Reciprocity relations and forward amplitude theorems for elastic waves

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Abstract
Relations are derived between the amplitudes of scattered elastic waves from obstacles of arbitrary shape when the direction of observation and incidence are reversed and interchanged, similar to the reciprocity theorem for the scalar wave equation. For waves which undergo a polarization change on scattering (longitudinal to shear and vice versa), a new type of reciprocity relation is derived which is peculiar to elastic waves. Expressions for the scattering cross section are obtained for shear and longitudinal incident waves, and it is shown to be proportional to the amplitude of the scattered wave in the forward direction alone. Incident waves are restricted to plane, monochromatic waves.

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