  We study a linear model for the propagation of hydro-acoustic waves and
tsunami in a stratified free-surface ocean. A formulation was previously
obtained by linearizing the compressible Euler equations. The new formulation
is obtained by studying the functional spaces and operators associated to the
model. The mathematical study of this new formulation is easier and the
discretization is also more efficient than for the previous formulation. We
prove that both formulations are well posed and show that the solution to the
first formulation can be obtained from the solution to the second. Finally, the
formulations are discretized using a spectral element method, and we simulate
tsunamis generation from submarine earthquakes and landslides.
