Incomplete acoustic time reversal, frequency shifting, and matched field processing

Abstract

In a reciprocal time-invariant medium, sound can travel in both directions along acoustic paths. This bi-directionality enables acoustic retrofocusing via time reversal (TR) and acoustic source localization via matched field processing (MFP). Given this common basis, the simplest frequency-domain formulations of acoustic TR and MFP are essentially identical; both involve a quadratic product of forward- and backward-propagating complex fields. For this presentation, all scenarios begin with the acoustic field from a remote source that propagates forward through a potentially-complicated acoustic environment to a transducer array where it is recorded. The difference between TR and MFP then arises because the second backward-propagating (time-reversed) acoustic field may be (i) a genuine field in the actual environment as in acoustic TR, or (ii) a predicted field developed from a model of the environment as in MFP. This presentation describes a third possibility, frequency-difference MFP or incomplete acoustic TR, that combines (i), (ii), and a multiplicative property of harmonic plane waves to produce frequency-downshifting. The resulting unconventional formulation involves a cubic product of complex fields and allows robust reduced-resolution source localization with sparse arrays in complicated uncertain environments. Example results from simulated, laboratory, and ocean propagation data are shown. [Sponsored by ONR, NAVSEA, NSF].