Complex effective depth of the ocean bottom

Abstract

The effective depth approximation is extended to allow for energy loss on reflection at an attenuating, low shear speed, solid ocean bottom. The resulting complex effective depth leads to a novel and efficient algorithm for finding the exact complex eigenvalues for the normal modes in isovelocity water over an attenuating fluid or solid bottom while avoiding numerical searches. The method gives rapid normal mode solutions for shallow water propagation including the effects of leaky modes.