Using the T matrix method, or the extended boundary condition, the solution for a class of problems involving an SH line source in an elastic wave guide is determined. The boundaries of the wave guide may be periodically corrugated and the wave guide may be embedded between elastic media. Numerical results are given for a seismically interesting case of wave propagation in a one-layer crustal model over a mantle half-space with a corrugated free surface representing the Basin and Range topography in the Western United States. Analysis of the scattered fields at the surface, and of the fields radiated into the half-space, shows complicated field behavior, even with sinusoidal free surface corrugation. These results are directly applicable to regional wave propagation and scattering.

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