Green´s Function Extraction for Interfaces With Impedance Boundary Conditions

Theory and experiments to obtain the response between two receivers from cross correlations of wave fields recorded at these receivers are well established. The principle relies on mutually spatial and temporal uncorrelated contributions from sources on a boundary enclosing the two receivers, which upon cross correlation interfere only constructively for signals traveling between the two receivers. It has, therefore, become generally known as interferometry. The theory includes situations with flow, mechanical, and electromagnetic field fluctuations, and their mutual coupling. Here, we present an electromagnetic theory for Green´s function retrieval from cross correlations that incorporates general bianisotropic media in which interfaces are present where bianisotropic impedance boundary conditions apply. The derived Green´s function representation shows that in lossless media and for interfaces with lossless impedance boundary conditions the Green´s function between two receivers is obtained by cross correlating the recordings of these receivers from sources on a boundary enclosing them. We show numerical examples in 2-D where proper solutions are numerically tractable and practical approximations illustrate that numerically less intensive algorithms lead to acceptable results and accurate extraction of reflections from impedance boundary surfaces. Because the method is data driven, it is suitable for experimental Green´s function extraction from measured data.