Reverberation Data Research Articles

Reverberation modeling workshops.

To evaluate progress made in basic and applied underwater acoustic reverberation modeling and to make recommendations for transitions to operational systems, a series of two reverberation modeling workshops (RMWs) was held (the last in May 2008). A basic goal of the RMWs was to provide well-defined problems and consensus solutions to support verification and validation for new models, upgrades to Navy Standard models, and geoacoustic inversion techniques based on reverberation data. The basic problem in designing the workshop was that even the simplest reverberation problems of interest to the Navy do not have closed form solutions and are still (essentially) beyond our computational capabilities to solve using standard “exact” numerical techniques. All current, practical underwater reverberation models replace the physical problem by employing scattering and loss functions or tables. We discuss the development of a sequence of well-defined problems (physics-based), with the equivalent loss/scattering input, which increases in complexity. We also discuss the lessons learned in this process and point out some of the unexpected results from the workshops, and make recommendations for future benchmarking workshops. [Work supported by the Office of Naval Research.]

Bayesian inversion of seabed reverberation and scattering data.

This paper describes a Bayesian approach to the inversion of ocean acoustic reverberation data for scattering and geoacoustic parameters of the seabed. The seabed is modeled as a sediment layer over a semi‐infinite basement. Interface scattering occurs at the (rough) upper and lower boundaries of the sediment layer, and volume scattering occurs within the layer (the scattering mechanisms are considered to be independent and are modeled using perturbation theory and the Born approximation). Unknown parameters include geoacoustic properties (sediment‐layer thickness and sound speeds, densities, and attenuations for sediments and basement) and scattering properties (roughnesses and scattering strengths for upper and lower sediment boundaries, and volume scattering strength). One dimensional (1‐D) and two‐dimensional (2‐D) marginal probability distributions are computed from the multidimensional posterior probability density (PPD) using Metropolis–Hastings sampling applied in a principal‐component parameter space to provide efficient sampling of correlated parameters. Results indicate that reverberation inversion is a strongly nonlinear inverse problem, with highly multimodal marginal distributions and strong interparameter correlations. Addressing this nonlinearity is of key importance to understanding the information content of reverberation data. [Work funded by the ONR.]

Improved space time prewhitener for linear frequency modulation reverberation using fractional Fourier transform

This letter presents an improved space time prewhitening method for linear frequency modulation (LFM) reverberation. The proposed method transforms the reverberation to fractional Fourier domain to whiten using fractional Fourier transform. The linear varying frequency in LFM reverberation is focused on a stationary frequency, and the adjacent block signal is used as the reference signal of prewhitening. Finally, experiment results with real reverberation data verify that the proposed method improves the detection performance of active sonar in shallow sea significantly.

A NEW ENERGY-FLUX MODEL OF WAVEGUIDE REVERBERATION BASED ON PERTURBATION THEORY

The modal shallow water reverberation theory and the energy-flux shallow water reverberation theory were combined to get a new energy-flux model of waveguide reverberation based on Perturbation theory. There are only three environmental parameters (P, Q, μ) in the new reverberation model. It has clear physical picture and it is satisfied the waveguide constraint without any adjustable parameters. The new energy-flux reverberation model was compared with the modal reverberation model (full-wave reverberation model). The results show that the new model can explain the shallow water reverberation in most cases. It is shown that the contributions of parameter P and Q are mutual compensated (coupled) for a fixed reverberation data, therefore it is hard to extract both of them simultaneously. Finally, parameters P and μ at different frequencies were extracted from the reverberation data of "Qingdao-2005 experiment" in Yellow sea shallow-water area where the parameter Q has been extracted from mode filtering approach previously.

Interference structure of shallow water reverberation in time-frequency distribution

The striations of the reverberation spectrum in the time-frequency distribution were observed in a shallow water acoustic experiment in 2002. A model following the coherent reverberation model developed in 2002 is presented to explain the observed striations. To examine the consistency between the measured data and numerical predictions, we have used a method based on Radon transform for determining the slope of the striations to the measured reverberation data and numerical predictions. The results indicate that the previously developed coherent reverberation model can predict the interference structure of the reverberation intensity in the time-frequency distribution.

Spectral roughness inferred from measured reverberation time series.

Reverberation data are often interpreted in terms of either Lambert’s law or a scattering kernel representation with a specified roughness spectrum. The parameters in these descriptions are adjusted and combined with a propagation model to produce simulated reverberation time series that fit the data. An alternative is to retain the scattering description with two separable factors: a well-defined physics-based vertical angle factor that can be justified analytically and a roughness spectrum factor that is adjusted to reproduce the measured data. For this purpose the scattering description is based on a two-way coupled-mode formalism that was shown to accurately produce reverberation time series for a two-dimensional, rough-bottom Pekeris waveguide [Knobles, Reverberation Workshop I, Austin, TX (November 2006)]. For water-sediment interface scattering, the off-diagonal components of the vertical angle factor in the Born approximation were shown to be equivalent to the kernel adopted by the Reverberation Workshop [Stotts and Koch, JASA Exp. Lett., EL242–EL248 (2008)]. Examples from the Reverberation Workshop problem sets will be used to demonstrate the fitting process for specific roughness spectra.

NUMERICAL SIMULATION ON SEARCHING THE OPTIMUM SOURCE-DEPTH DISTRIBUTION FOR REVERBERATION INVERSION BY SIMULATED ANNEALING

To extract the intrinsic bottom back-scattering information from the reverberation data in shallow water has been a challenge topic for long time. It is shown that the modal back-scattering matrix (MBSM) is the intrinsic description of the bottom scattering.1 The optimum source-depth distribution for inverting MBSM from the reverberation data has been discussed with a Pekeris waveguide.2 In the present work, we extend the procedure to the general case of non-Pekeris waveguide by using the simulated annealing (SA) approach. Numerical simulated examples on searching the optimum source-depth distribution for MBSM inversion are presented. It is shown that: (1) the SA is an effective approach for searching the optimum source-depth distribution for MBSM inversion (2) the MBSM inverted from the optimal source-depth distribution has the strong stability against noise.

Bayesian inversion of reverberation and propagation data for geoacoustic and scattering parameters

This paper applies nonlinear Bayesian inference theory to quantify the information content of reverberation and short-range propagation data, both individually and in joint inversion, to resolve seabed geoacoustic and scattering properties. The inversion of reverberation data alone is shown to poorly resolve seabed properties because of strong multi-dimensional correlations between parameters. Inversion of propagation data alone is limited by different correlations, but better constrains the geoacoustic parameters. However, propagation data are insensitive to scattering parameters such as Lambert's scattering coefficient. In each case the parameter correlations are inherent in the physics of the forward problem (reverberation and propagation) and cannot be overcome by processing or inversion techniques; rather, the inversion of more informative data is required. This is accomplished here by joint inversion of reverberation and propagation data, weighted according to their respective maximum-likelihood error estimates. Joint inversion of reverberation and propagation data collected on the Malta Plateau (Strait of Sicily) resolves both geoacoustic and scattering properties and achieves smaller uncertainties for all parameters than obtained by the inversion of either data set alone.

Coherent backscattering effect from mid‐frequency reverberation measurements in shallow‐water.

The coherent backscattering (or backscattering enhancement) effect is a persistent interference effect which occurs between waves propagating in random media such as randomly distributed scatterers and rough surfaces. Previous experimental and theoretical studies in optics, acoustics, or seismology have demonstrated that the coherent backscattering results in a doubling of the recorded intensity reflected exactly in the backward direction with respect to any other direction. We will present experimental observations of the coherent backscattering effect from mid‐frequency reverberation data (3–4 kHz) collected in shallow water off the west coast of Italy using various sensor array configurations. This demonstrates the presence of coherent effects in shallow water reverberation recordings from rough sea‐beds. Hence, coherent reverberation effects need to be accounted for to obtain accurate predictions of sea clutter levels. Furthermore, accurate rendering of the coherent backscattering effect could be used to simply verify and validate physics‐based undersea clutter models. Practical implementation for the design of active sonar systems will be discussed. [Work supported by ONR, Code 321.]

Extracting bottom information from towed-array reverberation data: Part I: Measurement methodology

Long-range reverberation data were gathered on towed arrays during the NATO Rapid Response exercises (1996–1998) and the Boundary Characterization experiments (2000–2004). The primary tools were various SACLANTCEN/NURC arrays towed by the NATO Research Vessel Alliance. Most of the sites were in the Mediterranean, in both deep and shallow water, but there were sites on the east and west Atlantic continental shelves. This paper describes the experimental measurements, data processing, and quick-look analyses that were used in our REA (rapid environmental assessment) approach. Polar plots of the beam time series, overlaid on the bathymetry of the region, were extremely useful in providing an immediate analysis of the area. The reverberation highlights are usually correlated with bottom bathymetry and known scattering features. However, it was found that the polar plots often showed scattering features not on the charts, but which could often be identified by detailed follow-on bottom surveys. Thus the polar-plot technique is a valuable survey tool. Examples from a number of the sites are illustrated. The reverberation beam time series data, from areas with few scattering features, were used with model predictions to extract estimates of bottom loss and backscattering strength. An example is given here, but details of the modelling procedure and parameter extraction are left to a companion paper. [Work supported in part by the US Office of Naval Research, DRDC Atlantic and NATO SACLANTCEN/NURC].

Extracting bottom information from towed-array reverberation data. Part II: Extraction procedure and modelling methodology

Reverberation data were gathered on the NATO Research Vessel Alliance, using the SACLANTCEN/NURC towed arrays, during the Rapid Response Exercises (1996–1998) and the Boundary Characterization experiments (2000–2004). Most of the sites were in the Mediterranean, but there were shallow-water sites on the east and west Atlantic continental shelves. A companion paper discusses the data gathering, polar-plot displays, and at-sea rapid environmental assessment of the reverberation and scattering features. This paper describes our efforts to use reverberation data from beam time series without prominent scattering features to extract estimates of bottom loss and scattering strength. The emphasis of this paper is on the procedure for extraction of the geoacoustic properties of the seafloor and on the modelling methodology used for the model-data comparisons. Towed-array beam patterns are included in the modelling, so polar plots of model-data differences can be used to provide a crude scattering map of the area. A manual inversion procedure was used at sea during the experiments for extracting bottom properties; the results compared reasonably well with post-trial measurements and estimates using an automated version of the extraction procedure. [Work supported in part by the US Office of Naval Research, DRDC Atlantic, and NATO SACLANTCEN/NURC].

Combined Geoacoustic Inversion of Propagation and Reverberation Data

Sonar performance predictions in shallow water are strongly dependent on good knowledge of the geoacoustic and scattering properties of the seabed. One technique to extract information about the bottom is to use a towed source and a towed horizontal array. This towed system has been shown to be applicable for characterizing the bottom properties locally by inversion of the acoustic signals received directly on the towed array at short ranges. The same towed system has also been applied to extract bottom properties from long-range reverberation data providing effective bottom properties over a large area. However, independent geoacoustic inversion of the short-range propagation and long-range reverberation data can introduce low sensitivity and uncertainty in the extracted bottom properties. An attempt to resolve this low sensitivity and ambiguity is made by a simultaneous geoacoustic inversion of short-range propagation and long-range reverberation data with the intention of constraining the possible solutions of the bottom properties.

Linear frequency modulation reverberation suppression using difference of singular values

This letter proposes a reverberation suppression method to improve the target detection probability in reverberation environment induced by a linear frequency modulation signal. Using the singular value decomposition and an assumption of local spatial stationarity, the proposed algorithm suppresses reverberation utilizing the difference of singular values between the reference beam and the current beam of interest. Several experiments using real oceanic reverberation data justify the validity of the proposed algorithm.

Slabs and shear wave reflectors in the midmantle

An extensive analysis of multiple ScS reverberation data sets sampling regions of active or recent subduction reveals evidence of midmantle reflections apparently stemming from fragments of subducted slabs or from the interaction between subducted slabs and the surrounding mantle. Transition zone reflectors are detected beneath the southwest Pacific Ocean and Melanesia with mean depths of ∼850 and 1100 km in the majority of source–receiver corridors crossing the study area. The observations are most spatially coherent beneath the Coral and Tasman Seas. Coincident observations of the two reflectors along most seismic corridors suggests (but does not mandate) the existence of two distinct reflectors rather than bimodal depth distribution of a single reflector or distributed scatterers. Beneath North America, reflectors at depths of ∼1380 and 1530 km are seen in the midcontinent region; further east, the reflections are shallower, with depths near 940 and 1130 km. Unlike the southwest Pacific, the reflectors are not paired in any of the individual source–receiver corridors. This and the depth variability of the observations indicate that the reflector (or reflectors) in the Americas is (are) fragmented from west to east (transecting source–receiver corridors). The impedance contrasts of these features rival that of the 660‐km discontinuity, suggesting that individual fragments of the reflecting surfaces must be relatively continuous and flat from north to south (along individual corridors) to maintain a strong apparent impedance contrast. The reflections in both study areas are unlikely to be the result of slabs interacting with a chemical boundary layer or small‐scale scatterers within the midmantle. More likely these reflectors result from a pressure–temperature‐dependent phase transition within or around subducting slabs.

Fitting data, but poor predictions: Reverberation prediction uncertainty when seabed parameters are derived from reverberation measurements

For many decades, researchers have been developing inverse techniques for estimating seabed parameters from reverberation data, notably scattering strength. Generally, the angular dependence of the scattering kernel is unknown and is either solved for or assumed fixed. In either case, agreement is typically quite good between the measured reverberation and that modeled (by fitting scattering parameters). However, what are the resulting uncertainties in a reverberation prediction if the ocean or geometry changes? The main results of the paper are that (1) these prediction uncertainties are surprisingly large, of order 10 dB at 10 km and thus (2) traditional/current methods for reverberation inversion should be augmented, mitigating the large prediction uncertainties by an additional measurement. Several options for additional measurements are discussed.

Combined inversion of mid‐frequency propagation and reverberation sonar data

Sonar performance predictions in shallow‐water regions are strongly dependent on a good knowledge of the geoacoustic and scattering properties of the seabed. The bottom properties are probably the most difficult parameters to determine, but inversion of measured acoustic data to infer the geoacoustic and scattering properties is a feasible technique. One of these techniques relies on inverting: (1) propagation data to estimate local bottom properties and (2) long‐range reverberation data providing effective bottom properties over larger areas. A matched‐field inversion approach is applied to propagation and reverberation data received on a towed horizontal array during the BASE'04 experiment conducted on the Malta Plateau, Mediterranean Sea. A total of 30 transmissions along a 10‐km track were used to capture eventual range‐dependent bottom properties. The inversion algorithm is composed of efficient prediction tools which can provide environmental parameter estimates within tactical time frames for in‐situ sonar performance predictions. The experimental set‐up mimics a mid‐frequency active sonar system using only the suite of sensors available on the vessel towing the sonar system; also known as the through‐the‐sensor technique. The impact on sonar performance utilizing the environmental characterization approach is shown for various experimental scenarios and seasons. [Research sponsored by NURC and the BOUNDARY Partners].

Characterization of seabed geo‐acoustic structure for a shallow water environment

Full‐field inversion methods over large frequency bands and spatial scales attempt to exploit the sensitivity of the frequency and spatial dependence of the acoustic field of the properties to the seabed. A comprehensive set of broadband impulsive and narrowband tonal acoustic recordings in the 5‐3000 Hz band from two L‐arrays separated by 20 km were made in a shallow water area on the New Jersey continental shelf during the Shallow Water 2006 (SW06) experiment. In addition, surface ship of opportunity passages on both arrays were recorded along with noise during the passage of tropical storm Ernesto. Reverberation and transmission loss data in the 25‐9200 Hz band from explosive sources were also collected at a nearby site prior to the SW06 experiment. Numerous full‐field geo‐acoustic inversion methods and analyses of all these acoustic data with supporting range and azimuth‐dependent geo‐physical measurements are employed to characterize the seabed properties. For example, the analyses of these data permit inferences about the frequency‐dependence of the seabed sound speed and attenuation to be made. The overlapping data types act to reduce the intrinsic ambiguities associated with inversion, quantify the spatial variability, and serve as independent validation.

Constrained comparison of ocean acoustic reverberation: Theory and observations

Measurements of long-range (order 104 m) shallow-water reverberation in the Straits of Sicily at 900 and 1800 Hz are compared with theoretical predictions. All of the required environmental inputs for the theory are obtained independently, that is to say there are no free parameters. The reflection coefficient and the scattering strength are measured by direct path methods; both quantities show strong frequency dependence. The theoretical reverberation predictions using these measurements are in good agreement with directional reverberation data, i.e., within the expected uncertainty bounds. The good agreement suggests that the supporting environmental measurement techniques are robust and that the physics associated with reverberation in a waveguide is reasonably well understood, at least in simple environments. The ability to independently measure the seabed scattering strength and reflection coefficient is a crucial step for the advancement of inverse methods using reverberation (e.g., rapid environmental assessment) inasmuch as it provides the means for quantitatively measuring the robustness of those methods. [Research supported by the Office of Naval Research OA321 and the NATO Undersea Research Centre.]

Frequency and angular dependence of bottom scattering strength in shallow water with a sandy seabed

The bottom scattering strength at low frequencies and small grazing angles is difficult to directly measure in shallow water. It is generally derived from mid- and long-range reverberation measurements. Reliable estimation of the bottom scattering strength from shallow-water reverberation requires a correct reverberation model, quality reverberation data, and an appropriate seabed geo-acoustic model that controls two-way sound propagation. In this paper, an effective Biot model for sand-silt bottoms, derived from low-frequency field measurements at 18 locations in different coastal zones around the world is used [J. X. Zhou and X. Z. Zhang, J. Acoust. Soc. Am. 117, 2494 (2005) and 119, 3447 (2006)]. A simple closed form expression for the reverberation in shallow isovelocity water [J. X. Zhou, Acta Acustica 5(2), 86–99(1980) in Chinese] as well as the normal-mode expression for the reverberation in shallow water with an arbitrary sound speed profile are used to derive the bottom scattering strength. The bottom scattering strength as a function of frequency and angle, derived from broadband reverberation data, will be reported and discussed. [Work supported by ONR.]

The optimum source depth distribution for reverberation inversion in a shallow-water waveguide

An approach for extracting the modal backscattering matrix from reverberation data in shallow water was proposed recently (Shang, Gao, and Tang, 2002). The kernel matrix of the inversion is constructed using the square of the modal functions. The singularity of this matrix (or the stability of the inversion) is the crucial issue to be considered. In this paper, we discuss this issue analytically for a Pekeris waveguide with the limited mode number M. The method that we used for singularity analysis is to calculate the maximum value of the determinant of this kernel matrix. We found that there is an optimum source depth distribution corresponding to the maximum value of the determinant of the kernel matrix. That means that, by choosing the optimum source depth distribution, we can get the most stable inversion. The conclusion is that, under a quite tolerant condition, the matrix is not singular, and the backscattering matrix can be inverted.