Underwater sound propagation is primarily driven by a nonlinear forward model relating variability of the ocean sound speed profile (SSP) to the acoustic observations (e.g., eigenray arrival times). Ocean acoustic tomography (OAT) methods aim at reconstructing SSP variations (with respect to a reference environment) from changes of the acoustic measurements between multiple source-receiver pairs. This article investigates the performance of three different OAT methods: (1) model-based methods (i.e., classical ray-based OAT using a linearized forward model), (2) data-driven methods (such as deep learning) to directly learn the inverse model, and (3) a hybrid solution [i.e., the neural adjoint (NA) method], which combines deep learning of the forward model with a standard recursive optimization to estimate SSPs. Additionally, synthetic SSPs were generated to augment the variability of the training set. These methods were tested with modeled ray arrivals calculated for a downward refracting environment with mild fluctuations of the thermocline. Idealized towed and fixed source configurations are considered. Results indicate that merging data-driven and model-based methods can benefit OAT predictions depending on the selected sensing configurations and actual ray coverage of the water column. But ultimately, the robustness of OAT predictions depends on the dynamics of the SSP variations.

A library of broadband (100–1000 Hz) channel impulse responses (CIRs) estimated between a short bottom-mounted vertical line array (VLA) in the Santa Barbara channel and selected locations along the tracks of 27 isolated transiting ships, cumulated over nine days, is constructed using the ray-based blind deconvolution algorithm. Treating this CIR library either as data-derived replica for broadband matched-field processing (MFP) or training data for machine learning yields comparable ranging accuracy (∼50 m) for nearby vessels up to 3.2 km for both methods. Using model-based replica of the direct path only computed for an average sound-speed profile comparatively yields∼110 m ranging accuracy.

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Ray-based acoustical tomography typically provides estimates of local ocean sound speed profile (SSP) fluctuations from precise measurements of acoustic travel times (AT) fluctuations (with respect to a reference environment) between multiple sources and receiver arrays along with a model of the ray propagation in the reference (i.e., fluctuation-free) environment. Classically, inverting the forward model (if available) yielding SSPs from ATs can be done by computing the pseudo-inverse (expensive) or using an iterative-method (e.g., gradient descent); however, including any acoustic forward model (e.g., ray-tracing) in an optimization loop is non-trivial because the nonlinear mapping between SPP and AT is computationally expensive to differentiate. Instead, we use a Neural Adjoint (NA) approach [Ren et al., NeurIPS (2020)] to circumvent this problem by replacing the physics-based forward model with a deep neural network approximation, allowing for an inexpensive way to compute a gradient through backpropagation. The iterative nature of the NA method permits thorough exploration of the solution space depending on the initialization, as opposed to outputting a single point estimate. Here, we continue the discussion of data-driven methods presented in the companion presentation by Saha et al. and show that NA has the potential to further refine existing data-driven SSP estimation techniques.

Underwater source localization is often achieved with a purely model-based approach such as matched-field processing with simulated replica-field. However, such approaches only yield reasonable predictions if the complex and dynamic ocean environment is sufficiently known – often a daunting task. Alternatively, it has been suggested that channel impulse responses (CIRs) estimated from measurements of sources of opportunity (such as commercial shipping vessels) can feed a data-driven approach to source localization that forgoes the need for precise model-parameters [Durofchalk et al., JASA 146(4), 2691–2691 (2019)]. In this presentation, multiple vertical line array (VLA) data from the SBCEx16 experiment conducted in the vicinity of shipping lanes in the Santa Barbara channel (580 m depth, downward refracting profile) are first used to a construct a library of estimated CIRs between selected locations along opportunistic shipping tracks and VLA receivers using ray-based blind deconvolution (RBD) [Byun et al., JASA 141(2), 797–807 (2017)]. Subsequently, this library of data derived CIRs is used to localize other surface sources with traditional matched-field processing techniques and as training data for a machine learning algorithm. The average localization error and computational efficiency of the different methods are compared.