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.

Emergence of the Green's Functions from Noise and Passive Acoustic Remote Sensing of Ocean Dynamics

“…Our theoretical approach is based on the flow reversal theorem (Godin, 1997), which is an extension of the reciprocity principle to moving media. The approach proved to be instrumental in deriving exact representations of the noise fields and their statistics in arbitrarily inhomogeneous, moving media in terms of deterministic GFs (Godin, 2006(Godin, , 2007(Godin, , 2009a(Godin, , 2010a. Moreover, the flow reversal theorem leads to important identities (often termed Ward identities), which relate surface and volume integrals of certain products of GFs to the GF value at a point and underlie exact and asymptotic local relations between diffuse noise cross-correlations and deterministic GFs (Godin, 2006(Godin, , 2007(Godin, , 2009a(Godin, , 2010a.…”

“…Emergence of the deterministic GFs from cross-correlations of noise due to sources distributed in a volume and on boundaries in inhomogeneous, fluid-solid environments with dissipation has been demonstrated theoretically (Godin, 2009a(Godin, , 2010a.…”

“…In underwater acoustics and other geophysical applications, noise fields are often diffuse but, with the exception of thermal noise (Rytov, 1953;Godin, 2007Godin, , 2009a, are never the "perfectly diffuse" wave fields for which exact relations between noise cross-correlations and deterministic Green's functions hold. Asymptotic approaches based on the stationary phase approximation (Snieder, 2004;Godin, 2006) and its extensions (Godin, 2009d(Godin, , 2010a have been used to determine the information content of two-point cross-correlation function of acoustic noise in the ocean.…”

Extracting the Green’s function from measurements of the energy flux

“…[1][2][3][4][5][6][7] Traditionally the Green's function is retrieved from cross correlation of measured field fluctuations. In this work we present a different method that allows extraction of the Green's function of acoustic waves by considering a sequence of three experiments with time-harmonic sources at two locations, r A and r B .…”

Noise interferometry in an inhomogeneous environment in the geometric limit

“…The connection between G x a jx b ; t ð Þand C ab (t) was first noted by Rytov. 1 Subsequent theoretical investigations of sound waves in solids, stationary fluids, and moving fluids has focused on arguments based on normal modes, 2,3 time-reversal considerations, 4 reciprocity considerations, [5][6][7][8] and asymptotic methods. [9][10][11][12][13][14][15][16] Also, many experimental results 2,3 including applications to seismology [17][18][19] and ocean bottom remote sensing [20][21][22] have been reported.…”