Autoproducts and out-of-band acoustic fields in refracting multipath environments with caustics

Abstract

Autoproducts are nonlinear mathematical constructions developed from a given acoustic field with non-zero bandwidth that can—with some limitations—mimic lower and higher frequency acoustic fields lying outside the bandwidth of the given acoustic field. The autoproducts’ mimicry of out-of-band fields is often sufficient for successful beamforming and/or source localization at below- or above-band frequencies chosen to correct array sparseness, suppress random scattering, mitigate environmental mismatch, and/or enhance resolution. While the limitations of autoproducts developed from acoustic fields well-described by ray acoustics are understood, what is less studied are the effects of diffraction and refraction. In this presentation, acoustic waveguide environments are defined which contain strong refraction, and form caustics—regions where nearby ray paths cross—which results in a phase shift in the propagating waves. These caustic phase shifts are not found in autoproduct fields and are detrimental for autoproduct-based remote sensing, especially in regions that are reached by multiple rays that have passed through different numbers of caustics. Multiple refracting environments are considered, including n2-linear and n2-quadratic sound speed profiles, and the ability of autoproducts to mimic out-of-band fields in these environments is assessed. Implications for autoproduct-based source localization are discussed. [Sponsored by ONR and NSF.]