摘要:

In underwater acoustics, the parabolic wave equation is often solved by employing techniques based on finite difference techniques. A major drawback of the finite difference treatment of interfaces to date is that mesh points have been required to lie exactly on the interface. With regularly spaced, predetermined meshes this can be a serious computational restriction. Previous treatments of the parabolic wave equation using finite differences have assumed an equispaced mesh and that at interfaces a mesh point will lie precisely on the interface. In this paper we remove both of these restrictions. This approach also makes it apparent that mesh points can be added or deleted during the solution process, and so presents a more general model to work with.

ISSN:0001-4966    

DOI:10.1121/1.391099

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

A hybrid numerical/analytic technique is presented for computing the field due to a monochromatic point source in a horizontally stratified medium. It is based on the exact Hankel transform relationship between the field in the range domain and the associated depth‐dependent Green’s function in the horizontal wavenumber domain. The method uses a numerical evaluation of the Hankel transform. It is shown that a major source of error in such an evaluation arises from undersampling of the Green’s function at points where it becomes infinite. This error is described in terms of aliasing, analogous to the aliasing that has been well‐described for the discrete Fourier transform. It is shown that the error can be substantially reduced by removing the infinities, calculating the Hankel transform of the remaining portion of the Green’s function numerically, and adding to it the analytically computed Hankel transform of the infinities. The sum of the analytic terms and the remaining Hankel transform always exactly equals the true field with no errors introduced other than those associated with the numerical evaluation of the Hankel transform, and the method is accurate in both the near‐ and farfield regions. The technique is developed in detail for the acoustics problem of a monochromatic point source and receiver in an isovelocity fluid half‐space overlying a horizontally stratified fluid medium. It is found that under circumstances of interest in ocean bottom acoustics, where the Green’s function has only a few singularities along the real horizontal wavenumber axis, the technique is efficient and extremely accurate.

ISSN:0001-4966    

DOI:10.1121/1.391100

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The method of normal modes is frequently used to solve acoustic propagation problems in stratified oceans. The propagation numbers for the modes are the eigenvalues of the boundary value problem to determine the depth dependent normal modes. Errors in the numerical determination of these eigenvalues appear as phase shifts in the range dependence of the acoustic field. Such errors can severely degrade the accuracy of the normal mode representation, particularly at long ranges. In this paper we present a fast finite difference method to accurately determine these propagation numbers and the corresponding normal modes. It consists of a combination of well‐known numerical procedures such as Sturm sequences, the bisection method, Newton’s and Brent’s methods, Richardson extrapolation, and inverse iteration. We also introduce a modified Richardson extrapolation procedure that substantially increases the speed and accuracy of the computation.

ISSN:0001-4966    

DOI:10.1121/1.391101

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The time‐frequency structure of broadband pulses propagating to long ranges is analyzed with the stationary phase approximation. A method based on this analysis is proposed for measuring the fine structure of the frequency dispersion. The new method determines the mode frequencies to a precision of 0.5 Hz whereas the precision of the sonogram method is typically several Hz. Implications of this improved frequency dispersion measurement are discussed.

ISSN:0001-4966    

DOI:10.1121/1.391102

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

A method of estimating the source to receiver range of wideband underwater acoustic pulses is critically examined in this paper. The method is based on the time–frequency dispersion of broadband signals received at a single hydrophone. Shot data recorded at field locations in the Arctic are analyzed by this technique. The resulting range predictions are compared with the observed ranges. Good agreement is found for those cases in which the bottom depth along the propagation path is greater than 1 km. At these depths, the upward refraction feature of Arctic sound propagation minimizes the effects of bottom topography. As long as the signal is above the noise level, the method is insensitive to the type of background noise and to the source spectrum shape. The frequency dispersion for anN2bilinear sound‐speed profile is investigated analytically. This profile yields a very close and useful approximation to the Arctic underwater sound field. The results are used to interpret the experimental data and to identify the factors which may influence the range estimation method.

ISSN:0001-4966    

DOI:10.1121/1.391103

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The nonlinearity parameterB/Aof seawater from 25%oto 40%ohas been calculated in the temperature range from 0° to 35 °C and at pressure of up to 1000 bars by use of the acoustic and thermodynamic approaches. Their agreement with an accuracy of 2% is within ±0.1 over most of the range from 0° to 35 °C up to 800 bars. The ratioB/Aat each concentration increases monotonically with pressure in the range covered. The increase rate at higher temperatures becomes slower than that at low temperatures. It is found that theB/Aat low pressure increases with increasing temperature, and at higher pressures decreases. However, the quantityB/Aat moderate pressure near 500 bars is relatively insensitive to temperature changes and then reveals a small temperature minimum. Although theB/Aat a fixedPandTincreases with increasing salinity, the increment ofB/Adecreases as pressure increases. To find a relationship betweenB/AandTorP, we obtained the thermodynamic expressions for [∂(B/A)/∂T]Pand [∂(B/A)/∂P]T, respectively.

ISSN:0001-4966    

DOI:10.1121/1.391113

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

Acoustic diffraction of plane impulsive waves is considered for free‐field, baffled, and pressure release boundary conditions, in the case of an arbitrary spatial distribution of combined, amplitude‐time delay modulation in an aperture. The method is based on the impulse response analysis of parallel aperture lines, the line impulse responses being then integrated to give an aperture impulse response. A closed‐form, analytical expression is derived for lines having an arbitrary amplitude modulation. In the case of nonmodulated apertures of an arbitrary shape, the aperture impulse response is also of an analytical form, directly involving the aperture contour line. The analysis is performed with emphasis on maintaining clear physical sense of successive evaluation steps.

ISSN:0001-4966    

DOI:10.1121/1.391115

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The half‐order derivative (d/dt)1/2s(t) is calculated fors(t) given by a burst of sine waves. The burst isNcycles in length, whereNis an integer or a half‐odd‐integer. The result contains Fresnel integrals; it may be written in a compact form by using the auxiliary Fresnel‐integral function usually denoted byg. Some novel properties ofgwere derived to facilitate a discussion of the result. The calculation is applicable to several dissipationless acoustical models for which the response to an exp(−iωt) input is proportional to ω1/2 exp(−iωt−iπ/4). Some examples include the pressure radiated by two‐dimensional sources such as the optoacoustic radiation from a thin modulated laser beam. Another example is the pressure from virtual ringlike sources such as those present in focused backscattering from large spheres and a torus. The scattering from a large torus is modeled for the case of an incident plane wave which propagates parallel to the symmetry axis.

ISSN:0001-4966    

DOI:10.1121/1.391014

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

A self‐consistent multiple scattering approach with suitable pair‐correlation function has been employed to study the frequency‐dependent properties of rubber materials containing a random distribution of voids. Numerical results indicate that for a certain range of concentration of voids, the resonance of the voids controls the frequency‐dependent effective properties such that the imaginary part of the effective wavenumber becomes greater than the real part. This indicates that the propagating wave will be damped out over a distance smaller than a wavelength. The so‐called ‘‘superviscous’’ propagation seems to occur over a bandwidth controlled by the concentration of voids (c). The bandwidth increases with increasing concentrations in the range 0

ISSN:0001-4966    

DOI:10.1121/1.391116

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The Schur algorithm is a signal processing algorithm which works on a layer‐stripping principle. Its time‐domain version, the fast Cholesky recursion, is a fast and efficient algorithm well‐suited for high‐speed data processing. In this paper, these algorithms are applied to the inverse problem for a continuous layered acoustic medium. Three different excitations of the medium are considered: impulsive plane waves at normal incidence, impulsive plane waves at oblique incidence, and spherical waves emanating from an impulsive point source. The fast algorithms obtained for each of these problems seem to be computationally superior to past work done on these problems that employed Gelfand–Levitan theory to reconstruct the potential of a Schrödinger equation.

ISSN:0001-4966    

DOI:10.1121/1.391062

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP