Waves at fluid–solid interfaces: explicit versus implicit formulation of the boundary condition

The correct simulation of wave propagation with direct grid methods at fluid–solid interfaces requires a proper implementation of the boundary condition, which involves continuity of the normal component of the particle velocity and traction. The horizontal component of the particle velocities can differ (slip) and the tangential traction vanishes. The challenge is to model the interface waves, which are relevant when the source and receiver are located close to the interface, in particular the Scholte and leaky (or pseudo, or generalized) Rayleigh waves. The explicit modelling is based on a domain-decomposition technique (one mesh for the fluid and another mesh for the solid) and the Fourier and Chebyshev differential operators along the horizontal and vertical directions, respectively. On the other hand, two implicit modelling algorithms are based on a single mesh and the fluid is described by setting to zero the shear wave velocity above the interface. The modelling is verified by comparisons with the analytical solution for a fluid–solid interface in lossless media, with source and receiver away from and at the interface. To our knowledge, the latter comparison, mainly involving the interface waves (Scholte and leaky-Rayleigh), has not been performed with other grid methods so far. It is shown that the implicit simulation yields erroneous results.