Rough surface scattering is a problem of interest in underwater acoustic remote sensing applications. To model this problem, a fully three-dimensional (3D) finite element model has been developed, but it requires an abundance of time and computational resources. Two-dimensional (2D) models that are much easier to compute are often employed though they don't natively represent the physical environment. Three quantities have been developed that, when applied, allow 2D rough surface scattering models to be used to predict 3D scattering. The first factor, referred to as the spreading factor, adopted from the work of Sumedh Joshi [1], accounts for geometrical differences between equivalent 2D and 3D model environments. A second factor, referred to as the perturbative factor, is developed through the use of small perturbation theory. This factor is well-suited to account for differences in the scattered field between a 2D model and scattering from an isotropically rough 2D surface in 3D. Lastly, a third composite factor, referred to as the combined factor, of the previous two is developed by taking their minimum. This work deals only with scattering within the plane of the incident wave perpendicular to the scatterer. The applicability of these factors are tested by comparing a 2D scattering model with a fully three-dimensional Monte Carlo finite element method model for a variety of von Karman and Gaussian power spectra. The combined factor shows promise towards a robust method to adequately characterize isotropic 3D rough surfaces using 2D numerical simulations.

Interface roughness can have a significant effect on the scattering of sound energy, and therefore an understanding of the effects of roughness is essential to making predictions of sound propagation and transmission underwater. Many models of roughness scattering currently in use are two dimensional (2D) in nature; three dimensional (3D) modeling requires significantly more time and computational resources. In this work, an effort is made to quantify the effects of 3D scattering in order to assess whether or under what conditions 3D modeling is necessary. To that end, an exact 3D roughness scattering model is developed based on a commercially available finite element package. The finite element results are compared with two approximate scattering models (the Kirchhoff approximation and first order perturbation theory) to establish the validity and regimes of applicability of each. The rough surfaces are realizations generated from power spectra measured from the sea floor. However, the surfaces are assumed to be pressure release (as on an air-water interface). Such a formulation is nonphysical, but allows the assessment of the validity of the various modeling techniques which is the focus of this work. The comparison between the models is made by calculating the ensemble average of the scattering from realizations of randomly rough surfaces. It is shown that a combination of the Kirchhoff approximation and perturbation theory models recovers the 3D finite element solution.

The objective is to understand the theory of acoustic scattering from rough surfaces, with applications to ocean surfaces. It is necessary to develop multiple scattering models that are able to treat larger values of roughness, as well as to incorporate as much information as possible into a statistical description of the surface. The mathematical methods we have developed are generic in the sense that they can also be applied to any rough surface. Enhanced backscattering can result when the surfaces are very rough. We have found additional new results for the coherent (specular) intensity and the backscatter enhancement effect for the direct scattering problem. In addition, we have reconstructed surface profiles from scattered field data using two different approaches.

Contents:Light Scattering Problems in Astrophysics (J M Perrin)Surface Integral Operators and their Use in Acoustics and Electromagnetics (A Berthon)Acoustic Diffraction by Slender Bodies of Arbitrary Shape (M Tran-Van-Nhieu)High and Low Energy Approximations for the Electromagnetic Scattering by Irregular Objects (B Torresani)Electromagnetic Scattering and Mutual Interactions Between Closely Spaced Spheroids (J Dalmas & R Deleuil)Acoustical Imaging of 2D Fluid Targets Buried in a Half Space: A Diffraction Tomography Approach Using Line-Sources Insonification (B Duchene et al)Contribution of Radar Polarimetry in Radar Target Discrimination. The “Poincaré Planisphere”: a New Representation Method (E Pottier)Electromagnetic and Acoustic Waves in Random Media: from Propagation to Anderson Localization (B Souillard)Weak Disorder: Homogeneisation Method and Propagation (C Bardos)Coherent Propagation of Surface Acoustic Waves in Quasi-Periodic and Random Arrays of Grooves (D Sornette et al)On Asymptotic Behaviour of Waves States in Random Media (F Bentosela & R Rodriguez)A Study of Acoustic Transmission of Transient Signal in a Inhomogeneous Medium with the Help of a Wavelet Transform. Application to an Air-Water Plane Interface (G Saracco & Ph Tchamitchian)Three-Dimensional Impedance Scattering Theory (P Sabatier)Survey of Optimization Algorithms Applied to Inverse Problems (A Roger)A Linearized Inverse Problem: Acoustic Impedance Tomography of Biological Media (J P Lefebvre)and others Readership: Electrical engineers and mathematicians.

A poroelastic finite element formulation originally derived for modeling porous absorbing material in air is adapted to the problem of acoustic scattering from a poroelastic seafloor with a one-dimensional randomly rough interface. The developed formulation is verified through calculation of the plane wave reflection coefficient for the case of a flat surface and comparison with the well known analytical solution. The scattering strengths are then obtained for two different sets of material properties and roughness parameters using a Monte Carlo approach. These numerical results are compared with those given by three analytic scattering models---perturbation theory, the Kirchhoff approximation, and the small-slope approximation---and from those calculated using two finite element formulations where the sediment is modeled as an acoustic fluid.

Abstract: This dissertation presents a Monte-Carlo multidomain pseudospectral time-domain (MPSTD) algorithm developed for the analysis of scattering from a two dimensional (2D) and three dimensional (3D) object buried below a random rough surface separating two half spaces. In the development, special attention is paid to the 3D computation domain decomposition, PML derivations, filtering technique and subdomain mapping involving the random rough surface as well as the subdomain patching along the rough surface. The Mote-Carlo MPSTD algorithm is then employed to determine the scattering of objects of various shapes and electromagnetic properties; embedded in the lower half space with different permittivity and the roughness of the random rough surface may vary. Sample numerical results are presented, validated, and analyzed. Then, scattering of objects buried in layered structure with random rough surface is studied using MPSTD algorithm. Through the analysis, it is observed that the roughness of the random rough surface and the electromagnetic properties of the lower half space can significantly affect the scattered signature of the buried object.