A single-sided representation for passive and active Green's function retrieval, time-reversal acoustics, and holographic imaging

Abstract

The homogeneous Green's function, defined as the superposition of the Green's function and its time-reversal, plays an important role in a variety of acoustic applications, such as passive and active acoustic Green's function retrieval, seismic interferometry, time-reversal acoustics, and holographic imaging. An exact representation of the homogeneous Green's function originates from the field of optical holographic imaging (Porter, 1970, JOSA). In this representation, the homogeneous Green's function between two points A and B is expressed as an integral along an arbitrary boundary enclosing A and B. This implies that the Green's function between A and B can be retrieved from measurements carried out at a closed boundary, or, via reciprocity, from passive observations at A and B of the responses to sources on a closed boundary. In practical situations, the closed-boundary integral usually needs to be approximated by an open-boundary integral. This can lead to significant artifacts in the retrieved Green's function. I will discuss a new, single-sided, representation of the homogeneous Green's function, which obviates the need for omnidirectional access. Like the classical closed-boundary representation, this new single-sided representation fully accounts for multiple scattering. I will indicate applications of this new representation in the aforementioned fields.