Abstract
For acoustic applications in which there is a ‘‘preferred direction of propagation’’ (the axial direction) it is useful to arrange the two-way and one-way wave equations into the same matrix-vector formalism. In this formalism, axial variations of the wave vector are expressed in terms of lateral variations of the same wave vector. The two-way wave vector contains the field quantities pressure and velocity (axial component only), whereas the one-way wave vector contains waves propagating in the positive and negative axial direction. By exploiting the equivalent form of the two-way and one-way matrix-vector equations, it appears to be possible to derive two-way and one-way reciprocity theorems that have an equivalent form but a different interpretation. The main differences appear in the boundary integrals for unbounded media, in the contrast terms, and (for the correlation-type theorems) in the handling of evanescent waves.
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