Efficient numerical simulation for long range wave propagation

Abstract

We develop an efficient algorithm for simulating wave propagation over long distances with both weak and strong scatterers. In domains with weak heterogeneities the wave field is decomposed into forward propagating and back scattered modes using two coupled parabolic equations. In the region near strong scatterers, the Helmholtz equation is used to capture the strong scattering events. The key idea in our method is to combine these two regimes using a combined domain decomposition and wave decomposition method. A transparent interface condition is derived to couple these two regions together. Numerical examples show that the simulated field is close to the field obtained using the full Helmholtz equation in the whole domain.

Random Backscattering in the Parabolic Scaling

“…We see that longitudinal scattering is not captured well leading to poor approximation of the wave heterogeneity and an artificially smooth approximation. In the right plot the dashed line corresponds to an approximation of the system (4-5) that captures the important "right" and "left" coupling [13,14]. The latter approximation corresponds to iterative right and left sweeps implementation of (4-5) when the coupling correction associated with exp(±2ikz/ε q )L 2 is neglected, giving convergence after a few iterations.…”

“…The latter approximation corresponds to iterative right and left sweeps implementation of (4-5) when the coupling correction associated with exp(±2ikz/ε q )L 2 is neglected, giving convergence after a few iterations. The boundary condition at the depth of the embedded scatterer is implemented via a domain decomposition approach with the inclusion located in a small domain numerically resolved via a discretization of the Helmholtz equation (see [13] for details). Motivated by this computational example we Fig.…”

“…withν(z, κ) the partial Fourier transform of ν(z, x) as defined by (13). This system is supplemented by the initial conditionŝ…”

Estimating a Green's Function from “Field-Field” Correlations in a Random Medium

“…In recent decades the parabolic or paraxial wave equation has emerged as the primary tool to describe small scale scattering situations as they appear in radiowave propagation, radar, remote sensing, propagation in urban environments, and in underwater acoustics [29,32,41], as well as in propagation problems in the earth's crust [9]. The paraxial equation models wave propagation if the dominant scattering occurs in the direction(s) transverse to a principal propagation direction.…”

A two-way paraxial system for simulation of wave backscattering by a random medium

“…In this paper we address situations in which backscattering is not negligible, which requires more elaborate schemes than the paraxial wave equation. After the pioneering work [5] an iterative two-way paraxial scheme was proposed to solve the full wave equation by an iteration of forward-going and backward-going paraxial wave equations in [12,13]. Comparisons between numerical simulations of the full wave and numerical simulations of the two-way paraxial system have shown very good agreement, with the overall conclusion being that the twoway paraxial scheme has the same numerical complexity as the standard oneway paraxial equation, but it also takes into account random backscattering.…”