A program of continuing application of waveform modeling to recover the detailed nature of the boundaries in the earth is proposed. It is based on an ability to model and thereby interpret the considerable complications of observed record sections caused by propagation through a complex earth. We propose to develop P and S velocity models from broad-band data with boundaries constrained to be at the same depths for the most uniform regions, shields, young and old oceans, and detailed two-dimensional cross-sections through regions of rapid variations. The recent tomographic results can be used to great advantage in collecting key data-sets where complete seismic sections, including surface waves, can be compared with synthetics appropriate for laterally varying earth models and proper evaluations made. Effects on surface waves due to lateral variation will be examined by applying a modified generalized ray code and by a finite-difference code modified to treat earthquake sources with three-dimensional spreading. The well established teleseismic travel time and amplitude (WWSSN long period) fluctuation patterns will be examined by comparing synthetics for the appropriate paths taken from detailed whole mantle tomographic results such as Grand (1986). This testing of proposed models will be conducted on core-mantle phases as well as the usual direct P and S waves. Particular attention will be given to (SKS - Sdif) seismic sections which show considerably more scatter from region-to-region than can be easily explained by variations in the mantle alone.
