Reciprocity relations for scattering of plane, elastic waves

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Abstract
The reciprocity relations that apply to the scattering of plane, elastic waves that are incident upon an obstacle of finite extent are investigated. In these relations, the particle‐displacement radiation characteristics of the scattered waves occur. The elastic medium outside the obstacle is assumed to be homogeneous, isotropic, and perfectly elastic. Hence, two kinds of acoustic waves can propagate in it, viz., irrotational, compressional or P waves and solenoidal, shear or S waves; each of these two waves has its own radiation characteristic. It is shown that the far‐zone scattered wave due to an incident wave propagating in the direction ? and observed in the direction −? is related to the far‐zone scattered wave due to an incident wave propagating in the direction ? and observed in the direction −?. This reciprocity property is next applied to two incident P waves, two incident S waves, and an incident P wave and an incident S wave. The resulting reciprocity relations hold under the assumption that the scattering obstacle is linear and reciprocal in its elastic behavior.

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