Unified wave field retrieval and imaging method for inhomogeneous non-reciprocal media

Abstract

Acoustic imaging methods often ignore multiple scattering. This may lead to false images in cases where multiple scattering is strong. Marchenko imaging has recently been introduced as a datadriven way to deal with internal multiple scattering. Promising results have been obtained with geophysical and ultrasonic data. Given the increasing interest in non-reciprocal materials, both for acoustic and electromagnetic applications, we propose to modify the Marchenko method for imaging of such materials.We start by formulating a unified wave equation for non-reciprocal materials, exploiting the similarity between acoustic and electromagnetic wave phenomena. This unified wave equation forms the basis for deriving reciprocity theorems that interrelate wave fields in a non-reciprocal medium and its adjoint. Next, we reformulate these theorems for downgoing and upgoing wave fields. From these decomposed reciprocity theorems we derive representations of the Green's function inside the non-reciprocal medium, in terms of the reflection response at the surface and focusing functions inside the medium and its adjoint. These representations form the basis for deriving a modified version of the Marchenko method for imaging of non-reciprocal media. We illustrate the proposed method at the hand of the numerically modeled reflection response of a horizontally layered medium.The appendices contain a detailed derivation of the unified wave equation for non-reciprocal media and the decomposition of the reciprocity theorems.

Non-reciprocal acoustics in a viscous environment

“…Distribution of acoustic pressure pAfalse(boldrboldfalse) produced by a point source at position r A in an inhomogeneous fluid with arbitrary distribution of scatterers satisfies a reciprocity relation formulated in its simplest form by Rayleigh [1] pAfalse(boldrBboldfalse)bold=pBboldfalse(boldrAboldfalse)bold. This relation expresses a symmetry between emitter and receiver upon switching their positions. More general reciprocity relations valid for distributed sources, such as anisotropic, moving and porous media and transient signals have been reported, expressed in the form of convolution or correlation integrals [2–12]. One more important characteristic of acoustic fields is the vector of the local velocity of an oscillating fluid.…”

“…(1.1) This relation expresses a symmetry between emitter and receiver upon switching their positions. More general reciprocity relations valid for distributed sources, such as anisotropic, moving and porous media and transient signals have been reported, expressed in the form of convolution or correlation integrals [2][3][4][5][6][7][8][9][10][11][12]. One more important characteristic of acoustic fields is the vector of the local velocity of an oscillating fluid.…”

A modified Marchenko method to retrieve the wave field inside a layered metamaterial from reflection measurements at the surface

“…To date, the Marchenko method has almost exclusively been applied to naturally occurring materials (with the exception of an application to non-reciprocal materials [23]), but it…”

Introduction to the special issue on non-reciprocal and topological wave phenomena in acoustics

“…Attarzadeh et al (2019) take a different route to breaking reciprocity in a) Electronic mail: haberman@utexas.edu a one-dimensional system by introducing an angular momentum bias associated with gyroscopic elements and Wiederhold et al (2019) consider the use of flow to introduce a momentum bias and thus beak reciprocity and suggest an associated acoustic device. Wapenaar and Reinicke (2019) present a unified wave equation for non-reciprocal materials and employ it to extend well-known approaches to seismic imaging in the presence of non-reciprocal effects. Zangeneh-Nejad and Fleury ( 2019) then introduce a model and experimental demonstration of a linear four-port acoustic device, termed a rat-race coupler, which displays novel excitation and isolation behavior through destructive interference.…”