Interferometric electromagnetic Green's functions representations using propagation invariants

Abstract

Creating new responses from cross-correlations of responses measured at different locations is known as interferometry. Each newly created response represents the field measured at one of the receiver locations as if there were a source at the other. Here, we formulate electromagnetic interferometric Green's functions representations in open configurations. There are in principle no restrictions on the heterogeneity and anisotropy of the medium inside or outside the domain. Time-correlation type formulations rely on conservation of total wave energy and they cannot be used for media showing relaxation of some form in a straightforward way. Time-convolution type propagation invariants are independent of the medium relaxation mechanisms and they can be used for interferometry by cross-correlating a measured response with the time-reverse of another response. This type of interferometry can only be formulated in the configuration with one receiver outside the domain. For time-convolution interferometry no restrictions on the medium heterogeneity, anisotropy or relaxation mechanisms are made. For these interferometric formulations to be of practical use, the main simplification is to make a high-frequency approximation for the normal derivative in the source coordinate. These approximations of the exact result lead to two different types of errors. We discuss the causes and consequences of these errors and illustrate them with numerical examples. © 2007 The Authors Journal compilation © 2007 RAS.