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The generation of T waves in a deep ocean by an earthquake in its epicentral region is often observed, but the mechanism of the excitation of the acoustic waves travelling horizontally with the speed of sound remains controversial. Here, the hypothesis is investigated that the abyssal T waves are generated by the scattering of ballistic sound waves by surface and internal gravity waves in the ocean. Volume and surface scattering are studied theoretically in the small perturbation approximation. In the 3-50 Hz typical frequency range of the observed T waves, the linear internal waves are found to lack the necessary horizontal spatial scales to meet the Bragg scattering condition and contribute appreciably to the T-wave excitation. In contrast, the ocean surface roughness has the necessary spatial scales at typical sea states and wind speeds. The efficiency of the acoustic normal modes' excitation at surface scattering of the ballistic body waves by wind seas and sea swell is quantified and found to be comparable to that of the established mechanism of the T-wave generation at downslope conversion at the seamounts. The surface scattering mechanism is consistent with key observational features of the abyssal T waves, including their ubiquity, low-frequency cutoff, presence on seafloor sensors, and weak dependence on the earthquake focus depth.

17 USC 105 interim-entered record; under review. The article of record as published may be found at https://doi.org/10.1121/10.0003601 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 inter- nal 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 cur- rents up to 20 cm/s have potential acoustical consequences. This research was supported by the Office of Naval Research (ONR) and M.K. was supported by an ONR Ocean Acoustics Graduate Student Fellowship under Award No. N00014-19-1-2203. The 600kHz ADCP and IPS ice draft data were supported by the ONR Arctic and Global Prediction Program (ONR 322AG) under Award No. N00014-15-1-2782. This material is based on work supported by the ONR under Award No. N00014-15-2068

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.

Sound speed characteristics in the upper ocean are sometimes thought to be set by a combination of mostly one-dimensional vertical mixing processes and (slow) mesoscale advection and stirring. However, a series of recent projects have showcased the role of small-scale (tens of meters to tens of km horizontally), rapidly evolving (hours to days) submesoscale instabilities in setting both stratification and sound speed properties. The observations also reveal that sound speed structure set by such processes is fundamentally three dimensional, with significant lateral gradients at a broad range of scales. Some relevant processes are frontogenetic and create sometimes rapid secondary circulations near lateral density gradients. Some are associated with wind-driven near-inertial oscillations or internal waves. Some of the more interesting recent observations concern the intersection of submesoscale and internal wave processes. Here, I will review a few highlights from the last decade of observations on unbalanced, nonlinear processes that conspire to set density, spice, and sound speed profiles in several contrasting oceans.

An automated method was developed to align underwater acoustic measurements taken at various depths and ranges to a reference model of acoustic arrival structure. Data used to demonstrate the method were collected by four autonomous underwater vehicles deployed in the Philippine Sea as part of an ocean acoustic tomography experiment. The arrivals were measured in the upper 1000 m of the ocean at ranges spanning several hundred kilometers from 5 moored acoustic tomography sources. The primary objective is to accomplish automatic source-receiver ranging by aligning measurements of long range acoustic arrivals to a single reference model. Acoustic arrival time structure for pulse compressed signals at long ranges is relatively stable, yet real ocean variability presents challenges in acoustic arrival matching. The presence of internal waves scatters the acoustic arrival structure and can introduce spurious arrivals in the measured data. This method takes advantage of simple projections of the measured structure onto the model space with constraints informed by scattering statistics consistent with the Garrett Munk internal wave energy spectrum. Compared to manual matching of the measured arrivals to eigenray models, more than 90% of the automatically obtained range estimates were within 150 m of the manually obtained range estimates.

A network of sound sources, hydrophone arrays and physical oceanography and biological survey equipment was established at the southern edge of the New England Shelf in May 2021 to investigate how the oceanic processes at shelfbreak regions affect underwater sound propagation. The ocean processes of particular interest include shelfbreak fronts, shelf water streamers, thermohaline intrusions, and internal waves along with other significant marine geological features and biological factors, such as seafloor slopes, submarine canyons, variable seabed properties, and fish schooling and shoaling. With fixed propagation paths, acoustic fluctuations can be correlated with environmental variations between the network nodes. The temporal scale of the acoustic measurements ranges from minutes to weeks, and the spatial coverage is up to 20–30 km. Adaptive sampling and tracking of acoustic sensitivity “hot spots” was also conducted during the experiment to assist real-time joint ocean acoustics and circulation modeling. This presentation will review the design concept of this ocean acoustic network experiment and provide an overview the preliminary results. [Work supported by the Office of Naval Research.]

Upper ocean variability depends on tides and wind forcing. The barotropic tide creates baroclinic internal tides and internal gravity waves (IGWs) that can propagate long distances and dissipate, impacting mixed layer and thermocline depths, vertical thermal gradients, and mixing. In the last decade, there has been an effort to include tidal motions in global HYCOM (HYbrid Coordinate Ocean Model). Here, we look at the impacts of tidally driven motions on acoustic propagation along the Amazon shelf by comparing acoustic transmission loss and key acoustic parameters in 1/25 deg Global HYCOM model runs with and without tides. Acoustic runs were performed at mid-frequencies using Bellhop3D at depths above and below the sonic-layer depth (SLD). Key acoustic parameters assessed include the SLD and vertical sound-speed gradients. Although the impacts of the internal waves and tides on acoustics are intermingled with the effects of other stochastic ocean processes (e.g., mesoscale eddies, fronts, and atmospheric forcing), timeseries analysis indicates that there is acoustic sensitivity to tidally forced variability. These ocean-acoustic results can be used for future development of machine learning algorithms to model coupled oceanographic and acoustical processes.

The effects of dynamic oceanographic processes in the upper ocean mixed layer on acoustic propagation are investigated using at-sea sound speed observations and acoustic transmission simulations. The sound speed environment is based on a 400 m deep and 1000 km long East-West salinity and temperature transect that was collected during April of 2005 in the North Pacific where there is a mixed layer acoustic duct with a mean depth of 89 m. The deterministic baseline of this sound speed measurement is first estimated from the observations using a spatial lowpass filter with a cut off length scale of 50-km. The remaining small length scale variations in sound speed are assumed to have two physically distinct contributions: one due to the vertical displacement of isopycnals caused by eddies and internal waves and another due to compensating temperature and salinity anomalies along isopycnals termed spice. These two contributions can be separated yielding three distinct sound speed fields: i(1) the deterministic background; (2) thedisplacement field; and (3) the spice field. Acoustic transmission loss calculations are carried out on these three fields for frequencies of 400 and 1000 Hz for sources both in and below the mixed layer duct. Statistical and deterministic results for acoustic normal modes and full field transmission loss are presented, which quantify the relative importance of displacement and spice for acoustic propagation in the upper ocean.

The three-dimensional Monterey–Miami parabolic equation model is used to simulate a nonlinear internal wave (NIW) crossing the sound field in a shallow water environment. The impetus for this research stems from acoustic measurements taken during the Shallow Water '06 (SW06) field experiment, where a NIW traversed the water column such that soliton wavecrests were nearly parallel to the source–receiver path. Horizontal refraction effects are important in this scenario. A sound speed profile adapted from experimental SW06 data is used to simulate the NIW, assuming variations along the wavecrests (e.g., curvature) are negligible. Broadband and modal energy metrics show acoustic fluctuations due to internal wave activity. Repeated model runs simulate the NIW crossing the parabolic equation (PE) field over space and time. Statistical analysis shows the PE data are best fit by a lognormal distribution but tends to an exponential distribution during certain scenarios. Small angle differences between the acoustic track and the propagating NIW cause substantial differences in energy distribution throughout the PE field. While refraction effects due to the leading edge of the NIW's arrival are important in all cases, the impacts of focusing and defocusing in the perfectly parallel case dominate the field fluctuations. In the non-parallel case, the strong fluctuations introduced by the passage of the NIW are of similar order to the refraction off the leading edge.The three-dimensional Monterey–Miami parabolic equation model is used to simulate a nonlinear internal wave (NIW) crossing the sound field in a shallow water environment. The impetus for this research stems from acoustic measurements taken during the Shallow Water '06 (SW06) field experiment, where a NIW traversed the water column such that soliton wavecrests were nearly parallel to the source–receiver path. Horizontal refraction effects are important in this scenario. A sound speed profile adapted from experimental SW06 data is used to simulate the NIW, assuming variations along the wavecrests (e.g., curvature) are negligible. Broadband and modal energy metrics show acoustic fluctuations due to internal wave activity. Repeated model runs simulate the NIW crossing the parabolic equation (PE) field over space and time. Statistical analysis shows the PE data are best fit by a lognormal distribution but tends to an exponential distribution during certain scenarios. Small angle differences between the acousti...

Nonlinear internal waves in shallow water have significant acoustic impacts and cause three-dimensional ducting effects, for example, energy trapping in a duct between curved wavefronts that propagates over long distances. A normal mode approach applied to a three-dimensional idealized parametric model [Lin, McMahon, Lynch, and Siegmann, J. Acoust. Soc. Am. 133(1), 37–49 (2013)] determines the dependence of such effects on parameters of the features. Specifically, an extension of mode number conservation leads to convenient analytical formulas for along-duct (angular) acoustic wavenumbers. The radial modes are classified into five types depending on geometric characteristics, resulting in five distinct formulas to obtain wavenumber approximations. Examples of their dependence on wavefront curvature and duct width, along with benchmark comparisons, demonstrate approximation accuracy over a broad range of physical values, even including situations where transitions in mode types occur with parameter changes. Horizontal-mode transmission loss contours found from approximate and numerically exact wavenumbers agree well in structure and location of intensity features. Cross-sectional plots show only small differences between pattern phases and amplitudes of the two calculations. The efficiency and accuracy of acoustic wavenumber and field approximations, in combination with the mode-type classifications, suggest their application to determining parameter sensitivity and also to other feature models.Nonlinear internal waves in shallow water have significant acoustic impacts and cause three-dimensional ducting effects, for example, energy trapping in a duct between curved wavefronts that propagates over long distances. A normal mode approach applied to a three-dimensional idealized parametric model [Lin, McMahon, Lynch, and Siegmann, J. Acoust. Soc. Am. 133(1), 37–49 (2013)] determines the dependence of such effects on parameters of the features. Specifically, an extension of mode number conservation leads to convenient analytical formulas for along-duct (angular) acoustic wavenumbers. The radial modes are classified into five types depending on geometric characteristics, resulting in five distinct formulas to obtain wavenumber approximations. Examples of their dependence on wavefront curvature and duct width, along with benchmark comparisons, demonstrate approximation accuracy over a broad range of physical values, even including situations where transitions in mode types occur with parameter changes...

The relation between high-frequency broadband acoustic signal variability and two types of internal waves (short-period internal solitary waves; ISWs, and semidiurnal internal tides; ITs) is investigated using data collected during the shallow-water acoustic variability experiment 2015 in the northeastern East China Sea. In this flat (∼100 m depth) region, an underwater sound channel with sound speed profile (SSP) variability observed during the experiment significantly affects the acoustic variability induced by the ISW, and the arrival structure of the channel impulse response (CIR) modeled by ray tracing. To model the range-dependent SSP due to ISW, the location and characteristics of the mode-1 ISW of wavelength (0.5–1 km) are estimated and verified based on the two-layer Korteweq–de Vries theory and by analyzing the observed temperature fluctuations. It is found from comparison between the measured and modeled CIRs that the ISW scatters the arrival structures of refracted rays. Meanwhile, semidiurnal ITs change the channel size modeled as range-independent considering the wavelengths (15–40 km) longer than the model range (3 km). Higher centroid of acoustic arrival time is found with lower isotherm depressions owing to the multimode ITs, indicative of acoustic energy focusing at the lower channel region.

Internal-wave induced sound-speed perturbations cause phase and intensity fluctuations of time-fronts. This paper focuses on predictions for broadband Transmission Losses (TL), time wander, and Scintillation Index (SI), along various sections of a typical deep water time-front. These statistics are usually predicted using Monte-Carlo Parabolic Equation (PE) simulations, or the high frequency based path-integral method. A physics based model that fully connects the wave-field statistics, and the internal wave spectrum, to the broadband statistics is not yet available. This paper uses the mode-based transport theory approach to predict the pressure field scattering at different frequencies, and from that the broadband statistics. This requires calculations for cross-modal correlations over mode number and frequency, which becomes computationally intensive for large bandwidths. This paper considers the adiabatic phase coherence to simplify the computations, and tests the final predictions against PE simulations and observations from the Philippine Sea 2010 experiment.

A scaled experiment in a water tank was conducted to study effects of medium heterogeneities on underwater acoustic propagation while controlling the so-called fluctuations. An ultrasonic wave is transmitted (a pulse train at center frequency f = 2.25 MHz) throughout an acoustic lens presenting a plane input face and a randomly rough output face inducing spatial fluctuations of the sound pressure field. The roughness statistics are tuned so that the fluctuating pressure field presents features comparable to what can be observed in the case of acoustic waves propagating through a fluctuating ocean. Generally speaking, disturbances can include path propagation delays, multipath dependent Doppler spreading, scattering from the sea surface or bottom, and coherence loss over the array aperture arising from dynamic wave-front fluctuations due to internal waves. This last topic is the main focus of our study. Signal snapshots received at a virtual, vertical line array of 64 sensors may be corrupted by impulsive (heavy-tailed) additive noise and high resolution outlier-resistant arrival angle identification is desirable. Recent advances in robust techniques such as Sparse Bayesian Learning and L1 -norm Principal Component Analysis motivate this work. We compare the performance of these innovative techniques to the classical MUSIC and Bartlett processors. [This work is supported by DGA, NSF Grant CNS1753406, ONR.]

Seismic oceanography is a new interdiscipline which uses “legacy” marine seismic reflection data collected by the oil industry to image ocean water columns like eddies and internal waves. Unlike seafloor reflections, ocean water-column reflections are typically weak due to the low acoustic impedance contrast, which challenges seismic oceanography. Utilization of the acoustic characteristics of low-frequency, broadband airgun source can enhance water-column signals for better ocean seismic imaging. Acoustics characteristics of received direct-path, water-column, and seafloor signals are analyzed and applied to design adaptive filtering process to enhance water-column signals. The processing increases the signal-to-noise ratio of water-column signal and attenuates the direct waves without changing the spectral content of the airgun source. The results can be useful to improve seismic oceanography by providing better imaging of ocean water columns.

Random matrix theory originated as the statistical theory of strongly interacting quantum systems, and has since been applied in an extremely broad range of applications. For example, it has been developed to accurately and efficiently model long range acoustic propagation in the ocean, including the construction of propagating acoustic time fronts. This problem can be viewed as dynamical symmetry breaking, i.e., the breaking of integrability, which has been explored in a variety of quantum mechanical contexts. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. In addition to its efficiency, the theory helps identify which information about the ocean environment can be deduced from the timefronts and how to connect features of the data to that environmental information. It also makes direct connections to methods used in other disordered wave guide contexts where the use of random matrix theory has a multi-decade history.

The variability of the interference pattern of a narrow-band sound signal in a shallow water waveguide in the horizontal plane in the presence of horizontal stratification, in particular due to linear internal waves, is studied. It is shown that lines of constant phase (a phase front) and lines of constant amplitude/envelope (an amplitude front) for each waveguide mode may have different directions in the spatial vicinity of the point of reception. The angle between them depends on the waveguide's parameters, the mode number, and the sound frequency. Theoretical estimates and data processing methodology for obtaining these angles from experimental data recorded by a horizontal line array are proposed. The behavior of the angles, which are obtained for two episodes from the Shallow Water 2006 (SW06) experiment, show agreement with the theory presented.

Ocean acoustic tomography depends on a suitable reference ocean environment with which to set the basic parameters of the inverse problem. Some inverse problems may require a reference ocean that includes the small-scale variations from internal waves, small mesoscale, or spice. Tomographic inversions that employ data of stable shadow zone arrivals, such as those that have been observed in the North Pacific and Canary Basin, are an example. Estimating temperature from the unique acoustic data that have been obtained in Fram Strait is another example. The addition of small-scale variability to augment a smooth reference ocean is essential to understanding the acoustic forward problem in these cases. Rather than a hindrance, the stochastic influences of the small scale can be exploited to obtain accurate inverse estimates. Inverse solutions are readily obtained, and they give computed arrival patterns that matched the observations. The approach is not ad hoc, but universal, and it has allowed inverse estimates for ocean temperature variations in Fram Strait to be readily computed on several acoustic paths for which tomographic data were obtained.

The coherence length of a horizontal array is the maximum separation between two points where coherent processing gives useful gain when a distant source is at broadside. In shallow water, the coherence length is limited by the environmental variability caused by several relevant oceanographic processes. In the present study, a statistical model is developed that quantifies how one oceanographic process, linear internal waves, affects the coherence length. A key input to the ocean sub-model is the vertically integrated energy density of the internal wave field. The acoustic sub-model is based on the adiabatic normal mode approximation and so should be reasonable for frequencies under 1 kHz. Numerical calculations using environmental data from the Shallow Water 2006 Experiment (SW06) show how the coherence length of individual modes varies with consequent effects on array coherence. The coherence length is shown to be a strong function of where the source and array are positioned in the water column. For a bottom-mounted array above a moderately lossy seabed, the model predicts a coherence length that depends only weakly on range, an effect observed in field experiments.

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.

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.

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.

The tympanic membrane model as developed by Parent and Allen [(2007). J. Acoust. Soc. Am. 122(2), 918–931] is shown to have active, lossy, and non-reciprocal properties despite being described as lossless. These properties are traced back to its scattering junction formulations. Some impedance parameters are shown to have ambiguous values which complicate interpreting the physics of the model's internal wave propagation. Certain model parameters omitted from the original paper have been derived from the original computer simulation source code used by Parent and Allen.

A fully three-dimensional coupled mode approach is used in this paper to describe the physics of low frequency acoustic signals propagating through a train of internal waves at an arbitrary azimuth. A three layer model of the shallow water waveguide is employed for studying the properties of normal modes and their coupled interaction due to the presence of nonlinear internal waves. Using a robust wave number integration technique for Fourier transform computation and a direct global matrix approach, an accurate three-dimensional coupled mode full field solution is obtained for the tonal signal propagation through straight and parallel internal waves. This approach provides accurate results for arbitrary azimuth and includes the effects of backscattering. This enables one to provide an azimuthal analysis of acoustic propagation and separate the effects of mode coupled transparent resonance, horizontal reflection and refraction, the horizontal Lloyd's mirror, horizontal ducting and anti-ducting, and horizontal tunneling and secondary ducting.

The authors present an acoustic system, designed by DGA Naval Systems, dedicated to the study of sound propagation in challenging environments. The system is called ALMA for Acoustic Laboratory for Marine Applications. Shallow and coastal waters, where oceanographic phenomena (such as linear internal waves, tides and 3-D effects) interact with acoustic propagation, represent the main area of deployments. Since 2014, 5 at-sea campaign have been successfully conducted in the Mediterranean Sea and in the Atlantic Ocean. They mainly consisted in propagating sound waves in the 1–15 kHz frequency band using fixed or towed sources towards a modular passive acoustic array. The latter is composed of 8 rigid arms carrying 16 hydrophones each. These arms can be, and actually were, arranged in various shapes, depending on the goal of the experiment. Environmental sensing using thermistor strings and CTD cast complete the experimental equipment. The analysis of the 2016 campaign demonstrates the ability of the system ...

We consider the problem of robust direction-of-arrival (DoA) estimation in dynamic ocean environments. Robust direction finding of underwater acoustic signals transmitted from known locations may enable accurate underwater localization and enhance link communication rate by instructing a receiver to listen for transmissions from a specific direction. We propose to estimate the DoA of underwater acoustic signals via subspace methods, executed at a very large receiver array, that involve performing what is known as principal-component analysis (PCA) for finding the L2-norm principal vector subspace of the recorded signal snapshots. However, in practice coherence loss, which typically arises from dynamic wavefront fluctuations due to internal waves, scattering from the sea surface and/or bottom and other unknown environmental parameters, may result in recorded signal snapshots that are corrupted by faulty measurements, leading to an inaccurate estimation of the DoA and source position. We propose to model the loss of coherence as multiplicative random noise applied to the measured acoustic signal. In such cases, L2-norm PCA methods suffer from significant performance degradation. Motivated by the resistance of novel L1-nrom-derived subspaces against the impact of irregular, highly deviating points in reduced-dimensionality data approximations, we propose to employ L1-norm (absolute error) maximum projection PCA of the antenna array measurements and evaluate the performance of a novel, outlier-resistant DoA estimation algorithm.

From April 2010 to March 2011, low frequency acoustic transmissions were carried out on a 330-km radius pentagonal acoustic array with a sixth transceiver in the middle in the Philippine Sea. Herein, we describe the fluctuation statistics of the signals originating on the six transceivers and recorded on a water column spanning receiver array located slightly off center of the pentagon. The signals analyzed here are interpretable in terms of specific acoustic ray paths clearly separable in time. Acoustic field statistics treated include (1) variances of phase and intensity, (2) vertical coherence and intensity covariance, (3) glinting and fade out rates, and (4) intensity probability density functions. Several of these observables are compared to predictions from Feynman path integral theory assuming the Garrett-Munk internal wave model suitably modified using Philippine Sea oceanographic observations. Data and theory differ by at most a factor of 2 and reveal the wave propagation regimes of unsaturated, and partially saturated.

Synthetic aperture sonar imagery often captures features that appear similar to sand waves but are actually pockets of denser water traveling as isolated waves along the seafloor. These pockets of cold water refract acoustic waves like a lens, causing intensity peaks and shadows that resemble medium to large scale sand waves. This work uses dynamic ray tracing to predict the intensity return as affected by refraction. First, we explore the nature of the intensity pattern created by internal waves of various shapes and sizes. Then, we use an optimization-based approach to solve the inverse problem: given an intensity pattern, determine the size, shape, and location of the internal wave that created it.Synthetic aperture sonar imagery often captures features that appear similar to sand waves but are actually pockets of denser water traveling as isolated waves along the seafloor. These pockets of cold water refract acoustic waves like a lens, causing intensity peaks and shadows that resemble medium to large scale sand waves. This work uses dynamic ray tracing to predict the intensity return as affected by refraction. First, we explore the nature of the intensity pattern created by internal waves of various shapes and sizes. Then, we use an optimization-based approach to solve the inverse problem: given an intensity pattern, determine the size, shape, and location of the internal wave that created it.

Deep seafloor (~5000 m) observations of seismoacoustic arrivals are presented from the Aloha Cabled Observatory (ACO), Hawaii-2 Observatory (H20), and Ocean Seismic Network-1 (OSN1). Acoustic observations of local earthquakes from the ACO 24 kHz hydrophone show extraordinarily high frequencies up to 165 Hz at distances to ~200 km—a unique window into earthquake source dynamics. Combined seismic and hydrophone observations show that the traditional T wave propagates as a seismoacoustic polarized interface wave “Ti” coupled to the seafloor. Seismoacoustic Ti waves propagating at the sound speed of water are routinely observed over megameter distances at H2O between Hawaii and California, even though the seafloor site is within the shadow zone for acoustic wave propagation. Internal waves or thermohaline covariation may or may not be sufficient to scatter acoustic energy from the SOFAR channel to the deep seafloor. Ti has also been observed on seismometers SSW of Oahu at the OSN1 site at the seafloor and within an ODP borehole 242 m into the basalt basement. The observation of Ti from an earthquake in Guatemala at OSN1, whose path is blocked by the Island of Hawaii, is consistent with scattering from the vicinity of the Cross Seamount.

Recent technological advances in high-frequency (>10 kHz) sonar transducers, sonar transceivers, and sonar design have been accompanied by increased capabilities for observing ocean phenomena. These advances include the high range resolution and frequency-domain target classification capabilities associated with wideband acoustic echo sounders, the long-range high-resolution synoptic imaging capabilities associated with multibeam echo sounders and synthetic aperture sonar, and an increased focus on sensor calibration for all systems. High-frequency sonars are increasingly being used to quantify ocean phenomena at scales ranging from sub-centimeter (e.g., individual gas bubbles) to 100s of km (e.g., internal waves) to several 10s of km (e.g., thermohaline staircases). In this talk, we highlight some of the ocean processes that we have been investigating using high-frequency sonar systems, typically involving the transport of hydrocarbons, heat, energy, and fresh water into and through the ocean, and some of the (many) acoustic challenges that must be overcome to continue to increase the value of these observations.

Caustics are a form of natural focusing that occurs in deep water acoustic propagation, but acoustic intensity and position perturbations at caustics have not been investigated in detail. The positions, shapes, and intensities of caustics and cusps are controlled primarily by the large-scale sound speed profile, with perturbations primarily caused by deterministic features (fronts, eddies) and stochastic features (internal waves). We selected two representative deep water environments for our analysis: a north Pacific site and temperate profile. For each region, 100 independent and 100 time-coherent realizations of internal waves were generated. The model uses the statistics provided by the Garrett-Munk power spectrum to generate displacements, which are converted into sound speed realizations. In the north Pacific profile, internal waves were concentrated primarily in the upper 200 m of water. In the temperate profile, internal waves were concentrated in the upper 700 m of water. We used a Gaussian beam model to analyze position and intensity statistics of caustics for both types (independent and time-coherent) of internal wave fields at each site as a function of frequency, internal wave strength, and source depth. Simulations indicate that caustics are more stable than other portions of the acoustic field and that this stability is a function of internal wave strength and caustic location. This work is approved for public release, Distribution Unlimited.Caustics are a form of natural focusing that occurs in deep water acoustic propagation, but acoustic intensity and position perturbations at caustics have not been investigated in detail. The positions, shapes, and intensities of caustics and cusps are controlled primarily by the large-scale sound speed profile, with perturbations primarily caused by deterministic features (fronts, eddies) and stochastic features (internal waves). We selected two representative deep water environments for our analysis: a north Pacific site and temperate profile. For each region, 100 independent and 100 time-coherent realizations of internal waves were generated. The model uses the statistics provided by the Garrett-Munk power spectrum to generate displacements, which are converted into sound speed realizations. In the north Pacific profile, internal waves were concentrated primarily in the upper 200 m of water. In the temperate profile, internal waves were concentrated in the upper 700 m of water. We used a Gaussian beam ...

The mixed layer and upper ocean are a region of immense interest to physical oceanographers, meteorologists, and climate scientists because this is the boundary through which energy, momentum, buoyancy, and gasses are exchanged between the ocean and the atmosphere. The upper ocean is also a rich ecosystem for a vast array of ocean organisms and marine wildlife as well as a region of great Naval tactical importance. Given these factors, it is rather surprising that ocean acoustics has paid little attention to this significant region, aside from very high-frequency studies of bubble properties and gas entrainment. From the standpoint of transmission loss, the major work on the problem seems to go back to the Acoustic, Meteorological, Oceanographic Survey (AMOS) of the mid-50s. Here, a review is presented of relevant ocean processes that may be important for acoustic propagation at frequencies ranging from several hundreds of hertz to several kilohertz, where the foundation of the analysis is normal mode and transport theory. Processes of interest are surface gravity waves including subsurface currents, internal waves and tides, wind driven inertial oscillations and Langmuir circulations, eddies and submesoscale processes, turbulence and spice, bubbles, and fishes.

In this paper, acoustical noise intensity fluctuations recorded by single hydrophones (SHRUs) in the Shallow Water 2006 experiment are studied. The area of experiment (New Jersey Atlantic shelf) is characterized by a remarkable activity of internal waves, in particular, approximately twice per day trains of nonlinear internal waves (NIW) consisting of up to ten separate peaks with the amplitudes about 10–15 m and wave front parallel to the coastal line move toward the beach. During its motion trains of NIW cross positions of five SHRUs, located about 5–8 km to each other along line perpendicular to the coast as well as thermistor’s strings which allow us to estimate the shape and evolution of trains while they are propagating. It is shown that the appearance of irregular wideband sound field (amplitude by up to 20–40 dB greater than noise background) takes place when the train of NIW is passing through the location of the corresponding SHRUs. The nature of these signals is discussed, and the spectrum and specific temporal variations as well as other characteristics are analyzed. [Work was supported by ONRG, NSF, and BSF.] In this paper, acoustical noise intensity fluctuations recorded by single hydrophones (SHRUs) in the Shallow Water 2006 experiment are studied. The area of experiment (New Jersey Atlantic shelf) is characterized by a remarkable activity of internal waves, in particular, approximately twice per day trains of nonlinear internal waves (NIW) consisting of up to ten separate peaks with the amplitudes about 10–15 m and wave front parallel to the coastal line move toward the beach. During its motion trains of NIW cross positions of five SHRUs, located about 5–8 km to each other along line perpendicular to the coast as well as thermistor’s strings which allow us to estimate the shape and evolution of trains while they are propagating. It is shown that the appearance of irregular wideband sound field (amplitude by up to 20–40 dB greater than noise background) takes place when the train of NIW is passing through the location of the corresponding SHRUs. The nature of these signals is discussed, and the spectrum and...

In the spring of 2009, broadband transmissions from a ship-suspended source with a 284-Hz center frequency were received on a moored and navigated vertical array of hydrophones over a range of 107 km in the Philippine Sea. During a 60-h period over 19,000 transmissions were carried out. The observed wavefront arrival structure reveals four distinct purely refracted acoustic paths: One with a single upper turning point near 80 m depth, two with a pair of upper turning points at a depth of roughly 300 m, and one with three upper turning points at 420 m. Individual path intensity, defined as the absolute square of the center frequency Fourier component for that arrival, was estimated over the 60-h duration and used to compute scintillation index and log-intensity variance. Monte Carlo parabolic equation simulations using internal-wave induced sound speed perturbations obeying the Garrett-Munk internal-wave energy spectrum were in agreement with measured data for the three deeper-turning paths but differed by as much as a factor of four for the near surface-interacting path.

Clutter is related to false alarms for active sonar. It is demonstrated that, in shallow water, target-like clutter in reverberation signals can be caused by nonlinear internal waves. A nonlinear internal wave is modeled using measured stratification on the New Jersey shelf. Reverberation in the presence of the internal wave is modeled numerically. Calculations show that acoustic energy propagating near a sound speed minimum is deflected as a high intensity, higher angle beam into the bottom, where it is backscattered along the reciprocal path. The interaction of sound with the internal wave is isolated in space, hence resulting in a target-like clutter, which is found to be greater than 10 dB above the mean reverberation level.

Measurements of acoustic ray travel-times in the ocean provide synoptic integrals of the ocean state between source and receiver. It is known that the ray travel-time is sensitive to variations in the ocean at the transmission time, but the sensitivity of the travel-time to spatial variations in the ocean prior to the acoustic transmission have not been quantified. This study examines the sensitivity of ray travel-time to the temporally and spatially evolving ocean state in the Philippine Sea using the adjoint of a numerical model. A one year series of five day backward integrations of the adjoint model quantify the sensitivity of travel-times to varying dynamics that can alter the travel-time of a 611 km ray by 200 ms. The early evolution of the sensitivities reveals high-mode internal waves that dissipate quickly, leaving the lowest three modes, providing a connection to variations in the internal tide generation prior to the sample time. They are also strongly sensitive to advective effects that alter density along the ray path. These sensitivities reveal how travel-time measurements are affected by both nearby and distant waters. Temporal nonlinearity of the sensitivities suggests that prior knowledge of the ocean state is necessary to exploit the travel-time observations.

The article of record as published may be found at https://doi.org/10.1121/1.4789358 Internal waves and bathymetric variation create time- and space-dependent alterations in the ocean acoustic waveguide, and cause subsequent coupling of acoustic energy between propagating normal modes. In this paper, the criterion for adiabatic invariance is extended to the case of an internal solitary wave (ISW) encountering a sloping bathymetry (i.e., continental shelfbreak). Predictions based on the extended criterion for adiabatic invariance are compared to experimental observations from the Asian Seas International Acoustics Experiment. Using a mode 1 starter field, results demonstrate time-dependent coupling of mode 1 energy to higher adjacent modes, followed by abrupt coupling of mode 5–7 energy to nonadjacent modes 8–20, produces enhanced mode coupling and higher received levels downrange of the oceanographic and bathymetric features. Numerical simulations demonstrate that increasing ISW amplitude and seafloor slope enhance the coupling of energy to adjacent and nonadjacent modes. This enhanced coupling is the direct result of the simultaneous influence of the ISW and its proximity to the shelfbreak, and, compared to the individual effect of the ISW or shelfbreak, has the capacity to scatter 2–4 times the amount of acoustic energy from below the thermocline into the upper water column beyond the shelfbreak in realistic environments. The ASIAEX and NLIWI experiments were supported jointly by the National Science Council of Taiwan and the U.S. Office of Naval Research.

The hypothesis tested is that internal gravity waves limit the coherent integration time of sound at 1346 km in the Pacific ocean at 133 Hz and a pulse resolution of 0.06 s. Six months of continuous transmissions at about 18 min intervals are examined. The source and receiver are mounted on the bottom of the ocean with timing governed by atomic clocks. Measured variability is only due to fluctuations in the ocean. A model for the propagation of sound through fluctuating internal waves is run without any tuning with data. Excellent resemblance is found between the model and data's probability distributions of integration time up to five hours.

Acoustic tomography systems have been deployed in Fram Strait over the past decade to complement existing observing systems there. The observed acoustic arrival patterns are unusual, however, consisting of a single, broad arrival pulse, with no discernible repeating patterns or individual ray arrivals. The nature of these arrivals is caused by vigorous acoustic scattering from the small-scale processes that dominate ocean variability in Fram Strait. Simple models for internal wave and mesoscale variability were constructed and tailored to match the variability observed by moored thermisters in Fram Strait. The internal wave contribution to variability is weak. Acoustic propagation through a simulated ocean consisting of a climatological sound speed plus mesoscale and internal wave scintillations obtains arrival patterns that match the characteristics of those observed, i.e., pulse width and travel time variation. The scintillations cause a proliferation of acoustic ray paths, however, reminiscent of “ray chaos.” This understanding of the acoustic forward problem is prerequisite to designing an inverse scheme for estimating temperature from the observed travel times.

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

Internal Kelvin waves (IKWs) initiated by rotation of the Earth are one of the main hydrodynamic phenomena in large stratified lakes where baroclinic Rossby radius of deformation is smaller than the horizontal scale of the lake. IKWs can be identified using the spectra of internal waves, where in the presence of IKWs, the inertial frequency is at maximum. IKWs play a rather important role in the lake's dynamics for different processes, both in the water layer and sediment, especially at the periphery of lake. Due to influence of internal waves on the sound propagation, acoustical methods can be used for estimation of behaviour of IKWs. In this paper, the spatiotemporal variability of the mid-frequency (∼1 kHz) sound field in the presence of IKWs in a deep stratified Lake Kinneret is studied using numerical simulations based on normal-mode theory. Due to the specific character of perturbation of the water layer, IKWs can cause specific variations of interference pattern, in particular, a significant shift of the sound interference pattern both in spatial and frequency domain. These shifts can be easily measured and used for reconstruction of IKW parameters.

A theory of guided propagation of sound in layered, moving fluids is extended to include acoustic-gravity waves (AGWs) in waveguides with piecewise continuous parameters. The orthogonality of AGW normal modes is established in moving and motionless media. A perturbation theory is developed to quantify the relative significance of the gravity and fluid compressibility as well as sensitivity of the normal modes to variations in sound speed, flow velocity, and density profiles and in boundary conditions. Phase and group speeds of the normal modes are found to have certain universal properties which are valid for waveguides with arbitrary stratification. The Lamb wave is shown to be the only AGW normal mode that can propagate without dispersion in a layered medium.

Experimental observations and theoretical studies show that nonlinear internal waves occur widely in shallow water and cause acoustic propagation effects including ducting and mode coupling. Horizontal ducting results when acoustic modes travel between internal wave fronts that form waveguide boundaries. For small grazing angles between a mode trajectory and a front, an interference pattern may arise that is a horizontal Lloyd mirror pattern. An analytic description for this feature is provided along with comparisons between results from the formulated model predicting a horizontal Lloyd mirror pattern and an adiabatic mode parabolic equation. Different waveguide models are considered, including boxcar and jump sound speed profiles where change in sound speed is assumed 12 m/s. Modifications to the model are made to include multiple and moving fronts. The focus of this analysis is on different front locations relative to the source as well as on the number of fronts and their curvatures and speeds. Curvature influences mode incidence angles and thereby changes the interference patterns. For sources oriented so that the front appears concave, the areas with interference patterns shrink as curvature increases, while convexly oriented fronts cause patterns to expand.

The article of record as published may be found at https://doi.org/10.1121/1.3666014 Environmental sensors moored on the New Jersey continental shelf tracked constant density surfaces (isopycnals) for 35 days in the summer of 2006. Sound-speed fluctuations from internal-wave vertical isopycnal displacements and from temperature/salinity variability along isopycnals (spiciness) are analyzed using frequency spectra and vertical covariance functions. Three varieties of internal waves are studied: Diffuse broadband internal waves (akin to waves fitting the deep water Garrett/Munk spectrum), internal tides, and, to a lesser extent, nonlinear internal waves. These internal-wave contributions are approximately distinct in the frequency domain. It is found that in the main thermocline spicy thermohaline structure dominates the root mean square sound-speed variability, with smaller contributions coming from (in order) nonlinear internal waves, diffuse internal waves, and internal tides. The frequency spectra of internal-wave displacements and of spiciness have similar form, likely due to the advection of variable-spiciness water masses by horizontal internal-wave currents, although there are technical limitations to the observations at high frequency. In the low-frequency, internal-wave band the internal-wave spectrum follows frequency to the −1.81 power, whereas the spice spectrum shows a −1.73 power. Mode spectra estimated via covariance methods show that the diffuse internal-wave spectrum has a smaller mode bandwidth than Garrett/Munk and that the internal tide has significant energy in modes one through three. This work was supported by the Office of Naval Research, and Professor Colosi gratefully acknowledges his additional support from the Naval Postgraduate School’s Undersea Warfare Chair that he holds.

Oceanic intrusions and internal waves can each be imaged with echo sounders for dynamics and flux studies. We have recently investigated signatures of intrusions, while internal-wave imaging is long established, with Farmer as a leader. Intrusive flow at fronts with counteracting temperature and salinity gradients along isopycnals is one of many mixing phenomena in the ocean. Advection within the intrusions is accompanied by diapycnal mixing above and below that may provide buoyant forcing. Probable double-diffusive mixing processes can create sharp interfaces and microstructure that can provide intrusion-following echo patterns. This backscattering is weaker than that from shear-generated turbulence microstructure, but it can be spatially coherent along intrusions and thus robustly detectable. Mapping of intrusion features with a shipboard system using this method may enable targeted physical measurements within intrusions to advance our knowledge, and can provide 2D structure maps if augmenting dropped ...

Temporal coherence of acoustic signals propagating in a fluctuating ocean is important for many practical applications and has been studied intensively experimentally. However, only a few theoretical formulations of temporal coherence exist. In the present paper, a three-dimensional (3D) modal theory of sound propagation in a fluctuating ocean is used to derive closed-form equations for the spatial-temporal coherence function of a broadband signal. The theory is applied to the analysis of the temporal coherence of a monochromatic signal propagating in an ocean perturbed by linear internal waves obeying the Garrett-Munk (G-M) spectral model. In particular, the temporal coherence function is calculated for propagation ranges up to 10(4) km and for five sound frequencies: 12, 25, 50, 75, and 100 Hz. Then, the dependence of the coherence time (i.e., the value of the time lag at which the temporal coherence decreases by a factor of e) on range and frequency is studied. The results obtained are compared with experimental data and predictions of the path-integral theory.

Several recent field efforts have revealed surprisingly complex and dynamic thermohaline structure in the upper ocean of the Beaufort Sea. Solitary and compact eddies with strong temperature contrasts and currents have been observed in multiple locations and are associated with vigorous mixing, staircase structure and intrusive feature formation. While many of the eddies are primarily found in the upper 300-m of the water column, rare deep eddies with cores near 500 to 1000-m depth have also been observed. Internal waves are generally weak with energies an order of magnitude less than mid-latitude values and they show marked dominance by near inertial waves, intermittency, spatial inhomogeneity, and deviations from the Garrett-Munk model. Strong intrusive structure, termed spice, is observed in the upper 150-m of the water column and is associated with the mixed layer and eddy activity. Acoustic implications of the associated sound speed structure will be discussed.

Six acoustic sources arranged in a pentagon with a central point transmitted broadband signals in the frequency range 200–300 Hz to a water column spanning vertical array in the Philippine Sea from Spring 2010 to Spring 2011. The propagation ranges were 128, 210, 224, 379, 396, and 449 km. Observations of phase and intensity variance as well as vertical coherence were obtained for several ray identified wavefronts. These observations are compared to Feynman path integral theory predictions utilizing Garrett-Munk internal wave spectral fits to in-situ measurements of temperature, salinity, and current. The observations and theory suggest that the three shortest ranges are in the unsaturated regime while the three longer ranges are in the partially saturated regime. Vertical coherence lengths are well predicted by theory. Implications for future experiments designed to observe internal wave spectra acoustically will be discussed. Six acoustic sources arranged in a pentagon with a central point transmitted broadband signals in the frequency range 200–300 Hz to a water column spanning vertical array in the Philippine Sea from Spring 2010 to Spring 2011. The propagation ranges were 128, 210, 224, 379, 396, and 449 km. Observations of phase and intensity variance as well as vertical coherence were obtained for several ray identified wavefronts. These observations are compared to Feynman path integral theory predictions utilizing Garrett-Munk internal wave spectral fits to in-situ measurements of temperature, salinity, and current. The observations and theory suggest that the three shortest ranges are in the unsaturated regime while the three longer ranges are in the partially saturated regime. Vertical coherence lengths are well predicted by theory. Implications for future experiments designed to observe internal wave spectra acoustically will be discussed.

The travel time for end of the final finale is often used is in inversion algorithms for acoustic tomography experiments when there is impreciseness due to ship and mooring positions and/or motions. The rationale is the first mode has the maximum slowness and higher order ones must arrive earlier, so the finale must solely be composed of energy from the first mode. This places a constraint on the tomographic sections, e.g., on the summation of the ray path or mode group slownesses. In a two papers Dozier and Tappert (JASA, 1978) examined the re population of the mode space for signals propagating in a stochastic ocean described by a Garrett & Munk model for internal waves. In the limit of an energy conserving ocean, i.e. no loss through boundaries, the limit of the population goes to an equipartition population density which was verified by numerical experiments. For more realistic oceans with boundary losses, the limit is a race between loss and scattering. This complicates what can be well identified as mode one at long ranges at low SNR's. We perform a numerical experiment by spatial filtering for mode one along the range dependent path to select just its energy in the finale. Earlier NUMERICAL studies by the author, (JASA, 1998) suggests just five percent of the energy remained at one megameter ranges with a 1/2 Garrett/Munk ocean. [Work supported by ONR.]The travel time for end of the final finale is often used is in inversion algorithms for acoustic tomography experiments when there is impreciseness due to ship and mooring positions and/or motions. The rationale is the first mode has the maximum slowness and higher order ones must arrive earlier, so the finale must solely be composed of energy from the first mode. This places a constraint on the tomographic sections, e.g., on the summation of the ray path or mode group slownesses. In a two papers Dozier and Tappert (JASA, 1978) examined the re population of the mode space for signals propagating in a stochastic ocean described by a Garrett & Munk model for internal waves. In the limit of an energy conserving ocean, i.e. no loss through boundaries, the limit of the population goes to an equipartition population density which was verified by numerical experiments. For more realistic oceans with boundary losses, the limit is a race between loss and scattering. This complicates what can be well identified as...

Deep acoustic shadow-zone arrivals observed in the late 1990s in the North Pacific Ocean reveal significant acoustic energy penetrating the geometric shadow. Comparisons of acoustic data obtained from vertical line arrays deployed in conjunction with 250-Hz acoustic sources at ranges of 500 and 1000 km from June to November 2004 in the North Pacific, with simulations incorporating scattering consistent with the Garrett-Munk internal-wave spectrum, are able to describe both the energy contained in and vertical extent of deep shadow-zone arrivals. Incoherent monthly averages of acoustic timefronts indicate that lower cusps associated with acoustic rays with shallow upper turning points (UTPs), where sound-speed structure is most variable and seasonally dependent, deepen from June to October as the summer thermocline develops. Surface-reflected rays, or those with near-surface UTPs, exhibit less scattering due to internal waves than in later months when the UTP deepens. Data collected in November exhibit dramatically more vertical extension than previous months. The depth to which timefronts extend is a complex combination of deterministic changes in the depths of the lower cusps as the range-average profiles evolve with seasonal change and of the amount of scattering, which depends on the mean vertical gradients at the depths of the UTPs.