Jon M. Collis

A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Pade approximants

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness

Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534-3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808-813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment.

Horizontal coherence of low-frequency fixed-path sound in a continental shelf region with internal-wave activity

Sound at 85 to 450 Hz propagating in approximately 80-m depth water from fixed sources to a joint horizontal/vertical line array (HLA/VLA) is analyzed. The data are from a continental shelf area east of Delaware Bay (USA) populated with tidally generated long- and short-wavelength internal waves. Sound paths are 19 km in the along-shore (along internal-wave crest) direction and 30 km in the cross-shore direction. Spatial statistics of HLA arrivals are computed as functions of beam steering angle and time. These include array gain, horizontally lagged spatial correlation function, and coherent beam power. These quantities vary widely in magnitude, and vary over a broad range of time scales. For example, correlation scale can change rapidly from forty to five wavelengths, and correlation-scale behavior is anisotropic. In addition, the vertical array can be used to predict correlation expected for adiabatic propagation with cylindrical symmetry, forming a benchmark. Observed variations are in concert with internal-wave activity. Temporal variations of three coherence measures, horizontal correlation length, array gain, and ratio of actual correlation length to predicted adiabatic-mode correlation length, are very strong, varying by almost a factor of ten as internal waves pass.

Observed limiting cases of horizontal field coherence and array performance in a time-varying internal wavefield

Using a moored source and horizontal/vertical line array combination, horizontal coherence properties of high signal to noise ratio (> or =20 dB) 100-1600 Hz signals have been measured. Internal waves in the area of the measurement created moving episodic sound-speed anomaly structures, influencing coherence length. Measured horizontal coherence scales for 100 Hz ranged from 5 to 20 acoustic wavelengths, and were inversely related to the sound-speed anomaly strength. Horizontal field properties were compared with fields computed using modal decompositions of the vertical signals. The comparison allows azimuthal field coherence properties to be studied apart from normal-mode interference effects.

Characteristics of sound propagation in shallow water over an elastic seabed with a thin cap-rock layer

Measurements of low-frequency sound propagation over the areas of the Australian continental shelf, where the bottom sediments consist primarily of calcarenite, have revealed that acoustic transmission losses are generally much higher than those observed over other continental shelves and remain relatively low only in a few narrow frequency bands. This paper considers this phenomenon and provides a physical interpretation in terms of normal modes in shallow water over a layered elastic seabed with a shear wave speed comparable to but lower than the water-column sound speed. A theoretical analysis and numerical modeling show that, in such environments, low attenuation of underwater sound is expected only in narrow frequency bands just above the modal critical frequencies which in turn are governed primarily by the water depth and compressional wave speed in the seabed. In addition, the effect of a thin layer of harder cap-rock overlaying less consolidated sediments is considered. Low-frequency transmission loss data collected from an offshore seismic survey in Bass Strait on the southern Australian continental shelf are analyzed and shown to be in broad agreement with the numerical predictions based on the theoretical analysis and modeling using an elastic parabolic equation solution for range-dependent bathymetry.

Comparison of simulations and data from a seismo-acoustic tank experiment.

A tank experiment was carried out to investigate underwater sound propagation over an elastic bottom in flat and sloping configurations. The purpose of the experiment was to evaluate range-dependent propagation models with high-quality experimental data. The sea floor was modeled as an elastic medium by a polyvinyl chloride slab. The relatively high rigidity of the slab requires accounting for shear waves in this environment. Acoustic measurements were obtained along virtual arrays in the water column using a robotic apparatus. Elastic parabolic equation solutions are in excellent agreement with data.

Seismo-acoustic ray model benchmarking against experimental tank data

Acoustic predictions of the recently developed traceo ray model, which accounts for bottom shear properties, are benchmarked against tank experimental data from the EPEE-1 and EPEE-2 (Elastic Parabolic Equation Experiment) experiments. Both experiments are representative of signal propagation in a Pekeris-like shallow-water waveguide over a non-flat isotropic elastic bottom, where significant interaction of the signal with the bottom can be expected. The benchmarks show, in particular, that the ray model can be as accurate as a parabolic approximation model benchmarked in similar conditions. The results of benchmarking are important, on one side, as a preliminary experimental validation of the model and, on the other side, demonstrates the reliability of the ray approach for seismo-acoustic applications.

Elastic parabolic equation solutions for underwater acoustic problems using seismic sources

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

Extension of the Rotated Elastic Parabolic Equation to Beach and Island Propagation

Improvements in the capability of handling sloping interfaces and boundaries with the parabolic equation method have been an active area of research. Recent progress in accurately treating range-dependent seismoacoustic problems has involved coordinate transformation techniques. The variable-rotated parabolic equation is among recent advances in this area. The solution rotates the coordinate axes to achieve greater accuracy in the presence of range-dependent bathymetry. At points of slope change the rotated solution interpolates and extrapolates the field into adjacent regions. This approach is extended to solve problems involving variable topography (above-ocean-surface sediments) by accounting for the transition and boundary conditions at the water/solid/air interfaces. It is applied to range-dependent problems of sound transmission up a beach and through an island. The method is benchmarked for accuracy against a finite-element solution.

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.