Cost-effective seafloor mapping at high resolution is yet to be attained. A possible solution consists of using a mobile, wide-aperture, sparse array with subarrays distributed across multiple autonomous surface vessels. Such wide-area mapping with multiple dynamic sources and receivers require accurate modeling and processing systems for imaging the seabed. In this paper, we focus on computational schemes and challenges for such high-resolution acoustic imaging or migration. Starting from the imaging condition from the adjoint-state method, we derive a closed-form expression for Gaussian beam migration in stratified media. We employ this technique on simulated data and on real data collected with our novel acoustic array over shipwrecks in the Boston Harbor. We compare Gaussian beam migration with diffraction stack and Kirchhoff migration, and we find that Gaussian beam migration produces the clearest images with the fewest artifacts.

The multi-scale dynamics of oceanic processes and the complex propagation of acoustic waves are fundamental challenges in marine sciences and operations. Recent computing advances enable such multiresolution ocean and acoustic modeling, but a fully integrated system for sustained coupled predictions and Bayesian data assimilation remains needed. In this study, we integrate the MSEAS Primitive Equation (PE) ocean modeling system and the MSEAS acoustic Parabolic Equation (ParEq) solver, enabling real-time coupled ocean and acoustic predictions. Realistic applications in Massachusetts Bay, the Norwegian Sea, the western Mediterranean Sea, and the New York Bight are used to demonstrate capabilities and validate predictions in diverse shallow and deep-water environments. Results provide the foundation for an end-to-end system for coupled ocean-acoustic probabilistic modeling, Bayesian inversion, and learning.

Developing accurate and computationally efficient models for underwater sound propagation in the uncertain, dynamic ocean environment is inherently challenging. In this work, we evaluate the potential of dynamic reduced-order modeling for stochastic ray tracing. We obtain and implement the stochastic dynamically-orthogonal (DO) differential equations for Ray Tracing (DO-Ray). With stochastic DO-Ray, we can start from non-Gaussian environmental uncertainties and compute the stochastic acoustic ray fields in a dynamic reduced order fashion, all while preserving the dominant complex statistics of the ocean environment and the nonlinear relations with ray dynamics. We develop varied algorithms and discuss implementation challenges and solutions, using direct Monte Carlo for comparison. We showcase results in an uncertain deep-sound channel example and observe the ability to represent the stochastic ray trace fields in a dynamic reduced-order fashion.

Accurate and computationally efficient acoustic models are needed for varied marine applications. In this paper, we focus our attention on forward models, which are essential to inverse problems such as imaging and mapping. First, we introduce new dynamically orthogonal (DO) equations for the acoustic wave equation in full generality, allowing for stochastic and spatially heterogeneous parameters. These equations may be spatially discretized and integrated in time numerically. Alternatively, the DO equations may be discretized themselves, admitting a non-intrusive reduced-order approach to solve the stochastic wave equation. We demonstrate the latter with a test case of an acoustic pulse traveling through the ocean with an uncertain sound speed. Second, we adapt the spatially discrete DO approach, typically used to reduce the stochastic dimension, to efficient reduced-order modeling of deterministic 3D acoustic propagation. We solve the 3D parabolic wave equation and show that low-rank solutions rapidly converge to the full-rank solution. Together, these approaches offer novel ways to solve stochastic and deterministic problems with strong or weak scattering at a reduced computational cost.

The widely-used Global Positioning System (GPS) does not work underwater. This presents a severe limitation on the communication capabilities and deployment options for undersea assets such as AUVs and UUVs. To address this challenge, the Positioning System for Deep Ocean Navigation (POSYDON) program aims to develop an undersea system that provides omnipresent, robust positioning across ocean basins. To do so, it is critically important to accurately model sound waves and signals under diverse, and often uncertain, undersea environmental conditions. Probabilistic estimates of the four-dimensional variability of the fields of sound speed, salinity, temperature, and currents are thus needed. In this paper, we employ our MSEAS primitive-equation and error subspace data-assimilative ensemble ocean forecasting system during two real-time POSYDON sea exercises, one in winter 2017 and another in August 2018. We provide real-time high-resolution estimates of sound speed fields and their uncertainty, and describe the ocean conditions from submesoscales eddies and internal tides to warm core rings and larger-scale circulations. We verify our results against independent data of opportunity; in all cases, we show that our probabilistic forecasts demonstrate skill.

The reliability of sonar systems in the littoral environment is greatly affected by the variability of the surrounding nonlinear ocean dynamics. This variability occurs on multiple scales in space and time, and involves multiple interacting processes, from internal tides and waves to meandering fronts, eddies, boundary layers, and strong air-sea interactions. We utilize our high-resolution MSEAS-PE ocean modeling system to hindcast the ocean physical environment off the New Jersey continental shelf for the end of June 2009, and then utilize our new MSEAS probabilistic acoustic NAPE and WAPE solvers in a coupled ocean physics-acoustic modeling fashion to predict the transmission and integrated transmission losses, respectively. The coupled models are described, and their predictions verified against independent ocean physics observations and sound propagation measurements from acoustic sources and receivers in the region. Our high-resolution ocean simulations are shown to substantial reduce the RMSE and bias of the coarser simulations. Our acoustic simulations of deterministic and stochastic TL fields also show significant skill.

Covering the vast majority of our planet, the ocean is still largely unmapped and unexplored. Various imaging techniques researched and developed over the past decades, ranging from echo-sounders on ships to LIDAR systems in the air, have only systematically mapped a small fraction of the seafloor at medium resolution. This, in turn, has spurred recent ambitious efforts to map the remaining ocean at high resolution. New approaches are needed since existing systems are neither cost nor time effective. One such approach consists of a sparse aperture mapping technique using autonomous surface vehicles to allow for efficient imaging of wide areas of the ocean floor. Central to the operation of this approach is the need for robust, accurate, and efficient inference methods that effectively provide reliable estimates of the seafloor profile from the measured data. In this work, we utilize such a stochastic prediction and Bayesian inversion and demonstrate results on benchmark problems. We first outline efficient schemes for deterministic and stochastic acoustic modeling using the parabolic wave equation and the optimally-reduced Dynamically Orthogonal equations and showcase results on stochastic test cases. We then present our Bayesian inversion schemes and its results for rigorous nonlinear assimilation and joint bathymetry-ocean physics-acoustics inversion.

During naval operations, sonar performance estimates often need to be computed in-situ with limited environmental information. This calls for the use of fast acoustic propagation models. Many naval operations are carried out in challenging and dynamic environments. This makes acoustic propagation and sonar performance behavior particularly complex and variable, and complicates prediction. Using data from a field experiment, we have investigated the accuracy with which acoustic propagation loss (PL) can be predicted, using only limited modeling capabilities. Environmental input parameters came from various sources that may be available in a typical naval operation.

The outer continental shelf shallow-water experimental area featured internal tides, packets of nonlinear internal waves, and a meandering water mass front. For a moored source/receiver pair separated by 19.6 km, the acoustic propagation loss for 800 Hz pulses was computed using the peak amplitude. The variations in sound speed translated into considerable PL variability of order 15 dB. Acoustic loss modeling was carried out using a data-driven regional ocean model as well as measured sound speed profile data for comparison. The acoustic model used a two-dimensional parabolic approximation (vertical and radial outward wavenumbers only). The variance of modeled propagation loss was less than that measured. The effect of the internal tides and sub-tidal features was reasonably well modeled; these made use of measured sound speed data. The effects of nonlinear waves were not well modeled, consistent with their known three-dimensional effects but also with the lack of measurements to initialize and constrain them.

Over the last four decades the use of numerical flow models in oceanography has vastly increased. Models are run operationally for regional locations, ocean basins, and the entire earth. In addition, specialized research models targeting specific processes and areas are routinely produced. These models are often coupled with biological and chemical models for research into biological-physical and biogeochemical-physical interactions. The role of some models is to create conditions close to reality, in a deterministic sense, whereas others have the role of imitating mean behavior or fluctuation behavior. The role of yet another family of models is to alter conditions from reality to study the ramifications, examples being interdisciplinary climate models [1-3]. All of these models provide full access to time- evolving three-dimensional fields (4-D fields) for process studies, or for predictive purposes. There is strong motivation for using these models for ocean acoustic studies. Suitably formulated models can include the important flow and water-mass features of the ocean, with the important features covering a wide dynamic range. Each feature has its own acoustic propagation or scattering signature, with some signatures having an interfering effect on underwater acoustic activities. The signature can be in the temporal domain, the spatial domain, or both. An important part of ocean acoustics research at this time is identifying which processes are dominant at specific times and places, and models are well suited to this. Significant acoustic effects of water-column and seafloor features occur in concert. However, they have traditionally been studied individually, sometimes in idealized or very simple form. Despite the isolation of the processes, many of these studies have been very successful. Examples are the analysis of the Pekeris waveguide [4], adiabatic mode propagation in a smoothly varying waveguide [5], and propagation through idealized internal waves [6-8]. The state of our knowledge now demands that the full complexity be analyzed, as can be done using the ocean models. Initial efforts that have coupled four-dimensional ocean fields with 2D acoustics modeling include data assimilation and uncertainty studies [9, 10], end-to-end computations [11], real-time at-sea predictions [12] and coupled adaptive sampling [13]. In the present work, a specific focus is on 3D acoustic effects coupled to 4D ocean predictions. We have thus motivated the use of oceanographic flow models as a straightforward approach for objective and comprehensive study of sound propagation in realistic environments, which we refer to as coupled ocean/acoustics modeling. The alternative of investigating the overall effects of simultaneously occurring feature types by constructing idealized process models with multiple features (straight line internal waves in two-layer fluid over a uniformly sloped bottom and one eddy, for example) is likely to lack objectivity or completeness. In fact, such feature models are mainly utilized to initialize ocean models or describe/assimilate specific features [14]. Coupled ocean/acoustics modeling can have high value, under the condition that the synthesized environments are sufficiently inclusive, representative, and accurate. This is a nontrivial condition; many challenges remain for flow models in terms of boundary conditions and data assimilation, resolution of near-boundary effects and mixing effects, and three-dimensional nonlinear gravity waves with hydrostatic pressure. Note that making acoustic propagation predictions, without analysis of the behavior or the mechanisms at work, is a byproduct of coupled ocean-acoustic modeling. Coupled ocean/acoustics modeling is becoming more common. Nevertheless, the approach is relatively recent and the best research path to take at this time deserves discussion. In this paper we discuss the potential of this method, and inform the discussion with some example computations from recent work in the Mid Atlantic Bight.

Today’s situational awareness requirements in the undersea environment present severe challenges for acoustic communication systems. Acoustic propagation through the ocean environment severely limits the capacity of existing underwater communication systems. Specifically, the presence of internal waves coupled with the ocean sound channel creates a stochastic field that introduces deep fades and significant intersymbol interference (ISI) thereby limiting reliable communication to low data rates. In this paper we present a communication architecture that optimally predistorts the acoustic wave via spatial modulation and detects the acoustic wave with optimal spatial recombination to maximize reliable information throughput. This effectively allows the system to allocate its power to the most efficient propagation modes while mitigating ISI. Channel state information is available to the transmitter through low rate feedback. New results include the asymptotic distribution of singular values for a large number of apertures. Further, we present spatial modulation at the transmitter and spatial recombination at the receiver that asymptotically minimize bit error rate (BER). We show that, in many applications, the number of apertures can be made large enough so that asymptotic results approximate finite results well. Additionally, we show that the interference noise power is reduced proportional to the inverse of the number of receive apertures. Finally, we calculate the asymptotic BER for the sparse aperture acoustic system.

Ocean science and ocean acoustics today are engaged in coupled interdisciplinary research on both fundamental dynamics and applications. In this context interdisciplinary data assimilation, which melds observations and fundamental dynamical models for field and parameter estimation is emerging as a novel and powerful methodology, but computational demands present challenging constraints which need to be overcome. These ideas are developed within the concept of an interdisciplinary system for assessing sonar system performance. An end-to-end system, which couples meteorology-physical oceanography-geoacoustics-ocean acoustics-bottom-noise-target-sonar data and models, is used to estimate uncertainties and their transfers and feedbacks. The approach to interdisciplinary data assimilation for this system importantly involves a full, interdisciplinary state vector and error covariance matrix. An idealized end-to-end system example is presented based upon the Shelfbreak PRIMER experiment in the Middle Atlantic Bight. Uncertainties in the physics are transferred to the acoustics and to a passive sonar using fully coupled physical and acoustical data assimilation.

The uncertainties in the predicted acoustic wavefield associated with the transmission of low- frequency sound from the continental slope, through the shelfbreak front, onto the continental shelf are examined. The locale and sensor geometry being investigated is that of the New England continental shelfbreak with a moored low-frequency sound source on the slope. Our method of investigation employs computational fluid mechanics coupled with computational acoustics. The coupled methodology for uncertainty estimation is that of Error Subspace Statistical Estimation. Specifically, based on observed oceanographic data during the 1996 Shelfbreak Primer Experiment, the Harvard University primitive-equation ocean model is initialized with many realizations of physical fields and then integrated to produce many realizations of a five-day regional forecast of the sound speed field. In doing so, the initial physical realizations are obtained by perturbing the physical initial conditions in statistical accord with a realistic error subspace. The different forecast realizations of the sound speed field are then fed into a Naval Postgraduate School coupled-mode sound propagation model to produce realizations of the predicted acoustic wavefield in a vertical plane across the shelfbreak frontal zone. The combined ocean and acoustic results from this Monte Carlo simulation study provide insights into the relations between the uncertainties in the ocean and acoustic estimates. The modeled uncertainties in the transmission loss estimate and their relations to the error statistics in the ocean estimate are discussed.

The estimation of oceanic environmental and acoustical fields is considered as a single coupled data assimilation problem. The four-dimensional data assimilation methodology employed is Error Subspace Statistical Estimation. Environmental fields and their dominant uncertainties are predicted by an ocean dynamical model and transferred to acoustical fields and uncertainties by an acoustic propagation model. The resulting coupled dominant uncertainties define the error subspace. The available physical and acoustical data are then assimilated into the predicted fields in accord with the error subspace and all data uncertainties. The criterion for data assimilation is presently to correct the predicted fields such that the total error variance in the error subspace is minimized. The approach is exemplified for the New England continental shelfbreak region, using data collected during the 1996 Shelfbreak Primer Experiment. The methodology is discussed, computational issues are outlined and the assimilation of model-simulated acoustical data is carried out. Results are encouraging and provide some insights into the dominant variability and uncertainty properties of acoustical fields.

The efficient interdisciplinary 4D data assimilation with nonlinear models via Error Subspace Statistical Estimation (ESSE) is reviewed and exemplified. ESSE is based on evolving an error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. A specific focus here is the use of ESSE in interdisciplinary smoothing which allows the correction of past estimates based on future data, dynamics and model errors. ESSE is useful for a wide range of purposes which are illustrated by three investigations: (i) smoothing estimation of physical ocean fields in the Eastern Mediterranean, (ii) coupled physical-acoustical data assimilation in the Middle Atlantic Bight shelfbreak, and (iii) coupled physical-biological smoothing and dynamics in Massachusetts Bay.

An interdisciplinary team of scientists is collaborating to enhance the understanding of the uncertainty in the ocean environment, including the sea bottom, and characterize its impact on tactical system performance. To accomplish these goals quantitatively an end-to-end system approach is necessary. The conceptual basis of this approach and the framework of the end-to-end system, including its components, is the subject of this presentation. Specifically, we present a generic approach to characterize variabilities and uncertainties arising from regional scales and processes, construct uncertainty models for a generic sonar system, and transfer uncertainties from the acoustic environment to the sonar and its signal processing. Illustrative examples are presented to highlight recent progress toward the development of the methodology and components of the system.