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.

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

Frequency-domain spatial-correlation analysis of recorded acoustic fields is typically limited to the bandwidth of the recordings. A previous study [Lipa, Worthmann, and Dowling (2018) J. Acoust. Soc. Am. 143(4), 2419-2427] suggests that limiting such analysis to in-band frequencies is not strictly necessary in a Lloyd's mirror environment. In particular, below-band field information can be retrieved from the frequency-difference autoproduct, a quadratic product of measured complex pressure-field amplitudes from two nearby frequencies. The frequency-difference autoproduct is a surrogate field that mimics a genuine acoustic field at the difference frequency. Here, spatial-correlation analysis is extended to deep-ocean acoustic fields measured during the PhilSea10 experiment. The frequency-difference autoproduct, at difference frequencies from 0.0625 to 15 Hz, is determined from hundreds of Philippine Sea recordings of 60 or 100 Hz bandwidth signals with center frequencies from 172.5 to 275 Hz broadcast to a vertical receiving array 129-450 km away. The measured autoproducts are cross correlated along the array with predicted acoustic fields and with predicted autoproduct fields at corresponding below-band frequencies. Stable measured cross correlations as high as 80%-90% are found at the low end of the investigated difference-frequency range, with consistent correlation loss due to mismatch at the higher below-band frequencies.

High-resolution acoustic localization of changes in spatially-distributed coherent sources for structural health monitoring.

Localization of acoustic sources is a common remote sensing goal. When multiple sources are present and coherent, high-resolution localization typically becomes more challenging. The spectral estimation method with additive noise (SEMWAN) is an existing technique for high-resolution localization of incoherent monopole sources in low-signal-to-noise environments. SEMWAN utilizes a reference measurement to incoherently suppress background noise, but its performance suffers in applications involving spatially-distributed coherent sources, such as like a vibrating plate. However, by subtracting a reference measurement and using subarray averaging, SEMWAN can be extended to localization of small changes in distributed coherent sources. This revised approach, the spectral estimation method with coherent background removal (SEMCBR), permits remote acoustic localization of damage in a vibrating structure. A simple multi-source experiment using an 8-by-8 planar square microphone array with 6-cm spacing in both horizontal directions was performed to validate SEMCBR at a frequency of 5.0 kHz. Additional SEMCBR experimental results are reported for the same array placed 1.0 m above a 30 cm × 30 cm vibrating plate with and without damage. Cuts, boundary failures and delamination of a composite plate were successfully located with conventional spherical-wave beamforming and SEMCBR using a 0.1 to 6.0 kHz bandwidth. However, SEMCBR provides 4 to 6 times better resolution.

Autoproducts in and near acoustic shadow zones created by barriers.

The autoproducts are nonlinear mathematical constructs developed from acoustic fields with non-zero bandwidth. When averaged through the field's bandwidth, the autoproducts may mimic a genuine acoustic field at frequencies that are lower or higher than the original field's bandwidth. The resulting opportunity to extend signal processing to user-selectable below- or above-band frequencies is intriguing for many signal processing algorithms. Based on prior work, the limitations of the autoproducts' mimicry of out-of-band fields are understood when the in-band acoustic field is well-represented by ray acoustics. Thus, the focus in this study is on autoproducts in acoustic shadow zones behind barriers containing only diffracted acoustic fields where a sum of ray-path contributions is not an adequate field description. Diffraction is expected to be a detriment to autoproduct techniques due to its sensitivity to frequency. Two ideal shadow-zone environments with exact analytic Helmholtz-equation solutions are considered: Sommerfeld's half-plane problem, also known as knife-edge diffraction, and Mie scattering from a sphere with ka = 40, where k is the wavenumber and a is the sphere's radius. With the exception of the shadow regions, autoproducts experience only mild degradation in field-mimicry performance when compared to what the ray-based theory would predict.

The effects of refraction and caustics on autoproducts.

Quadratic products of complex amplitudes from acoustic fields with nonzero bandwidth, denoted "autoproducts," can mimic acoustic fields at frequencies lower or higher than the bandwidth of the original field. While this mimicry has been found to be very promising for a variety of signal processing applications, its theoretical extent has, thus far, only been considered under the most elementary ray approximation. In this study, the combined effects of refraction and diffraction are considered in environments where refraction causes neighboring rays to cross and form caustics. Acoustic fields on and near caustics are not well-predicted by elementary ray-acoustic theory. Furthermore, caustics introduce frequency dependence to the nearby acoustic field and a phase shift on the acoustic waves that passes through them. The effects these caustics have on autoproducts is assessed here using two simple, range-independent waveguides with index of refraction (n) profiles that are n2-quadratic and n2-linear. It is found that in multipath regions where rays have passed through differing numbers of caustics, the ability of autoproducts to mimic out-of-band fields is substantially hindered.

Long-range frequency-difference source localization in the Philippine Sea.

Matched field processing (MFP) refers to a variety of source localization schemes for known complicated environments and involves matching measured and calculated (replica) fields to identify source locations. MFP may fail for several reasons, most notably when the calculated fields are insufficiently accurate. This error commonly prevents MFP-based long-range (>100 km) source localization in the deep ocean (from 5 to 6 km depth) for signal frequencies of hundreds of Hz, even when extensive high-signal-to-noise ratio field measurements are available. Recently, below-band MFP utilizing the frequency-difference autoproduct [Worthmann, Song, and Dowling (2015). J. Acoust. Soc. Am, 138(6), 3549-3562] achieved some shallow-ocean localization success at a 3 km source-to-array range with signal frequencies in the tens of kHz. The performance of this technique, when extended to matching the measured frequency-difference autoproduct with a composite mode-ray replica, is described here for deep ocean source localization. The ocean propagation data come from the PhilSea10 experiment and involve source-to-array ranges from 129 to 379 km and nominal 100-Hz-bandwidth signals having center frequencies from 250 to 275 Hz. Based on an incoherent average of five signal samples, the frequency-difference technique was 90%-100% successful at four different source-to-array ranges using single-digit-Hz difference frequencies.

Remote acoustic detection of cuts in a vibrating plate with stochastic input forcing in a reverberant environment.

A mechanical structure subject to vibratory forcing will often radiate sound. When remotely recorded, this sound depends on the vibratory forcing, the structure's frequency response function, and the structure-to-receiver acoustic propagation. Thus, successful remote acoustic detection of changes in a structure's vibration response between baseline and subsequent test recordings may require compensation for possible baseline-to-test changes in vibratory forcing and acoustic propagation. Compensation schemes for unknown structural forcing in an unknown reverberant environment that allow such remote detection are described here and found to be successful when the random forcing has a consistent power spectrum and the structure-radiated sound is recorded with an array of receivers. In particular, experimental results are presented for remote acoustic detection of 13-76 mm cuts in a vibrating 0.30-m-square by 3-mm-thick edge-clamped aluminum plate subject to 0.1-2 kHz base excitation in a reverberant laboratory. Radiated sound from the plate is recorded remotely with a 15-element microphone array and processed with the synthetic time reversal blind deconvolution algorithm to compensate for unknown reverberation. Cut detection success is compared for frequency-sweep and random-input forcing when this forcing is known and unknown, and when there are plate-to-array geometric changes between the baseline and test measurements.

Frequency-difference beamforming in the presence of strong random scattering.

Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029] is a nonlinear, out-of-band signal processing technique used to beamform non-zero bandwidth signals at below-band frequencies. This is accomplished with the frequency-difference autoproduct AP(Δω)=P(ω2)P*(ω1), a quadratic product of complex field amplitudes that mimics a genuine field at the difference frequency, Δω=ω2-ω1. For frequency-difference beamforming, AP(Δω) replaces the in-band complex field in the conventional beamforming algorithm. Here, the near-field performance of frequency-difference beamforming is evaluated in the presence of 1 to 30 high-contrast spherical scatterers with radius a placed between, and in the plane defined by the source and a 12-element linear receiving array with element spacing d. Based on the center frequency wave number, k, of the 150-200 kHz frequency sweep source signal, the scatterers are large, ka ≈ 15; the array is sparse, kd = 37; and the average source-to-receiver distance is up to 4.3 mean-free-path lengths. Beamforming results from simulations and experiments show that in-band beamforming loses peak-to-sidelobe ratio and fails to reliably locate the source as the scatterer count increases. Using the same signals, frequency-difference beamforming with difference frequencies from 5 to 25 kHz localizes sources reliably with higher peak-to-side-lobe ratios, though with reduced resolution.

Effect of bevel angle on the reflection coefficient from open unflanged pipes.

Pipes terminating in bevel angled cuts are popular for automotive and motorcycle exhaust systems. This letter provides measured reflection coefficients and end impedances obtained from two-microphone experiments using unflanged open-ended pipes with bevel angles of 0°, 30°, and 60° for 0.03 < ka < 0.27, where k is the acoustic wave number and a is the pipe radius. The measurements at 0° match classical pipe reflection coefficient results within uncertainty. However, as the bevel angle increases to 60°, the magnitude of the reflection coefficient decreases by 2%, the end reactance increases by 130%, and the end resistance increases by 24%.

Remote acoustic detection of mechanical changes in a vibrating plate in an unknown reverberant environment.

Acoustic radiation from a vibrating mechanical structure subject to broadband forcing is inherently dependent on the structure's material, geometry, and boundary conditions. Remote measurements of radiated sound can be used to detect mechanical changes (i.e., defects) when compared to known baseline measurements from the same structure. However, proper determination of a structure's acoustic signature may not be possible in highly reverberant environments due to reverberation contamination. Herein, experimental results are presented for the remote acoustic detection of clamped-boundary defects in a nominally 30 × 30 × 0.3 cm aluminum plate in a reverberant environment. Synthetic Time Reversal (STR) is used to estimate the free-field acoustic signature of the plate from recordings made in a reverberant environment with a 15-element microphone array at signal-to-reverberation ratio levels of -7 to -13 dB in a 100 Hz to 2.0 kHz bandwidth. These reconstructed time domain signals are then cross-correlated with baseline measurements of a known fully-clamped plate and classified as either changed or unchanged. Using common classifier statistics, this approach to remote acoustic damage detection using STR is found to be superior to equivalent waveform correlation approaches based on unprocessed signals and conventional time-domain beamforming outputs.

Measurement of autoproduct fields in a Lloyd's mirror environment.

Conventional frequency-domain acoustic-field analysis techniques are typically limited to the bandwidth of the field under study. However, this limitation may be too restrictive, as prior work suggests that field analyses may be shifted to lower or higher frequencies that are outside the field's original bandwidth [Worthmann and Dowling (2017). J. Acoust. Soc. Am. 141(6), 4579-4590]. This possibility exists because below- and above-band acoustic fields can be mimicked by the frequency-difference and frequency-sum autoproducts, which are quadratic products of frequency-domain complex field amplitudes at a pair of in-band frequencies. For a point source in a homogeneous acoustic half-space with a flat, pressure-release surface (a Lloyd's mirror environment), the prior work predicted high correlations between the autoproducts and genuine out-of-band fields at locations away from the source and the surface. Here, measurements collected in a laboratory water tank validate predictions from the prior theory using 40- to 110-kHz acoustic pulses measured at ranges between 175 and 475 mm, and depths to 400 mm. Autoproduct fields are computed, and cross-correlations between measured autoproduct fields and genuine out-of-band acoustic fields are above 90% for difference frequencies between 0 and 60 kHz, and for sum frequencies between 110 and 190 kHz.

Frequency-sum beamforming for passive cavitation imaging.

Beamforming includes a variety of spatial filtering techniques that may be used for determining sound source locations from near-field sensor array recordings. For this scenario, beamforming resolution depends on the acoustic frequency, array geometry, and target location. Random scattering in the medium between the source and the array may degrade beamforming resolution with higher frequencies being more susceptible to degradation. The performance of frequency-sum (FS) beamforming for reducing such sensitivity to mild scattering while increasing resolution is reported here. FS beamforming was used with a data-dependent [minimum variance (MV)] or data-independent (delay-and-sum, DAS) weight vector to produce higher frequency information from lower frequency signal components via a quadratic product of complex signal amplitudes. The current findings and comparisons are based on simulations and passive cavitation imaging experiments using 3 MHz and 6 MHz emissions recorded by a 128-element linear array. FS beamforming results are compared to conventional DAS and MV beamforming using four metrics: point spread function (PSF) size, axial and lateral contrast, and computation time. FS beamforming produces a smaller PSF than conventional DAS beamforming with less computation time than MV beamforming in free space and mild scattering environments. However, it may fail when multiple unknown sound sources are present.

Far-field coherent backscatter enhancement from random aggregations of scatterers and comparisons to backscattering from single isolated spheres.

Coherent backscatter enhancement (CBE), a multiple scattering phenomenon, may cause an enhancement of up to a factor of two in the average intensity backscattered from a random aggregation of scatterers. In the ocean, CBE may occur when a fish school or a bubble cloud is remotely illuminated. The research reported here explored the possibility that CBE might be used to remotely discriminate between an aggregation of many scatterers and a single isolated scattering object. For this investigation, the far-field harmonic acoustic pressure backscattered from aggregations of randomly placed omnidirectional point scatterers was determined from numerical solution of the equations from Foldy [(1945) Phys. Rev. 67(3,4), 107-119], and compared to equivalent results from single spherical scatterers having hard surfaces, pressure-release surfaces, or aggregation-matched effective-medium properties. Interestingly, CBE causes a spherical aggregation to backscatter as much or more sound than a single perfectly reflecting sphere of the same size when (ka)1/2(ks)-4/5(kσs1/2)3/4 ≥ 2.3, where k is the acoustic wave number, a is the aggregation radius, s is the average spacing between scatterers, and σs is a scatterer's cross section. And, backscattered intensity samples (in dB) from all simulated aggregations followed an extreme value distribution, a finding that supports the conventional use of backscatter statistics for remote aggregation-versus-single-object discrimination.

The frequency-difference and frequency-sum acoustic-field autoproducts.

The frequency-difference and frequency-sum autoproducts are quadratic products of solutions of the Helmholtz equation at two different frequencies (ω+ and ω-), and may be constructed from the Fourier transform of any time-domain acoustic field. Interestingly, the autoproducts may carry wave-field information at the difference (ω+ - ω-) and sum (ω+ + ω-) frequencies even though these frequencies may not be present in the original acoustic field. This paper provides analytical and simulation results that justify and illustrate this possibility, and indicate its limitations. The analysis is based on the inhomogeneous Helmholtz equation and its solutions while the simulations are for a point source in a homogeneous half-space bounded by a perfectly reflecting surface. The analysis suggests that the autoproducts have a spatial phase structure similar to that of a true acoustic field at the difference and sum frequencies if the in-band acoustic field is a plane or spherical wave. For multi-ray-path environments, this phase structure similarity persists in portions of the autoproduct fields that are not suppressed by bandwidth averaging. Discrepancies between the bandwidth-averaged autoproducts and true out-of-band acoustic fields (with potentially modified boundary conditions) scale inversely with the product of the bandwidth and ray-path arrival time differences.

Adaptive frequency-difference matched field processing for high frequency source localization in a noisy shallow ocean.

Remote source localization in the shallow ocean at frequencies significantly above 1 kHz is virtually impossible for conventional array signal processing techniques due to environmental mismatch. A recently proposed technique called frequency-difference matched field processing (Δf-MFP) [Worthmann, Song, and Dowling (2015). J. Acoust. Soc. Am. 138(6), 3549-3562] overcomes imperfect environmental knowledge by shifting the signal processing to frequencies below the signal's band through the use of a quadratic product of frequency-domain signal amplitudes called the autoproduct. This paper extends these prior Δf-MFP results to various adaptive MFP processors found in the literature, with particular emphasis on minimum variance distortionless response, multiple constraint method, multiple signal classification, and matched mode processing at signal-to-noise ratios (SNRs) from -20 to +20 dB. Using measurements from the 2011 Kauai Acoustic Communications Multiple University Research Initiative experiment, the localization performance of these techniques is analyzed and compared to Bartlett Δf-MFP. The results show that a source broadcasting a frequency sweep from 11.2 to 26.2 kHz through a 106 -m-deep sound channel over a distance of 3 km and recorded on a 16 element sparse vertical array can be localized using Δf-MFP techniques within average range and depth errors of 200 and 10 m, respectively, at SNRs down to 0 dB.

Performance comparisons of frequency-difference and conventional beamforming.

Frequency-difference beamforming [Abadi, Song, and Dowling (2012b). J. Acoust. Soc. Am. 132, 3018-3029] is an unconventional beamforming method for use with sparse receiver arrays. It involves beamforming a quadratic product of complex field amplitudes, P(ω2)P*(ω1), at the difference frequency, ω2-ω1, instead of beamforming the complex field amplitude P(ω) at frequencies ω within the signal bandwidth. Frequency-difference beamforming is readily implemented with ordinary transducer array recordings of non-zero bandwidth signals. Results for, and comparisons of, frequency-difference beamforming from simulations and experiments are reported herein. In particular, spherical-wave beamforming is investigated using 15 and 165 kHz pulse signals in a 1.07-m-diameter water tank with a linear array having 14 elements spaced 5.08 cm apart. Here, frequency-difference beamforming using the high-frequency pulses provides comparable results to conventional beamforming at 15 kHz. Plane-wave beamforming is investigated using 11.2-32.8 kHz frequency-sweep signals broadcast 3 km through a 106-m-deep ocean sound channel to a vertical array having 16 elements spaced 3.75 m apart. Here, frequency difference beamforming in the 1.7-2.3 kHz difference frequency band provides results comparable to conventional beamforming in this band.

Simulating acoustic coherent backscattering enhancement from random aggregations of omnidirectional scatterers.

Coherent backscatter enhancement (CBE) is a multiple scattering phenomenon that can lead to a doubling of the backscattered field intensity from a random aggregation of scatterers. It may be useful for remote sensing of scatterer aggregations, such as fish schools. This paper presents simulations of acoustic CBE from randomly placed omnidirectional point scatterers based on Foldy's field equations. The simulations are verified and validated through comparisons with Bragg scattering and Foldy's effective-medium theory, assessments of acoustic energy conservation, and comparisons with prior optical and acoustical CBE results. To make CBE comparisons with prior optics results, a CBE coherence function was postulated to account for resolution differences between the optics and simulation studies. For the higher-resolution optics studies, the postulated coherence function yields a CBE of 1.68, which matches optical CBE measurements. For the lower-resolution simulations, the same coherence function yields a CBE of 1.034, which agrees with appropriately extrapolated CBE simulation results, 1.030 ± 0.005. Assuming comparable resolution, the acoustics experiment and simulations both produce a CBE of approximately 1.5. The CBE peak is found to increase approximately monotonically with (k(2)σs)(1/4)(ks)(-1), where k is the wave number, s is the average spacing between scatterers, and σs is a scatterer's cross section.