Time-reversing array retrofocusing in simple dynamic underwater environments

Abstract

A time-reversing array (TRA) has the ability to retrofocus acoustic energy, in both time and space, to the original sound-source location without any information about the acoustic environment in which it is deployed. This unique capability may be limited or lost when the acoustic medium or its boundaries are time dependent, or propagation losses are prevalent. In this paper, predictions are made for the size, field-amplitude decay rate (or time), and location of the retrofocus for a TRA deployed in the presence of three dynamic acoustic propagation complexities commonly present in shallow ocean waters: (i) volume scattering from a random superposition of linear internal waves convecting a gradient in the sound speed profile; (ii) reflection and volume scattering from a deterministic soliton internal wave traveling on the thermocline between two water masses with differing sound speed; and (iii) surface scattering from a wind-driven dynamic random rough ocean surface. Analytical propagation models for narrow-band signals are used to highlight separately the influence of each propagation complexity on TRA retrofocusing. As expected, internal wave time scales are long enough so that TRA retrofocusing should persist for several minutes for source-array ranges of several kilometers at frequencies approaching 1 kHz. However, the comparatively rapid motion of ocean surface waves should prevent TRA exploitation of acoustic scattering from a wind-driven ocean surface at ranges greater than a few hundred meters, independent of acoustic frequency. Interestingly, multiple time-invariant propagation paths are not found to consistently enhance retrofocusing unless the TRA has sufficient angular resolution to distinguish them.