Intrinsic Modes in a Wedge-Shaped Ocean with Stratified Elastic Bottom

Abstract

Propagation of low frequency acoustic signals in an ocean environment with weak lateral variation in the sound speed and (or) bottom profile can be modeled effectively in terms of local intrinsic modes (Arnold and Felsen, to be published in Wave Motion). At any lateral location (x,y), these local modes have a depth (z) variation like a normal mode in a laterally homogeneous ocean defined by conditions at (x,y), and they propagate in the (x,y)-plane along lateral ray trajectories. Local intrinsic modes differ from adiabatic modes, first, by incorporating some adiabatic mode coupling effects and, second, by uniformly accommodating the transition through cutoff from trapped to radiating during upslope propagation. It has previously been shown that local intrinsic modes become exact for the prototype problem of a homogeneous water column separated from a homogeneous fluid bottom by a plane slanted interface. The model is now generalized to allow for stratification of the slanted bottom along planes parallel to the water-bottom interface, and for elastic properties in these layers. Examined in detail is the special case where the bottom is an elastic half space. Upslope propagation in the water, perpendicular to the coast line, now involves transformation of a locally trapped mode downslope into a partly leaky and then into a totally leaky mode due to the separately occurring compressional and shear wave transitions. The numerically computable generalized intrinsic mode spectral integral for the acoustic field in the water and the seismic field in the bottom describes these transitions, as well as the reduction to adiabatic modes in the totally trapped regime.