Transmission and Reflection of Surface Waves at a Vertical
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.
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
ILR, TMIN, TMAX, NT, MINVAL
THICK1(1), ALPHA1(1), BETA1(1), RHO1(1)
THICK1(2), ALPHA1(2), BETA1(2), RHO1(2)
THICK1(NZ1), ALPHA1(NZ1), BETA1(NZ1), RHO1(NZ1)
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
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.
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.