A three-dimensional ray method is used to compute three components of ground motion for complex structures involving curved boundaries. The method of principal curvature is developed to compute geometrical spreading of rays. This method, commonly used in electromagnetic wave propagation problems, employs phase matching at model interfaces and analysis of the wave front surface metric as the ray propagates throughout the model. It is an elegant way to examine the characteristics of three-dimensional caustics. Results computed for a two-dimensional canonical basin model with a plane SH-wave source are compared and are found to be in good agreement with those previously obtained by other independent numerical methods. Relaxing the restriction that the incident wave be perpendicular to the basin symmetry axis gives rise to large amplitude vertical and radial motions for incident SH waves and large tangential motions for incident P waves. As in the two-dimensional case, seismic energy is geometrically focused in the central region of the basin but strong later arrivals from the curved boundaries are not well developed in the three-dimensional case. The method is of direct use in analyzing three-dimensional crustal structure from off-azimuth P to S and S to P conversions.

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