Daniel Wurmser

Calculations of acoustic scattering from the ocean surface

The problem of acoustic scattering from the ocean surface can be solved using the formalism that has been developed to describe the scattering of a wave off a finite object. A refined version of this formalism is used to generate various approximation schemes. The validity of these approximations are investigated and their relative merits are discussed. The scattering cross section is evaluated numerically and it is concluded that the observed cross section for scattering near the ocean surface cannot be explained by ocean surface scattering alone.

A new theory for scattering from a surface

A new formal approach to the problem of scattering from a rough surface is derived. The first ingredient of this approach is a formal statement of the composite model. This consists of an approximate expression for the change in the scattering amplitude corresponding to a perturbation of a reference surface. It is good to first order in the perturbation, and exact with respect to the reference surface. The derivation of this result makes use of the general asymptotic form of the scattering solution. The expression is simplified using the boundary conditions. When the formal composite model is applied to an unfinitesimal translation, a new representation of the scattering amplitude is obtained. Unlike the traditional representation, this expression depends on two full solutions to the wave equation, and it manifestly exhibits reciprocity. This article is the first in a series. Application of the results will be considered in future papers.

Small-slope scattering from rough elastic ocean floors: General theory and computational algorithm

In this article acoustic scattering by a random rough interface that separates a fluid incident medium from an underlying uniform scattering medium, either fluid or elastic solid, in cases for which the Bragg scale lies within the power-law tail of the roughness spectrum is dealt with. The physical foundation is an inherently reciprocity-preserving, local small-slope theory. A fully bistatic formulation is developed for the scattering strength, together with a robust numerical implementation that allows a wide range of spectral exponent values. The practical result for ocean acoustics is a significantly improved description of the interface component of sea floor scattering. Calculations are presented to demonstrate the advantage of this approach over perturbation theory, and to illustrate its dependence on frequency and environmental parameters as well as its operation in bistatic geometries.

Approximate representations of the scattering amplitude

This is the second in a series of articles about the theory of scattering from a rough surface. A symmetric representation of the scattering amplitude and a formal statement of the composite model, both derived in the previous article, are used to approximate the scattering amplitude in terms of the known results for a reference surface. When the reference surface is a plane, the small slope approximation follows, while the traditional composite model is obtained if the curvature of the reference surface is neglected. The medium is assumed to be homogeneous, and the calculation is performed for scalar waves obeying Dirichlet or Neumann boundary conditions, electromagnetic waves obeying perfect conductor boundary conditions and the interface between two media for both types of waves. Finally, the requirement that the formal composite model must reproduce the traditional composite model in the appropriate limit is used to obtain a new approximation to the scattering amplitude. This is done for the Dirichlet...

A new strategy for applying the parabolic equation to a penetrable rough surface

The range‐dependent parabolic equation (PE) propagates an auxiliary field that roughly corresponds to the square root of the downrange flux. At the ocean bottom, the interface is broken into stair steps, and this auxiliary field is conserved at the vertical interfaces. Because of its success in matching benchmark solutions, this method is widely used to model standard propagation problems in underwater acoustics. However, when the interface is rough at the wavelength scale, the physics of the problem changes, and the standard approach ceases to be practicable. This talk presents a new approach specifically designed to handle this important problem. The Foldy–Wouthuysen transformation generates the PE for this auxiliary field, complete with a full suite of boundary conditions. In the discrete problem, the boundary conditions are used to evaluate the Hamiltonian on the interface, and the result is used to perform the next downrange step. At lowest order, the new theory streamlines the stair step method, and...

Applications of the new scattering formalism: The Dirichlet boundary condition

This is the third in a series of articles concerning the theory of scattering from a rough surface. Consideration of the scattering problem for a scalar wave obeying Dirichlet boundary conditions enables one to investigate the formalism developed in the previous work. The advantages of this new representation of the scattering amplitude is discussed. This result is supplemented with an improved integral equation for the desired solutions on the surface. This new equation not only allows one to reproduce the approximations for the scattering amplitude obtained previously, but it can also be used to extend those results to higher orders. This is illustrated with a derivation of the second‐Born approximation. The correction to the scattering amplitude due to a distribution of point scatters is also obtained. To the order under consideration, this phenomenon is shown to be equivalent to a perturbation of the surface. A similar result is found when the index of refraction is allowed to vary near the scattering...

Application of the Foldy–Wouthuysen transformation to the reduced wave equation in range-dependent environments

The Foldy–Wouthuysen transformation can be used to reduce the relativistic Klein–Gordon equation to the nonrelativistic Schrodinger equation. This technique is modified and applied to the problem of wave propagation through media with a range-dependent index of refraction. The forward and backward propagating components of the field are decoupled order-by-order to produce a perturbative expansion of the range-dependent parabolic equation. The result includes energy-conserving correction terms that can be associated with a rapid fluctuation of energy between forward and backward propagating solutions of the Helmholtz equation. The approach selects out physical processes which accumulate over the entire range of propagation, distinguishing them from effects which depend solely on the initial and final values of the index of refraction and its derivatives. It is also shown that the corresponding backscatter mechanism is fundamentally nonperturbative, so that the parabolic equation technique as applied to the...

Applications of the Foldy–Wouthuysen transformation to acoustic modeling using the parabolic equation method

The application of the Foldy–Wouthuysen transformation on the Helmholtz equation has been previously demonstrated [J. Acoust. Soc. Am. 96, 3343 (A) (1994)]. The result provides an asymptotic expansion for correction terms to the parabolic equation (PE). These terms include contributions from the coupling of the forward propagating and backward propagating solutions to the Helmholtz equation, caused by propagation through range‐dependent media. The new correction terms have been found to depend on the curvature of the local index of refraction and can be calculated from available environmental parameters. A finite element PE (FEPE) has been modified to include these new correction terms. This new PE is used to model propagation of an acoustic field through an ocean with fluctuating sound‐speed profiles caused by internal waves and other range‐dependent oceanographic properties. The effects of these new terms and the circumstances under which they are expected to be most important are discussed, with specia...

A manifestly reciprocal theory of scattering in the presence of elastic media

The role of elastic waves in the scattering problem is examined in the context of modern field theory. This effort builds upon a previously published, and since successfully applied formalism for solving the acoustic and electromagnetic scattering problems. It specifically addresses the scattering of acoustic waves from a fluid‐solid interface, as well as the scattering of elastodynamic waves from surfaces satisfying the zero‐displacement, stress‐free, and solid–solid boundary conditions. Expressions for the change in the scattering amplitude due to a perturbation in the scattering surface are derived directly from the requirement of time reversal symmetry (also known as reciprocity). These results constitute formal statements of the composite (or two‐scale) model. In a typical application, the perturbation usually corresponds to Bragg scattering and is treated statistically, while the reference surface provides tilt, shadowing, and multiple scattering, and is usually treated deterministically. Used in th...

Assessing the Variability of Near-Boundary Surface and Volume Reverberation Using Physics-Based Scattering Models

The increased importance of responding to regional conflicts has focused Navy attention on littoral waters, with active sonar expected to be a favored mode of operation. Major performance drivers of such systems are the acoustic interactions with the ocean boundaries and fish. The vicinity of the air-sea interface is in particular a complex mix of scattering by surface roughness and scattering from bubble clouds and fish, coupled with boundary-interference effects. The Naval Research Laboratory has recently developed broadband, physics-based scattering strength models that both unify and advance our understanding of boundary scattering at low frequencies (< 5 kHz) by providing a physical basis for isolating scattering mechanisms. In this paper, these models are used to assess both the sensitivity of scattering strength to environmental variables and their utility as tools for estimating these variables. These efforts are supported by a series of data-model comparisons that demonstrate both the environmental variability of acoustic response with frequency and scattering angle, and the importance of using physics-based tools to predict these responses.