Showing papers in "Journal of Computational Acoustics in 1993"

A Study of the Short Wave Components in Computational Acoustics

Abstract: The feasibility of performing direct numerical simulations of acoustic wave propagation problems has recently been demonstrated by a number of investigators. It is easy to show that the computed acoustic wave solutions are good approximations of those of the exact solutions of the linearized Euler equations as long as the wavenumbers are in the long wave range. Computed waves with higher wavenumber, or the short waves, generally have totally different propagation characteristics. There are no counterparts of such waves in the exact solutions. The short waves are contaminants of the numerical solutions. The characteristics of these short waves are analyzed here by group velocity consideration. Numerical results of direct simulations of these waves are reported. To purge the short waves so as to improve the quality of the numerical solution, it is suggested that artificial selective damping terms be added to the finite difference scheme. It is shown how the coefficients of such damping terms may be chosen so that damping is confined primarily to the high wavenumber range. This is important for then only the short waves are damped leaving the long waves basically unaffected. The effectiveness of the artificial selective damping terms is demonstrated by direct numerical simulations involving acoustic wave pulses with discontinuous wave fronts.

A modal inversion scheme for ocean acoustic tomography

Abstract: An inversion scheme based on normal-mode representation of the acoustic field is applied in ocean acoustic tomography for a range-dependent reconstruction of the sound speed variations at a vertical slice. The scheme is based on the assumption that modal phase can be measured by suitable mode filtering at some range from the sound source. Two cases have been considered. The first of them makes no use of oceanographic information on the variability to be recovered, while the second one makes use of empirical orthogonal functions (EOFs) that describe sound speed variations in the ocean. The data used in the applications presented in this paper are synthetic ones. It is shown that both modal inversion schemes can be used for the recovery of range-dependent sound speed variations of compact support in the ocean, provided that a range dependent background environment is used to describe an initial guess of the variations. The scheme is more powerful when EOFs are used.

Theory of acoustic imaging in the ocean with ambient noise

Abstract: Following a recent experiment in which ambient noise (acoustic daylight) was used as the sole source of acoustic illumination for detecting objects in the ocean, a full wave-theoretic analysis is presented in this article of the visibility of a pressure-release spherical target when illuminated by ambient noise showing various degrees of anisotropy. The basis of the analysis is a new, accurate approximation for the Green's function representing the field around the sphere. From this expression, an analysis of the acoustic contrast is developed, as observed at the output of an endfire line array, which constitutes the acoustic lens. Our essential conclusion is that, even in isotropic noise, which presents one of the least favourable conditions for incoherent imaging, the visibility of the sphere (i.e. the ratio of intensities with the sphere present and absent) is approximately 4 dB. This is consistent with our early experimental observations, and is adequate to form the basis of an acoustic daylight imaging system.

Two versions of quasi-newton method for multidimensional inverse scattering problem

Abstract: 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.

Wavelet solutions for time harmonic acoustic waves in a finite ocean

Abstract: In this paper, we show how wavelet analysis may be used to solve the parabolic approximate wave equation. The paper is naturally subdivided into three parts. The first entails a crash course in wavelet analysis with the aim of using it to solve partial differential equations. The second part develops the wavelet-Galerkin approximation for solving partial differential equations in variational form. Finally, the third section derives a range-depth adaptive wavelet approach, and, moreover, provides an algorithm for solving the propagation problem.

A 3d boundary element method for determination of acoustic eigenfrequencies considering admittance boundary conditions

Abstract: A 3D boundary element method for the determination of the acoustic eigenfrequencies of car compartments, characterized by a unified treatment of Robin, Dirichlet, and Neumann boundary conditions, is presented. The drawback of frequency-dependent matrices of the eigenvalue problem is overcome by means of the Particular Integral Method. Thus, the standard numerical algorithms for the extraction of eigenvalues can be applied. The numerical study contains both a comparison of numerical results with analytical solutions of a simple problem with different types of boundary conditions and a comparison of numerical results of a large-scale problem with respective numerical results, computed on the basis of the finite element method. In addition, for the latter example, different numerical algorithms for the eigenvalue extraction are examined.

Acoustic travel time computation based on pe solution

Abstract: We propose the modal spectrum of the PE field (MOSPEF) method for computing modal travel time under strong mode coupling environments. Instead of dealing with the coupled equations governing the complex modal amplitudes, the coupled modal amplitudes and phases are obtained from the spectral expansion of the full wave field given by the PE solution. Consequently, the method is very efficient and is free of problems at critical coupling points. Numerical simulations for computing modal travel time perturbations caused by a mesoscale eddy are conducted. A case which illustrates the failure of the adiabatic mode theory is also presented, the result of which raises an important issue for ocean acoustic tomography schemes.

On the conditions for uniqueness and existence of the solution to an acoustic inverse problem i: theory

Abstract: 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 nonlinear plane-wave algorithm for diffractive propagation involving shockwaves

Abstract: A new algorithm for nonlinear plane-wave propagation is presented. The algorithm uses a novel time domain representation to account for nonlinearity, while accounting for absorption in the frequency domain. The new algorithm allows for accurate representations of diffractive shockwave propagation in the framework of an existing nonlinear beam propagation model using far fewer harmonics (and thus time) than alternative algorithms based on a frequency domain solution to Burgers' equation. The new algorithm is tested against the frequency domain solution to Burgers' equation in a variety of cases and then used to model a focused ultrasonic piston transducer operating at very high source intensities.

A new lattice gas model for 1-d sound propagation

Abstract: A new lattice gas model for sound propagation in one space dimension is proposed. This model has zero truncation error, and the group velocity is independent of wave number as is required from the continuum limit. Conventional finite difference approaches do not have these properties in general. Boundary condition treatments, applicable to the lattice gas formulation, are also given. Both the boundary between two fluid media and an impedance boundary are considered.

Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems

Abstract: In this paper, a new method for the numerical solution of the two-dimensional parabolic equation of Tappert in horizontally-stratified media is presented. This method uses orthogonal cubic spline collocation for the semidiscretization with respect to depth, and the resulting system of differential-algebraic equations is solved using the NAG Library routine D02NNF. In the present application, orthogonal spline collocation, which has been exceedingly effective in the approximate solution of a broad class of problems, has the advantage that it systematically incorporates the requisite interface conditions. The state-of-the-art routine D02NNF, which implements backward differentiation formulas, has been used successfully in the solution of related problems.

An approximate boundary integral method for acoustic scattering in shallow oceans

Abstract: The problem of a time-harmonic acoustic wave scattering from a cylindrical object in shallow oceans is solved by an approximate boundary integral method In the method we employ a Green's function of the Helmholtz equation with sound soft sea level and sound hard sea bottom conditions, and reformulate the problem into a boundary integral equation on the surface of the scattering object The kernel of the integral equation is given by an infinite series, and is approximated by an appropriate truncation The integral equation is then fully discretized by applying a quadrature rule The method has an O(N−3) rate of convergence Various numerical examples are presented

The influence of the reference wavenumber in computational ocean acoustics

Abstract: A class of ocean acoustic propagation problems can be solved efficiently by the Parabolic Equation (PE) approximation method. The application of the PE method for the prediction of wave propagation introduces a new parameter, the reference wavenumber k0. This requires selection of the most appropriate k0, which is related to the reference sound speed c0. The influence on the acoustic field by the choice of c0 is rarely visible under weak range-dependent environments. Even if it is visible, the difference is small and is usually negligible since the present judicious choice of the c0 seems to provide acceptable results. When the environment is not weakly range-dependent, the choice of c0 will likely affect the computation of acoustic results. This paper examines a few different choices of c0 and analyzes how these different choices can influence the acoustic results. An application is given where the farfield wave equation represents a realistic range-dependent environment. Different choices of c0 were made for the computation of the acoustic field; as a consequence, different choices of c0 produce different acoustic results. These numerical results are not in agreement with a known reference exact solution. The differences are not too small and may be considered non-negligible. So, there is a need to make an appropriate choice of c0 in order to produce reasonable results. For the purpose of achieving satisfactory and acceptable acoustic results dealing with a PE-type equation, the requirements of the reference wavenumber will be discussed both mathematically and physically. Then, a number of computational choices of c0 will be examined, especially the k0-formula. An analysis as well as an assessment of the k0-formula will be given.

Parameter sensitivities in two-layer isospeed models of shallow water channels

Abstract: Sensitivities of relative intensity, interference wavelength, and horizontal wave number predictions to input parameters in two-layer isospeed models of shallow-water, low-frequency (less than 100 Hz) acoustic propagation problems are examined. The investigation is directed toward environmental parameter values corresponding generally to those near the site of a recent New Jersey shelf experiment. Typical parameter uncertainties in the environment of the experiment site are used to determine effects of parameter sensitivities on the accuracy of propagation model predictions. Also, analytic expressions for rates of change of wave numbers with respect to parameters are used to compute wave number and interference wavelength changes caused by parameter variations corresponding to the uncertainties. It is found that channel depth variations cause the largest change in intensity, while water sound speed variations have the greatest effect on wave numbers. Variabilities of the parameter sensitivities in regions about the base parameter sets are also examined, with the rates of change generally staying of the same order of magnitude throughout the regions considered. However, wave numbers which are close to cutoff can produce rates of change which vary by as much as three orders of magnitude.

Quasi-linear elastodynamic equations for finite difference solutions in discontinuous media

Abstract: The linear elastodynamic equations are ill-posed for models which contain high contrast density discontinuities. This paper presents a quasi-linear superset of the linear equations that is well-posed for this situation. The extended system contains a conservation of mass equation and a quasi-linear convective term in the momentum equation. Density, momentum, and stress are the field variables in the quasi-linear system, which is cast in a first order form. Using a Lax–Wendroff finite difference approximation, the utility of the quasi-linear system is demonstrated by modeling underwater acoustic scattering from a truncated ice sheet. The model contains air, ice, and water with a density contrast between air and ice or water of O(103). Superlinear convergence of the Lax–Wendroff scheme is demonstrated for his heterogeneous medium problem.

Boundary element solution of a body's exterior acoustic field near its internal eigenvalues

Abstract: A relatively straightforward Boundary Element Method (BEM) for the numerical solution of the exterior Helmholtz problem is specified in a tutorial fashion. The algorithm employs the Combined Helmholtz Integral Equation Formulation (CHIEF) and then Singular Value Decomposition (SVD) to solve the resulting system. Its accuracy and convergence characteristics are examined, and compared to the simplest boundary element method for exterior acoustics, the Helmholtz Integral Equation Formulation or HIEF. Boundary element and auxiliary (CHIEF) point requirements to obtain BEM solutions of a desired accuracy are described. This particular CHIEF algorithm is found to largely avoid the numerical difficulties of the HIEF technique while retaining theoretical and practical implementation simplicity.

Radiation boundary conditions for vertically heterogeneous acoustic media

Abstract: Several radiation boundary conditions for inhomogeneous acoustic media are investigated. Previous investigators have developed various approximate radiation conditions and have studied their accuracy by calculating an effective reflection coefficient for plane waves incident on such radiating boundaries. In this paper, it is shown that effective reflection coefficients can be calculated for a class of parabolic approximations to the Helmholtz equation. These results are valid for vertically heterogeneous media. Comparison of these radiation conditions is given through numerical examples.

Scattering of transient waves by finite cracks in an anti-plane strain elastic solid

Abstract: The transient problem of finite cracks with vanishing thickness in an anti-plane strain solid is investigated by finite element method. The infinitesimally thin crack with traction free on both faces of the crack is simulated by the energy-sharing-node technique. The following cases are considered: (a) One finite line crack in a whole space subjected to (i) a concentrated line source and (ii) an inclined incident SH plane wave. (b) Two cracks in a whole space subjected to an inclined incident SH plane wave. Emphasis has been laid on the quantitative evaluation of the dynamic disturbances for the problem in the interference stage, which is generally difficult to be obtained by analytical approaches. The synthetic seismograms for displacements along the crack surfaces, which cover a period up to an instant of time during which the second order scattering from crack tips can be observed, are presented. Snapshots of the scattered displacement field for each case are also displayed so that the generations of the scatterings and the processes of the wave propagations can be clearly visualized. The two-dimensional wave propagation for transient acoustic problem and electromagnetic problem with the same nature of boundaries can be analogously obtained.

Numerical interfaces in finite difference methods for hyperbolic equations with discontinuous coefficients

Abstract: 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.

Dynamic simulation of sound field created by a motion of a monopole along a curved path and related physical phenomena

Abstract: 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.