Woods Hole Oceanogr. Inst., Woods Hole, MA 02543
MIT, Cambridge, MA 02139
This work is the study of acoustic wave propagation in a range-dependent waveguide, where either the interfaces or the medium parameters are functions of horizontal dimensions. 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 been 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. At the ASA Ottawa meeting [Tang and Guo, J. Acoust. Soc. Am. 93, 2284(A) (1993)], Tang and Guo presented the spectrum formalism and an application of the formalism to an ideal wedge. Here the approximate spectral formalism is further developed for more general weakly range-dependent problems. Special attention is paid to the ``transition regions'' of the waveguide where the discrete part of the spectrum borders the continuous part of the spectrum. Near such regions, different parts of the spectrum interact strongly with each other, resulting in apparent changes of the acoustic fields. Some examples will be discussed to elucidate the advantages of this approach.