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.
Frequency selective scattering of water-borne acoustic waves by the rough sea surface ͑Bragg scattering͒ has been observed, in particular during the Critical Sea Test series. The directional nature of the gravity wave spectrum observed by Mitsiyasu, Donelan, Banner and others implies that the interface scattering will be directional, that is, depend upon azimuth relative to the receiver. During the ocean exercise Critical Sea Test 4, Bragg scattering was observed at 250 Hz over a wide range of azimuths using a linear hydrophone array with approximately one degree azimuthal resolution. The amplitude of the Bragg scattering and its dependence on azimuth closely matched model predictions based on the Donelan 2-D wave spectrum, first-order perturbation theory and a normal mode reverberation model.
During an at-sea encounter, signatures of interest can exhibit characteristics that differ from those observed in previously recorded data. These differences can occur due to variations in a number of factors including encounter geometry, propagation channel, and receiving sensor configuration. This paper presents a simulation technique that imposes low-frequency propagation effects on a time-domain signal using a normal mode method. High-quality, time-varying recorded signatures are used as inputs into the algorithm, which outputs band-limited time-series data for a selected geometry and environment. The output time-series are phased to simulate the time-varying pressure amplitudes that would be received by a towed array or any multielement passive sensor configuration operating in a realistic multipath environment. These capabilities enable the simulation of signatures of interest as captured under a broad range of littoral conditions by various passive sensors. These simulated data are used to augment scarce signature collections for training and assessing the performance of passive sonar automation.
Parabolic equations currently in use to predict acoustic intensity require a judicious choice of the reference wavenumber ko. A new parabolic equation (PE) is presented here which is independent of ko and capable of handling large variations in the index of refraction. This equation is similar to, and ostensibly simpler than, an earlier range refraction PE (RAR-EPE) reported recently by Tappert and Lee. The modified refraction parabolic equation (MOREPE) is obtained by a transformation approach, and operator and multiscale formalisms are also described to validate the equation. Principal properties of MOREPE are discussed. An exact solution with only range variation in sound speed is presented to illustrate differences between standard PE and MOREPE. Propagation examples in range-independent environments demonstrate close agreement between MOREPE and standard PE, while examples with strong range dependence exhibit significant differences between the two equations in their predictions of acoustic intensity. [Work supported by ONR.]
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