It is shown that a diffuse field is not devoid of phase information, but has a correlation function equal to the Green's function. More specifically, the cross-correlation between diffuse signals in two transducers is very nearly equal to the direct response of one transducer to an impulse applied to the other. This is true whether the diffuse field is one that was created by a distant source, or (if the detectors are sufficiently sensitive) created by thermal fluctuations in the specimen. Here we outline and review proofs, and laboratory demonstrations, from three recent archival publications.

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Noise generated in an ultrasonic receiver circuit consisting of transducer and amplifier is usually ignored, or treated as a nuisance. Here it is argued that acoustic thermal fluctuations, with displacement amplitudes of 3 fm, contain substantial ultrasonic information. It is shown that the noise autocorrelation function is the waveform that would be obtained in a direct pulse/echo measurement. That thesis is demonstrated in experiments in which direct measurements are compared to correlation functions. The thermal nature of the elastodynamic noise that generates these correlations is confirmed by an absolute measurement of their strength, essentially a measurement of the sample temperature.

Equipartition is a first principle in wave transport, based on the tendency of multiple scattering to homogenize phase space. We report observations of this principle for seismic waves created by earthquakes in Mexico. We find qualitative agreement with an equipartition model that accounts for mode conversions at the Earth's surface.

We study the temperature dependence of diffuse reverberant ultrasound in elastic bodies. Transient wave forms are found to undergo an almost pure dilation of 0.0277% per degree, related to the temperature dependence of wave speeds. The wave forms also suffer a distortion that, we argue, depends on the rate of conversion between the dilatational (P) and shear (S) waves. Distortion is found to scale in a manner consistent with theoretical arguments but also appears to be a function of the degree of ray chaos in the body, indicating that the mixing rates are slower in more regular bodies.