Transmission and Reflection of Surface Waves at a Vertical Contact


Program objectives

The transmission and reflection coefficients of surface waves at a vertical contact can be obtained with this program. The vertical contact between two media is considered as a welded contact between two layered media. The surface waves propagation across this contact is considered as normal incidence at the interface of the vertical contact. Thus, with these hypotheses the problem of the transmission and reflection of surface waves, at a vertical contact, can be simplified and easily solved (Corchete, 2011). The method used to obtain the transmission and reflection coefficients of the surface waves, propagated across a vertical contact like this, has been detailed by Keilis-Borok (1989). You can compute the transmission and reflection coefficients of the surface waves at this vertical contact, by means of the present program, as it will be described below.

Program description

The CONTACT program and its data file are enclosed into a ZIP file named "contact.zip". When you have got the ZIP file and you have uncompressed this file, you have two files named contact.exe and contact.dat. The file contact.exe contains a program (in FORTRAN code for PC) for the computation of the transmission and reflection coefficients of surface waves at a vertical contact. All the program capabilities are controlled by parameters enclosed in the file named contact.dat. The file contact.dat must be in the free format and must contain the parameters:

ILR, TMIN, TMAX, NT, MINVAL
NZ1
THICK1(1), ALPHA1(1), BETA1(1), RHO1(1)
THICK1(2), ALPHA1(2), BETA1(2), RHO1(2)
...
...
...
THICK1(NZ1), ALPHA1(NZ1), BETA1(NZ1), RHO1(NZ1)
NZ2
THICK2(1), ALPHA2(1), BETA2(1), RHO2(1)
THICK2(2), ALPHA2(2), BETA2(2), RHO2(2)
...
...
...
THICK2(NZ2), ALPHA2(NZ2), BETA2(NZ2), RHO2(NZ2)

The description of all parameters is as follows:

ILR = With value 1 the transmission and reflection coefficients will be computed for Love waves, with value 0 for Rayleigh waves and with value 2 for Love and Rayleigh waves.
TMIN, TMAX, NT = Period range (in seconds) in which the computations will be performed. TMIN is the minimum and TMAX is the maximum of this interval. The maximum value for NT is 100.
NZ1,2 = Number of layers of the earth model considered in each medium (maximum 100).
THICK1,2(i), ALPHA1,2(i), SVEL1,2(i), RHO1,2(i) = Thickness (km), P-wave velocity (km/s), S-wave velocity (km/s) and density (g/cm3); for the ith layer of the earth model considered in each medium. The NZ1,2 layer is the semi-infinite medium and its thickness must be given as zero.

Running the program

Figures 1 to 10 show the transmission and reflection coefficients resulting for the sample file contact.dat, in which a ocean-continent contact has been considered. In this example, Love and Rayleigh waves have been considered with normal incidence at a ocean-continent contact, considered as a welded vertical contact between both media.

Fig. 1. Transmission and reflection coefficients resulting for the sample file contact.dat. The incident mode is the fundamental mode for Love and Rayleigh waves.

Fig. 2. Transmission and reflection coefficients resulting for the sample file contact.dat. The incident mode is the first higher mode for Love and Rayleigh waves.

Fig. 3. Transmission and reflection coefficients resulting for the sample file contact.dat. The incident mode is the second higher mode for Love and Rayleigh waves.

References

Corchete V. (2011). Review of the methodology for the computation of transmission and reflection coefficients for surface waves propagated through a vertical contact. Computational Geosciences, 15, 579-586.

Keilis-Borok V. I. (1989). Seismic surface waves in a laterally inhomogeneus Earth. Kluwer, Dordrecht.