Approximations for surface-wave propagation in laterally varying media

Abstract

A number of techniques which exploit the waveforms of seismic surface waves depend on simple approximations for the character of the propagation process from source to receiver based on the representation for a stratified medium. Commonly the propagation path is assumed to lie along a great circle and to be representable by a path-averaged structure. The influence of structure near the source and near the receiver is included by using local modal formulations. However, the terms that depend on source depth and receiver depth in the stratified medium results are not purely local in character, and so care has to be taken to ensure a simple mapping between the modal shapes for the different structures. For frequencies less than 0.03 Hz, different crustal structures can be used at the source, near the receiver, and along the propagation path, provided that the change in crustal thickness is not more than 10 km between contiguous structures. Furthermore, for frequencies up to 0.035 Hz, it should be possible to use a single modal set in non-linear waveform inversions for perturbations of up to 5 per cent in lithospheric velocities along the propagation path. For propagation paths of length from 1000 to 4000 km, typical of a continental scale, the path-averaged structure approximation should be suitable for waveform fitting for frequencies in the range 0.01-0.03 Hz. The lower limit depends on the use of asymptotic approximations and the upper on the influence of heterogeneity on the modal content of the seismograms. Where surface waves cross a major structural boundary such as the continent-ocean transition, some aspects of the wavefield can still be represented using the path-averaged approximation.