Perturbative inversion of geoacoustic parameters in a shallow waterenvironment

In many strategic shallow water areas, the geoacoustic properties of the sub-bottom are largely unknown. This paper demonstrates that inverse theory and measured data from a single hydrophone can be used to accurately deduce the geoacoustic properties of the sub-bottom, even when the initial background geoacoustic model is a highly inaccurate estimate. Since propagation in shallow water is very sensitive to the geoacoustic properties of the sub-bottom the inverse technique is a vitally important, practical, and inexpensive means to improve sonar performance prediction in a potentially hostile environment. To provide ground truth for the inverse technique, measured data collected during Project GEMINI were compared to the inverse solutions. Detailed, site-specific geoacoustic models were developed for two array locations and the finite-element parabolic equation (FEPE) model was used to estimate transmission loss (TL). The model estimates from FEPE compared well with the measured data and the detailed geoacoustic models were considered as “ground truth.” To test the efficacy of the technique, initial background geoacoustic models were constructed assuming no a priori information of the bottom. The resultant inverse solution was used to predict the geoacoustic properties at each of the sites. The final results were in excellent agreement with the measured data and the resulting TL estimates derived from the inverse technique were as good or better than the TL estimates obtained from the detailed, site-specific geoacoustic models     

Performance comparison between vertical and horizontal arrays for geoacoustic inversion

Most of the research on model-based geoacoustic inversion techniques has concentrated on data collected using moored vertical receiver arrays. However, there are many advantages to considering geoacoustic inversion using a towed horizontal array. Towed arrays are easily deployed from a moving platform; this mobility makes them well suited for surveying large areas for sea-bed properties. Further, if a model-based geoacoustic inversion scheme uses both a towed source and array, the separation between the two can be kept short, which reduces the requirement for range-dependent modeling. Range-independent modeling is used for inverting all the horizontal array data considered in this paper. Using the Inversion Techniques Workshop Benchmark Test Cases, the performance of a horizontal (simulated towed) and vertical arrays are compared and found to be very similar. However, it will be shown that, for Benchmark Test Case 3, where the bathymetry is flat and a hidden bottom intrusion exists, a towed horizontal array is ideal for determining the range-dependent sea-bed properties. The practical advantages of using a towed array are clear and the purpose of this paper is to show that the performance is similar (and in some cases better) than using moored vertical arrays.     

Broad-band geoacoustic inversion in shallow water from waveguideimpulse response measurements on a single hydrophone: theory andexperimental results

The paper discusses an inversion method that allows the rapid determination of in situ geoacoustic properties of the ocean bottom without resorting to large acoustic receiving apertures, synthetic or real. The method is based on broad-band waterborne measurements and modeling of the waveguide impulse response between a controlled source and a single hydrophone. Results from Yellow Shark '94 experiments in Mediterranean shallow waters using single elements of a vertical array are reviewed, inversion of the bottom parameters is performed with an objective function that includes the processing gain of a model-based matched filter (MBMF) receiver relative to the conventional matched filter. The MBMF reference signals incorporate waveguide Green's functions for known geometry and water column acoustic model and hypothesized bottom geoacoustic models. The experimental inversion results demonstrated that, even for complex environmental conditions, a single transmission of a broad-band (200-800 Hz) coded signal received at a single depth and a few hundred forward modeling runs were sufficient to correctly resolve the bottom features. These included the sound speed profile, attenuation, density, and thickness of the top clay sediment layer, and sound speed and attenuation of the silty clay bottom. Exhaustive parameter search proved unequivocally the low-ambiguity and high-resolution properties of the MBMF-derived objective. The single-hydrophone results compare well with those obtained under identical conditions from matched-field processing of multitone pressure fields sampled on the vertical array. Both of these results agree with expectations from geophysical ground truth. The MBMF has been applied successfully to a field of advanced drifting acoustic buoys on the Western Sicilian shelf, demonstrating the general applicability of the inversion method presented     

Quantifying data information content in geoacoustic inversion

This paper examines the information content in matched-field geoacoustic inverse problems as a function of a variety of experiment factors, with the aim of guiding data collection and processing to achieve the best possible inversion results. The information content of the unknown geoacoustic parameters is quantified in terms of their marginal posterior probability distributions, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. When sampled to convergence, the marginal distributions are found to have simple, smooth shapes that facilitate straightforward comparisons. The approach is general; the specific examples considered here include factors such as the number of sensors in the receiving array, array length, source-receiver range, source frequency, number of frequencies, source bandwidth, and signal-to-noise ratio     

Matched-field inversion for geoacoustic model parameters in shallowwater

Matched-field inversion is used to, estimate geoacoustic properties from data obtained in an experiment with a vertical line array (VLA). The experiment was carried out using broad-band sources (shots) in water depths of about 200 m on the continental shelf off Vancouver Island. The data were processed to obtain spectral components of the field for frequencies near the bubble frequency for the shot. The ocean bottom in this region consists of a layer of mainly sandy sediments (about 100 m thick) overlying older consolidated material. Consequently, the inversion was designed to estimate the parameters of a two-layer elastic sediment model. In the inversion, an adaptive global search algorithm was used to investigate the multidimensional space of geoacoustic models in order to determine the set of values corresponding to the best replica field. Convergence is driven by adaptively guiding the search to regions of the parameter space associated with above-average values of the matched field correlation between the measured and replica fields. The geoacoustic profile estimated by the inversion consisted of a 125-m layer with compressional speed ~1700 m/s and shear speed ~400 m/s, overlying a layer with compressional speed ~1900 m/s. This model is consistent with the results from conventional seismic experiments carried out in the same region     

An investigation of algorithm-induced variability in geoacoustic inversion

This paper investigates the inherent variability in the results of matched-field geoacoustic inversion algorithms. This algorithm-induced variability must be considered when interpreting inversion results in terms of environmental changes as a function of time or space. Fast simulated annealing (FSA), genetic algorithms (GA), and a hybrid algorithm (adaptive simplex simulated annealing; ASSA) are compared by performing multiple inversions of benchmark synthetic data (noise free and noisy) and acoustic data measured over both low- and high-speed sea-bed sediments in the MAPEX 2000 experiment. ASSA produced the lowest variability in inversion results for all cases, followed by GA and FSA. For the high-speed MAPEX 2000 case, the variability is essentially negligible, while for the low-speed case the variability is significant as compared with environmental variations reported in the literature.     

Effective parameters for matched field geoacoustic inversion in range-dependent environments

Using the well-established technique of geoacoustic inversion, one can estimate a set of acoustic sea-bed parameters from sonar array data. Simultaneously, one can search for geometric parameters such as range, water depth, and hydrophone depth. When the technique is applied in a range-dependent environment, there is a potentially much larger set of parameters to match, unless one has perfect knowledge of the bathymetry. From the point of view of optimization, one needs to handle uncertainties in bathymetry without hugely increasing the amount of computation. A simple time-domain view (which is shown to be equivalent to the adiabatic approximation) suggests that it is sufficient to use a range-independent model with an empirical "effective" depth even when the bottom is not flat. In fact, there is a set of effective environments that will suffice; one can choose whichever is the most convenient. The success of this concept is demonstrated with some test cases from a recent Geoacoustic Inversion Techniques Workshop.     

Modal evolution and inversion for seabed geoacoustic properties inweakly range-dependent shallow-water waveguides

In a shallow-water ocean environment, the range dependent variation of the geoacoustic properties of the seabed is one of the crucial factors affecting sound propagation. Since the local modes of propagation depend on the spatial changes in the bottom sediments, the local eigenvalues of these modes are useful as tools for examining the range dependence of the sediment properties. In order to extract the local eigenvalues from measurements of the pressure field in a laterally inhomogeneous waveguide, the zeroth-order asymptotic Hankel transform with a short sliding window is utilized. The local peak positions in the output spectra differ from the local eigenvalues due to both the range variation of the local modes and the interference of adjacent modes. The departure due to the former factor is evaluated analytically by using the stationary phase method. In order to reduce the error induced by the latter factor, mode filtering is utilized by incorporating data from a fixed vertical array of receivers. The methods developed are applied to simulated pressure field data as well as experimental field data, and it is shown that the range evolution of the local modes can be successfully estimated. In addition, field measurements are used to demonstrate that the modal trajectories in range can be used to infer the range-dependent geoacoustic properties of the seabed     

Geoacoustic inversion of broad-band acoustic data in shallow water on a single hydrophone

The inversion of broad-band low-frequency acoustic signals received on sparse arrays can lead to robust and efficient estimations of sea-bed properties. This paper describes a shallow-water geoacoustic inversion scheme based on the use of a model-based matched-impulse response on a single hydrophone. Results from the INTIMATE'96 experiment on the Portuguese shelf break are reviewed. In order to minimize the effects of strong time variability due to internal tides, only the time-stable waterborne bottom-surface reflected arrivals are exploited. A quasi-linear inversion algorithm is first applied to refine the geometry of the experiment. Then, inversion of bottom parameters is performed with an objective function that only makes use of the bottom-surface reflected arrivals' amplitudes. The experimental results show that broad-band transmissions (300-800 Hz) received on a single hydrophone, combined with the use of a simple eigenray code, are sufficient to correctly resolve geometrical parameters and bottom features. The analysis of the reflection coefficients both on simulated and real data helps to understand the validity of the inverted parameters and to derive the basis of an equivalent medium concept for geoacoustic inversion based on a "through-the-sensor" approach.     

Experimental matched-field localization results using a short vertical array and mid-frequency signals in shallow water

Traditionally, matched-field processing (MFP) has been used to localize low-frequency sources (e.g., <300 Hz) from their acoustic signals received on long vertical arrays. However, some sources emit acoustic signals of much higher frequency. Applying MFP to signals in the mid-frequency range (e.g., 1-4 kHz) is a very challenging problem because MFP's sensitivity to environmental parameter mismatch becomes more severe with increasing frequency. Robust MFP techniques are required to process signals in the mid-frequency range. As a practical issue, short vertical arrays are more convenient to work with than are long vertical arrays; they are easier to deploy and are less prone to large amounts of deformation. However, short vertical arrays undersample the water column, which can result in severely degraded MFP performance. In this paper, we present experimental data results for this nonconventional paradigm. Using the environmentally robust broad-band L/sub /spl infin//-norm estimator, MFP results are given using shallow-water experimental data. This data consisted of broad-band signals in the 3-4-kHz band collected on an eight-element 2.13-m vertical array. These results serve to demonstrate that good localization performance can be attained for this difficult problem. Guidelines on the appropriate use of ray and normal-mode propagation models are also presented.     

Calculation of the added mass of elliptical cylinders with vertical fins in shallow water

In order to carry out any studies of ship motions, concerning either seakeeping or manoeuvring, it is usually necessary to have knowledge of the added mass of the hull section shapes. In deep water, the added mass can be found using conformal mapping techniques combined with residue calculus, or by means of surface singularity distributions. In shallow water, the need to utilise an infinite number of mirror images, to represent the effects of the seabed and the free surface, precludes the use of the deep-water methods in this case. In previous papers, the author presented methods to evaluate the added mass of semi-circular and elliptical body sections. Now, using a similar Schwarz–Christoffel method, the added mass of elliptical body sections with vertical fins in shallow water is evaluated.     

Estimates of geoacoustic model parameters from inversions of horizontal and vertical line array data

This paper describes results from geoacoustic inversion of low-frequency acoustic data recorded at a receiving array divided into two sections, a sparse bottom laid horizontal array (HLA) and a vertical array (VLA) deployed in shallow water. The data are from an experiment conducted by the Norwegian Defence Research Establishment (FFI) in the Barents Sea, using broadband explosives (shot) sources. A two-layer range-independent geoacoustic model, consistent with seismic profiles from the area, described the environment. Inversion for geoacoustic model parameters was carried out using a fast implementation of the hybrid adaptive simplex simulated annealing (ASSA) inversion algorithm, with replica fields computed by the ORCA normal mode code. Low-frequency (40-128 Hz) data from six shot sources at ranges 3-9 km from the array were considered. Estimates of sediment and substrate p-wave velocities and sediment thickness were found to be consistent between independent inversions of data from the two sections of the array.     

Geoacoustic inversion by matched-field processing combined with vertical reflection coefficients and vertical correlation

The wide-band source (WBS) signals measured in the Asian Seas International Acoustics Experiment (ASIAEX) in the East China Sea (ECS) were used to invert for geoacoustic parameters. Sound speed and density were inverted using the matched-field processing method combined with the vertical reflection coefficients and sea-bed attenuation coefficients were inverted from the vertical correlation data. For a half infinite liquid sea-bottom model, the inverted equivalent bottom sound speed is 1610/spl plusmn/12 m/s and the bottom density is 1.86 g/cm/sup 3/. The inverted attenuation coefficients are well described by a nonlinear relationship of the form /spl alpha//sub b/=0.28f/sup 1.58/ dB/m (f is in units of kilohertz) in the frequency range of 100-600 Hz.     

High-frequency reverberation in shallow water

Monostatic reverberation measurements were collected in shallow water, over a coarse gravel and cobble bottom, 100 m deep, off the coast of Nova Scotia. Data were collected at frequencies of 21, 28, and 36 kHz using linear FM pulses of 2-kHz bandwidth and 0.160-s duration. An anchored, high-frequency active sonar array deployed at a depth of 42 m was used to collect the data. The reverberation measurements were compared with estimates computed with the NUWC generic sonar model (GSM). The data were reasonably well modeled for times greater than 0.2 s after pulse transmission by neglecting surface reverberation and using Lambert's rule for bottom backscattering with a scattering coefficient of -27 dB, independent of frequency. At all three frequencies, the data and model show a peak approximately 0.9 s after pulse transmission. This peak results from a focusing effect that the downward-refracting sound-speed profile has on the interaction of the rays with the bottom     

Seismo-acoustic field statistics in shallow water

The spatial statistics of the acoustic field in shallow water are strongly affected by interfacial roughness and volume fluctuations in the water column or the seabed. These features scatter energy, reducing the coherence of the acoustic field. This paper introduces a consistent, mode-based modeling framework for ocean scattering. First, the rough surface scattering theory of Kuperman and Schmidt is reformulated in terms of normal modes, resulting in computation times which are reduced by several orders of magnitude. Next, a perturbation theory describing scattering from sound speed and density fluctuations in acoustic media is developed. The scattering theories are combined with KRAKEN, creating a unified normal mode code for wave theory modeling of shallow-water spatial statistics. The scattered field statistics are found to be a complicated function of scattering mechanism, scatterer statistics, and acoustic environment. Bottom properties, including elasticity, strongly influence the scattered field     

Wave height distribution in shallow water

Probability distribution of shallow water wave heights, obtained from a pressure type recorder, are examined. It is tested with the theoretical distributions of (a) Rayleigh, (b) Weibull, (c) Gluhovski, (d) Ibrageemov and (e) Goda. The best fit is shown by the Gluhovski probability density function with a correlation coefficient greater than 0.8. The functions of Weibull, Ibrageemov and Goda fit only half of the tested cases. The role of wave steepness in the wave height distribution is found to be negligible.     

Bound waves and triad interactions in shallow water

Boussinesq type equations with improved linear dispersion characteristics are derived and applied to study wave-wave interaction in shallow water. Weakly nonlinear solutions are formulated in terms of Fourier series with constant or spatially varying coefficients for two purposes: to derive higher order boundary conditions for regular and irregular wave trains and to derive evolution equations on constant or variable water depth. Wave transformation of monochromatic, bichromatic and irregular waves is studied and comparison with measurements and direct time domain solutions shows good agreement. The improvement relative to classical models from the literature is discussed.     

Coupled scattering and reflection measurements in shallow water

The characteristics of shallow-water reverberation are often controlled by scattering from the seabed. While scattering mechanisms are understood in general, the state-of-the-art falls far short of predicting the correct angular and frequency dependence of scattering in a given region. A series of acoustic and supporting geoacoustic measurements were conducted over a large area in the Straits of Sicily in order to study seabed scattering in a complex littoral environment. The hypothesis was that exploiting direct path reflection coefficient measurements, in conjunction with the scattering measurements, could help illuminate the underlying scattering mechanisms. The sediment at the seabed interface was found to be a fine silty clay with nearly uniform properties across the area. Notwithstanding this spatial homogeneity, 1-6-kHz reflection and scattering measurements showed significant spatial variability. The coupled reflection-scattering approach resolved this apparent discrepancy, revealing that the reflection and scattering processes are largely controlled by the sediment properties below, rather than at, the water sediment interface. Measurements at 3600 Hz show that site-to-site variability is in part controlled by the thickness of the silty-clay layer. Layers up to 10 m below the water sediment interface contribute to the scattering at 3600 Hz.