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Coupled perturbed modes over a sloping penetrable bottom.

The development of coupled perturbed mode theory--the combination of conventional coupled modes and perturbation theory for problems of sound speed range dependence--is extended using a transformation of the normal modes to include a range-dependent penetrable bottom. The result is a fast, direct, and accurate range-dependent modal solution of the acoustic field in the water column. The method is applied to upslope propagation in shallow water wedge waveguides.