NZ is the number of depth points computed. The top of the halfsp.tmp file:

   HALFSP.F OUTPUT:
  RHO=0.1600E+04
  MU=0.6400E+08
  LAME=0.8960E+09
  FREQ=0.1500E+02
  P-WAVE VELOCITY=0.8000E+03
  S-WAVE VELOCITY=0.2000E+03
  RAYLEIGH WAVE PHASE VEL=  190.2245
 R1=Horiz. Displacement R2=Vertical Displacement
 R3=Horiz. Stress       R4=Vertical Stress


     DEPTH      R1         R2         R3         R4

       0.0   0.2241030E+00  -0.3974480E+00   0.3780026E+01  -0.0000000E+00
       0.6   0.1236450E+00  -0.4410695E+00   0.4977292E+07   0.2806469E+07
       1.2   0.5226342E-01  -0.4611813E+00   0.8269704E+07   0.4662912E+07
       1.8   0.2325356E-02  -0.4647821E+00   0.1033810E+08   0.5829188E+07
       2.4  -0.3185774E-01  -0.4570187E+00   0.1152439E+08   0.6498086E+07
       3.0  -0.5452060E-01  -0.4416587E+00   0.1208169E+08   0.6812320E+07
       3.6  -0.6881093E-01  -0.4214445E+00   0.1219681E+08   0.6877232E+07
       4.2  -0.7706446E-01  -0.3983572E+00   0.1200719E+08   0.6770310E+07
       4.8  -0.8101030E-01  -0.3738140E+00   0.1161344E+08   0.6548294E+07
       5.4  -0.8192512E-01  -0.3488157E+00   0.1108883E+08   0.6252494E+07
       6.0  -0.8074815E-01  -0.3240562E+00   0.1048634E+08   0.5912774E+07

To make a quick plot of the motion vectors, you can do something like this. Copy the halfsp.tmp file to a file like data.dat:


cp halfsp.tmp data.dat

Delete the first lines down to the first depth. So the top of the file becomes just columns of data:

       0.0   0.2241030E+00  -0.3974480E+00   0.3780026E+01  -0.0000000E+00
       0.6   0.1236450E+00  -0.4410695E+00   0.4977292E+07   0.2806469E+07
       1.2   0.5226342E-01  -0.4611813E+00   0.8269704E+07   0.4662912E+07
       1.8   0.2325356E-02  -0.4647821E+00   0.1033810E+08   0.5829188E+07
       2.4  -0.3185774E-01  -0.4570187E+00   0.1152439E+08   0.6498086E+07
       3.0  -0.5452060E-01  -0.4416587E+00   0.1208169E+08   0.6812320E+07

Then write a short Gnuplot script to plot the second and third columns as a function of the negative of the depth. Call it plot.gp:

 
set grid
set ylabel 'Depth (meters)'
p 'data.dat' u ($2):(-1)*($1) w l t 'horiz',\
'data.dat' u 3:(-1)*($1) w l t 'vert'
set terminal pdf
set output 'plot.pdf'
replot

Run the Gnuplot program from a terminal command line to produce Figure 49:
gnuplot -p plot.gp

Figure 49: Gnuplot image created by the plot.gp script. The -p command line option of the gnuplot command makes the X11 plot persistent. Press the q key while mouse focus is in the figure to end the display. Then view the plot.pdf file with your favorite PDF viewer.
\includegraphics[scale=1.1]{Figurehalfsp.pdf}