ihree-dimensional variability Occurs in the ocean volume and bottom on length scales that are important for acoustic propagation.There fore, there are situations when it is necessary to use 3-dimensional propagation models for accurate predictions.A recent propagation model (called 101731)) that has three dimensional capability is reviewed.A summary of the theoretical development, numerical solution procedures, and computer implementation of this model will be presented.An application of the model to propagation through the somd speed field from a mesoscale ocean prediction model will be discussed.It is important to describe both the capabilities of NR3!) (what it can do) and its limitations (what it cannot do).Its current limitations suggest some enhancements which can improve its capabilities and performance.These enhancements will be discussed along with a mmber of research topics in the area of three-dimensional propagation modeling.1 .

This paper reviews research developed since 2007 at BU and RPI, with leadership by the late W.M. Carey, on acoustic properties of mud. Marine mud consists primarily of small clay mineral platelets, which are comprised of crystalline layers and usually carry charge because of isomorphous substitution. Because of resulting electrical forces, the physical nature of mud is considerably different from sand sediments. In particular, as platelets settle under gravity, electrical forces repel face-to-face contact while strong van der Waals forces permit edge-to-face attachment. This platelet aggregation results in card-house structures, for which a tentative quantitative model has been analyzed (J.O. Fayton, RPI Ph.D. thesis). The model preserves basic physics of platelet interactions and leads to low shear wave speed predictions that are consistent with observations. However, because compressional sound speed is independent of the electrostatic interactions, accurate sound speed estimates are available from the Mallock-Wood formula, which also incorporates bubble effects. The basic physical concepts and semi-empirical formulas derived for shear attenuation and its frequency dependence in sandy sediments do not apply for mud, nor do assumptions behind the often cited Biot theory for poro-elastic media. Consideration is given to incorporating geoacoustic models into equations for acoustic propagation in mud.

Doctoral and master’s students in Rensselaer’s Department of Mathematical Sciences have had opportunities for research in Ocean Acoustics since 1957. Since then only one or two faculty members at any time were directly involved with OA education. Consequently, collaboration with colleagues at other centers of OA research has been essential. The history will be briefly reviewed, focusing on the education of a small group of OA doctoral students in an environment with relatively limited institutional resources. Graduate education in OA at RPI has persisted because of sustained support by the Office of Naval Research.

A complete energy conservation correction is derived to improve the accuracy of the elastic parabolic equation for range-dependent problems. The correction is complete in the sense that it is valid for problems involving a broad spectrum of horizontal wave numbers. It is a linear condition that associates the incident and transmitted fields on a vertical interface with arrays of point sources having the appropriate energy flux densities. It is a generalization of a complete energy conservation correction for the acoustic parabolic equation [J. Acoust. Soc. Am. 94, 975–982 (1993)].

A model which provides a connection between deep-ocean temperature data and convergence zone phenomena is presented. Temperature variability below the mixed layer of the thermocline and SOFAR channel is modeled parametrically. A sound-speed profile is used which has closed form ray solutions in a range-independent ocean. By incorporating the environmental parameters into the sound speed and using the ray formulas for acoustic sources below the mixed layer, expressions for convergence zone widths and ranges are developed. Temperature profile data from the Sargasso Sea is used to construct a parameter domain representative of statistically homogeneous deep-water masses. A parabolic equation model is used to assess the accuracy of the convergence zone formulas. Good agreement is seen between the two models over the entire parameter domain. By varying the temperature parameters individually, convergence zone feature sensitivities to the parameters are characterized.

A parabolic equation (PE) method for the prediction of coherent low-frequency acoustic propagation through small-scale atmospheric turbulence is presented. Frequency constraints on the applicability of stochastic parabolic approximations are avoided by first averaging the stochastic Helmholtz equation and then applying a parabolic approximation to the resulting deterministic equation. Turbulence effects are incorporated by means of spatially varying effective wave numbers. Comparison of exact solutions in the case of infinite-space propagation demonstrates the advantages and limitations of this approach. A uniform asymptotic expression for the effective wave-number profile in the case of isotropic turbulence is used to develop a half-space PE formulation that is valid in the limit of low-frequency, small-scale inhomogeneity. For anisotropic turbulence that is correlated more strongly in range than height, a modified mean-value theorem for the 2-D Helmholtz operator is used to find the effective wave number. Numerical examples demonstrate that excess attenuation due to the imaginary component of the effective wave number is the primary effect of weak turbulence on coherent low-frequency propagation. [Work supported by the U.S. Army Atmospheric Sciences Laboratory through the United States Military Academy and by NASA.]

Previous studies have shown that the parabolic approximation method, widely used in ocean acoustics, can be successfully applied to low-frequency long-range atmospheric sound propagation over a locally reacting boundary, an important problem with many applications. This work models cw acoustic signals as they propagate over horizontal ground surfaces with impedance discontinuities. An implicit finite-difference implementation of the parabolic approximation sound propagation model incorporating locally reacting, variable-impedance ground surfaces is employed to compute estimates of the sound field excess attentuation for a variety of flow resistivities and source frequencies. Both windy and stationary atmospheres are considered. An accuracy benchmark and several example problems in which the sound propagation path includes an idealized lake will be discussed. [Work supported by NASA.]

A new parabolic equation (PE) is presented that is independent of k0 and capable of handling relatively large range variations in the index of refraction. This equation is similar to, and ostensibly simpler than, an earlier range refraction PE (RAREPE). The modified range refraction parabolic equation (MOREPE) is obtained by a transformation approach, and operator and multiscale formalisms are described to validate the equation. Principal properties of MOREPE are developed, including energy conservation and possession of the correct (Helmholtz) rays in the high-frequency, small-angle limit. Exact solutions with range variation in sound speed are presented to illustrate differences between standard PE (SPE) and MOREPE. Propagation examples in range-independent environments demonstrate close agreement between MOREPE and SPE, while examples with strong range dependence exhibit significant differences between the two equations in their predictions of acoustic intensity. Analytical and numerical comparisons of solutions to the one-way Helmholtz equation (HE1), MOREPE, and SPE demonstrate the increased accuracy of MOREPE over SPE in range-dependent environments.

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.

The effects on low-frequency acoustic propagation resulting from ideal atmospheric flow over a large ridge are investigated using the parabolic approximation. The ridge is taken to be triangularly shaped with a horizontal earth-air interface on both sides. A Schwarz-Christoffel transformation is employed to calculate the wind speeds that are then used to compute the effective sound-speed profiles. These profiles are used by an implicit finite-difference implementation of the parabolic approximation to estimate the intensity of the sound field. Several examples are examined to determine the effects of this wind-modeling method on sound pressure levels over rigid earth-air boundaries. [Work supported by NASA.]

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.

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.

In most environments, the prediction of acoustic wave propagation is carried out with two-dimensional propagation models. This should NOT mislead anyone to believe that three-dimensional models are not needed. In this paper, sound-speed information from eddy models is used to examine three-dimensional effects. This examination was carried out employing the IFD (two-dimensional) and the FOR3D (three-dimensional) models. A set of numerical results from these two models will be discussed. Interesting findings will be reported. These findings provide stimulation for continued three-dimensional model development.

The influence on ray propagation of including both attenuation and beam displacement at the bottom of a shallow-water isospeed channel is determined. Attenuation is incorporated using the Mackenzie-bottom model, rather than the commonly used Rayleigh reflection theory. Properties of displacement are studied as a function of launch angle and parameters such as bottom-to-water density, channel depth in wavelengths, and channel aspect ratio. Differences in beam displacement for the two bottom models are shown to affect the number and geometry of rays between surfaced source and receiver. Formulas for per-ray amplitude and phase shift and for incoherent total-field intensity are developed. Comparisons are made between these quantities for both modified and classical ray theory with a Mackenzie bottom, and also for both Mackenzie- and Rayleigh-bottom models using modified rays. Numerical computations show significant phase and amplitude differences arising in both types of comparisons.