### ASA 125th Meeting Ottawa 1993 May

## 2aAO4. Spectral formalism of wave propagation in a range-dependent
shallow-water waveguide.

**Dajun Tang
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*Woods Hole Oceanographic Inst., Woods Hole, MA 02543
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**Yue-Ping Guo
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*MIT, Cambridge, MA 02139
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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.