A hybrid grid method in an auxiliary coordinate system for irregular fluid-solid interface modelling

Seismic wave propagation in a fluid-solid environment cannot be simulated with a single wave equation, but can be described by use of the acoustic and viscoelastic wave equations for their respective fluid and solid parts. Proper boundary conditions at the fluid-solid interface based on the relationship between pressure and stress are crucial when combining the two different wave equations. Traditional finite difference methods have had difficulties in dealing with the irregular fluid-solid interface topography. The Cartesian grids discretization leads to artificial reflections and diffractions during the conversion between acoustic wave and elastic waves. We propose a variable coordinate transformation methodology to simulate seismic waves in a fluid-solid environment. An irregular fluid-solid interface can be transformed into a horizontal interface, so that pressure and stress can be well converted. We also introduce a multiblock coordinate transformation (MCT) method which meshes each layer with curvilinear grids to transform the interface topography into a horizontal one, thereby allocating vertical sampling points adaptively. The grid size is determined adaptively based on the shape and the parameters of the target area, which reduces in size in when the layers are thin or exhibit low velocities. A Lebedev-standard staggered grid scheme is applied to the MCT method to reduce both the computational cost associated with the Lebedev grid scheme and the instability in the auxiliary coordinate system when using a standard staggered grid scheme.