Love’s formula and H/V-ratio (ellipticity) of Rayleigh waves

Abstract The ellipticity of Rayleigh surface waves, which is an important parameter characterizing the propagation medium, is studied for several models with increasing complexity. While the main focus lies on theory, practical implications of the use of the horizontal to vertical component ratio ( H / V -ratio) to study the subsurface structure are considered as well. Love’s approximation of the ellipticity for an incompressible layer over an incompressible half-space is critically discussed especially concerning its applicability for different impedance contrasts. The main result is an analytically exact formula of H / V for a 2-layer model of compressible media, which is a generalization of Love’s formula. It turns out that for a limited range of models Love’s approximation can be used also in the general case.