M. J. Jacobson

Current and current shear effects in the parabolic approximation for underwater sound channels

The effect of currents on the acoustic pressure field in an underwater sound channel is investigated. Based on fundamental fluid equations, model equations are formulated for sound pressure while including nonuniform currents in the source–receiver plane. Application of parabolic‐type approximations yields a collection of parabolic equations. Each of these is valid in a different domain determined by the magnitudes of current speed, current shear, and depth variation of sound speed. Under certain conditions, it is possible to interpret current effects in terms of an effective sound speed. Using this effective sound speed in an existing numerical code, we examine sound speed in a shallow water isospeed channel with a simple shear flow and a lossy bottom. It is found that even small currents can induce very substantial variations in relative intensity. The degree of variation depends upon current speed, source and receiver geometry, and acoustic frequency. Particular emphasis is placed on intensity‐differen...

Predictability of acoustic intensity and horizontal wave numbers in shallow water at low frequencies using parabolic approximations

Accuracy of relative intensity and horizontal wave‐number predictions from parabolic approximation models of shallow water, low‐frequency (less than 100 Hz) acoustic propagation problems is examined. Effects of input parameter uncertainties and basic approximations in parabolic equation models are investigated. Environmental parameters and uncertainties considered correspond generally to those from a recent New Jersey Shelf experiment. Parameter uncertainties are found to impose the greatest limitations on prediction accuracy, with sediment sound‐speed uncertainties causing the largest restrictions. Issues associated with modeling the sediment sound speed, such as using isospeed layers to approximate sound‐speed variations, are also resolved. Weak range dependence in the channel depth and sound speed, of similar type as at the experiment site, is found to be well approximated by range‐independent models. Comparisons of the experimental results with model predictions illustrate how parameter uncertainties ...

Low‐frequency sound propagation modeling over a locally reacting boundary with the parabolic approximation

There is substantial interest in the analytical and numerical modeling of low‐frequency, long‐range atmospheric acoustic propagation. Ray‐based models, because of their frequency limitations, do not always give an adequate prediction of quantities such as sound pressure or intensity levels. However, the parabolic approximation method, widely used in ocean acoustics, and often more accurate than ray models for frequencies of interest, can be applied to acoustic propagation in the atmosphere. Modifications of an existing implicit finite‐difference implementation for computing solutions to the parabolic approximation are discussed. A locally reacting boundary is used together with a one‐parameter (the flow resistivity) ground impedance model. Intensity calculations are performed for a number of flow resistivity values in both quiescent and windy atmospheric sound channels. Variations in the value of this parameter are shown to have substantial effects on the spatial variation of the acoustic signal. [Work su...

Acoustical effects of ocean current shear structures in the parabolic approximation

In a previous article [Robertson et al., J. Acoust. Soc. Am. 77, 1768–1780 (1985)], the authors developed a family of parabolic equations that includes effects due to the presence of a time‐dependent, depth‐dependent current. Some of these equations contain a new term that explicitly depends on current gradient. In this article, certain effects of this new term are studied. By transforming the parabolic equations, it is possible to convert them to forms that can be directly solved numerically using existing IFD or FFT implementations. Ocean currents with vertical fine structure present situations that can require these new types of parabolic approximations. Propagation in a shallow isospeed channel is examined, with both rigid and lossy bottoms, and use is made of a shear flow with features of an actual ocean current. The vertical current variation can cause changes in relative intensity that are substantial and that depend on bottom loss, source and receiver locations, and acoustic frequency. Intensity d...

Acoustical effects of a large ridge on low-frequency sound propagation in stationary and moving atmospheres

Abstract The effects of a ridge on a low-frequency acoustic propagation in quiescent and windy atmospheres are investigated using a parabolic approximation. A logarithmic wind-speed profile, commonly employed to model atmospheric wind currents, is modified and used to model two-dimensional atmospheric flow over a triangularly shaped hill. The parabolic equation is solved using an implicit finite-difference algorithm. Several examples are examined to determine the combined effects of source-ridge distance, ridge dimensions, wind-speed profile, and cw source frequency on the received acoustic field.

A treatment of three‐dimensional underwater acoustic propagation through a steady shear flow

The effect of a steady, depth‐dependent, horizontal shear current in an underwater sound channel is considered. Because the source–receiver direction and current direction need not lie in the same vertical plane, the propagation problem is inherently three dimensional. A three‐dimensional (3‐D) parabolic approximation for this channel is formulated by extending a two‐dimensional result obtained previously [Robertson et al., J. Acoust. Soc. Am. 77, 1768–1780 (1985)]. It is shown that, if the azimuthal derivatives are small enough to be neglected in the farfield, azimuthal effects appear only as coefficients in the parabolic equation. Therefore, an N×2‐D technique can be used to solve the parabolic equation. Numerical examples are used to examine cross‐current propagation. It is shown that substantial intensity variations can occur as the angle between the source–receiver direction and current varies from 0 to 180 deg.

Effects of a sediment scattering layer in underwater‐acoustic studies of intensity sensitivity and data matching

A scattering layer is introduced at a horizontal water–bottom interface to account for effects of attenuation due to bottom volume scattering. Using a wide‐angle parabolic equation, a formula for the local mean intensity level is found for a shallow‐ocean model consisting of three isospeed fluid layers: water, scattering layer, and bottom. The sensitivity of the theoretical mean to environmental parameters is studied, and the standard deviation of intensity is examined also. Comparisons are made between intensity statistics of the three‐layer model and of other isospeed models. Also, comparisons are made between three‐layer model statistics and data from a recent New Jersey Shelf experiment. Results from the inclusion of a scattering layer for the prediction of relative intensity statistics are evaluated over a wide range of acoustic frequencies. It is found that, with parameter values representative of the experimental site, the three‐layer model can successfully match the local mean and standard deviati...

An Efficient Enhancement of Finite-Difference Implementations for Solving Parabolic Equations

The parabolic approximation method is widely recognized as useful for accurately analyzing sound transmissions in diverse ocean environments. One reason for its attractiveness is because solutions are marched in range, thereby avoiding the massive internal storage required when using the full wave equation. Present implementations employ a range step size that is prescribed either by the user or by the code and remains fixed for the duration of the computation. An algorithm is presented in which the range step is adaptively selected by a procedure within the implicit finite‐difference (IFD) implementation of the parabolic approximation. An error indicator is computed at each range step, and its value is compared to a user‐specified error tolerance window. If the error indicator falls outside this window, a new range step size is computed and used until the error indicator again leaves the tolerance window. For a given tolerance, the algorithm generates a range step size that is optimal in a specified sens...

Parabolic approximation predictions of underwater acoustic effects due to source and receiver motions

The effects of uniform horizontal source and receiver motion on the intensity of an underwater‐acoustic pressure field are investigated. For simplicity, the surface and bottom of a stationary ocean are taken to be horizontal, the sound speed may be range‐and‐depth dependent, and the source emits a continuous‐wave (cw) signal. A Galilean transformation is used to convert the source‐receiver motion problem into a fixed receiver‐moving source problem in an ocean with a horizontal current. The effects of the transformation on the course, position, and speed of the source are discussed. A parabolic equation incorporating an apparent current due to receiver motion and an approximate Doppler frequency shift due to source and receiver motion is derived from the wave equation. All motion effects are seen to manifest themselves in a single parameter, the ‘‘effective’’ sound speed, once an appropriate time‐interval limit is found. Several numerical examples illustrate that the effects of different source and receive...

OS2IFD: A microcomputer implementation of the parabolic equation for predicting underwater sound propagation

Abstract Underwater acoustic signals are powerful scientific tools for probing large regions of the ocean which would otherwise be inaccessible. Oceanographers and other scientists use acoustic energy as a mechanism to examine the structure of ocean regions for a variety of purposes. Predicting the behavior of sound in different types of ocean environments is an extraordinarily difficult problem which has been studied intensely for many decades. The parabolic approximation, introduced to the oceanographic community more than a decade ago has proven to be a powerful and effective ocean acoustics propagation model. Whereas these models were once exclusively run on mainframe computers, the advent of fast microcomputer chips, together with operating systems that can exploit the powerful features of these chips, now makes personal computers an attractive tool for performing many propagation prediction computations. This paper describes a full-featured version of one such widely used underwater acoustic propagation model which runs on PCs under the OS/2 operating system.