Green's Function Retrieval by Crossconvolutions

Abstract

Several formulations exist for retrieving the Green's function from cross correlation of (passive) recordings at two locations. Usually these formulations retrieve Green's functions from sources on a closed boundary. Then they apply to media without losses inside the domain spanned by the sources. Until recent, these formulations were only developed for wave phenom- ena. Now Green's function representations for Green's functions for electromagnetic flelds in matter exist. When they exploit cross correlations, the sources must lie on a boundary of a lossless medium and outside this boundary the medium can be lossy. Then such methods can be exploited for passive applications using transient or ambient noise sources, either natural or man-made. For seabed logging methods this is not a realistic scenario because possible are nec- essarily located in the conductive medium. A second formulation employs cross convolutions to retrieve the Green's function and this formulation remains valid when the media in the domain spanned by the sources is conductive. We derive here general exact electromagnetic Green's function retrieval and simplify the obtained results for practical applications. DOI: 10.2529/PIERS060907163222