Love and Rayleigh waves in non-uniform media

Abstract

This paper is concerned with the dispersion of Love and Rayleigh waves in multilayered models with smooth and weakly non-parallel boundaries. Perturbation formulae for the phase, frequency, wavenumber, phase velocity, group velocity and amplitude are derived from first-order perturbation theory of Whitham's equation for dispersive waves in non-uniform media. Derivation of the average Lagrangian for Love and Rayleigh waves is obtained as required by the perturbation formulae. Explicit formulae are given for Love waves in the long-wavelength limit and comparisons with related studies are made. In order to demonstrate the results, numerical calculations for the perturbation in frequency, wavenumber, amplitude and phase are performed. The models consist of non-uniform media of one and two layers over a half-space. The perturbed parameter is the layer depth, sampled at different locations.