Seismic representation theorem coupling: synthetic SH mode sum seismograms for non-homogeneous paths

In this paper the methods for representation theorem coupling of finite-element or finite difference calculations and propagator matrix method calculations (Harkrider) are developed. The validity and accuracy of the resulting hybrid method are demonstrated. The resulting hybrid technique can be used to study the propagation of any phase that can be represented in terms of an SH mode sum seismogram, across regional transition zones or other heterogeneities. These heterogeneities may exist in regions which form subsegments of a longer, mostly plane-layered, path. Examples of structures of interest through which such waves can be propagated using these techniques include, regions of crustal thickening or thinning such as continent-ocean transitions or basins,' anomalous bodies of any shape located in the path, and sudden transitions from one layered structure to another. Examples of the types of phases that may be propagated through these structures include Love waves, L,, S, and S,.