The long-distance propagation of shallow water waves over an ocean of random depth

An investigation is made of the scattering effect of a random ocean bottom of constant average depth upon the propagation of shallow water waves. Of particular concern is the case of long-distance propagation, in which the conventional perturbation schemes fail to apply. The approximation scheme employed is basically one of selective summation of the type used in other areas of physics such as the theory of many-body interactions. Results are obtained for the average wave and the two-point correlation function of the wave field for the case when the ocean statistics are homogeneous and isotropic. The application of the results to the case of a tsunami is discussed.