Acoustic waves in a perturbed layered ocean

The study of acoustic wave propagation in an ocean is of interest due to our need to understand naval detection and marine seismology. If the ocean is assumed to be homogeneous with a plane seabed, normal mode analysis can be employed to the depth equation obtained by separation of variables from the acoustic wave equation. The analysis is simpler if a rigid seabed is assumed. In practical situations, however, the ocean may have depth-dependent properties due to an increase in density due to depth, salinity, or a change in temperature. This change can often be modeled by considering a layered model of ocean. Moreover, the seabed may not be rigid, but may satisfy reflecting-type boundary conditions. One interesting situation can arise if the seabed undergoes undulation so that separation of variables is no longer feasible. We use the layered model of an ocean and employ the perturbation method to discuss the solution of the depth equation arising from these situations.