Retrieval of Green’s functions of elastic waves from thermal fluctuations of fluid-solid systems

Abstract

Fluctuation-dissipation and flow reversal theorems are used to study long-range correlation of thermal phonons in a stationary heterogeneous mechanical system comprised of arbitrary inhomogeneous fluid flow and anisotropic solid. At thermal equilibrium, with an appropriate choice of physical observables to characterize thermal fluctuations within the fluid and within the solid, the general integral expression for the two-point correlation function of the fluctuations reduces to a linear combination of deterministic Green's functions, which describe wave propagation in opposite directions between the two points. It is demonstrated that the cross-correlation of thermal noise contains as much information about the environment as can be obtained in active reciprocal transmission experiments with transceivers placed at the two points. These findings suggest a possible application of ambient noise cross-correlation to passive acoustic characterization of inhomogeneous flows in fluid-solid systems in laboratory and geophysical settings.