Layer1

The purpose here is two fold - to make synthetics and then to make receiver functions from them. We examine a horizontal profile with observations at the surface between x-coordinates if 0 and 200 km. The source is placed at (100,100), e.g., an x-coordinate of 100 km and a depth of 100 km.

The velocity model is contained within the DOIT file. The receiver positions are also defined in this file. The sequence of commands to make the Sac files is just 

cprep96 -M model.d -d dfile -HS 100 -XS 100 -HR 0 -DOALL  -DOCONV
cseis96 -R > cseis96.out
cpulse96 -V -p -l 4 -EXF -DELAY 10  | f96tosac -B
cray96 -XMIN -50 -XMAX 250 -ZMIN 0 -ZMAX 150

cprep96 creates the following two plots
CPREP96M.PLT
CPREP96R.PLT

  cprep96 creates two plot files. CPREP96M.PLT is a plot of the model and CPREP96R.PLT is a plot of the rays.

cray96 creates the following plot:

CRAY96.PLT

which shows all of the ray paths. In the example Layer2 the results for just one ray will be shown.

After the computations are completed the script DOPLT is run to plot record sections, and in this simple case compare the receiver function from the synthetic at receiver position 200 km to the analytic value using hrftn96. The plots are in the next two figures.

ZEX.PLT
REX.PLT

This is the output of cpulse96. gsac was used to make the plot. Note that this is a relative amplitude plot. The peak amplitude of each traces has the same amplitude on the plot. In the plots, a positive amplitude is to the left. At the station at 200 km, the initial Z and R are positive. The initial P wave is in a direction upward and to the right away from the source. At a distance of 0 km, the ray leaves the source up and to the left. The initial P motion here is up on the vertical and down on the horizontal, meaning in the negative z-direction,  which is what is expected. The normal use of R meaning Radial away form the source does not apply here.

The computation of the receiver function presents an opportunity to better understand the meaning of the entry in column 8 of cseis96.amp. For the receiver distance of 200 km, this line for the direct P ray is 

    1   21  0.19849E+02  0.11161E-01  0.13669E-01  0.31416E+01  0.00000E+00 -0.696068E+00    1  0.33000E+01  0.80000E+01  0.00000E+00  0.28000E+01  0.60000E+01

The angle -0.696068E+00 in radians is measured with respect to the horizontal and corresponds to 39.3968 degrees. The angle required for the ray parameter is measured with respect to the vertical and is thus 50.083 degrees. The ray parameter is sin(50.083 degrees)/8.0 = 0.09587 s/km. Since this is a plane layered model, time96 can be used to get the plane wave ray parameter and the travel time by the commands 
time96 -EVDP 100 -DIST 100 -M model.d -P -RAYP 
time96 -EVDP 100 -DIST 100 -M model.d

From these two commands one obtains 9.59405228E-02 s/km for the ray parameter and 19.8530426s for the travel time.
in addition the negative value indicates that this ray goes up from the source. Since it is greater than -π/2, the ray goes upward and to the right of the source.
RFTN.PLT

Exercises