Wave-field representations with Green's functions, propagator matrices, and Marchenko-type focusing functions

TL;DR

This paper introduces a unified matrix-vector wave equation framework that reformulates classical wave-field representations using Green's matrices, propagator matrices, and Marchenko focusing functions, enabling boundary-limited integral representations for improved inverse scattering and imaging.

Contribution

It develops a unified matrix-vector formalism that replaces volume and boundary integrals with boundary-limited representations involving propagator matrices and focusing functions.

Findings

Boundary integrals are limited to a single boundary.

Propagator matrices can be expressed via Marchenko focusing functions.

Framework facilitates advanced inverse scattering and imaging methods.

Abstract

Classical acoustic wave-field representations consist of volume and boundary integrals, of which the integrands contain specific combinations of Green's functions, source distributions and wave fields. Using a unified matrix-vector wave equation for different wave phenomena, these representations can be reformulated in terms of Green's matrices, source vectors and wave-field vectors. The matrix-vector formalism also allows the formulation of representations in which propagator matrices replace the Green's matrices. These propagator matrices, in turn, can be expressed in terms of Marchenko-type focusing functions. An advantage of the representations with propagator matrices and focusing functions is that the boundary integrals in these representations are limited to a single open boundary. This makes these representations a suitable basis for developing advanced inverse scattering, imaging and monitoring methods for wave fields acquired on a single boundary.