Interest in measurement of Green's function by correlating ambient noise has seen enormous growth in recent years. That the technique determines wave responses without using a source is especially attractive in seismology inasmuch as active seismic sources are typically either uncontrolled or inconvenient.
The recent activity has its origins in ultrasonic theory and experiments done here at Illinois. These were followed by some stunning applications in seismology. The method now has whole sessions devoted to it at the annual American Geophysical Union meeting.
Retrieval has its theoretical basis in the concept of wave equipartition; alternatively it can be derived as a consequence of the fluctuation dissipation theorem of statistical thermal mechanics. Proofs, and demonstrations, that Green's function is found in the correlations of noise is simplest and most elegant in the thermal case, for which the noise is equipartitioned. But seismic noise is not equipartitioned like a thermal field is, and those proofs do not apply. Nevertheless correlations of seismic noise do seem to give the Green function. Retrieval is often strikingly feasible under practical conditions, although certain additional caveats apply. This talk will review some of the history of retrieval in acoustics, its analytic proofs, some of its laboratory demonstrations, and its seismic applications. Particular attention will be paid to the consequences of using imperfectly equipartitioned noise.