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One‐way wave propagation methods in direct and inverse scalar wave propagation modeling
Author(s) -
Fishman Louis
Publication year - 1993
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/93rs01632
Subject(s) - helmholtz equation , inverse scattering problem , scalar field , mathematical analysis , mathematics , reflection (computer programming) , wave propagation , operator (biology) , wave equation , inverse problem , scalar (mathematics) , physics , computer science , optics , geometry , biochemistry , chemistry , repressor , transcription factor , programming language , mathematical physics , gene , boundary value problem
Wave field splitting, invariant imbedding, and phase space methods reformulate the Helmholtz wave propagation problem in terms of an operator scattering matrix characteristic of the modeled environment. The subsequent equations for the reflection and transmission operators are of first‐order (one‐way) in range, nonlinear (Riccati‐like), and, in general, nonlocal. The reflection and transmission operator equations provide the framework for constructing inverse algorithms based on, in principle, exact solution methods.