Multiple reflection of plane SH waves by a dipping layer

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Abstract
The problem of a plane SH wave incident at the base of a dipping layer has been considered. A solution by multiple reflection for waves incident at any angle perpendicular to strike has been obtained for the amplitude, phase and phase velocity. Numerical values are calculated on the surface. For waves propagating in the up-dip direction the amplitude versus frequency curves for a constant depth to the interface change slowly with increasing dip for dip angles less than 20°. However, for waves propagating in the down-dip direction, the character of the amplitude curves changes rapidly. It is found in these cases that the diffracted wave plays an important role. In addition to satisfying the boundary conditions at the surface and between the media, the diffracted wave must also satisfy additional conditions along a dipping surface lying between the free surface and the boundary between the two media due to the geometrical nature of the reflected wave solution. It is found that the phase velocities vary rapidly with both period of the wave and depth to the interface, particularly for propagation directions close to an angle which corresponds to vertical incidence in the horizontally layered case.

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