Using long-range transmissions in the Beaufort Gyre to test the sound-speed equation at high pressure and low temperature.

An ocean acoustic tomography array with a radius of 150 km was deployed in the central Beaufort Gyre during 2016-2017 for the Canada Basin Acoustic Propagation Experiment. Five 250-Hz transceivers were deployed in a pentagon, with a sixth transceiver at the center. A long vertical receiving array was located northwest of the central mooring. Travel-time anomalies for refracted-surface-reflected acoustic ray paths were calculated relative to travel times computed for a range-dependent sound-speed field from in situ temperature and salinity observations. Travel-time inversions for the three-dimensional sound-speed field consistent with the uncertainties in travel time [∼2 ms root mean square (rms)], receiver and source positions (∼ 3 m rms), and sound speed calculated from conductivity-temperature-depth casts could not be obtained without introducing a deep sound-speed bias (below 1000 m). Because of the precise nature of the travel-time observations with low mesoscale and internal wave variability, the conclusion is that the internationally accepted sound-speed equation (TEOS-10) gives values at high pressure (greater than 1000 m) and low temperature (less than 0 °C) that are too high by 0.14-0.16 m s-1.

Observations of ocean spice and isopycnal tilt sound-speed structures in the mixed layer and upper ocean and their impacts on acoustic propagation.

A 400-m deep and 970 km long conductivity, temperature, depth section in the Northeast Pacific Ocean is decomposed into sound-speed variations associated with tilting isopycnals and ocean spice. The vertical distribution of sound-speed variance from these two processes shows significant fluctuations in the mixed layer (ML) and transition layer (TRL) below. Acoustic simulations at 400 and 1000 Hz are conducted with the decomposed fields to quantify their relative impact on upper ocean propagation for source locations in the ML and TRL. The low frequency simulations show that localized scattering processes dominate the propagation while higher frequencies experience more diffuse scattering. For propagation in the ML, spice generates the most loss while tilt can reduce loss when combined with spice. Statistics further show that energy can couple into and out of the ML duct depending on source depth and frequency.

Acoustic travel-time variability observed on a 150-km radius tomographic array in the Canada Basin during 2016-2017.

The Arctic Ocean is undergoing dramatic changes in response to increasing atmospheric concentrations of greenhouse gases. The 2016-2017 Canada Basin Acoustic Propagation Experiment was conducted to assess the effects of the changes in the sea ice and ocean structure in the Beaufort Gyre on low-frequency underwater acoustic propagation and ambient sound. An ocean acoustic tomography array with a radius of 150 km that consisted of six acoustic transceivers and a long vertical receiving array measured the impulse responses of the ocean at a variety of ranges every four hours using broadband signals centered at about 250 Hz. The peak-to-peak low-frequency travel-time variability of the early, resolved ray arrivals that turn deep in the ocean was only a few tens of milliseconds, roughly an order of magnitude smaller than observed in previous tomographic experiments at similar ranges, reflecting the small spatial scale and relative sparseness of mesoscale eddies in the Canada Basin. The high-frequency travel-time fluctuations were approximately 2 ms root-mean-square, roughly comparable to the expected measurement uncertainty, reflecting the low internal-wave energy level. The travel-time spectra show increasing energy at lower frequencies and enhanced semidiurnal variability, presumably due to some combination of the semidiurnal tides and inertial variability.

Observations of the space/time scales of Beaufort sea acoustic duct variability and their impact on transmission loss via the mode interaction parameter.

The Beaufort duct (BD) is a subsurface sound channel in the western Arctic Ocean formed by cold Pacific Winter Water (PWW) sandwiched between warmer Pacific Summer Water (PSW) and Atlantic Water (AW). Sound waves can be trapped in this duct and travel long distances without experiencing lossy surface/ice interactions. This study analyzes BD vertical and temporal variability using moored oceanographic measurements from two yearlong acoustic transmission experiments (2016-2017 and 2019-2020). The focus is on BD normal mode propagation through observed ocean features, such as eddies and spicy intrusions, where direct numerical simulations and the mode interaction parameter (MIP) are used to quantify ducted mode coupling strength. The observations show strong PSW sound speed variability, weak variability in the PWW, and moderate variability in the AW, with typical time scales from days to weeks. For several hundreds Hertz propagation, the BD modes are relatively stable, except for rare episodes of strong sound speed perturbations. The MIP identifies a resonance condition such that the likelihood of coupling is greatest when there is significant sound speed variability in the horizontal wave number band 1/11

Beaufort Sea observations of 11 to 12.5 kHz surface pulse reflections near 50 degree grazing angle from 2016 to 2017.

Sea-surface acoustic scattering is investigated using observations from the 2016-2017 Canada Basin Acoustic Propagation Experiment. The motions of the low-frequency acoustic source and/or receiver moorings were measured using long-baseline acoustic navigation systems in which the signals transmitted once per hour by the mooring instruments triggered high-frequency replies from the bottom-mounted transponders. The moorings recorded these replies, giving the direct path and single-bounce surface-reflected arrivals, which have grazing angles near 50°. The reflected signals are used here to quantify the surface scattering statistics in an opportunistic effort to infer the changing ice characteristics as a function of time and space. Five scattering epochs are identified: (1) open water, (2) initial ice formation, (3) ice solidification, (4) ice thickening, and (5) ice melting. Significant changes in the ice scattering observables are seen using the arrival angle, moment of reflected intensity and its probability density function, and pulse time spread. The largest changes took place during the formation, solidification, and melting. The statistical characteristics across the experimental region are similar, suggesting consistent ice properties. To place the results in some physical context, they are interpreted qualitatively using notions of the partial and fully saturated wave fields, a Kirchhoff-like approximation for the rough surface, and a thin elastic layer reflection coefficient model.

Sensitivity of mixed layer duct propagation to deterministic ocean features.

Here, the problem of mode coupling in a mixed layer (ML) surface duct is considered where the coupling is induced by deterministic upper ocean features such as eddies, filaments, and/or density compensated temperature and salinity anomalies (spice). The single scatter Dyson series solution for mode energy is used to define a non-dimensional mode interaction parameter Γmn that quantifies the strength of coupling between modes m and n as a function of environmental factors and frequency. Direct coupled mode simulations at 400 and 1000 Hz show weak, first order coupling and small ML transmission loss (TL) variability when Γmn<1, while for Γmn>1, there is strong, higher order coupling with large changes in ML TL. Importantly, there is a frequency dependent resonance condition associated with the range width of the perturbations, Δ, such that Γmn→0 as Δ→0 and ∞.

Observations of sound-speed fluctuations in the Beaufort Sea from 2016 to 2017.

Due to seasonal ice cover, acoustics can provide a unique means for Arctic undersea communication, navigation, and remote sensing. This study seeks to quantify the annual cycle of the thermohaline structure in the Beaufort Sea and characterize acoustically relevant oceanographic processes such as eddies, internal waves, near-inertial waves (NIWs), and spice. The observations are from a seven-mooring, 150-km radius acoustic transceiver array equipped with oceanographic sensors that collected data in the Beaufort Sea from 2016 to 2017. Depth and time variations of the sound speed are analyzed using isopycnal displacements, allowing a separation of baroclinic processes and spice. Compared to lower latitudes, the overall sound speed variability is small with a maximum root mean square of 0.6 m/s. The largest source of variability is spice, most significant in the upper 100 m, followed by eddies and internal waves. The displacement spectrum in the internal wave band is time dependent and different from the Garret-Munk (GM) spectrum. The internal wave energy varied with time averaging 5% of the GM spectrum. The spice sound-speed frequency spectrum has a form very different from the displacement spectrum, a result not seen at lower latitudes. Because sound speed variations are weak, observations of episodic energetic NIWs with horizontal currents up to 20 cm/s have potential acoustical consequences.

A seminal paper linking ocean acoustics and physical oceanography.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Observations of upper ocean sound-speed structures in the North Pacific and their effects on long-range acoustic propagation at low and mid-frequencies.

Three 1000-km long, high resolution conductivity, temperature, depth sections in the North Pacific Ocean obtained by the ship towed vehicle SeaSoar are analyzed to quantify 2005 March/April upper-ocean sound-speed structure and determine the effects on low to mid-frequency transmission loss (TL) through numerical simulation. The observations reveal a variable mixed layer acoustic duct (MLAD) with a mean sonic layer depth of 91-m, and an even higher variability, 80-m-average-thickness transition layer connecting the mixed layer (ML) with the main thermocline. The sound-speed structure is hypothesized to be associated with thermohaline processes such as air-sea fluxes, eddies, submesoscale, fronts, internal waves, turbulence, and spice, but the analysis does not isolate these factors. Upper-ocean variability is quantified using observables of layer depth, ML gradient, and sound speed to compute low order moments, probability density functions, horizontal wavenumber spectra, and empirical orthogonal function decomposition. Coupled mode acoustic propagation simulations at 400 and 1000 Hz were carried out using the sound-speed observations from the upper 400-m appended to climatology, which reveal propagation physics associated with diffraction, random media effects, and deterministic feature scattering. Statistics of TL reveal important energy transfers between the MLAD and the deep sound channel.

Temporal and spatial dependence of a yearlong record of sound propagation from the Canada Basin to the Chukchi Shelf.

The Pacific Arctic Region has experienced decadal changes in atmospheric conditions, seasonal sea-ice coverage, and thermohaline structure that have consequences for underwater sound propagation. To better understand Arctic acoustics, a set of experiments known as the deep-water Canada Basin acoustic propagation experiment and the shallow-water Canada Basin acoustic propagation experiment was conducted in the Canada Basin and on the Chukchi Shelf from summer 2016 to summer 2017. During the experiments, low-frequency signals from five tomographic sources located in the deep basin were recorded by an array of hydrophones located on the shelf. Over the course of the yearlong experiment, the surface conditions transitioned from completely open water to fully ice-covered. The propagation conditions in the deep basin were dominated by a subsurface duct; however, over the slope and shelf, the duct was seen to significantly weaken during the winter and spring. The combination of these surface and subsurface conditions led to changes in the received level of the sources that exceeded 60 dB and showed a distinct spacio-temporal dependence, which was correlated with the locations of the sources in the basin. This paper seeks to quantify the observed variability in the received signals through propagation modeling using spatially sparse environmental measurements.

Observations of low-frequency, long-range acoustic propagation in the Philippine Sea and comparisons with mode transport theory.

The year-long Philippine Sea (2010-2011) experiment (PhilSea) was an extensive deep water acoustic propagation experiment in which there were six different sources transmitting to a water column spanning a vertical line array. The six sources were placed in an array with a radius of 330 km and transmitted at frequencies in the 200-300 Hz and 140-205 Hz bands. The PhilSea frequencies are higher than previous deep water experiments in the North Pacific for which modal analyses were performed. Further, the acoustic paths sample a two-dimensional area that is rich in internal tides, waves, and eddies. The PhilSea observations are, thus, a new opportunity to observe acoustic modal variability at higher frequencies than before and in an oceanographically dynamic region. This paper focuses on mode observations around the mid-water depths. The mode observations are used to compute narrowband statistics such as transmission loss and broadband statistics such as peak pulse intensity, travel time wander, time spreads, and scintillation indices. The observations are then compared with a new hybrid broadband transport theory. The model-data comparisons show excellent agreement for modes 1-10 and minor deviations for the rest. The discrepancies in the comparisons are related to the limitations of the hybrid model and oceanographic fluctuations other than internal waves.

Observations of phase and intensity fluctuations for low-frequency, long-range transmissions in the Philippine Sea and comparisons to path-integral theory.

In the Philippine Sea, from April 2010 to March 2011, a 330-km radius pentagonal acoustic transceiver array with a sixth transceiver in the center transmitted broadband signals with center frequencies between 172 and 275 Hz and 100 Hz bandwidth eight times a day every other day. The signals were recorded on a large-aperture vertical-line array located near the center of the pentagon at ranges of 129, 210, 224, 379, 396, and 450 km. The acoustic arrival structures are interpretable in terms of ray paths. Depth and time variability of the acoustic observations are analyzed for six ray paths (one from each transceiver) with similar vertical sampling properties in the main thermocline. Acoustic-field statistics treated include: (1) variances of phase and intensity, (2) vertical coherence and intensity covariance, (3) glinting and fadeout rates, and (4) intensity probability density functions. Several observed statistics are compared to predictions using Feynman path-integral theory assuming the Garrett-Munk internal-wave spectrum. In situ oceanographic observations support this assumption and are used to estimate spectral parameters. Data and theory differ at most by a factor of two and reveal the wave propagation regimes of unsaturated, partially saturated, and fully saturated. Improvements to the evaluation of path-integral quantities are discussed.

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

Broadband classification and statistics of echoes from aggregations of fish measured by long-range, mid-frequency sonar.

For horizontal-looking sonar systems operating at mid-frequencies (1-10 kHz), scattering by fish with resonant gas-filled swimbladders can dominate seafloor and surface reverberation at long-ranges (i.e., distances much greater than the water depth). This source of scattering, which can be difficult to distinguish from other sources of scattering in the water column or at the boundaries, can add spatio-temporal variability to an already complex acoustic record. Sparsely distributed, spatially compact fish aggregations were measured in the Gulf of Maine using a long-range broadband sonar with continuous spectral coverage from 1.5 to 5 kHz. Observed echoes, that are at least 15 decibels above background levels in the horizontal-looking sonar data, are classified spectrally by the resonance features as due to swimbladder-bearing fish. Contemporaneous multi-frequency echosounder measurements (18, 38, and 120 kHz) and net samples are used in conjunction with physics-based acoustic models to validate this approach. Furthermore, the fish aggregations are statistically characterized in the long-range data by highly non-Rayleigh distributions of the echo magnitudes. These distributions are accurately predicted by a computationally efficient, physics-based model. The model accounts for beam-pattern and waveguide effects as well as the scattering response of aggregations of fish.

Internal tides and deep diel fades in acoustic intensity.

A mechanism is presented by which the observed acoustic intensity is made to vary due to changes in the acoustic path that are caused by internal-tide vertical fluid displacements. The position in range and depth of large-scale caustic structure is determined by the background sound-speed profile. Internal tides cause a deformation of the background profile, changing the positions of the caustic structures-which can introduce intensity changes at a distant receiver. Gradual fades in the acoustic intensity occurring over timescales similar to those of the tides were measured during a low-frequency (284-Hz) acoustic scattering experiment in the Philippine Sea in 2009 [White et al., J. Acoust. Soc. Am. 134(4), 3347-3358 (2013)]. Parabolic equation and Hamiltonian ray-tracing calculations of acoustic propagation through a plane-wave internal tide environmental model employing sound-speed profiles taken during the experiment indicate that internal tides could cause significant gradual changes in the received intensity. Furthermore, the calculations demonstrate how large-scale perturbations to the index of refraction can result in variation in the received intensity.

Low-frequency pulse propagation over 510 km in the Philippine Sea: A comparison of observed and theoretical pulse spreading.

Observations of the spread of wander-corrected averaged pulses propagated over 510 km for 54 h in the Philippine Sea are compared to Monte Carlo predictions using a parabolic equation and path-integral predictions. Two simultaneous m-sequence signals are used, one centered at 200 Hz, the other at 300 Hz; both have a bandwidth of 50 Hz. The internal wave field is estimated at slightly less than unity Garrett-Munk strength. The observed spreads in all the early ray-like arrivals are very small, <1 ms (for pulse widths of 17 and 14 ms), which are on the order of the sampling period. Monte Carlo predictions show similar very small spreads. Pulse spread is one consequence of scattering, which is assumed to occur primarily at upper ocean depths where scattering processes are strongest and upward propagating rays refract downward. If scattering effects in early ray-like arrivals accumulate with increasing upper turning points, spread might show a similar dependence. Real and simulation results show no such dependence. Path-integral theory prediction of spread is accurate for the earliest ray-like arrivals, but appears to be increasingly biased high for later ray-like arrivals, which have more upper turning points.

A test of deep water Rytov theory at 284 Hz and 107 km in the Philippine Sea.

Predictions of log-amplitude variance are compared against sample log-amplitude variances reported by White, Andrew, Mercer, Worcester, Dzieciuch, and Colosi [J. Acoust. Soc. Am. 134, 3347-3358 (2013)] for measurements acquired during the 2009 Philippine Sea experiment and associated Monte Carlo computations. The predictions here utilize the theory of Munk and Zachariasen [J. Acoust. Soc. Am. 59, 818-838 (1976)]. The scattering mechanism is the Garrett-Munk internal wave spectrum scaled by metrics based on measured environmental profiles. The transmitter was at 1000 m depth and the receivers at nominal range 107 km and depths 600-1600 m. The signal was a broadband m-sequence centered at 284 Hz. Four classes of propagation paths are examined: the first class has a single upper turning point at about 60 m depth; the second and third classes each have two upper turning points at roughly 250 m; the fourth class has three upper turning points at about 450 m. Log-amplitude variance for all paths is predicted to be 0.04-0.09, well within the regime of validity of either Born or Rytov scattering. The predictions are roughly consistent with the measured and Monte Carlo log-amplitude variances, although biased slightly low. Paths turning in the extreme upper ocean (near the mixed layer) seem to incorporate additional scattering mechanisms not included in the original theory.

Entropy rate defined by internal wave scattering in long-range propagation.

The reduction of information capacity of the ocean sound channel due to scattering by internal waves is a potential problem for acoustic communication, navigation, and remote sensing over long ranges. In spite of recent progress in research on acoustic signal scattering by random internal waves and the fact that random internal waves are ubiquitous in the world oceans, there is no clear understanding of how these waves influence data communication performance. The entropy decrease resulting from scattering by internal waves is an important measure of information loss. Here a rigorous calculation of the entropy is carried out using second moment transport theory equations with random sound-speed perturbations obeying the Garrett-Munk internal-wave model. It is shown that full-wave rate of entropy is of the same order of magnitude as the Kolmogorov-Sinai entropy and Lyapunov exponents for the relevant ray trajectories. The correspondence between full-wave and ray entropies suggests a correspondence between full-wave scattering and ray chaos near statistical saturation. The relatively small level of entropy rate during propagation through the random internal-wave field shows that scattering by internal waves is likely not an essential limitation for data rate and channel capacity.

A reformulation of the Λ-Φ diagram for the prediction of ocean acoustic fluctuation regimes.

The Λ-Φ diagram was a tool introduced in the late 1970s to predict ocean acoustic fluctuation regimes termed unsaturated, partially saturated, and fully saturated, where internal wave sound speed fluctuations play a dominant role. The Λ-Φ parameters reflect, respectively, the strength of diffraction and the root-mean-square phase fluctuation along a ray path. Oceanographic knowledge of the small scale part of the internal wave spectrum and high angle Fresnel zone formulations now allow a more stable and accurate calculation of these parameters. An empirical relation between the variance of log-intensity and Λ-Φ provides a more accurate border between the unsaturated regime and stronger fluctuations. The diagram is consistent with six short range, deep water experiments in the Pacific, Atlantic, and Arctic oceans with frequencies ranging from 75 to 16 000 Hz. The utility of the Λ-Φ diagram is that it provides one of the few means to inter-compare experiments at different geographic locations, and at different frequencies and ranges.

High-frequency normal-mode statistics in shallow water: the combined effect of random surface and internal waves.

In an earlier article, the statistical properties of mode propagation were studied at a frequency of 1 kHz in a shallow water environment with random sound-speed perturbations from linear internal waves, using a hybrid transport theory and Monte Carlo numerical simulations. Here, the analysis is extended to include the effects of random linear surface waves, in isolation and in combination with internal waves. Mode coupling rates for both surface and internal waves are found to be significant, but strongly dependent on mode number. Mode phase randomization by surface waves is found to be dominated by coupling effects, and therefore a full transport theory treatment of the range evolution of the cross mode coherence matrix is needed. The second-moment of mode amplitudes is calculated using transport theory, thereby providing the mean intensity while the fourth-moment is calculated using Monte Carlo simulations, which provides the scintillation index. The transport theory results for second-moment statistics are shown to closely reproduce Monte Carlo simulations. Both surface waves and internal waves strongly influence the acoustic field fluctuations.