Journal of Computational Acoustics

In this paper, we discuss the interface problems arising in using finite difference methods to solve hyperbolic equations with discontinuous coefficients. The schemes developed here can be used to handle four important types of numerical interfaces due to: (1) the discontinuity of the coefficients of the PDE, (2) using artificial boundary, (3) using different finite difference formulae in different areas, and (4) using different grid sizes in different areas. Stability analysis for these schemes is carried out in terms of conventional l₁, l₂, and l_∞ norms so that the convergence rates of these schemes are obtained. Several numerical examples are supplied to demonstrate properties of these schemes.

A combination of the Neumann series and the modified Cagniard method is used to derive a theoretically exact space-time domain solution for the 3-D acoustic wave propagation problem in horizontally continuously layered media. Firstly, integral transformations (among which is a one-sided temporal Laplace transformation) are applied to the space-time domain basic acoustic equations. Secondly, a system of transform domain integral equations is derived, which is solved using a convergent Neumann series. Finally, the individual terms of this series are transformed back to the space-time .domain using the modified Cagniard method. The space-time domain series turns out to be convergent for every continuously layered configuration and at any time instant. In contrast to the standard angular wave number-frequency domain analysis, in the present analysis, difficulties due to turning points, etc., are avoided.

Suppose that a medium with slowly changing spatial properties is enclosed in a bounded 3-dimensional domain and is subjected to a scattering by plane waves of a fixed frequency. Let measurements of the wave scattering field induced by this medium be available in the region outside of this domain. We study how to extract the properties of the medium from the information contained in the measurements. We are concerned with the weak scattering case of the above inverse scattering problem (ISP), that is, the unknown. spatial variations of the medium are assumed to be close to a constant. Examples can be found in the studies of the wave propagation in oceans, in the atmosphere, and in some biological media.

Since the problems are nonlinear, the methods for their linearization (the Born approximation) have been developed. However, such an approach often does not produce good results. In our method, the Born approximation is just the first iteration and further iterations improve the identification by an order of magnitude. The iterative sequence is defined in the framework of a Quasi-Newton method. Using the measurements of the scattering field from a carefully chosen set of directions we are able to recover (finitely many) Fourier coefficients of the sought parameters of the model. Numerical experiments for the scattering from coaxial circular cylinders as well as for simulated data are presented.

This paper which is Part I of a sequence deals with the problem of determining a radially dependent coefficient n (r) in the equation ∆ u − n² (r) u = 0, in the unit disk Ω from the Dirichlet–Neumann data pair . We prove that the sufficiency condition for uniqueness established in Ref. 2 is, in some instances, also a necessity for uniqueness. We also discuss the solvability of this inverse problem. In Part II numerical experiments will be presented which illustrate the theory developed here.

A model is described and numerical results are shown for the far-field scatter of a plane wave from an acoustically hard surface with a periodic roughness profile function that is continuous everywhere, but is nondifferentiable at a finite number of points within a period, and that may have a large maximum amplitude or slope. Scattering from these types of surfaces is modeled by approximating the roughness profile by truncating its Fourier series representation, and using the integral equation scattering formalism of Holford [J. Acoust. Soc. Am.70, (1981) 1116–1128]. To determine the effects of this approximation on the far-field scatter, the exact profile function and the scattering formalism of DeSanto [Radio Sci.16, (1981) 1315–1326], which is not an integral equation formalism, is also used to calculate the far-field scatter. Both formalisms are used to calculate plane wave scattering from sinusoidal surface roughness and from nondifferentiable periodic surface roughness constructed from (1) a trapezoid, (2) a rectified sinusoid, (3) concave upward and concave downward semi-ellipses, and (4) a power law spectrum. It is shown that the amplitudes of the plane wave modes scattered from a continuous and nondifferentiable surface and from its truncated Fourier series representation are essentially identical for all surfaces considered and over a wide range of incident grazing angles, wavenumbers, and surface roughness. In addition, it is shown that the Holford formalism may be used to calculate scattering from surfaces considerably rougher and at grazing angles lower than the DeSanto formalism, but that the Holford formalism is more computationally intensive than the DeSanto formalism, and that in the regions where both theories are numerically stable, the DeSanto formalism is preferable.

The paper deals with sound fields created by sources moving along a curved path in the open atmosphere. The theory presented here is used for computer simulation in time steps in order to discover some general acoustic phenomena which appear during the motion of the sound source. Specifically, the modified "Doppler effect" of such motions is investigated rather than the motion along a straight line (which is a specific case). This includes the influence of condensation and rarefication of the sound waves on the amplitudes in front and behind the source. Conclusively, it has been found that generalization of the sound field radiated by a moving source along a straight line to motion along curved lines does not avoid a clear appearance of the known "Doppler effect". Enhancement 01 weakening of the waves is distinguished in a manner similar to that of a motion along a straight line, as related to the actual location of the source. Finally, examples of motion of a sound source along a circular orbit, a parabolic orbit, and others in the free space illustrate the proposed approach and highlight the possibility of its use.