Progressive waves in a compressible-ocean with an elastic bottom

The mathematical solution for the two-dimensional linear problem of acoustic-gravity waves in a compressible ocean with an elastic bottom is presented. The physical properties of these waves are studied, and compared with those for waves over rigid ground. The solutions for constant water depth, together with the assumption of constant energy flux, are used to study the shoaling of acoustic-gravity waves over a slowly-varying bathymetry. The present work enriches our knowledge about acoustic-gravity waves in a way that could assist, among others, in the early detection of tsunami. •The leading acoustic-gravity mode dominates the solution.•At large enough depths, the solution for the leading mode is only slightly affected by the elasticity of the ground.•At relatively small water depths only the Scholte wave outlasts.•Light is shed on mechanisms involved in transforming energy from the ocean to the crust as part of the microseisms phenomenon.•The depth at which an acoustic-gravity wave attains its maximum intensity can be estimated.•Knowledge of the behavior of acoustic-gravity waves with depth can be applied for the early detection of tsunami.