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.
Highlights
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
The propagator matrix has been used in a seismic imaging method, which accounts for multiple scattering in a model-driven way.[40]
Building on a one-dimensional (1D) acoustic autofocusing method, it has been shown that the wave field inside a laterally invariant layered medium can be retrieved with the Marchenko method from the singlesided reflection response at the surface of the medium.[41–43]
Summary
The aim of this paper is to give a systematic treatment of different types of wave-field representations (with Green’s functions, propagator matrices, and Marchenkotype focusing functions), discuss their mutual relations, and indicate some new applications. Building on a one-dimensional (1D) acoustic autofocusing method, it has been shown that the wave field inside a laterally invariant layered medium can be retrieved with the Marchenko method from the singlesided reflection response at the surface of the medium.[41–43] This concept was extended to a threedimensional (3D) Marchenko wave-field retrieval method for laterally varying media.[44].
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call