Anthony P. Lyons

Novel physical interpretations of K-distributed reverberation

Interest in describing and modeling envelope distributions of sea-floor backscatter has increased recently, particularly with regard to high-resolution active sonar systems. Sea-floor scattering that results in heavy-tailed-matched-filter-envelope probability distribution functions (i.e., non-Rayleigh distributions exemplified by the K, Weibull, Rayleigh mixture, or log-normal distributions) is often the limiting factor in the performance of these types of sonar systems and in this context is referred to as reverberation or acoustic clutter analogous to radar clutter. Modeling of reverberation has traditionally entailed fitting various candidate distributions to time samples of the envelope of the scattered sonar (or radar) returns. This type of descriptive analysis and the asymptotic (infinite number of scatterers) analysis defining the K-distribution yield little insight into the environmental mechanisms responsible for heavy-tailed distributions (e.g., distributions and, clustering of discrete scatterers, patchiness in geo-acoustic properties, scattering strength of scatterers, etc.) and do not allow evaluation of the effect of changing sonar system parameters such as bandwidth and beamwidth. In contrast, we derive the envelope distribution for the scattered returns starting from simple physical descriptions of the environment with a finite number of scatterers. It is shown that plausible descriptions of the environment can lead to K-distributed reverberation. This result explains, at least partially, the success of the K-distribution in the modeling of radar clutter and sonar reverberation at a variety of frequencies and scales. The finite-number-of-scatterers model is then used to predict how the shape parameter of the K-distribution will change as the beamwidth of a towed-array receiver is varied. Analysis of reverberation data from a low-frequency (450-700 Hz) active sonar system illustrates that, within our ability to estimate it, the shape parameter of the K-distribution is proportional to the beamwidth of the towed-array receiver, a result important for sonar simulation and performance prediction models. These results should prove useful in developing methods for modeling, predicting and mitigating reverberation on high-resolution sonar systems.

Statistical characterization of high-frequency shallow-water seafloor backscatter

Knowledge of the background reverberation environment is a prerequisite for the design of any target detection scheme. While the problem of understanding and predicting high-frequency background seafloor reverberation level or mean energy scattered per unit area of the seabed has received considerable attention, studies of high-frequency reverberation amplitude statistics are relatively scarce. Of these studies, many have dealt with scattering from more or less homogeneous seafloors in terms of bottom type, whereas most shallow-water areas will not be homogeneous but will have patchiness in space and time which will have a strong influence on scattered amplitude statistics. In this work, a comparison is presented between 80-kHz seafloor backscatter statistics obtained at shallow-water sites around Sardinia and Sicily. The data include measurements from several distinct bottom provinces, including sites with Posidonia Oceanica sea grass and sites covered with live shellfish. Results of the analysis are cast both in terms of mean power level or backscattering coefficient as well as of the amplitude statistics. The reverberation statistics did not always exhibit a Rayleigh probability distribution function (PDF), but exhibited statistical distributions with heavier tails. Several more appropriate models of reverberation PDF were examined in order to better describe the measured amplitude distributions. The Rayleigh mixture and the K models were found to be the most robust in describing the observed data.

ACOUSTIC SCATTERING FROM THE SEAFLOOR : MODELING AND DATA COMPARISON

An existing model of seafloor backscattering [D. R. Jackson, D. P. Winebrenner, and A. Ishimaru, J. Acoust. Soc. Am. 79, 1410–1422 (1986)] was implemented with the additions of volume scattering from a random inhomogeneous continuum and scattering from subbottom interfaces. Results of computer simulations with the extended model were compared with values of scattering strength obtained from processed GLORIA data from the Monterey Fan off the coast of California. Regions of well‐delineated high and low backscatter are seen in the GLORIA imagery. The geoacoustic input parameters for the simulation runs were either taken directly from or estimated from core data obtained by ground truth sampling in the image area. From the model simulation results it appears that the main factor causing the observed dichotomous character of the strength of returns in the Fingers Area is the presence or absence of a topmost, inhomogeneous silt‐clay layer (with a thickness of around 1–1.5 m). In the high backscatter areas, inh...

Simulation of non-Rayleigh reverberation and clutter

The simulation of active sonar reverberation time series has traditionally been done using either a computationally intensive point-scatterer model or a Rayleigh-distributed reverberation-envelope model with a time-varying power level. Although adequate in scenarios where reverberation arises from a multitude of scatterers, the Rayleigh model is not representative of the target-like non-Rayleigh reverberation or clutter commonly observed with modern high-resolution sonar systems operating in shallow-water environments. In this paper, techniques for simulating non-Rayleigh reverberation are developed within the context of the finite-number-of-scatterers representation of K-distributed reverberation, which allows control of the reverberation-envelope statistics as a function of system (beamwidth and bandwidth) and environmental (scatterer density and size) parameters. To avoid the high computational effort of the point-scatterer model, reverberation is simulated at the output of the matched filter and is generated using efficient approximate methods for forming K-distributed random variables. Finite impulse response filters are used to introduce the effects of multipath propagation and the shape of the reverberation power spectrum, the latter of which requires the development of a prewarping of the K distribution parameters to control the reverberation-envelope statistics. The simulation methods presented in this paper will be useful in the testing and evaluation of active sonar signal processing algorithms, as well as for simulation-based research on the effects of the sonar system and environment on the reverberation-envelope probability density function.

Predictions of the acoustic scattering response of free‐methane bubbles in muddy sediments

The response of the sediments of Eckernfoerde Bay, Germany to acoustic remote sensing previously has been attributed qualitatively to gas features which were postulated to exist in situ within the sediment. The existence of features as small as 0.5‐mm equivalent spherical radius has now been confirmed by x‐ray computed tomography of cores taken and scanned at in situ pressures. The interaction of an acoustic pulse from the acoustic sediment classification system (ASCS) with this type of gassy sediment was modeled and the results are presented here. The bubble scattering response model includes both the effects of nonspherical bubbles and of sediment resistance to shear deformation (as expressed by the dynamic shear modulus). Model predictions made using the observed gas bubble distribution agree with normal incidence ASCS data, exhibiting extended returns (i.e., greater than the source pulse length) from the seafloor bubble layers as well as high attenuation within the bubble layers. Spectrograms of ASCS ...

Reverberation envelope statistics and their dependence on sonar bandwidth and scattering patch size

Increasing transmit waveform bandwidth in an active sonar-system results in an increase in the signal-to-reverberation power ratio in reverberation-limited environments, but also changes the probability density function of the reverberation envelope. A recent model that relates a description of the sonar system and environment to the parameters of the K-distribution predicts that the shape parameter (/spl alpha/) is proportional to range, beamwidth, and the density of scattering patches on the sea floor and is inversely proportional to bandwidth. In this paper, the bandwidth relationship is examined with real data from a low-frequency active sonar system with a towed array receiver. The inverse proportionality is observed at low bandwidths as a trend away from a Rayleigh-distributed envelope (decreasing /spl alpha/) as bandwidth increases. However, a trend back toward Rayleigh reverberation (increasing /spl alpha/) is observed as bandwidth continues to increase. Hypothesizing that the increase in /spl alpha/ arises from over-resolving scattering patches in range and not in angle, the model of is extended to account for patch size relative to that of the sonar-resolution cell. The shape parameter of a moment-matched K-distribution derived from the extended model is then seen to provide a good fit to that estimated from the data.

Reliable Methods for Estimating the

Parameter estimation for the K-distribution is an essential part of the statistical analysis of non-Rayleigh sonar reverberation or clutter for performance prediction, estimation of scattering properties, and for use in signal and information processing algorithms. Computational issues associated with maximum-likelihood (ML) estimation techniques for K-distribution parameters often force the use of the method of moments(MoM). However, as often as half the time, MoM techniques will fail owing to a noninvertible equation relating the shape parameter (α) to a particular moment ratio, which is equivalent to the detection index (D) of the matched-filter envelope. In this paper, a Bayesian approach is taken in developing a MoM-based estimator for D, and therefore a, that reliably provides a solution and is less computationally demanding than the ML techniques. Analytical-approximation (AA) and bootstrap-based (BB) approaches are considered for approximating the likelihood function of D and forming a posterior mean estimator, which is compared with the standard MoM and ML techniques. Computational complexity (in the form of execution time) for the Bayes-MoM-AA estimator is on the order of the standard MoM estimator while the Bayes-MoM-BB estimator can be 1-2 orders of magnitude greater, although still less than ML techniques. Performance is seen to be better than the standard MoM approach and the ML techniques, except for very small α (<; 3) where the ML techniques remain superior. Advantages of the Bayesian approach are illustrated through the use of alternative priors, the formation of Bayesian confidence intervals, and a technique for combining estimates from multiple experiments.

K

Abnormally high levels of methane gas in seafloor sediments could pose a major hazard to coastal populations within the next 100 years through their impact on climate change and sea level rise. Marine scientists have known for many years that biogenic methane (CH4) is generated in shallow seabed sediments on continental margins, especially in rapidly deposited muddy sediments with high organic matter content (see Methane Flux Control in Ocean Margin Sediments (METROL) project in Mienert et al., [2004]). Gassy sediments are found in river deltas, estuaries, and harbors, but also in deeper waters on continental shelves and slopes. Human activities can accelerate natural seafloor gas generation by increasing the supply of sediments and organic matter from rivers through deforestation and intensive farming, and also by the disposal of human waste at sea. When this extra organic matter becomes buried to about one meter beneath the seabed, biogeochemical processes start to convert it to CH4 [Floodgate and Judd, 1992]. The impact of this extra CH4 could be felt within the next 100 years, assuming a one-centimeter-per-year sediment accumulation rate.

-Distribution Shape Parameter

Recent backscattering measurements made in the Gulf of La Spezia, Italy, using a sonar operating at 140 kHz combined with thorough characterization of seabed interface and volume properties illustrate the importance of seabed volume scattering. Three-dimensional fluctuation statistics of density variability and vertical density gradients, both of which are attributed to the level of bioturbation (e.g., sea shell fragments, burrows, pockets of water) have been quantified using X-Ray computed tomography. Two-dimensional interface roughness spectra have also been determined using a digital stereo photogrammetry system. The combined ground truth has allowed a backscattering model to be fully constrained. Measured backscattering strength versus angle is compared to a model that includes the effects of varying density and sound speed. Data-model comparisons show that scattering from the volume of strongly inhomogeneous sediments can often be a primary contributor to seafloor scattering away from normal incidence.

Shallow seabed methane gas could pose coastal hazard

This paper examines the impact that a thin layer of varying density would have on high-frequency reflection, forward loss, and backscattering of acoustic plane waves from the seafloor. A functional form for density stratification was found by examination of several high-resolution density profiles obtained from X-ray computed tomography (CT) scans of seafloor cores. A solution based on these general profiles was used to estimate the reflection coefficient. The influence of the density profile on reflection loss and backscatter was then calculated using the estimated reflection coefficient. Parameter values used in simulations were obtained from the literature or from the CT scans of cores. It was found that inclusion of a density profile adds a strong frequency dependence to estimates of the reflection coefficient and forward loss. The largest effect on total scattering strength is near normal incidence where returns are dominated by interface scattering. The effect of the density profile on the strength of acoustic returns suggests that care should be taken when using high-frequency systems for measuring sediment properties, especially near normal incidence.