A boundary element approach to ocean seismoacoustic facet reverberation Peter Gerstoft •degaard and Danneskiold-Sams•e, Kroghsgade I, 2100 Copenhagen, Den mark and Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Honrik Schmidt Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received 27 July 1990; accepted for publication 29 October 1990) A numerically efficient, hybrid method is introduced for modeling of shortand longrange seismoacoustic facetreverberation in the ocean environment. The method combines the global matrix approach to the solution of the wave equation in horizontally stratified media with a boundary element formulation of the boundary conditions at a contour surrounding the facet. The present paper describes a two-dimensional formulation for facets within an elastic seabed or an elastic ice cover, but allows for simulation of the reverberant field within the water column aswell. The approach is directlyextendable to treat reverberation from seabed- penetrating facets aswell asthree-dimensional elastic facets. In contrast to discrete methods such asthe finite element andfinitedifference approaches, the solution obtained with the present hybrid approach is not only efficient for short-aswell aslong-range reverberation, but inherently decomposes the total solution in the temporal and spatial spectral components, of importance to the basic physical understanding of the factors affecting seismoacoustic facet reverberation. PACS numbers: 43.30.Gv, 43.30.Bp, 43.30. Ma INTRODUCTION The effect of noise correlation on the performance of ocean acoustic array processing iswell established, makingit importantto include such effects in theoretical evaluations of signal processing algorithms.• The effect of thenoise is obviously more severe the more "signal-like"the noise is. Thus the "white" electronic noise is less of a problemthan surface generated noise 2 or shipping noise. Another correlatednoise component is that generated by the signal itself through scattering and reverberation. However,in contrast to the, e.g., surface generated ambient noise,the reverberantfield is directly associated with and dependent onthesignal to be extracted by thesignal process- ing.Therefore, the reverberant fieldwill bothbeproportion- al to the signal strength and often have spatialcorrelation characteristics that are more "signal-like" than those of the ambient noise, in turn providing moreproblems for the sig- nal processing performance. The degradation of the signal processing performance is closely related to the degree and natureof the correlation. To enable performance analysis of signal processing algorithms, it is thereforeessential to be able to accuratelymodel the array response to scattering and reverberation in realistic ocean environments. Based on the temporal and spatialcorrelationcharac- teristics,the reverberation is divided into two main catego- ries, diffuseandfacet reverberation. The diffusereverbera- tion is due to scattering by the small-scale, stochastic structureof the oceanwaveguide, e.g., surface and bottom roughness, and bottom inhomogeneity. Thefacet reverbera- tion is dueto abrupt changes in the environment, e.g., by seamounts andsubbottom faults anddiapirs. Due to its sto- chastic nature, thediffuse reverberation ischaracterized by a relatively lowcorrelation. The ocean facets areof more de- terministic nature and therefore give rise to extremely "sig- nal-like" reverberation. Due to theoretical and computational limitations, the numerical modeling tools applied in underwater acoustics have untilrecently been limited to one-way, two-dimension- al propagation scenarios, capable of treating thereverbera- tion problem only interms of"target strength," incapable of representing real ocean reverberation. Thus available theo- ries cannot explain the reverberation received from the con- tinental margins as well as the reverberant field observed in apparently smooth ocean environments. Onthis background there has been a significant effort in recent years toimprove the modeling capabilities toincorpo- rate scattering and reverberation effects. Most theoretical work ondtffuse scattering has been fo- cusing on the rough sea surface, where various scattering theories have been developed. A verythorough review of these approaches was recently given by Thorsos and Jack- son. 3 Theelastic properties ofthe ocean bottom become im- portant at lowfrequencies in particular, butnotuntil very recently have elastic effects been incorporated in thetheo- retical analysis of rough bottom scattering. 4'• A review of earlier work on bottom scattering isgiven byOgilvy. 6 The facet reverberation is due to local, distinct features in theenvironment. Thecoupled mode approach of Evans ? is capable of modeling the reverberation from two-dimen- 1629 J. Acoust. Sec. Am. 89 (4), Pt. 1, April1991 0001-4966/91/041629-14500.80 •) 1991 Acoustical Society of America 1629 ownloaded 06 Aug 2010 to 137.110.8.118. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.js