EFFECTS OF IRREGULAR BOUNDARIES IN A LAYERED HALF-SPACE ON SEISMIC WAVES

Abstract

Seismic waves through a layered half-space with geometrically irregular boundaries (surface and/or interfaces) are investigated. Wave scattering occurs at these irregular boundaries, resulting in coupling between P-SV and SH waves, which is not the case in a perfectly layered half-space. A first order perturbation technique is applied to solve such a three-dimensional wave scattering problem. Specifically, the total wave field, generated by a seismic dislocation source buried in the layered half-space, is decomposed into two wave fields. One is a mean wave field, which is response field in a perfectly layered half-space subjected to a seismic dislocation source. This can be solved using a reflectivity method; i.e., an approach combining integral transform and wave propagation analysis in terms of reflection and transmission properties of portions of the layers. The other is a scattered wave field, which is due to the existence of irregular boundaries. The effects of the irregular boundaries on the scattered wave field are equivalent to those of fictitious discontinuity sources acting on the corresponding perfectly boundaries. The intensity of the fictitious discontinuity source depends on both the mean wave field and the irregularities. The solution for the scattered wave field is then obtained using the same approach as for the mean wave response field. The effects of the irregular boundaries on the seismic wave responses, especially on the ground motion responses, are evaluated qualitatively and quantitatively. This is fundamentally important to the issue that whether the irregular boundaries can or cannot be approximately considered as flat ones, which is associated with the simplification of a complex model for the real earth media subjected to the seismic waves. Numerical examples are presented for illustration.