Exact formula for the horizontal-to-vertical displacement ratio of Rayleigh waves in layered orthotropic half-spaces.

Abstract

This paper is concerned with the propagation of Rayleigh waves in a compressible orthotropic half-space coated by a compressible orthotropic layer. The main purpose of the paper is to establish an explicit exact formula for the H/V ratio (the horizontal-to-vertical displacement ratio) of the Rayleigh wave. This formula is derived by using the transfer matrix for an orthotropic elastic layer and by the effective boundary condition technique. The formula recovers the H/V formula by Malischewsky and Scherbaum [(2004). Wave Motion 40, 57-67] for the compressible isotropic case and the H/V formula by Love [(1911). Some Problems of Geodynamics (Cambridge University Press, Cambridge)] for the incompressible isotropic case. The effect of anisotropy on the H/V ratio's properties is examined and it is numerically shown that the anisotropy strongly affects the peak and zero frequency of the H/V ratio and its prograde domain as well. As the H/V ratio is a dimensionless quantity and it is easily experimentally measured, the obtained formula will be a useful tool for the nondestructive evaluation of mechanical properties of thin films deposited onto half-spaces. Two numerical examples are performed to show how the obtained formula can be used to extract the material properties of deposited layers from measured values of the H/V ratio.