Emergence of the deterministic Green's function from thermal noise in inhomogeneous solids and fluid‐solid structures

Abstract

S. M. Rytov [A Theory of Electrical Fluctuations and Thermal Radiation (USSR Academy of Sciences, Moscow, 1953)] was apparently the first to establish theoretically a simple relation between deterministic Green's function and cross‐correlation of fluctuations of wave fields generated by random sources. He used reciprocity considerations to analyze fluctuations of electromagnetic fields. An acoustic counterpart of the Rytov's approach was applied in [O. A. Godin, Emergence of the acoustic Green's function from thermal noise, J. Acoust. Soc. Am. 121, EL96‐EL102 (2007)] to derive exact and asymptotic relations between acoustic Green's functions and cross‐correlation of thermal noise in inhomogeneous moving or motionless fluids. In this paper, these results are extended to solid and fluid‐solid media and compared to experimental and theoretical results previously reported in the literature. It is shown that, with the averaging time being sufficiently large, the two‐point correlation function of thermal noise ...