Influence of Short Time-Scale Water-Column Temperature Fluctuations on Broadband Signal Angular Beam Spreading

Abstract

Temporal fluctuations in vertical thermocline structure and depth span (on a time scale of 30 to 40 min) are shown to affect the arrival angle, and focusing of measured broadband (22–28 kHz) non-surface-interacting acoustic signals at a depth of ~100 m. Measurements were taken in the Pacific Missile Range Facility near Kauai island, Hawaii, for a source-receiver range of 1.0 km. The arrival time and angular spread of acoustic beams are obtained for measured signals using a plane wave beamformer with a-prior gaussian weighting. The weighting process reduces ambiguity in angular measurements due to spatial aliasing from a vertical array with element spacing d much greater than half the acoustic wavelength $ \left(\frac{\lambda_{\mathrm{a}}}{2}\right) $ of the highest frequency in the broadband signal. Over two full periods of thermocline oscillation, 2 times of high and 2 times of low isotherm depth are selected to show fluctuations in angular beam spreading, focusing, and the robustness of the weighted beamformer routine. To benchmark the performance of the weighted beamformer, a two-dimensional (2D) Parabolic Equation (PE) model calculates the angular signal spread and focusing using parameters to satisfy spatial sampling requirements for broadband beamforming. In the absence of spatial aliasing, beamforming the output of the 2D PE can be conducted without weighting. Comparison of measured and modeled results shows less than a degree of difference in the angular beam spread of direct, bottom reflected, and refracted paths. It is shown that a vertical array with $ d\gg \left(\frac{\lambda_{\mathrm{a}}}{2}\right) $ and gaussian weighting can resolve changes in angular spread and beam focusing as a function of vertical isotherm displacement.

Keywords

Thermocline / Beamforming / Spatial aliasing / High-frequency / Shallow water / Broadband / Parabolic equation

References

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