The Application of Finite Element Analysis to Body Wave Propagation Problems

Abstract

The finite element method is shown to be a powerful tool for the numerical modelling of seismic body wave propagation problems. Applications extend to both problems on a scale of interest to engineers and also to large-scale seismological problems. Solutions are sought in the time domain. Efficient programs have been written to accomplish this. The scope of numerical solutions has been greatly enhanced by the use of a previously reported scheme for exactly cancelling reflections at the boundaries of the model. The finite difference results of Boore and the analytical results of Trifunac for the amplification due to a mountain and an alluvial valley respectively are compared with new finite element results. The new results agree well, although there are some difficulties with resonance in the alluvial valley problem. Boore's SH results have been extended to vertical P and SV incidence. A deep earthquake zone has been modelled realistically in two dimensions and earthquakes simulated at depth. It is suggested that the variation in observed amplitude across the top of the zone, due to refraction away from the slab, may be used to provide an estimate of the thickness of the slab from long-period observations of local earthquakes.