A geometrical ray method is developed for wave calculations involving three-dimensional planar dipping interfaces. Justification for the method is based on analogy with first-motion approximations derived from generalized ray theory where frequency dependence in the reflection-transmission coefficients is related to changes in the complex ray parameter. The method is applied to finding the teleseismic response of an arbitrarily oriented dislocation source in dipping layered media and for receiver calculations which assume an impinging P or S wave beneath a stack of dipping layers. Source results indicate that wave forms from fast azimuthally varying sources, such as strike-slip faults, are significantly distorted from the plane layered case for simple structures. A simple dipping Moho for dips up to 10° does not significantly distort vertical and radial P waves for the receiver response. However, due to azimuth anomalies introduced by interface dip a significant tangential P component is produced. In addition, the S-wave response becomes a function of source mechanism due to the need for specifying the incident polarization angle. Polarization studies are suggested for finding dipping structure.

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