Henry Weinberg

Horizontal ray theory for ocean acoustics

The solution of the reduced scalar wave equation for an almost stratified medium is written in the form of an asymptotic power series. The vertical structure of the solution is expressed as a linear combination of the normal‐mode eigenfunctions whose coefficients satisfy two‐dimensional eikonal and transport equations. Although smooth caustics may be treated for the two‐dimensional scalar wave equation, the problem of a uniform approximation near a point source has not yet been resolved. Finally, the theory is applied to acoustic propagation in a realistic model ocean and the results are compared with measurements.The solution of the reduced scalar wave equation for an almost stratified medium is written in the form of an asymptotic power series. The vertical structure of the solution is expressed as a linear combination of the normal‐mode eigenfunctions whose coefficients satisfy two‐dimensional eikonal and transport equations. Although smooth caustics may be treated for the two‐dimensional scalar wave equation, the problem of a uniform approximation near a point source has not yet been resolved. Finally, the theory is applied to acoustic propagation in a realistic model ocean and the results are compared with measurements.

Gaussian ray bundles for modeling high‐frequency propagation loss under shallow‐water conditions

An acoustical propagation model was developed to analyze high‐frequency propagation loss under shallow‐water conditions. The model is based on Gaussian ray bundles which are similar in form but somewhat simpler than Gaussian beams. After describing the approach, propagation loss predictions are compared with those of various ‘‘standard models’’ at lower frequencies where the latter models are accurate and efficient. If Gaussian ray bundles compare well at the lower frequencies, they should perform well at the higher frequencies as ray approximations improve.

Application of ray theory to acoustic propagation in horizontally stratified oceans

The acoustic pressure due to a point harmonic source in a horizontally stratified ocean is represented as a multipath expansion of the integral representation. Generalized Wentzel–Kramers–Brillouin–Jeffreys solutions are used to solve the depth‐dependent wave equation. By applying numerical integration in conjunction with stationary phase, the problem of caustics is eliminated. Computed predictions are compared with theoretical results and another computer model.Subject Classification: 30.20; 20.20; 85.84.

A Continuous‐Gradient Curve‐Fitting Technique for Acoustic‐Ray Analysis

A method of computing acoustic‐ray paths is developed. The velocity of sound is approximated by a function of depth that has a continuous gradient and allows one to evaluate the range and travel time integrals in closed form. The advantages of this technique over others are discussed, and some interesting phase effects are illustrated.

High‐frequency propagation modeling using HYPER

The hybrid parabolic equation‐ray (HYPER) model previously described [J. Acoust. Soc. Am. Suppl. 1 74, S96 (1983)] has been further developed both theoretically and numerically. The small‐angle Newtonian ray equation that is consistent with the parabolic approximation has been integrated numerically through strongly range‐dependent ocean environments and compared to the exact rays with satisfactory agreement. The modified parabolic equation that correctly describes amplitude and phase within a ray bundle has been integrated numerically at kHz frequencies through strongly range‐dependent ocean environments and the caustic structure at convergence zones has been examined. Comparisons to available caustic theories show that the HYPER model provides fully diffractive results that are uniformly valid.

Technical aspects of the comprehensive acoustic simulation system (CASS) reverberation model and comparisons with measured data

The Comprehensive Acoustic Simulation System (CASS) has recently received interim acceptance into the United States Navy’s Atmospheric and Oceanographic Master Library (OAML). This paper focuses on the application of the CASS to computing reverberation in shallow water. The first topic reviews the numerical approach. This is based on the usual assumption that reverberation received at a specific time can be found by integrating returns from ensonified scattering areas on the ocean boundaries and from ensonified volumes within the ocean proper. The same approach is used for monostatic and bistatic modes of operation. CASS contains various methods for integrating over bearing and frequency. The second topic compares computed results with torpedo data measured off the waters of southern California. This data confirms the requirement for including range‐dependent effects in shallow‐water reverberation modeling. Fortunately, the measured reverberation was accompanied by an excellent survey of bottom properties...

HYPER: A hybrid parabolic equation‐ray model for underwater sound propagation in the vicinity of smooth caustics

The hybrid parabolic equation‐ray model (HYPER) uses modified ray tracing of geometrical acoustics to locate important propagation paths. Then HYPER solves a modified parabolic equation in a small region near the rays to compute the pressure field. This paper applies the HYPER model to investigate acoustic propagation in the vicinity of smooth caustics. Results are compared with ordinary ray theory, modified ray theory, and the wave solution for a range‐independent case. Some range‐dependent examples are also presented. [Funding for this work was provided by the AEAS Program Office, ONR Detachment, Code 132.]

Convolving the impulse response of ocean reverberation.

The comprehensive acoustic system simulation, a range‐dependent standard model for predicting ocean reverberation, has the ability to simulate complex pulses. However, the method is inefficient if the acoustic system is aimed at numerous directions for various pulse shapes. A recent capability uses the standard approach to determine a numerical impulse response as a function of time and azimuth. The impulse response is then convolved with a complex pulse in order to obtain the actual response. Standard and convolved responses agree for the simple test cases that were tried. The standard approach is faster for one look direction and pulse shape. Convolution is an order of magnitude faster for realistic applications. At first glance, the impulse response appeared to be a significant advantage to the standard approach, but theoretical issues have not been resolved to the authors’ satisfaction. Some methods, including the one described here, convolve acoustic pressure squared. Others convolve acoustic pressure. References tend to quote basic convolution theory or require a significant background in signal processing. The former is probably an oversimplification. The latter is significantly more complicated than standard convolution.

Improving the efficiency of the comprehensive acoustic simulation system Navy standard reverberation model.

Research projects that use supercomputers and real‐time applications for at‐sea exercises would benefit from more efficient code. This paper describes various approaches that significantly reduced the run time of the comprehensive acoustic simulation system (CASS) Navy standard reverberation model. These include computer upgrades, parallel processing, and reconfiguring code. For example, typical CASS run times of two 3‐GHz computers differed by a factor of 10 because the faster computer had more efficient memory. Three types of parallelization were also tried. The easiest to implement used a platform that contained numerous blades with eight processors per blade. Reverberation runs were split along receiver bearing angles with several bearing angles per processor. The second parallelization attempted fine grain segmentation. This proved inefficient exchanging data between processors until the GRAB eigenray model was restructured. The third approach, OPENMP, has the advantage of using the same code on comp...

Modeling ocean reverberation under short pulse conditions

The Comprehensive Acoustic System Simulation (CASS) is a standard model for predicting ocean reverberation. However, the current version, CASS V4.1, is known to have theoretical and numerical difficulties when investigating short pulse lengths. This is due to two model requirements: (1) the time increment for sampling reverberation should not exceed the pulse length; and (2) the range increment for sampling the environment should not exceed half the sound speed‐pulse length product. Unless these requirements are met, certain phenomena, such as time splitting, may not be accurately modeled. In addition, the predicted results may have an unrealistic step function appearance. On the other hand, very small time and range increments often lead to excessive computational requirements. A simple modification to CASS V4.1 appears to have relaxed the current increment requirements substantially. The range increment must still be small enough to sample environmental features, but not to the extent dictated by small ...