Emergence of the acoustic Green’s function from thermal noise

Abstract

Recently proposed applications of noise cross-correlation measurements to passive remote sensing range from ultrasonics and acoustic oceanography to helioseismology and geophysics, at wave frequencies that differ by more than ten orders of magnitude. At the heart of these applications is the possibility to retrieve an estimate of a deterministic Green’s function from long-range correlations of diffuse noise fields. Apparently, S. M. Rytov [A Theory of Electrical Fluctuations and Thermal Radiation (USSR Academy of Sciences, Moscow, 1953)] was the first to establish theoretically a simple relation between the Green’s function and the two-point correlation function of fluctuations of wave fields generated by random sources. He used reciprocity considerations to analyze fluctuations of electromagnetic fields. In this paper, an acoustic counterpart of Rytov’s approach is applied to derive exact and asymptotic relations between respective acoustic Green’s functions and cross-correlation of thermal noise in inhomogeneous fluid, solid, and fluid-solid media. Parameters of the media are assumed to be time independent, but can be arbitrary functions of spatial coordinates. Theoretical results obtained are compared to those previously reported in the literature.