### ASA 125th Meeting Ottawa 1993 May

## 5pUW14. Exact reflection and transmission operator symbols in
two-dimensional, invariant imbedding-based, propagation modeling.

**Louis Fishman
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*Dept. of Math. and Computer Sci., Colorado School of Mines, Golden, CO
80401
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Recognizing that typical ocean propagation problems are essentially
scattering problems in terms of a transition region and transversely
inhomogeneous asymptotic half-spaces, wave-field splitting, invariant
imbedding, and phase space methods have reformulated the problem in terms of an
operator scattering matrix characteristic of the transition region. This
approach solves the elliptic (fixed-frequency) scattering problem by well-posed
marching (one-way) methods, and is centered on the reflection and transmission
operator symbol equations. For several nontrivial, two-dimensional, refractive
index profiles, these equations (and the wave-field equations) are solved
exactly and analyzed. These results provide benchmark cases to test both the
scattering operator and subsequent wave-field calculations, providing a severe
test of the stiff nonlinear solvers employed in the numerical implementation of
the method. The exactly solved models incorporate symmetric and asymmetric
wells, trapped modes, and sharp-gradient features. Numerical results will be
presented. [Work supported by NSF, AFOSR, ONR, ASEE, JEWC, and the S. N. Bose
Centre for Basic Sciences.]