PSV-wave propagation in a medium with local heterogeneities: a hybrid formulation and its application

Abstract

SUMMARY Hybrid methods, which combine so-called ‘numerical’ and ‘analytical’ methods, are a successful tool for computing synthetic seismograms for media with localized heterogeneous regions. Each of the two methods is applied in that part of the medium in which it can be employed efficiently. This paper deals with a combination of a finite-difference algorithm, applied in the neighbourhood of the heterogeneity, and a frequency–wavenumber filter for the PSV-wave equation applied outside. This method is an alternative to the use of Green's theorem as a wavefield-continuation method (e.g. van den Berg 1984). In the hybrid method presented here, absorption can be incorporated additionally. For different models with first-and second-order discontinuities the hybrid method was tested successfully against the reflectivity method. The hybrid method was applied to study the effects of a heterogeneous lower crust on the wavefield. This application has been inspired by recent deep seismic reflection profiling, which often reveals a highly reflecting lower crust. The scattering models have been divided into three groups: horizontal, vertical and isotropic scatterers. The comparison of the reflection responses of these models shows that thin horizontal or small isotropic scatterers yield high reflected energy, coherent over a few kilometres, in the time window of lower crustal reflections. Vertical structures, characterized by a small correlation length in horizontal direction, have less energy in this time window, but they can generate a complex Moho reflection with a strong Moho coda. It is also shown that the acoustic approximation is mostly not sufficient to describe the wave propagation in such complex media.