Impact of quadratically varying rigidity and linearly varying density on the Rayleigh wave propagation: An analytic solution

In this paper, a mathematical model of Rayleigh wave propagation in a sandy earth crust has been investigated under the influence of quadratically varying rigidity and linearly varying density in the incompressible half space. The upper boundary plane of the sandy crust has been assumed to be rigid. The displacement of the wave in two medium have been deduced separately and the dispersion equation has been found in the closed form. Numerical results analyzing the dispersion equation are discussed and presented graphically. It has been observed that the inhomogeneity parameter has a direct bearing on the phase velocity while it is also affected by the sandy parameter associated with the earth crust.