Effect of static compression on tsunami waves: Two-dimensional solution

This study provides an analytical solution for the surface wave profile resulting from an arbitrary temporal ocean bottom disturbance in a compressible ocean. The solution also considers the impact of static compression of the ocean background. The problem is formulated in two dimensions and solved using the Fourier transformation and eigenfunction matching method, which requires a new inner product and determining a particular solution to account for the non-homogeneous boundary condition. To verify the solution's validity, it is compared with the corresponding Green's function formulation, which employs the movement of the ocean floor as a source. The Green's function technique can handle the ocean floor's arbitrary spatial movement, which is demonstrated through two specific profiles. Additionally, the shallow water limit is derived to provide further validation. A time-domain simulation of the surface profile is presented, comparing the case with and without static compression. The effect of static compression is found to be small but non-negligible for typical ocean depths.