Rayleigh wave in an anisotropic heterogeneous crustal layer lying over a gravitational sandy substratum

The purpose of this paper is to study the propagation of Rayleigh waves in an anisotropic heterogeneous crustal layer over a gravitational semi-infinite sandy substratum. It is assumed that the heterogeneity in the crustal layer arises due to exponential variation in elastic coefficients and density whereas the semi-infinite sandy substratum has homogeneous sandiness parameters. The coupled effects of heterogeneity, anisotropy, sandiness parameters and gravity on Rayleigh waves are discussed analytically as well as numerically. The dispersion relation is obtained in determinant form. The proposed model is solved to obtain the different dispersion relations for the Rayleigh wave in the elastic medium of different properties. The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists.