Computing Body-Wave
Responses With Program


To model receiver functions, we use numerical calculation of plane-wave ground motions and apply the source equalization procedure to these "synthetic" seismograms before comparing with the observed receiver functions. Once you have generated the velocity model, you can compute the response of the structure to an incident P (or S) wave using the program "respknt". This program was written by George Randall and is based on Kennett's (1983) reflection matrix approach to computing the seismic response of a cylindrically symmetric medium.

The program uses interactive input to obtain the name of the velocity model file, the ray parameter, the duration and sampling rate of synthetic seismogram. The program computes the response using Kennett's reflection matrix method. The method allows truncation of the response after a certain number of reverberations. If you use the options "full" and "mode conversions" you will get all the arrivals that are excited by the incident plane wave.

Sample respknt Execution

 Velocity Model Name
List the site model? (y or n) y
 file: smp.mod    model:  simple       2 layers 
 lyr     vp      vs     rho      h     qp      qs     strike    dip
   1     6.00    3.46    2.69   35.00    0.00    0.00    0.00    0.00
   2     8.00    4.62    3.33    0.00    0.00    0.00    0.00    0.00
 incident P(1) or S(2) wave
 sampling interval
 signal duration
  enter slowness: 
  partial(p) or full(f) : 
  mode conversions? (y or n) 


The results of the calculation are SAC files, with the naming convention _sp.[z,r,t]. The model name is used as the prefix of the output file names. These files are the response to the incoming plane wave, not receiver functions. You have to perform the source equalization procedure on these files to calculate receiver functions.

The output files are sac files called:

 smp.mod_sp.r and smp.mod_sp.z 

To process these files using the pwaveqn code you have to tell the code that the data are "not real" by answering the "Real Data?" prompt negative. Then pwaveqn will expect files with the suffixes _sp.r, _sp.t, and _sp.z to perform the deconvolutions. You can safely ignore the error from pwaveqn that no "_sp.t" file was found - it will simply use zeros in place of the tangential response.LimitationsThe main limitation of respknt is that the technique is applicable to flat-lying layers. To compute the response for more complicated structures you will need to use ray3d (Tom Owens' ray tracer for dipping layers) a finite-difference code for complicated 2D or 3D structures, or a specialized code for anisotropic structures. An old version of ray3d is included with the codes in this package.Wrap-aroundTo avoid wrap around, you must make the seismograms long enough to contain all the reverberations in the structure. If the output response is too short, the later reverberations will wrap-around into the earlier part of the signal (this is a consequence of the periodic character of the FFT). The precise length that you need to make the code depends on the velocity structure. For example, a severe low-velocity layer near the surface can create a very long response.