Woods Hole Oceanographic Inst., Woods Hole, MA 02543
MIT, Cambridge, MA 02139
The study of acoustic wave propagation in a shallow-water environment invariably encounters the problem of range dependency, which usually comes in the forms of rough interfaces and medium inhomogeneity. For a range-independent, i.e., horizontally stratified problem where the wave equation can be solved using separation of variables, the well-established wave-number spectrum formulation has proved to be a powerful technique. When such a spectrum is known, the modal structure and its continuous component will completely determine the wave behavior in the waveguide. More importantly, knowledge of the spectral information can be used in inversion techniques to estimate environment parameters through acoustic probing. Here an approximate spectral formalism is developed for weakly range-dependent problems. More specifically, this approach is suitable for those cases where the change of environment is much slower than a horizontal wavelength. The formulation is based on an asymptotic expansion in which the lowest-order solution will result in the well-known adiabatic solution when the proper poles of the spectrum are evaluated. Since the field is expressed in the form of an approximate wave-number integral, a mode near its transition region where it changes from propagating to nonpropagating in the water column can be handled properly. In addition, higher-order solutions can be expressed in a simple recursive manner. Some examples will be discussed to elucidate this approach.