An approximate formula for the H/V ratio of Rayleigh waves in compressible pre-stressed elastic half-spaces coated with a thin layer

This paper is concerned with the propagation of Rayleigh waves in a compressible pre-stressed elastic half-space coated with a thin compressible pre-stressed elastic layer. The main purpose of the paper is to establish an approximate formula for the H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude one of Rayleigh waves at two sides of the interface between the layer and the half-space are created. From the continuity condition at the interface and these relations, the displacement amplitude vector of Rayleigh waves at the interface is determined. Then,  a third-order approximate formula for the H/V ratio has been derived by expanding the layer displacement amplitude vector at its traction-free surface into Taylor series at the interface. It is shown numerically that the obtained formula is a good approximate one.