SIMULATION OF ACOUSTICAL AND ELASTIC-WAVES AND THEIR INTERACTION

A method for numerical simulation of wave propagation through an interface separating two media, e.g., water and ocean bottom, is derived using Chebyshev spectral collocation. The propagation of acoustical waves in water is modeled by the Euler equations applied to a stratified fluid, while the elastic waves are modeled by the equations of linear elasticity. The transmission of the waves through the interface is based on the physical boundary conditions, continuous normal velocity component and normal stress, and implemented via characteristic boundary conditions. Domain decomposition procedures are used to solve the equations in each of the two physically different domains and to match the solutions at the boundary. At the interface modeling the ocean surface, free boundary conditions are used. The conditions at the lower and vertical boundaries are constructed to give free transmission of the wave modes, making no influence on the wave propagation. Some test cases are discussed, the simplest based upon a plane interface, the second with a piecewise linear interface made up of a horizontal and an inclined part.