A diffuse acoustic field is shown to have correlations equal to the Green’s function of the body. Simple plausibility arguments for this assertion are followed by a more detailed proof. A careful version of the statement is found to include caveats in regard to how diffuse the field truly is, the spectrum of the diffuse field, and the phase of the receivers. Ultrasonic laboratory tests confirm the assertion. The main features of the direct signal between two transducers are indeed recovered by cross correlating their responses to a diffuse field generated by a third transducer. The quality of the recovery improves with increased averaging and the use of multiple sources. Applications are discussed. © 2001 Acoustical Society of America . [DOI: 10.1121/1.1417528] PACS numbers: 43.40.Qi, 43.40.Hb, 43.35.Yb [DEC]

Abstract We review the history of diffuse ultrasonic waves in solids with emphasis on recent developments in field-field correlations and their identification with Green’s function. The basic principles appear to be well understood now, and the identity between these two waveforms has been proven under a variety of assumed conditions that guarantee a diffuse field. Promise for practical passive imaging is good; nevertheless, measurements sometimes fail to fully agree with theory. We ascribe this in some cases to incomplete convergence — insufficient amounts of data have been processed. In other cases, it is probably because of a lack of perfect diffuseness; ambient nonmultiply scattered fields are often not equipartitioned and imperfectly diffuse.