One-way Wave Equation Modeling in Two-way Wave Propagation Problems

The exact, well-posed, one-way reformulation of Helmholtz-type wave equations and the generalized Bremmer coupling series are applied to the two-way, scalar, multidimensional Helmholtz equation of mathematical physics. These two constructions provide complementary ways of incorporating one-way wave equation modeling into two-way wave propagation problems. The mathematical framework, for the explicit representation of the appropriate wave propagation operators, one-way wave equations, propagators (fundamental wave field solutions), and computational algorithms, follows upon exploiting the correspondences between the classical wave propagation problem, quantum mechanics, and microlocal analysis. Subsequent detailed, exact and uniform asymptotic constructions, which require going beyond the available results in both the quantum mechanical and microlocal analysis literatures, ultimately provide theoretical insight and computational viability to this approach.