A Time-Domain Model for Acoustic Scattering from the Sea Surface

R.S. Keiffer
Acoustics Division

Introduction: It is common for sonar systems to operate under conditions in which (unavoidably) some of the sound generated by the source travels upward and impinges on the wavy ocean surface. If the seas are rough enough, a significant fraction of the energy hitting this boundary may scatter toward the sonar receiver where it can act as a kind of noise that limits the sonar systems ability to detect a target. The current scientific literature contains descriptions of several computer models that can accurately predict the acoustic scattering from rough boundaries like the sea surface. These interface scattering models have overcome past difficulties presented by the broad band of spatial scales that exhibit significant roughness. However, a complete simulation of the surface reverberation problem must address the dynamic nature of the boundary and the inhomogeneity of the underlying medium. Difficulties in modeling these additional ocean-acoustic phenomena have kept the accurate calculation of the magnitude and spectral content of acoustic signals scattered from the sea surface as one of the outstanding unsolved problems in underwater acoustics.

Under the 6.1 Base Program, NRL has developed, benchmarked, and published the only computer model that predicts the 3-D acoustic scattering from sea surfaces in the time domain.¹ This model is called the Wedge Assemblage Scattering Program (WASP). Unlike some of the other highly accurate modeling approaches, it is efficient enough to be applied to the largest time-evolving 2-D sea surfaces of interest.

Fig7 Graph

FIGURE 7
A comparison between the WASP model and a benchmarkaccurate frequency domain solution (OE2) for the average intensity of sound backscattered from simulated 2-D seas that are due to a spatially uniform, steady, 20 m/s wind. The angle of insonification is 20° grazing and the scattered angles (qscat) are 90°, 45°, 20°, and 10° grazing.

Physical Basis of the Scattering Model: The basis of the WASP model is an exact time-domain solution for the scattered response of an impenetrable wedge-shaped boundary.² Because this solution has a clear and unambiguous physical interpretation, it is applicable (with some modification) to scattering problems involving complicated rough boundaries like the sea surface. NRL has extended this modeling approach from its original form for 1-D (corrugated) surfaces to fully 2-D surfaces. The WASP model for 2-D surfaces has been benchmarked against exact numerical solutions for scattering from simple objects (disks) and against highly accurate solutions for scattering from rough sea surfaces. Figure 7 shows results from this later benchmarking effort. Here we see comparisons between WASP and a benchmarkaccurate frequency-domain solution for the average intensity of sound backscattered from simulated 2-D seas that are due to a 20 m/s wind. The angle of insonification is 20° grazing and the scattered angles (qscat) in the comparison are 90°, 45°, 20°, and 10° grazing. Of particular significance is the high level of agreement between WASP and the benchmark over the large dynamic range of scattered intensities.

FIGURE 8
An example calculation made using the extension of the WASP model to moving surfaces. In this simulation, 2-D seas travel away from a stationary source and the backscattered signal is collected at a receiver that is advancing at a speed of 5 m/s while periodically (1 Hz) undergoing small (1 m) up and down excursions. The various motions involved cause frequency shifts in the average scattered power spectrum. This (Doppler) effect is calculated for a broad band of source frequencies. The modulation effect seen in this simulation is due to the periodic vertical displacement of the receiver.

Extension of WASP to Moving Surfaces: One of the promising attributes of the WASP model is the time-domain nature of its solution approach. While mathematically equivalent, frequency-domain solution approaches are, in practice, difficult to interpret under dynamic, time-varying conditions. The time-domain approach offers a conceptually straightforward algorithm for computing the scattered signal, even under circumstances in which the source, receiver, and surface all move in complicated ways. This motion induces an additional time variation in the scattered signal that manifests itself in the frequency domain as a frequency-shifting phenomenon called the Doppler effect. Using concepts from timevariant linear filter theory, the WASP model has been extended to address this dynamic scattering problem. Figure 8 shows an example of a simulation in which 2-D seas travel away from a static source and the backscattered signal is collected at a receiver that advances on the seas at a speed of 5 m/s. The WASP model supplies the average scattered power spectrum and the Doppler shift for a broad band of source frequencies. The modulation effect seen in this simulation is due to the receiver periodically (1 Hz) undergoing small excursions (1 m) up and down in the water as it advances on the seas.

Summary: NRL has developed and tested a unique time-domain scattering model that is being used to address many of the long-standing issues as- sociated with acoustic scattering from dynamic ocean surfaces. Further development of this capability, along with more comprehensive acoustic and environmental data, will help mitigate the critical impact that sea surface reverberation can have on sonar performance.

Acknowledgments: The author acknowledges the many helpful conversations he has had with frequent co-author J.C. Novarini (Planning Systems Inc). Also, the author recognizes the grants of computer time at two DOD High Performance Computing Shared Resource Centers (Stennis Space Center, Mississippi, and Vicksburg, Mississippi).

[Sponsored by ONR]

References
¹ R.S. Keiffer and J.C. Novarini, "A Time-Domain Rough Surface Scattering Model Based on Wedge Diffraction: Application to Low-Frequency Backscattering from Two-Dimensional Sea Surfaces," J. Acoust. Soc. Am. 107, 27-39 (2000).
² H. Medwin and C.S. Clay, Fundamentals of Acoustical Oceanography (Academic Press, New York, 1998), Chaps. 11- 12.