An explicit granular-mechanics approach to marine sediment acoustics.

Here, we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms, which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features.

The effect of seafloor roughness on passive estimates of the seabed reflection coefficient.

In this work, a model is developed for the effect of seafloor interface roughness on passive estimates of the reflection coefficient. The main result is an expression for the total intensity reflection coefficient, with separate coherent and incoherent contributions. Assumptions of this model include constant sound speed in the ocean, stationary and Gaussian seafloor roughness, and ambient noise. Numerical examples for the coherent, incoherent, and total contributions to the intensity reflection coefficient are presented for halfspace and layered environments-all using the small slope approximation. To illustrate the potential parameter errors that results from using a flat interface wave model when roughness is present, a geoacoustic inversion is performed using the proposed model as input data. A joint roughness-geoacoustic inversion of simulated data using the proposed model was also performed. It was found that the true roughness and geoacoustic parameters can be inverted using this model, but the sensitivity to the outer scale of the rough surface has the highest error compared to the other parameters.

Testing the theoreticians.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

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.

Beaufort Sea observations of 11 to 12.5 kHz surface pulse reflections near 50 degree grazing angle from 2016 to 2017.

Sea-surface acoustic scattering is investigated using observations from the 2016-2017 Canada Basin Acoustic Propagation Experiment. The motions of the low-frequency acoustic source and/or receiver moorings were measured using long-baseline acoustic navigation systems in which the signals transmitted once per hour by the mooring instruments triggered high-frequency replies from the bottom-mounted transponders. The moorings recorded these replies, giving the direct path and single-bounce surface-reflected arrivals, which have grazing angles near 50°. The reflected signals are used here to quantify the surface scattering statistics in an opportunistic effort to infer the changing ice characteristics as a function of time and space. Five scattering epochs are identified: (1) open water, (2) initial ice formation, (3) ice solidification, (4) ice thickening, and (5) ice melting. Significant changes in the ice scattering observables are seen using the arrival angle, moment of reflected intensity and its probability density function, and pulse time spread. The largest changes took place during the formation, solidification, and melting. The statistical characteristics across the experimental region are similar, suggesting consistent ice properties. To place the results in some physical context, they are interpreted qualitatively using notions of the partial and fully saturated wave fields, a Kirchhoff-like approximation for the rough surface, and a thin elastic layer reflection coefficient model.

A series approximation to the Kirchhoff integral for Gaussian and exponential roughness covariance functions.

The Kirchhoff integral is a fundamental integral in scattering theory, appearing in both the Kirchhoff approximation and the small slope approximation. In this work, a functional Taylor series approximation to the Kirchhoff integral is presented, under the condition that the roughness covariance function follows either an exponential or Gaussian form-in both the one-dimensional and two-dimensional cases. Previous approximations to the Kirchhoff integral [Gragg, Wurmser, and Gauss (2001) J. Acoust. Soc. Am. 110(6), 2878-2901; Drumheller and Gragg (2001) J. Acoust. Soc. Am. 110(5), 2270-2275] assumed that the outer scale of the roughness was very large compared to the wavelength, whereas the proposed method can treat arbitrary outer scales. Assuming an infinite outer scale implies that the root mean square (rms) roughness is infinite. The proposed method can efficiently treat surfaces with finite outer scale and therefore finite rms height. This series is shown to converge independently of roughness or acoustic parameters and converges to within roundoff error with a reasonable number of terms for a wide variety of dimensionless roughness parameters. The series converges quickly when the dimensionless rms height is small and slowly when it is large.

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, σbb, 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 σbb 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 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.

Scattering from layered seafloors: Comparisons between theory and integral equations.

Acoustic scattering from layered seafloors exhibits dependence on both the mean geoacoustic layering, as well as the roughness properties of each layer. Several theoretical treatments of this environment exist, including the small roughness perturbation approximation, the Kirchhoff approximation, and three different versions of the small slope approximation. All of these models give different results for the scattering cross section and coherent reflection coefficient, and there is currently no way to distinguish which model is the most correct. In this work, an integral equation for scattering from a layered seafloor with rough interfaces is presented, and compared with small roughness perturbation method, and two of the small slope approximations. It is found that the most recent small slope approximation by Jackson and Olson [J. Acoust. Soc. Am. 147(1), 56-73 (2020)] is the most accurate when the root-mean-square (rms) roughness is large, and some models are in close agreement with each other when the rms roughness is small.

The small-slope approximation for layered, fluid seafloors.

The small-slope approximation (SSA) for rough-interface scattering is most commonly applied to the upper boundary of either impenetrable media or uniform half-space media, but has been recently developed for layered media in the acoustic and electromagnetic cases. The present work gives an overview of three forms of the SSA for layered media. The first has been previously presented in the acoustics literature. The second is from the electromagnetics literature and in the present work is converted to the fluid-sediment problem. A missing proof is supplied of a key consistency condition demanded of the small-slope ansatz. As is usual, these small-slope results are expressed in k-space. A third SSA for layered seafloors follows from conversion of the usual half-space formulation from k-space to coordinate space. This form turns out to be useful for reverberation simulations. The three different approaches are compared with respect to scattering strength and the coherent reflection coefficient, but an assessment of their relative merits will require comparison with exact calculations.

Fast computation of time-domain scattering by an inhomogeneous stratified seafloor.

Marine sediment properties exhibit fluctuations on a very wide range of scales in all three spatial dimensions. These fluctuations lead to scattering of acoustic waves. Seabed scattering models that treat such fluctuations are reasonably well developed under the plane-wave assumption. A recent model, called TDSS (time domain model for seafloor scattering), accurately treats the important point-source-point-receiver geometry for generally stratified fluid sediments-important because this is the geometry employed in many seabed scattering measurements. The computational cost associated with this model is very high and scales roughly with the product of mean source-receiver height above the basement to the fifth power and both bandwidth and wavenumber to the second power. Thus, modeling deep ocean scattering from a near sea surface source and receiver is prohibitive at frequencies above a few tens of hertz. A computational approach was developed based on Levin's method of oscillatory integration, which is orders of magnitude faster than standard numerical integration techniques and makes deep ocean seabed scattering computations practical up to many kilohertz. This approach was demonstrated to agree with the narrowband sonar equation in several simple environments in the limit of small bandwidths, but the TDSS model is expected to be valid for a much wider range of environments.

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 the 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 a significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had a significant parameter correlation, but also contained multiple modes. It is concluded that the mixture between two K distributions is the most applicable to this dataset.

A point-based scattering model for the incoherent component of the scattered field.

A numerical model for calculation of the incoherent component of the field scattered from random rough surfaces is described. This model is based on the point scattering approach, where the mean scatterer amplitudes are calculated from deterministic models. These amplitudes are then scaled by a complex circular Gaussian random variable to simulate scattering from a surface with minimal coherence length. The resulting simulated fields are shown to agree with theory for the mean field, mean square field, statistical distribution, and the spatial coherence length.

Measurements of high-frequency acoustic scattering from glacially eroded rock outcrops.

Measurements of acoustic backscattering from glacially eroded rock outcrops were made off the coast of Sandefjord, Norway using a high-frequency synthetic aperture sonar (SAS) system. A method by which scattering strength can be estimated from data collected by a SAS system is detailed, as well as a method to estimate an effective calibration parameter for the system. Scattering strength measurements from very smooth areas of the rock outcrops agree with predictions from both the small-slope approximation and perturbation theory, and range between -33 and -26 dB at 20° grazing angle. Scattering strength measurements from very rough areas of the rock outcrops agree with the sine-squared shape of the empirical Lambertian model and fall between -30 and -20 dB at 20° grazing angle. Both perturbation theory and the small-slope approximation are expected to be inaccurate for the very rough area, and overestimate scattering strength by 8 dB or more for all measurements of very rough surfaces. Supporting characterization of the environment was performed in the form of geoacoustic and roughness parameter estimates.

Scattering measurements of rocky seafloors using a split-beam echosounder.

Scattering measurements were made off the coast of Pacific Grove, CA at 200 kHz, in an exposed fractured granite seafloor. Using inertial sensors and a split-beam transducer, data were processed to obtain a range of grazing angles corresponding to scattering strength, and signal processing techniques were used to extract the relevant portion of each ping. The ensonified angular width from a circular aperture is presented. Scattering strength measurements using different assumptions regarding the grazing angle were compared. The empirical Lommel-Seeliger model provided a good fit to measured data with a parameter of -18.4 dB.

Physics-Based Modelling and Simulation of Multibeam Echosounder Perception for Autonomous Underwater Manipulation.

One of the key distinguishing aspects of underwater manipulation tasks is the perception challenges of the ocean environment, including turbidity, backscatter, and lighting effects. Consequently, underwater perception often relies on sonar-based measurements to estimate the vehicle's state and surroundings, either standalone or in concert with other sensing modalities, to support the perception necessary to plan and control manipulation tasks. Simulation of the multibeam echosounder, while not a substitute for in-water testing, is a critical capability for developing manipulation strategies in the complex and variable ocean environment. Although several approaches exist in the literature to simulate synthetic sonar images, the methods in the robotics community typically use image processing and video rendering software to comply with real-time execution requirements. In addition to a lack of physics-based interaction model between sound and the scene of interest, several basic properties are absent in these rendered sonar images-notably the coherent imaging system and coherent speckle that cause distortion of the object geometry in the sonar image. To address this deficiency, we present a physics-based multibeam echosounder simulation method to capture these fundamental aspects of sonar perception. A point-based scattering model is implemented to calculate the acoustic interaction between the target and the environment. This is a simplified representation of target scattering but can produce realistic coherent image speckle and the correct point spread function. The results demonstrate that this multibeam echosounder simulator generates qualitatively realistic images with high efficiency to provide the sonar image and the physical time series signal data. This synthetic sonar data is a key enabler for developing, testing, and evaluating autonomous underwater manipulation strategies that use sonar as a component of perception.