Equipartition and retrieval of Green’s function.

Abstract

Research on retrieval of Green’s function by correlation of ambient noise has seen enormous growth in recent years, in particular in seismology, exploration geophysics, and ocean acoustics, and in general whenever receivers are convenient while active sources are not. As such it resembles various other methodologies such as daylight imaging, sound shadows, and correlations with noisy sources which are, in fact, different in principle. Retrieval has its theoretical origin in the concept of wave equipartition and the fluctuation dissipation theorem of statistical thermal mechanics. Proof that the Greens function is retrieved from the correlations of noise is the simplest and most elegant in the thermal case, but acoustic noise is rarely thermal and those proofs do not always apply. Nevertheless, diffuse acoustic wave fields will sometimes approximate equipartition (it is routinely assumed in room acoustics and statistical energy analysis), and retrieval is often strikingly feasible even where that approximation is weak. This talk will review some of the history of retrieval in acoustics, particularly its analytic proofs and its successful applications. Rates of convergence, the effect of non-stationarity of noise, and the practical effect of imperfect equipartition, will also be discussed.