Aaron M. Gunderson

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.

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.

Acoustic scattering enhancements for partially exposed cylinders in sand and at a free surface caused by Franz waves and other processes

Creeping waves on solid cylinders having slightly subsonic phase velocities and large radiation damping are described as Franz waves because of association with complex poles investigated by Franz. For free-field high frequency broadside backscattering in water, the associated echoes are weak due to radiation damping. It was recently demonstrated, however, that for partially exposed solid metal cylinders at a free surface viewed at grazing incidence, the Franz wave echo can be large relative to the specular echo when the grazing angle is sufficiently small [G. C. Eastland and P. L. Marston, J. Acoust. Soc. Am. 135, 2489–2492 (2014)]. The Fresnel zone associated with the specular echo is occluded making it weak while the Franz wave is partially reflected at the interface behind the cylinder. This hypothesis is also supported by calculating the exact backscattering by half-exposed infinitely long rigid cylinders viewed over a range of grazing angles. Additional experiments concern the high frequency backsca...

Numerical determination of Green's functions for far field scattering solutions

Typical finite element target scattering results are evaluated over a small physical domain and then propagated to the far field using the Helmholtz-Kirchhoff integral. This process allows for direct far field data-model comparison and is substantially faster than evaluation over a large domain. It does, however, require knowledge of the Green’s function of the target’s environment. For underwater buried targets, the two-medium Green’s function pertaining to the water and sediment is often not readily known and can be cumbersome to analytically solve or approximate, particularly when surface roughness or volume inhomogeneity is to be incorporated. Instead, the Green’s function can be determined directly through numerical methods. A direct process for numerical Green’s function determination in an arbitrary two-medium environment is proposed, and is used to determine the far field scattering from buried targets. Results are compared to experimental scattering records on buried elastic targets, and to other...

Three dimensional finite element modeling of scattering by objects at rough interfaces

Fully three-dimensional finite element models for buried objects and objects at interfaces have been extended to incorporate interface roughness. Near field results are solved using a fully scattered field formulation, in which all fields in the absence of the target are applied and the target scattering is solved. Results are extended to the far field through the Helmholtz-Kirchhoff integral, using a numerically determined Green’s function approach. Interface roughness is applied using a modified power law wavenumber spectrum. Previous model demonstrations evaluated the scattering in the flat interface limit, in which background fields were prescribed analytically. Now, the presence of the surface roughness forces background fields to be evaluated and prescribed numerically. Such models have strong applicability for predicting scattering by objects buried within or resting on a rough seafloor interface. Model results are compared with various experimental and other modeled results, demonstrating model validity over a wide frequency range. [Work supported by Applied Research Laboratories IR&D and ONR, Ocean Acoustics.]Fully three-dimensional finite element models for buried objects and objects at interfaces have been extended to incorporate interface roughness. Near field results are solved using a fully scattered field formulation, in which all fields in the absence of the target are applied and the target scattering is solved. Results are extended to the far field through the Helmholtz-Kirchhoff integral, using a numerically determined Green’s function approach. Interface roughness is applied using a modified power law wavenumber spectrum. Previous model demonstrations evaluated the scattering in the flat interface limit, in which background fields were prescribed analytically. Now, the presence of the surface roughness forces background fields to be evaluated and prescribed numerically. Such models have strong applicability for predicting scattering by objects buried within or resting on a rough seafloor interface. Model results are compared with various experimental and other modeled results, demonstrating model va...

Scattered field formulation applied to 3D models for buried targets

Calculation of the acoustic scattering from buried targets in a seafloor environment is a task ideally suited for finite element software. A complication arises though when the target’s environment is modeled as two infinite half spaces of water and sediment, each surrounded by perfectly matched layers (PML’s) to satisfy the Sommerfeld radiation condition. Each half space requires a surrounding PML tailored to its material properties, resulting in abrupt discontinuities in PML structure at the corners where the sand-water interface meets the edges of the physical domain. Acoustic energy incident on these corners results in nonphysical reflections directed back into the physical domain. It has previously been shown in a 2D axisymmetric geometry [Zampolli et al., JASA 122, 2007] that using a scattered field formulation, where the incident, reflected, and transmitted fields are applied as background fields, bypasses the discontinuity and eliminates these spurious reflections. Here, the theory is extended to full 3D geometries, allowing the scattering from 3D buried objects to be evaluated and tested against experimental and analytical benchmark results. Once complete, the 3D model template is easily modified to consider any target at any level of burial. [Work supported by Applied Research Laboratories IR&D and ONR, Ocean Acoustics.]Calculation of the acoustic scattering from buried targets in a seafloor environment is a task ideally suited for finite element software. A complication arises though when the target’s environment is modeled as two infinite half spaces of water and sediment, each surrounded by perfectly matched layers (PML’s) to satisfy the Sommerfeld radiation condition. Each half space requires a surrounding PML tailored to its material properties, resulting in abrupt discontinuities in PML structure at the corners where the sand-water interface meets the edges of the physical domain. Acoustic energy incident on these corners results in nonphysical reflections directed back into the physical domain. It has previously been shown in a 2D axisymmetric geometry [Zampolli et al., JASA 122, 2007] that using a scattered field formulation, where the incident, reflected, and transmitted fields are applied as background fields, bypasses the discontinuity and eliminates these spurious reflections. Here, the theory is extended to ...

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.

Kirchhoff approximation for scattering from solid spheres at flat interfaces: Improved description at large grazing angles

The Kirchhoff approximation has previously been used to model scattering from partially exposed elastic spheres breaking through a flat interface, with variable exposure level, grazing angle, and frequency [J. Acoust. Soc. Am. 136, 2087 (2014)]. The limits of the Kirchhoff integral are determined by the boundaries of illumination on the sphere for each scattering path. Recent adaptations to the methods of boundary determination within the Kirchhoff approximation have yielded faster numerical integration algorithms and higher similarity of results when compared to experimental scattering data and the exact solution at half exposure [J. Acoust. Soc. Am. 140, 3582-3592 (2016)]. Additional steps have been taken to account for the partial blocking of the interface by the partially exposed sphere, through inclusion of a new correction term. This correction is largest at high grazing angles, low frequencies, and low target exposures, and drastically improves the Kirchhoff approximation within these limits. [Work supported by ONR.]The Kirchhoff approximation has previously been used to model scattering from partially exposed elastic spheres breaking through a flat interface, with variable exposure level, grazing angle, and frequency [J. Acoust. Soc. Am. 136, 2087 (2014)]. The limits of the Kirchhoff integral are determined by the boundaries of illumination on the sphere for each scattering path. Recent adaptations to the methods of boundary determination within the Kirchhoff approximation have yielded faster numerical integration algorithms and higher similarity of results when compared to experimental scattering data and the exact solution at half exposure [J. Acoust. Soc. Am. 140, 3582-3592 (2016)]. Additional steps have been taken to account for the partial blocking of the interface by the partially exposed sphere, through inclusion of a new correction term. This correction is largest at high grazing angles, low frequencies, and low target exposures, and drastically improves the Kirchhoff approximation within these limits. [Work...

Bistatic scattering from underwater elastic spheres and cylinders: Interference and resonance phenomena

Scattering by underwater elastic spheres and cylinders is considered over a full range of scattering angles. Three models are presented in the frequency domain: an exact solution for scattering from an elastic sphere, a finite cylinder approximate solution, and a finite element simulation for the finite cylinder. Close agreement between the two cylinder models speaks to the strength of the finite cylinder approximate solution. Within each model, the dependence of the scattering on frequency and angle is discussed. Resonance structure is highlighted, and families of ridges and valleys in the data can be described by interference models between near-side and far-side Rayleigh paths and the specular reflection. A thorough understanding of bistatic scattering from elastic targets is helpful for data acquisition from moving sources (such as an AUV) or acoustic arrays, as well as studying monostatic scattering from targets at an interface, where the interface may direct bistatic paths to the receiver. [Work sup...

Time-domain acoustic scattering by elastic objects using finite element analysis

Finite element analysis provides an accurate way of calculating acoustic scattering from underwater objects. The method provides an exact solution to the Helmholtz equation to the order of the discretization. Although commercial finite element software is capable of solving fully 3D scattering problems, it has been previously shown by Zampolli et al. [J. Acoust. Soc. Am. 122, 1472–1485 (2007)] that 3D axisymmetric targets can be solved more efficiently using 2D geometry. This method uses an axial wavenumber decomposition technique, which simulates an incident plane wave from an off-axis direction. In this study, results from this analysis are converted from the frequency domain to the time domain using Fourier synthesis. Elastic spheres and cylinders are considered because the analytical solutions for scattering by these targets are known and can be used to verify the finite element results. The success of this model to simulate time domain scattering will inform the applicability of finite element analys...