International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 381-390
doi:10.1155/S0161171287000449
Rayleigh wave scattering at the foot of a mountain
Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
Received 3 March 1986
Copyright © 1987 P. S. Deshwal and K. K. Mann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A theoretical study of scattering of seismic waves at the foot of a mountain
is discussed here. A mountain of an arbitrary shape and of width a (0≤x≤a, z=0) in the surface of an elastic solid medium (z≥0) is hit by a Rayleigh wave. The method of solution is the technique of Wiener and Hopf. The reflected, transmitted and scattered waves are obtained by inversion of Fourier transforms. The scattered waves behave as decaying cylindrical waves at distant points and have a large amplitude near the foot of the mountain. The transmitted wave decreases exponentially as its distance from the other end of the mountain increases.