Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation. (English) Zbl 0551.76069
(Authors’ summary.) The reduced scalar Helmholtz equation for a transversely inhomogeneous half-space supplemented with an outgoing radiation condition and an appropriate boundary condition on the initial- value plane defines a direct acoustic propagation model. This elliptic formulation admits a factorization and is subsequently equivalent to a first-order Weyl pseudodifferential equation which is recognized as an extended parabolic propagation model. Perturbation treatments of the appropriate Weyl composition equation result in a systematic development of approximate wave theories which extend the narrow-angle, weak- inhomogeneity, and weak-gradient ordinary parabolic (Schrödinger) approximation. Through analysis the authors believe in that it can provide for the formulation and exact solution of a multidimensional nonlinear inverse problem appropriate for ocean acoustic and seismic studies. The wave theories foreshadow computational algorithms, the inclusion of range-dependent effects, and the extension to (1) the vector formulation appropriate for elastic media and (2) the bilinear formulation appropriate for acoustic field coherence.
Reviewer: Z.Qian
MSC:
| 76Q05 | Hydro- and aero-acoustics |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
outgoing radiation condition; acoustic propagation model; Weyl pseudodifferential equation; inverse problem; ocean acoustic; seismic studiesCitations:
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