A generalised inner product-based wave scattering from an underwater source in a compressible ocean

Motivated by applications to underwater explosions and volcanic eruptions, this paper considers the evolution of an initial pressure disturbance in the ocean, including effects due to the dynamic and static compression of water and the free surface. In order to solve the equations of motion of a linear compressible ocean, a special inner product is introduced, which allows us to apply self-adjoint operator theory. What results is a Hilbert space in which the acoustic–gravity modes are orthogonal