Geoacoustic Inversion Using Simple Hand-Deployable Acoustic Systems

This article proposes the use of a simple, low-cost, hand-deployable pair of experimental assets to conduct geoacoustic inversion at sea. The system consists of an expendable, fully mechanical acoustic source called a rupture induced underwater sound source (RIUSS) and a new ropeless passive acoustic mooring called a TOSSIT (not an acronym). Used together, RIUSS and TOSSIT enable the collection of acoustic data suitable to perform single-hydrophone geoacoustic inversion. The method is illustrated using data collected on the New England Mud Patch in May 2021 from a relatively small (22 m) and inexpensive chartered fishing vessel. Modal time-frequency dispersion from 15 to 385 Hz is extracted from the TOSSIT/RIUSS data using warping, and used as input for Bayesian transdimensional geoacoustic inversion. The inversion results compare favorably to results obtained with data collected on the same track with traditional assets (e.g., a vertical line array) during the 2017 Seabed Characterization Experiment, even when jointly inverting for the water-column sound speed profile and seabed geoacoustic parameters. This further demonstrates inversion repeatability in a given location using data sets collected years apart, and under different (and potentially unknown) oceanographic conditions.

Abstract-This article proposes the use of a simple, low-cost, hand-deployable pair of experimental assets to conduct geoacoustic inversion at sea. The system consists of an expendable, fully mechanical acoustic source called a rupture induced underwater sound source (RIUSS) and a new ropeless passive acoustic mooring called a TOSSIT (not an acronym). Used together, RIUSS and TOSSIT enable the collection of acoustic data suitable to perform single-hydrophone geoacoustic inversion. The method is illustrated using data collected on the New England Mud Patch in May 2021 from a relatively small (22 m) and inexpensive chartered fishing vessel. Modal time-frequency dispersion from 15 to 385 Hz is extracted from the TOSSIT/RIUSS data using warping, and used as input for Bayesian transdimensional geoacoustic inversion. The inversion results compare favorably to results obtained with data collected on the same track with traditional assets (e.g., a vertical line array) during the 2017 Seabed Characterization Experiment, even when jointly inverting for the water-column sound speed profile and seabed geoacoustic parameters. This further demonstrates inversion repeatability in a given location using data sets collected years apart, and under different (and potentially unknown) oceanographic conditions.

I. INTRODUCTION
M ODELING, understanding, and forecasting acoustic propagation at sea is an important engineering and research topic. Historically, acoustic propagation prediction was driven by Navy needs, particularly for sonar performance predictions. Today, it is also recognized that predicting ocean acoustic propagation is of paramount importance to understand, forecast and mitigate noise pollution at sea. In shallow coastal waters and other bottom-limited environments, predicting the waterborne propagation requires knowledge of the seabed geoacoustic properties. Estimating those properties from ocean acoustic Manuscript  measurements is known as geoacoustic inversion, which has been a vibrant research topic in the past three decades [1]. In parallel, over this time period, many engineering fields have changed their data collection paradigm to enter the Big Data era. Swarms of simple (and cheap) sensors are now used to replace sophisticated standalone (and expensive) systems; a flagship example being the development of miniaturized satellites CubeSat [2]. However, such trends have barely impacted the geoacoustic inversion community to date. Although some single-hydrophone methods have been proposed, e.g., [3], [4], [5], [6], [7], [8], traditional at-sea geoacoustic inversion experiments (e.g., matched-field inversion) often involves deploying one or more central array(s) of synchronous hydrophones, usually with a vertical aperture that spans as much of the water column as possible. Acoustic sources are then deployed, towed, or moored in the experimental area, providing data for geoacoustic inversion to be carried out along various source-receiver propagation tracks. Major inversion experiments using this setup include the 2001 Asian Seas International Acoustics Experiment (ASIAEX) [9], the Shallow Water 2006 (SW06) Experiment [10], and the 2017 Seabed Characterization Experiment (SBCEX17) [11].
In this article, we propose and investigate the use of a simple and low-cost pair of experimental assets to conduct geoacoustic inversion at sea. The setup relies on the use of a TOSSIT ("toss it") receiver mooring and a RIUSS (rupture induced underwater sound source). The TOSSIT is a hand-deployable, tetherless bottom lander with a single hydrophone, an autonomous recorder, and an acoustic release [12]. The RIUSS is a simple expendable source system based on an evacuated vacuum chamber with a membrane that ruptures under hydrostatic pressure, which produces a high-amplitude impulsive signal [13], [14]. Both TOSSIT and RIUSS are recent systems, which have not been used together previously for ocean acoustic experiments. This article demonstrates that the combination of TOSSIT and RIUSS enables simple and cost-effective at-sea data collection relevant for geoacoustic inversion. The tradeoff associated with the use of simple experimental assets is that data analysis requires advanced processing methods. Here, we suggest the use of warping data analysis [15] and trans-dimensional (trans-D) Bayesian inversion methods [16], the combination of which has been shown to be highly effective for single-hydrophone geoacoustic inversion [17], [18].
To validate the proposed system, a geoacoustic experiment was performed on the New England Mud Patch (NEMP) in May, 2021. Work was carried out from a comparatively small ( RIUSS hand-deployed from the back deck. The chosen location (NEMP) allows comparison with data collected 4 years earlier during SBCEX17 using traditional acoustic assets, notably vertical line arrays (VLAs), combustive sound sources (CSS), and a low-frequency towed source (J15). The specific track studied here is collocated with a well-studied SBCEX17 track. The present TOSSIT/RIUSS inversion results are found to compare favorably with previous SBCEX17 results, demonstrating the potential of the proposed experimental assets for fast, simple, and inexpensive geoacoustic surveys. Incidentally, the results also demonstrate inversion repeatability in a given location using data sets collected years apart, which, as far as we know, has not been studied in this way before.
Another interesting aspect of the 2021 TOSSIT/RIUSS experiment is that it was carried out during an oceanographic frontal intrusion, with warm waters from the continental shelf creeping onto the NEMP at depth and creating a highly stratified sound speed profile (SSP) in the water column. This phenomenon was discovered thanks to repeated CTD casts carried out during the experiment, and constitutes an important difference from SBCEX17, during which the water column was well mixed, resulting in a virtually isospeed SSP [11]. To account for the frontal intrusion in 2021, two different inversions are considered in this article. The first inversion uses a SSP derived from the CTD measurements as known in the inversion. The second inversion jointly estimates the water-column SSP and seabed geoacoustic parameters using wide uniform priors. Although the results of the second inversion (with unknown SSP) have slightly increased geoacoustic uncertainties (as expected), they are fully consistent with results from the first inversion (with known SSP), and provide a very good description of the NEMP seabed. Hence, this article also demonstrates that seafloor properties can be estimated without knowledge of the water-column SSP (provided it is included in the inversion), which further simplifies the experimental setup. To the best of our knowledge, this article is one of the first to consider joint inversion of water SSP and seafloor properties in a context where there is enough preexisting knowledge on the water column and seabed to evaluate the result qualitatively. For example, joint water-column and seabed inversion was reported previously for airgun data collected in the Arctic [19]. However, the Arctic airgun data had relatively low information content, and no external seafloor information was available to evaluate the inversion results. As an other example, joint water-column and seafloor inversion was performed by Potty et al. [20] using data collected on the New England shelf (Primer experiment). However, the water column SSP inversion was performed using empirical orthogonal functions, which requires strong prior information.
The rest of this article is organized as follows. Section II introduces the proposed acoustic assets: TOSSIT receiver and RIUSS. Section III presents the data processing chain used to perform geoacoustic inversion with TOSSIT/RIUSS data. Section IV describes an experimental data set collected with TOSSIT/RIUSS assets on the NEMP. Section V considers the geoacoustic inversion of these data, and Section VI discusses the results, including comparisons with previous inversions in the same location. Finally, Section VII concludes this article.

II. EXPERIMENTAL SYSTEM
The proposed experimental setup relies on a pair of assets: a RIUSS to generate a broadband underwater signal, and a TOSSIT to record this signal at a distant location. Those two assets are described below.

A. Autonomous Receiver: TOSSIT
A TOSSIT is a custom-made mooring developed at the Woods Hole Oceanographic Institution (WHOI), which can easily be deployed from platforms ranging from small (e.g., rigid-hull inflatable) boats to large oceanographic vessels or even commercial ships. It is bottom mounted, ropeless, and records acoustic pressure (and optionally temperature) in the water. The whole system is described in detail in [12], and its main features are summarized below. Note that [12] is an "open hardware" publication, which provides potential users with the full recipe to build their own TOSSIT. Note also that "TOSSIT" is not an acronym; the system is so named because it can literally be tossed over the side of small vessels. For somewhat larger vessel (such as the fishing boat used for this study), a better practice is to gently slide the mooring to the water line using a sling rope (see deployment photographs in [12]). No winch, crane nor A-frame is required. At the end of the experiment, once acoustically released from their anchor and on the sea surface, TOSSITs can easily be recovered by hand or using a boat hook.
A TOSSIT consists of a commercial off the shelf (COTS) passive acoustic recorder and a COTS underwater acoustic release, mounted on a rope-free and shackle-free polyoxymethylene (i.e., thermoplastic) frame with built-in buoyancy (syntactic foam plates). If needed, a small COTS temperature sensor/recorder can be clamped or taped on the frame. The TOSSIT mooring is specifically designed to be used with a Vemco Ascent AR acoustic release. On the other hand, the TOSSIT modular design enables the user to choose any COTS acoustic recorder with a diameter less than 125 mm; here a Soundtrap ST300 is used. One of the TOSSIT moorings used during the experiment presented in this article is shown in Fig. 1.
The TOSSIT system is designed for operations in water depths of up to 500 m. In practice, the deepest TOSSIT deployment to date took place on the New England Shelf Break at a location where water depth is about 400 m [12]. For the current study on the NEMP, the water depth is about 75 m.
When used with a Soundtrap ST300 recorder (as here), a potential limitation of the TOSSIT is the acoustic receiver clock, which seemed to undergo a nonlinear time drift. The reason for this behavior is out-of-scope for this study, but its direct impact is that a set of TOSSITs with this recorder cannot be spatially distributed to form a coherent array. However, this has no implications for the current study, which focuses on single-hydrophone geoacoustic inversion.

B. Expendable Sound Source: RIUSS
The RIUSS is a simple device used to create high amplitude, broadband acoustic pulses for underwater acoustics experiments and surveys [13]. The most basic form of the source utilizes a submersible vacuum chamber and a rupture disc, which is an expendable diaphragm generally used in industrial applications. These discs are fabricated such that they rupture at a specified pressure differential between the two faces of the disc. Rupture discs are commercially available in a variety of materials and sizes; however, the rupture discs used for this work were Mersen Series 3, Graphilor Burst Discs sized for a four-inch, Class 150 ANSI pipe flange.
The basic operation of the RIUSS is as follows. A rupture disc is secured over a hollow, submersible chamber. The chamber is then evacuated of any air through the use of a vacuum pump, and then lowered or dropped through the water column until the pressure differential between the two faces of the disc exceeds that of the disc's pressure rating. Upon rupture of the disc, a quick inrush of water collapses into the evacuated chamber, which creates a high amplitude, broadband acoustic pulse. This process is documented in a slow motion video provided as supplemental material in McNeese et al. [13].
The inherent modular nature of the RIUSS chambers allows for their deployment in differing manners. There are versions of the device that rely on a deployment framework capable housing multiple chambers. This framework also allows for the mounting of autonomous acoustic and oceanographic recorders to be deployed along with the sound source. This configuration allows for precise knowledge of source-receiver separation distances, depth of the acoustic event, and SSP measurements. However, this configuration can be cumbersome in some situations in that it requires a deployment platform with a sufficient winch and deployment framework (A-frame, davit). For the scope of this work, it was desired to have a configuration of chambers that could be deployed in a quick and easy expendable manner from a small fishing vessel [14]. For this, each expendable unit can be hand-carried and manually dropped over the side into the water at locations of interest (see right panel of Fig. 1).
The submersible chambers utilized for this work were fabricated from sections of steel pipe fittings. The body of the chambers were 12-inch long sections of Schedule 40, 4-inch diameter steel pipe. Four-inch, Class 150 pipe flanges were welded to the top of the pipe sections to provide a mounting surface for the rupture discs, and steel concentric pipe reducers (four inch to two inch) were welded to the bottom of the pipe sections. Two-inch steel pipe caps were welded to the base of the reducer to complete the hollow chamber. A 1/8-inch NPT hole was tapped through the pipe cap, such that a 1/8-inch NPT ball valve could be installed on the chamber for use when evacuating and sealing the chamber.

A. Modal Propagation and Time-Frequency Analysis
The inversion method used in this article focuses on the low-frequency portion (f < 500 Hz) of the RIUSS signal, with relevant applications in relatively shallow waters (depth D < 500 m). In this context, propagation is conveniently described using normal mode theory. Given a broadband source emitting a signal S(f ) at depth z s in a range-independent waveguide, the pressure field Y (f ) received at depth z r after propagation over a range r is given by [21] M is the number of propagating modes, Ψ m is the modal depth function of mode m, and k m is the mth horizontal wavenumber. The term Q is an multiplicative constant unimportant for this study.
Using a single TOSSIT system, it is convenient to analyze the received signal in the time-frequency (TF) domain. The TF positions of the modal-arrival curves (arrival time as a function of frequency) represent the modal dispersion data considered here, and are given by where v m (f ) = 2πdf /dk m is the group speed of mode m, and τ s (f ) is the source group delay (i.e., its time-frequency emission function). If the source is an impulse, then τ s (f ) = t s is the source emission time.

B. Modal Dispersion Estimation
As in previous studies [6], [17], [18], the modal dispersion data [(2)] are used here as input for geoacoustic inversion. Doing so requires the TF data be properly estimated from the TOSSIT acoustic recordings. This is carried out in two steps: source deconvolution and warping. The entire method is detailed in a tutorial article [15]. In short, deconvolution (based on a signal recorded very close to the RIUSS) removes the source signature, such that the deconvolved signal represents the waveguide impulsive response. In practice, modal dispersion data after deconvolution represent τ s (f ) = t s in (2). Modal filtering is then performed using warping, a physics-based nonlinear resampling of the signal. Warping tends to transform each mode into monochromatic signal. This drastically increases the TF separation between (warped) modes, enabling TF filtering. The filtered (warped) modes are then unwarped, which concludes the modal filtering scheme. Finally, modal dispersion data are determined from individual modes by estimating the first frequency moment (i.e., average time) of each line of the spectrogram of all individual (filtered) modes.

C. Bayesian Inversion and Implementation
The modal dispersion data estimated using warping are then used as input for a geoacoustic inversion algorithm. To briefly describe the Bayesian joint inversion for seabed geoacoustic and water-column SSP parameters developed here, let M represent the choice of model (e.g., the seabed and water-column parameterizations), with m the corresponding set of unknown model parameters, and let d be the acoustic data. Assuming these to be random variables, they are related by Bayes' theorem In (3), P (m|M) is the prior probability, representing information for the model parameters (given a choice of model) independent of the data. The term P (d|m, M) defines the data information. Interpreted as a function of d, this represents the residual error distribution; however, when d is taken to be (fixed) observed data, this term is interpreted as the likelihood of the parameters given the model L(m|M). On the left side of (3), P (m|d, M) defines the posterior probability density (PPD), representing the state of information for the model parameters given the data, prior, and model. The normalization term on the right, P (d|M), is referred to as the Bayesian evidence, and can be interpreted as the likelihood of model M given the observed data. Bayesian inversion generally involves two levels of inference: model selection, which considers appropriate choices for the model M, and parameter estimation, which quantifies the PPD for parameters m given a choice (or choices) for M. One approach to model selection is to seek the parameterization (out of a set of possibilities) that maximizes the evidence or an approximation thereto, such as the Bayesian information criterion (BIC). Once the choice is determined, parameter estimation is carried out for that model. Another approach is to sample probabilistically over models with different numbers of parameters (dimensions) in trans-D inversion. Trans-D inversion has the advantage that model selection is automated and combined with parameter estimation, and hence the uncertainty in the parameterization is included in the parameter uncertainty estimates. However, standard trans-D inversion as has been applied to seabed geoacoustic inversion is based on the assumption of layers with uniform properties, and is not applicable for a water-column SSP represented by layers with gradients as typically applied in propagation modeling (e.g., layers with 1/c 2 -linear gradients, where c is sound speed, as is common in normal-mode modeling). Here, an approach combining trans-D inversion for the seabed with the BIC for the water column is applied as described below.
Trans-D methods have been described elsewhere [16], [22], [23], [24], including geoacoustic inversion of modal-dispersion data [17], [18], [25], [26], and are only briefly summarized here. Bayes' rule for a trans-D model over a set of K model choices, indexed by k with corresponding parameters m k , is given by In (4), P (k) P (m k |k) is the prior probability of the state (k, m k ), P (d|k, m k ) is interpreted as the likelihood L(k, m k ), and P (k, m k |d) is the trans-D PPD. The PPD can be sampled numerically using the reversible-jump Markov-chain Monte Carlo (rjMCMC) algorithm, which accepts a proposed perturbation from the current state (k, m k ) to a proposed state (k, m k ) with an acceptance probability given by the Metropolis-Hastings-Green criterion [22] A(k, m k |k, m k ) where Q(k, m k |k, m k ) is the proposal probability density and |J k k | is the determinant of the Jacobian matrix for the transformation between dimensions. Geoacoustic inversions to date have applied the so-called birth-death approach to rjMCMC sampling. This approach adds and removes interfaces at random depths defining homogeneous sediment layers (birth and death steps, respectively) with other layers unchanged; perturbations are also applied to parameters with the parameterization unchanged. Efficiency is achieved by combining a proposal density based on principal-component reparameterization [24] with the method of parallel tempering [27], [28], which applies a series of interacting Markov chains with successively relaxed likelihoods that are raised to the power 1/T j , where T j ≥ 1 is the sampling temperature of the jth chain (only samples from the unbiased T = 1 chain are retained). The birth-death formulation has the benefit that the Jacobian determinant is identically unity and need not be considered explicitly in perturbation acceptance based on (5). However, this does not apply for a water-column SSP represented by layers with nonzero gradients, where adding or removing a layer changes the properties of neighboring layers such that the Jacobian is not unity (note that this issue was missed in an earlier work that considered trans-D SSP inversion [19]). While it is possible in principle to derive and evaluate the Jacobian for such trans-D steps, a simpler approach is employed here in which trans-D inversion is applied for uniform seabed layers while the BIC is applied to estimate the optimal number of gradient-based layers for the water-column SSP.
To consider the BIC more specifically, note that since the evidence is a normalizing factor in (3), it can be written However, this integral over the parameter space is generally difficult to evaluate numerically to sufficient precision for model selection in nonlinear inversion [29]. Commonly, an asymptotic point estimate of evidence, the BIC, is applied [30], [31], and N is the number of data. Since the BIC approximates the negative of evidence, the model with the smallest BIC over a set of possible models is selected as the most appropriate choice, balancing the preference for high likelihood (low data misfit) with a penalty for an excessive number of parameters. While employing the BIC avoids the difficult integral for evidence in (6), it requires solving a nonlinear optimization for the ML parametersm. The optimization applied here is based on a simulated-annealing (cooling) approach applied within the trans-D parallel-tempering algorithm, as described in [26]. Other elements of the inversion approach, such as the definition of the likelihood function based on a trans-D autoregressive (AR) error model, are also the same as described in [26]. Note that this error model considers an unknown standard deviation σ m and first-order AR coefficient a m for each of m = 1, . . . M modes; these parameters are estimated from the data as part of the inversion process.

IV. EXPERIMENTAL DATA
The complete processing chain presented above (modal dispersion data estimation using warping and Bayesian inversion of water SSP and seabed parameters) is used to analyze experimental marine data collected using a TOSSIT and RIUSS. This section describes the experimental area, the at-sea experiment, and the available environmental information, as well as the acoustic data that were collected.

A. Experimental Area
A TOSSIT/RIUSS experiment was performed on 21 May 2021, on the NEMP, which is located about 100 km south of Martha's Vineyard, MA, USA. The area is characterized by a relatively flat seafloor (with water depth D 75 m) and an upper 12-m-thick sediment layer of "mud" (fine-grained sediment with clay) [32]. Importantly, the NEMP is one of the main locations of SBCEX17, where many previous measurements were carried out. In short, a CHIRP sub-bottom reflection survey was conducted in 2015 [33] and core samples were collected in 2016 [34]. A suite of acoustic propagation measurements were obtained in March, 2017, and included multiple propagation tracks, with a variety of sources and receivers. The 2017 data were analyzed extensively by the SBCEX group [11], and used in many geoacoustic inversion studies, e.g., [25], [26], [35], [36], [37], [38], [39], [40], [41], [42].
As a result, the NEMP is one of the locations in the world where sediment geoacoustic properties are known best. The TOSSIT/RIUSS experimental location was chosen for this specific reason, with the objective of facilitating comparison of the proposed method with results documented in the literature. More specifically, the experimental track chosen here (see Fig. 2) largely overlaps with previous trans-D inversion studies of modal dispersion data from SBCEX17 [17], [18]. Indeed, the experimental track (red line on Fig. 2) is virtually identical to the track in [17] (white dotted-line on Fig. 2), and largely overlaps with the track in [18] (black line on Fig. 2). Still, although input data (modal dispersion), inversion method (trans-D), and acoustic tracks are similar, the TOSSIT/RIUSS data were collected 4 years after the SBCEX17 data and used much simpler instrumentation.  [17], [18], which are used to compare result with the current study.

B. At Sea Experiment
The TOSSIT/RIUSS experiment was performed from the F/V Kathryn Marie, a 22.5-m-long scallop fishing vessel. The entire experiments was carried out on 21 May 2021, and involved deploying/recovering 2 TOSSITs in various locations, and deploying a total of 12 RIUSSs. We focus here on a single TOSSIT/RIUSS pair, forming the acoustic track mentioned above (i.e., the red line in Fig. 2).
The first TOSSIT was deployed at (40.4576 • N; 70.5573 • W) at 15:09 UTC. Deployment was carried out by hand by two operators using a sling rope (see [12, Fig. 5] for a photograph of a TOSSIT deployment from the ship), allowing the instrument to be lowered gently to the water level before it was released to free fall to the seafloor. Acoustic communications between the TOSSIT's acoustic release and a dedicated deck-box allowed the instrument to be interrogated and to evaluate its depth, as well as the range between the release and the deck-box's hydrophone. This was done at three different stations forming a triangle around the TOSSIT, with each station 100-200 m away from the center position. The data collected in this manner were used to accurately localize the TOSSIT using the triangulation method, which indicated a 30 m horizontal drift between the TOSSIT's deployment location and its final position on the seafloor. The TOSSIT localization was finished by 15:23 UTC. Further, water depth at the TOSSIT location, D = 74 m, was obtained through communication with the acoustic release (which has a pressure sensor and sits on the seafloor). Overall, deployment and localization of the TOSSIT took less than 20 min, with most of the time spent maneuvering the ship into the requested locations.
The experiment continued with a second TOSSIT deployment and several RIUSS deployments. Of interest here is a RIUSS deployed at (40.4889 • N; 70.6338 • W) at 16:55 UTC, with source depth z s 40 m (this single event will be used for inversion). Although RIUSS can be hand-carried by a single operator (see Fig. 1), their deployment was again performed by two operators with a sling rope. An independent hydrophone was also lowered into the water to measure the near-field waveform of the source signal, which is required for source deconvolution (see Section III-B). Overall, a single RIUSS deployment can be carried out in a few minutes, once the vessel reaches the intended location.
The experiment also included two approximately collocated conductivity-temperature-depth (CTD) casts along the propagation track (see Fig. 2). The first cast was carried out at (40.4632 • N; 70.5777 • W) at 15:54 UTC as the ship opened range from the TOSSIT, and the second at (40.4648 • N; 70.5784 • W) at 18:20 as the ship returned. An autonomous CTD (RBRconcerto) was used, which was attached to a small fishing winch for ease of deployment, but could be hand-deployed if needed. The TOSSIT was then recovered (using a long carbonfiber pole with a hook), and back on deck around 19:00. The entire data set (acoustic and water-column measurements) used for this inversion study was collected in less than 4 h, excluding transit time from port to the NEMP.

C. Environmental Information
Sub-bottom layering information along the propagation track of this study is available from the 2015 CHIRP sub-bottom reflection survey mentioned in Section IV-A. Prominent reflectors in the survey were interpreted to form a 4-layer sub-bottom model [33]. Fig. 3 shows this model along the propagation track, with the vertical axis given in two-way travel time (TWTT). The four Sub-bottom interfaces are denoted the "mud base," "sand base," "deep base 1," and "deep base 2." The first two layers have been sampled with cores in various locations on the NEMP, and their respective compositions (mud and sand) are relatively well known. The other layers are too deep to have been sampled; hence, their composition is unknown. Overall, an important feature of the chosen propagation track is that it is largely range independent. Note that the Sub-bottom layering information is not used in the geoacoustic inversion method, but is given here as a guide in analyzing the results.
The SSPs from the collocated CTD casts carried out two hours apart during the experiment (see Section IV-B) are shown in Fig. 4. The two SSPs are very similar, and show a drastic increase in sound speed from about 1472 to 1486 m/s at depth z 55 m. This is interpreted as due to a frontal intrusion of warm water from the shelf creeping north along the seafloor of the NEMP. This indicates a highly dynamic water column, which is known to be a difficult context for geoacoustic inversion. To deal with this, two different inversion methods are used here. One method assumes that the SSP is known: the inversion is performed using a fixed SSP representing a simplified form of the measured SSPs (dashed line in Fig. 4). The other method assumes no SSP information is available: both water-column SSP and seabed geoacoustic parameters are considered unknowns in the inversion. Both inversion methods assume range-independent propagation with a constant water depth D = 74 m.

D. Acoustic Data
The acoustic recording considered here consists of the RIUSS signal recorded 7 km away on the TOSSIT. The time series of this received signal is shown in Fig. 5(a), and its spectrogram in 5(c). The near-field RIUSS waveform recorded on the monitor hydrophone deployed from the fishing boat is shown in Fig. 5(b). This waveform is used to perform source deconvolution before warping is applied to estimate the TF dispersion data (see Section III-B). The spectrogram of the received signal after deconvolution and the estimated modal dispersion data are shown in Fig. 5(d). The TF dispersion of 10 of the first 11 modes at frequencies from 15 to 385 Hz is used for inversion in this article. Note that mode 7 has a very low signal-to-noise ratio (likely because the source or receiver depth corresponded to a null for this mode); hence, its dispersion TF data are not estimated or used for inversion.

A. Practical Application of the Inversion Method
The 10-mode dispersion data set presented in Section IV-D is used as input for the Bayesian inversion method described in Section III-C. In practice, the environment is modeled as a range-independent waveguide with water depth D = 74 m. The water SSP is modeled using M nodes at depth z i with speed c i , and a 1/c 2 -linear gradient between nodes. The seafloor is modeled as a stack of k isospeed layers over a semi-infinite basement. Modal group velocities, required to simulate (predict) TF dispersion data [see (2)] are calculated using the normal mode code ORCA [43]. Two different inversions are run to examine the data information content. The first considers the water-column SSP profile as known, and uses the simplified version of the measured SSP (see Fig. 4). The second considers the SSP profile as unknown, and jointly estimates the SSP and seabed geoacoustic parameters. Both inversions carry out trans-D sampling for seafloor parameters with an unknown number of layers k and 3 parameters per layer (interface depth z k , sound speed c k , and density ρ k ) plus basement parameters c b and ρ b . Source-receiver range r and source emission time t s are also treated as unknowns. The trans-D error model includes an unknown standard deviation σ m for each of M acoustic modes, as well as a first-order AR coefficient a m for n a ≤ M modes that have a correlated error model (the inversion samples transdimensionaly between correlated and uncorrelated error processes for each mode). The inversion with unknown water-column SSP further estimates the number of nodes q required to describe the SSP, along with q nodal sound speeds and q − 2 nodal depths (since the first and last nodes are fixed at the sea surface and seafloor, respectively). Hence, the total number of parameters for the inversion with known SSP is 3k + M + n a + 5 and with unknown SSP is 3k + M + n a + 2q + 4. Uniform prior bounds are applied for all parameters, as given in Table I. Since priors for the number of water-column and seabed layers are q ∈ [2,5] and k ∈ [1,10], respectively, and the data set includes M = 10 modes (thus n a ∈ [0, 10]), the total number of parameters varies between 18 and 55 when the water SSP is known, and between 21 and 64 when the SSP is unknown. As in previous Bayesian inversion studies of modal dispersion data [18], [26], [35], the parameter space is further constrained using a joint prior on sediment sound speed and density at each depth to constrain the PPD to physically reasonable parameter combinations based on empirical relations developed by Hamilton [44].
The trans-D inversions presented in this article use eight rjMCMC chains in the parallel tempering algorithm. The sampling temperatures of the chains are given by a geometric series T i = α i−1 T 1 with T 1 = 1 and α = 1.3. All the results are based on 400 000 samples from the T 1 = 1 chain after discarding burn-in (initial values before stationary sampling is achieved, determined visually). Sampling convergence is examined by comparing the results (marginal probability profiles) computed separately for the first and second halves of the total ensemble of samples: the fact that those do not differ significantly provides confidence that convergent sampling is achieved. Results shown in this article are for the full ensemble of samples.

B. Inversion With Known Water Column
This section presents results for the modal inversion with known water SSP. The results are summarized as marginal Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  posterior probability profiles for the geoacoustic parameters as a function of sub-bottom depth, as shown in Fig. 6. In this figure, the left panel shows the probability of occurrence of a layer interface versus depth, while the middle and right panels show sound-speed and density probability profiles, respectively, with warm colors indicating high probability and cold colors indicating low probability (white is zero). Reflector depths estimated from the CHIRP refection survey (not used in the inversion) are plotted as black lines. These reflector depths were obtained by converting the (range-averaged) TWTTs from Fig. 3 into sub-bottom depth using the estimated posterior mean for the sediment SSP.
The inversion results in Fig. 6 resolve two low-speed sediment layers over a higher speed basement. The transition depth between the sediment and basement coincides with (overlaps) the The basement sound speed is much faster (c b 1775 m/s), and the data do not have information to resolve structure deeper than 12 m (e.g., the deep base 2 reflector from Fig. 3 is not detected). Density estimates follows a trend similar to sound speed, with respective values of 1.4, 1.7, and 1.9 g/cm 3 for the two mud layers and the basement. These results are fully consistent with previous studies of the same propagation track; a comparison with the literature is presented in Section VI-B.
The fit to the modal-dispersion data achieved in the inversion is illustrated in Fig. 7, which compares the measured data to a large ensemble of predicted data drawn at random from the PPD. The predictions closely fit the measurements for all modes. Sampling convergence and validation of statistical assumptions of the error model were successfully carried out using methods discussed in previous studies by the authors, e.g., [18], [26], [35]; details are not presented here for the sake of concision. Finally, the estimated source/receiver range is consistent with those measured during the experiment.

C. Inversion With Unknown Water Column
This section presents results for the inversion with unknown water-column SSP. As stated in Section III-C, the number of water SSP nodes is estimated using a BIC study. The BIC results are summarized in Fig. 8, and favor a water-column SSP with three nodes.
The marginal probability profile estimated for the unknown water-column SSP (with three nodes) is shown in Fig. 9. Detailed structure in the measured SSPs (cf., Fig. 4) are not well resolved by the inversion; however, the overall structure is captured, with a negative near-surface gradient overlaying an overall upward-refracting profile. The seabed geoacoustic results for the unknown-SSP inversion are shown in Fig. 10. Interestingly, the seabed estimation results are barely impacted by the watercolumn SSP uncertainty, with the geoacoustic marginal PPDs in Fig. 10 very similar to those for known-SSP inversion in

A. Comparison Between the Inversions With Known/Unknown Water SSP
As noted above, the geoacoustic inversion results obtained with known and unknown water-column SSPs are very consistent (Figs. 6 and 10, respectively). However, on close inspection, the inversion results, notably the mud sound speeds, are slightly more uncertain when the SSP is unknown. To illustrate this, Fig. 11 compares sound-speed uncertainties for the two inversions at three depths within the mud: z = 0 (the water/sediment interface), z = 2 m, and z = 8 m. Note that results at the water/sediment interface are given in terms of marginal PPDs for the sound-speed ratio, R c = c mud /c water , while deeper results are given as marginal PPDs for sediment sound speed. Since the two inversion results indicate essentially no interfaces or changes in sound speed between z = 0 and z = 2 m (Figs. 6 and 10), the upper two panels of Fig. 11 show virtually the same result in terms of sound-speed ratio and sound speed. Note also that the evaluation of R c involves c water , which is treated as known/fixed in one inversion (red marginals), and unknown/estimated in the other (blue marginals) in Fig. 11.
The comparison between the two inversions is summarized in Table II, which gives 95% highest-probability density credibility intervals (i.e., intervals of minimum width containing 95% of the probability) for the marginal PPDs in Fig. 11. These results Fig. 12. Comparison of the sound speed ratio estimated using transD modal inversion. A: J15 source (r 7 km, 6 modes with 52 < f < 248 Hz). B: CSS source (r 7 km, 7 modes with 15 < f < 300 Hz). C: CSS source (r 5 km, 7 modes with 20 < f < 350 Hz). D: CSS source (r 5 km, 15 modes with 20 < f < 440 Hz). E: CSS source (r 5 km, 21 modes with 20 < f < 550 Hz), F: RIUSS (r 7 km, 11 modes with 15 < f < 385 Hz). G: RIUSS (r 7 km, 11 modes with 15 < f < 385 Hz). Inversions A and B are from [17] (SBCEX17 data, black track on Fig. 2), inversion C, D, and E are from [18] (SBCEX17 data, red track on Fig. 2), and inversions F and G are from the present study using the TOSSIT/RIUSS data (F with known water SSP and G with unknown water SSP). Fig. 13. Solid lines: comparison of mud-layer posterior sound-speed mean estimates from this study (blue with known water SSP, red with unknown water SSP) and from the 21-mode SBCEX17 data set (green) [18]. Dashed lines: corresponding interval speeds to 10 m depth. (Note that the color codes are that same than in Fig. 12.). further indicate the slightly increased uncertainties associated with the unknown water SSP. Interestingly, the inversion with unknown water SSP tends to predict a smaller sound speed ratio than that with known SSP. This is mostly driven by the sound-speed estimate at the bottom of the water column, which tends to be greater (1490-1500 m/s) that of the simplified SSP (1487 m/s), see Fig. 13. For the inversion with unknown water SSP, the sound speed estimated in the mud may be a better indicator of geoacoustic properties than the sound-speed ratio.

B. Comparison With Other Trans-D Modal Inversions
This section compares the inversion results obtained here for RIUSS/TOSSIT modal TF data with those from previous SBCEX17 inversion studies carried out along the same propagation track (see Fig. 2), but at different times. Comparisons are considered for trans-D inversions of modal data in two previous studies [17], [18], which inverted five different data sets obtained with different acoustic assets (e.g., combustive sound source or J15 towed source, single receiver or vertical line array), leading to different frequency bands and numbers of modes, and therefore differing data information content.
A comparison of inversion results in terms of the estimated mud/water sound-speed ratio is given in Fig. 12. Previous studies have considered the dependence of R c on data information content [18], as well as on environment parameterization [26]. Fig. 12 shows that all the studies predict R c 1 with various degrees of uncertainty. The inversion based on RIUSS/TOSSIT data gives results that are no more uncertain than other inversions when the water-column SSP is known (see Fig. 12-F), but uncertainty increases somewhat when the SSP is unknown (see Fig. 12-G).
A comparison of the posterior mean sound speed profiles in the mud is presented in Fig. 13. This comparison considers the two inversions performed in this article, as well as the 21-mode inversion from [18], i.e., the most informative data set of those considered in Fig. 12. The estimated mud profiles obtained here using the TOSSIT/RIUSS data are generally consistent with the 21-mode inversion results [18], although the data considered there were obtained in a more involved experiment using a CSS and a VLA. Interestingly, the TOSSIT/RIUSS inversion with known SSP shows a surficial mud speed, which is nearly 10 m/s higher than the SBCEX17 21-mode result. While this difference is generally within uncertainties, it is possible it could be due to significant difference in water-column conditions: the May 2021 (RIUSS/TOSIT) experiment involved much higher bottom-water sound speeds (1487 m/s) than the March 2017 SBCEX17 experiment (1469 m/s). This water sound speed difference, largely driven by water temperature, may impact the surficial mud properties, and lead to the 10 m/s difference observed here.
Another interesting difference between the estimated profiles is that the RIUSS/TOSSIT inversion does not predict a sound speed increase slightly above the mud-base ( 9 m), which was an important feature of SBCEX17 trans-D modal inversions [17], [18], [25], [35]. Although modal dispersion inversions based on layered seabed models do not seem to be able to resolve a potential gradient at the base of the mud (such a gradient was resolved by acoustic cores [45] at other locations on NEMP, by reflection-coefficient inversion [36], as well as by modal dispersion inversion based on alternative seabed parameterization [26]), they usually show a significant sound speed increase just above the mud base [17], [18], [25], [35]. However, this is not the case here, likely because the estimated 2-step SSP in the mud allows for a slightly deeper transition to the basement in predicting the observed modal dispersion. Interestingly, the two differences between the SBCEX17 and the 2021 TOSSIT/RIUSS profiles (at the water/mud interface and above the mud base) compensate each other and lead to interval speeds within the mud that are within 2 m/s of each other.

VII. CONCLUSION
This article presented the use of a simple and low-cost pair of experimental assets to conduct geoacoustic inversion at sea: a RIUSS and a TOSSIT receiver mooring. These two systems are simple enough to be hand deployed from any ships/boats. In this article, the TOSSIT/RIUSS combination is used to collect at-sea data, and the data are used to perform geoacoustic inversion.
The experiment took place in May 2021 on the New England Mud Patch, a location specifically chosen because a previous extensive geoacoustic inversion experiment (SBEX17) was carried out there in 2017. Inversion results obtained using the TOSSIT/RIUSS data compares favorably with results from SBCEX17, obtained with data collected with more complex assets. This demonstrates the relevance of the proposed system.
Further, the TOSSIT/RIUSS data were collected at a time period when a frontal intrusion was present in the water column at the experimental site. This was discovered thanks to CTD data collected during the experiment, showing that the water SSP is highly stratified with a high-speed near-bottom layer caused by a warm water intrusion at depth. To cope with this phenomenon, two different inversion methods were applied. A first inversion assumes that the water SSP is known, while a second inversion jointly estimates water column and seabed properties. A comparison of the results shows that results obtained with known/unknown water-column SSPs are very consistent, although mud sound speeds are slightly more uncertain when the SSP is unknown. This further demonstrates the capacity to estimate relevant seafloor geoacoustic parameters in a dynamic ocean with unknown water column conditions. Last but not least, this study revisits the SBCEX17 location after a 4-year time period. As such, it sheds some light on geoacoustic inversion consistency at a given location over time. This article is thus a landmark before reporting results from 2022 Seabed Characterization Experiment (SBCEX22), which took place in May 2022 in the same experimental area, with the objective of thoroughly revisiting the mud geoacoustic properties, five years after the initial SBCEX17.