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arXiv · 1401.4557

The Green-function transform and wave propagation

Colin J. R. Sheppard·Shan Shan Kou·Jiao Lin
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Abstract

Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogenous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.

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Colin J. R. Sheppard, Shan Shan Kou, Jiao Lin. 2014-01-18. The Green-function transform and wave propagation. https://arxiv.org/abs/1401.4557

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