Method of numerical Green's function determination for far-field scattering solutions from objects at a water-sediment interface.

A method is presented for numerically determining Green's functions for the purpose of calculating the far-field scattering from objects resting on or buried within the seafloor. To obtain the far-field scattering, initial evaluation of the three-dimensional near-field solution is required, through finite element analysis or other means. The Green's function and its spatial derivatives are then numerically evaluated for input into the Helmholtz-Kirchhoff integral, yielding the far-field scattering solution. This numerical technique determines the Green's function directly and avoids requiring analytic forms of Green's functions, which may be difficult or time consuming to evaluate for complex environments. This paper demonstrates the effectiveness of applying the numerical Green's function determination technique in conjunction with near-field results from finite element models to determine the far-field scattering for various elastic targets in free-field and flat seafloor environments. The method may be generalizable to arbitrary targets at complicated interfaces, incorporating interface roughness, layering, and volume inhomogeneities.

Observation and modeling of acoustic scattering from a rubber spherical shell.

Acoustic backscattering from a rubber spherical shell in water is observed to contain a delayed enhancement, demonstrated to be associated with a waveguide path along the shell. This path is somewhat analogous to that of the Lamb wave observed on metallic shells. Rubber is a unique material because of its subsonic sound speed relative to water, and because shear coupling is often small enough to be neglected in typical models, making it fluid-like. This makes rubber a material of interest for coating and cloaking underwater devices and vehicles. Both fluid and elastic rubber partial wave series models are tested, using experimentally measured longitudinal and shear speeds, attenuation, and rubber density. A finite element model for the shell is also developed. Comparison of the models and experiments highlights the importance of the waveguide path to the overall scattering. Estimates for the group and phase velocities of the lowest order propagating mode in the shell are determined through waveguide normal mode analysis and Sommerfeld-Watson theory, and are shown to give good agreement with experiments in predicting the time of arrival of the waveguide path.

Spectral analysis of bistatic scattering from underwater elastic cylinders and spheres.

Far field sound scattering from underwater elastic spheres and finite cylinders is considered over the full range of scattering angles. Three models for the frequency response of the scattered field are evaluated: a hybrid finite element/propagation simulation for a finite cylinder with broadside illumination, an approximate solution for the finite cylinder, and the exact solution for a sphere. The cylinder models are shown to give comparable results, attesting to the strength of the finite cylinder approximate solution. Interference and resonance structure present in the frequency response of the targets is identified and discussed, and the bistatic spectra for a variety of elastic sphere materials are presented. A thorough understanding of the complicated angle and frequency dependence of the scattering from simple elastic targets is helpful for interpretation of backscattering data from targets at or near an interface, or for scattering data taken by moving automated underwater vehicles, acoustic arrays, or other forms of data collection involving bistatic scattering.

Kirchhoff approximation for backscattering from a partially exposed rigid sphere at a flat interface.

The Kirchhoff approximation (KA) is used to model backscatter of sound from a partially exposed, rigid sphere at a flat free interface of two homogenous media. Scattered wavefields are calculated through numerical integration on the sphere of the Kirchhoff integral, requiring detailed knowledge of the illuminated region for each scattering path. This approach avoids amplitude discontinuities resulting from geometric transitions in the number of reflected rays. Reflections from the interface are modeled through use of an image source, positioned symmetrically relative to the real source. Results are compared to experimentally obtained backscattering records from elastic spheres at an air-water interface, as well as to an exact partial wave series for a half exposed sphere. These comparisons highlight the omission of Franz-type reflections from consideration within the KA, and the consequences of this omission are discussed. The results can be extended to boundary conditions beyond the ideal free surface limit, and are applicable to the problem of scattering by underwater objects partially buried in sand.

Validation and verification of three-dimensional finite element target scattering models and Green's functions.

A configurable three-dimensional (3D) finite element framework is used for modeling acoustic scattering from various elastic targets on seabed and for the numerical determination of Green's functions used in far-field target scattering prediction. The 3D selection is chosen for possible inclusion of complex seafloor geometries, such as rough, rippled, cluttered, or variably layered seabeds, in which two-dimensional modeling approaches cannot capture the full acoustic interaction with the target and the seabed. Model results are verified and validated against analytic scattering theories and measured results from the 2013 Target and Reverberation Experiment (TREX) and the 2017 CLUTTEREX experiment.