Attenuation of ocean waves due to random perturbations in the seabed profile

We employ linear wave theory to study long range attenuation of ocean waves caused by small, random perturbations in the seabed. The phenomenon in an example of localization in random media. A multiple-scale method is used, in which the solution is expanded over a local scale, on the order of the perturbations, and an observation scale. However, it is not clear how the properties of the random seabed profile, such as probability density, autocorrelation and spectral density, affect the expansion directly or indirectly. We will discuss how the solutions can be obtained numerically so that the effects of each instance of random seabed on the solution can be studied