Measurements of the correlation of the frequency-difference autoproduct with acoustic and predicted-autoproduct fields in the deep ocean

Coherence of the frequency-difference autoproduct deduced from high-frequency acoustic fields scattered from a rough sea surfacea)

The prevalence of random scattering from a rough ocean surface increases with increasing χ=kh cos θ, where k is the acoustic wavenumber, h is the root-mean-square surface height, and θ is the incidence angle. Generally, when χ≫1, coherence between incident and surface-scattered fields is lost. However, such coherence may be recovered when χ≫1 by considering the frequency-difference autoproduct of the surface-scattered field, a quadratic product of complex fields at nearby frequencies. Herein, the autoproduct's coherent reflection coefficient for χ> 20 is determined from surface-scattered sound fields obtained from 50 independent realizations of the rough ocean surface measured in pelagic waters off the coast of California in January 1992. The recordings were made with a source at a depth of 147 m that broadcasted 30 and 40 kHz signals to a single receiver 576 m away at depth of 66 m. An analytic formula for the coherent reflection coefficient of the frequency-difference autoproduct, based on the Kirchhoff approximation and a Gaussian surface autocorrelation function, compares favorably with measurements. Improved agreement with the single-receiver measurements is possible via a minor adjustment to the surface autocorrelation length. The adjustment identified here matches that determined previously from horizontal spatial coherence estimates utilizing the experiment's eight-element receiving array.

Coherent reflection recovery in scattering from the ocean surface using the frequency-difference autoproducta)

The coherence of rough sea-surface-scattered acoustic fields decreases with increasing frequency. The frequency-difference autoproduct, a quadratic product of acoustic fields at nearby frequencies, mimics a genuine field at the difference frequency. In rough-surface scattering, the autoproduct's lower effective frequency decreases the apparent surface roughness, restoring coherent reflection. Herein, the recovery of coherent reflection in sea surface scattering via the frequency-difference autoproduct is examined for data collected off the coast of New Jersey during the Shallow Water '06 (SW06) experiment. An acoustic source at depth 40 m and receiver at depth 24.3 m and range 200 m interrogated 160 independent realizations of the ocean surface. The root mean square surface height h was 0.167 m, and broadcast frequencies were 14-20 kHz, so that 2.5 ≤kh cos θ≤ 3.7 for acoustic wavenumber k and incidence angle θ. Measured autoproducts, constructed from scattered constituent fields, show significant coherent reflection at sufficiently low difference frequencies. Theoretical results, using the Kirchhoff approximation and a non-analytic surface autocorrelation function, agree with experimental findings. The match is improved using a numerical strategy, exploiting the relationship between autoproduct-based coherence recovery, the ocean-surface autocorrelation function, and the ocean-surface height spectrum. Error bars computed from Monte Carlo scattering simulations support the validity of the measured coherence recovery.

Localization of a remote source in a noisy deep ocean sound channel using phase-only matched autoproduct processing

Long-range passive source localization is possible in the deep ocean using phase-only matched autoproduct processing (POMAP) [Geroski and Dowling (2021). J. Acoust. Soc. Am. 150, 171-182], an algorithm based on matched field processing that is more robust to environmental mismatch. This paper extends these prior POMAP results by analyzing the localization performance of this algorithm in the presence of environmental noise. The noise rejection performance of POMAP is assessed using both simulated and measured signal data, with noise data based on environmental noise measurements. Herein, signal and noise measurements are from the nominally one-year-long PhilSea10 ocean acoustic propagation experiment. All signals were recorded from a single moored source, placed near the ocean sound channel 129.4 km away from a nearly water-column-spanning distributed vertical line array. The source transmitted linear frequency modulated chirps with nominal bandwidth from 200 to 300 Hz. The noise measurements used in this study were collected in the months after this source stopped transmitting, and synthetic samples of noise are calculated based on the characteristics of this measured noise. The effect that noise rejection algorithms have on the source localization performance of POMAP is also evaluated, but only 1 dB of performance improvement is achieved using these.

Recovery of coherent reflection from rough-surface scattered acoustic fields via the frequency-difference autoproduct

The acoustic field reflected from a random rough surface loses coherence with the incident field in the Kirchhoff approximation as kh cos θ increases, where k is the incident field wavenumber, h is the root mean square roughness height, and θ is the incidence angle. Thus, for fixed rough-surface properties and incidence angle, a reflected field at lower wavenumber should retain more coherence. Recent results suggest that the frequency-difference autoproduct formed from complex acoustic field amplitudes at two nearby frequencies can recover acoustic information at the difference of those frequencies even when the difference frequency is below the recorded field's bandwidth. Herein analytical, computational, and experimental results are presented for the extent to which the frequency-difference autoproduct recovers coherence from randomly rough-surface-scattered constituent fields that have lost coherence. The analytical results, developed from the Kirchhoff approximation and formal ensemble averaging over randomly rough surfaces with Gaussian height distributions and Gaussian correlation functions, indicate that the coherence of the rough-surface-reflected frequency-difference autoproduct depends on the surface correlation length and Δkh cos θ, where Δk is the difference of the autoproduct's constituent field wavenumbers. These results compare favorably with Monte Carlo simulations of rough surface scattering, and with laboratory experiments involving long surface correlation lengths where 1  ≤kh cos θ≤ 3.

Robust long-range source localization in the deep ocean using phase-only matched autoproduct processing

Passive source localization in the deep ocean using array signal processing techniques is possible using an algorithm similar to matched field processing (MFP) that interrogates a measured frequency-difference autoproduct instead of a measured pressure field [Geroski and Dowling, J. Acoust. Soc. Am. 146, 4727-4739 (2019)]. These results are extended herein to a new MFP-style algorithm, phase-only matched autoproduct processing, that is more robust at source-array ranges as large as 225 km. This new algorithm is herein described and compared to three existing approaches. The performance of all four techniques is evaluated using measured ocean propagation data from the PhilSea10 experiment. These data nominally span a 12-month period; include six source-array ranges from 129 to 450 km; and involve signals with center frequencies between 172.5 and 275 Hz, and bandwidths of 60 to 100 Hz. In all cases, weight vectors are calculated assuming a range-independent environment using a single sound-speed profile measured near the receiving array. The frequency-differencing techniques considered here are capable of localizing all six sources, with varying levels of consistency, using single-digit-Hz difference frequencies. At source-array ranges up to and including 225 km, the new algorithm requires fewer signal samples for success and is more robust to the choice of difference frequencies.