Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

Comparison of model selection techniques for seafloor scattering statistics

In quantitative analysis of seafloor imagery, it is common to model the collection of individual pixel intensities scattered by the seafloor as a random variable with a given statistical distribution. There is a considerable literature on statistical models for seafloor scattering, mostly focused on areas with statistically homogeneous properties (i.e. exhibiting spatial stationarity). For more complex seafloors, the pixel intensity distribution is more appropriately modeled using a mixture of simple distributions. For very complex seafloors, fitting 3 or more mixture components makes physical sense, but the statistical model becomes much more complex in these cases. Therefore, picking the number of components of the mixture model is a decision that must be made, using a priori information, or using a data driven approach. However, this information is time consuming to collect, and depends on the skill and experience of the human. Therefore, a data-driven approach is advantageous to use, and is explored in this work. Criteria for choosing a model always need to balance the trade-off for the best fit for the data on the one hand and the model complexity on the other hand. In this work, we compare several statistical model selection criteria, e.g., the Bayesian information criterion. Examples are given for SAS data collected by an autonomous underwater vehicle in a rocky environment off the coast of Bergen, Norway using data from the HISAS-1032 synthetic aperture sonar system.Comment: Paper presented at the 5th International Conference on Synthetic Aperture Radar and Sonar, Lyric Italy, September 202

THE ANGULAR DEPENDENCE OF ACOUSTIC SCATTERING STATISTICS FOR ROCKY SEAFLOORS

Understanding the performance of automatic detection algorithms requires a thorough understanding of the physical processes that affect the acoustic scattering statistics of sonar imagery. Many studies have reported on the scattering statistics of the seafloor generally, and recent work has quantified the dependence of scintillation index (SI) on range for sandy seafloors. This study examined the angular dependence of acoustic scattering statistics for rocky seafloors, which display complex spatial texture. Synthetic aperture sonar (SAS) images of rocky outcrops near Bergen, Norway, were categorized by texture and analyzed using scintillation index, relative scattering strength, and mixture model parameters with respect to grazing angle. The different rock textures displayed distinct scattering statistics across all methods of analysis. SI was generally found to increase with decreasing grazing angle and scattering strength was found to increase with increasing grazing angle, though variation was seen between textures. A three component model was found to perform the best for the smooth and weathered/pitted textures whereas a four component model performed the best for the stepped texture. All textures were best represented by less complex models at higher grazing angles, consistent with studies conducted on sandy seafloors. SAS imagery was provided by the Norwegian Defence Research Establishment.Distribution Statement A. Approved for public release: Distribution is unlimited.Outstanding ThesisLieutenant Commander, United States NavyOffice of Naval Research, Arlington, VA 2220

CHARACTERIZATION OF SURFACE ROUGHNESS ALONG THE ROCKY COASTLINE USING STEREO PHOTOGRAPHY TECHNIQUES

High-resolution images have been used to estimate and characterize the roughness of the rocky seafloor in terms of small-scale roughness and power spectral density. The application of this work is acoustical modeling of scattering from the sea floor. Two camera systems were designed and built to collect images of the ten different types of surfaces along the rocky shoreline on the Monterey Peninsula at low tide. Using commercial photogrammetry software, the images were processed to calculate height Digital Elevation Maps, which were then used to estimate 1-D and 2-D roughness power spectra. A power-law model was fit to the spectrum and had two parameters, the spectral strength and spectral slope. These roughness power spectra parameters were compared to previously collected parameter data on sandy seafloor, and the scattering strength values were compared to recently collected data along the same rocky coastline of the Monterey Bay. The lower-frequency rocky seafloor spectral strength and slope showed overlap with some of the sand surfaces at varying spatial scales. These parameters were used as inputs into a small-scale roughness perturbation theory model to predict scattering strength of the ten different surfaces for a frequency of 200 kHz and three different grazing angles. The predictions using this scattering strength method were within 10 dB of measurements collected within the same area in the Monterey Bay.Lieutenant Commander, United States NavyApproved for public release. distribution is unlimite

TEXTURAL ANALYSIS AND STATISTICAL INVESTIGATION OF PATTERNS IN SYNTHETIC APERTURE SONAR IMAGES

Textural analysis and statistical investigation of patterns in synthetic aperture sonar (SAS) images is useful for oceanographic purposes such as biological habitat mapping or bottom type identification for offshore construction. Seafloor classification also has many tactical benefits for the U.S. Navy in terms of mine identification and undersea warfare. Common methods of texture analysis rely on statistical moments of image intensity, or more generally, the probability density function of the scene. One of the most common techniques uses Haralick’s Grey Level Co-occurrence Matrix (GLCM) to calculate image features used in the applications listed above. Although widely used, seafloor classification and segmentation are difficult using Haralick features. Typically, these features are calculated at a single scale. Improvements based on the understanding that patterns are multiscale was compared with this baseline, with a goal of improving seafloor classification. Synthetic aperture sonar (SAS) data was provided by the Norwegian Research Defense Establishment for this work, and was labeled into six distinct seafloor classes, with 757 total examples. We analyze the feature importance determined by neighborhood component analysis as a function of scale and direction to determine which spatial scale and azimuthal direction is most informative for good classification performance.Office of Naval Research, Arlington, VA , 22217Lieutenant, United States NavyApproved for public release. Distribution is unlimited

Modeling the Effect of Random Roughness on Synthetic Aperture Sonar Image Statistics

A model has been developed to predict the effect of random seafloor roughness on synthetic aperture sonar (SAS) image statistics, based on the composite roughness approximation–a physical scattering model. The continuous variation in scattering strength produced by a random slope field is treated as an intensity scaling on the image speckle produced by the coherent SAS imaging process. Changes in image statistics caused by roughness are quantified in terms of the scintillation index (SI). Factors influencing the SI include the seafloor slope variance, geo-acoustic properties of the seafloor, the probability density function describing the speckle, and the signal-to-noise ratio. Example model-data comparisons are shown for SAS images taken at three different sites using three different high-frequency SAS systems. Agreement between the modeled and measured SI show that it is possible to link range-dependent image statistics to measurable geo-acoustic properties, providing the foundation necessary for solving problems related to the detection of targets using high-frequency imaging sonars, including performance prediction or adaptation of automated detection algorithms. Additionally, this work illustrates the possible use of SAS systems for remote sensing of roughness parameters such as root mean square slope or height

Resolution dependence of rough surface scattering using a power law roughness spectrum

Contemporary high-resolution sonar systems use broadband pulses and long arrays to achieve high resolution. It is important to understand effects that high-resolution sonar systems might have on quantitative measures of the scattered field due to the seafloor. A quantity called the broadband scattering cross section is defined, appropriate for high-resolution measurements. The dependence of the broadband scattering cross section, $\sigma_{bb}$ and the scintillation index, $SI$ on resolution was investigated for one-dimensional rough surfaces with power-law spectra and backscattering geometries. Using integral equations and Fourier synthesis, no resolution dependence of $\sigma_{bb}$ was found. The incoherently-averaged frequency-domain scattering cross section has negligible bandwidth dependence. $SI$ increases as resolution increases, grazing angle decreases, and spectral strength increases. This trend is confirmed for center frequencies of 100 kHz and 10 kHz, as well as for power-law spectral exponents of 1.5, 2, and 2.5. The hypothesis that local tilting at the scale of the acoustic resolution is responsible for intensity fluctuations was examined using a representative model for the effect of slopes (inspired by the composite roughness approximation). It was found that slopes are responsible in part for the fluctuations, but other effects, such as multiple scattering and shadowing may also play a role.Comment: 22 pages, 10 figures, preprint version of paper published in the Journal of the Acoustical Society of America, at \url{https://doi.org/10.1121/10.0002974

SUSHIMAP (Survey strategy and methodology for marine habitat mapping)

Bathymetrical mapping performed using multibeam sonar systems is widely used in marine science and for habitat mapping. The incoherent part of the multibeam data, the backscatter data, is less commonly used. Automatic classification of processed backscatter has a correlates well with three sediment classes, defined as fine-(clay-silt), medium- (sand) and coarse- (gravel–till) grained substrates. This relation is used directly as a theme in a modified habitat classification scheme, while a more detailed substrate classification is incorporated as another theme. This theme requires a manual interpretation and comprehensive knowledge of the substrate. This can partly be obtained by a newly developed technique using the backscatter strength plotted against the grazing angle. These plots make it possible to determine the critical angle and thereby calculate the compressional acoustic speed in seabed sediments. Marching a theoretical modeled backscatter curve to the measured backscatter strength at lower grazing angles provides estimates of four additional geoacoustic parameters

5th Annual Jackson School Research Symposium

Geological Science