We implemented Biot-type porous wave equations in a pseudo-spectral
numerical modeling algorithm for the simulation of Stoneley waves
in porous media. Fourier and Chebyshev methods are used to compute
the spatial derivatives along the horizontal and vertical directions,
respectively. To prevent from overly short time steps due to the
small grid spacing at the top and bottom of the model as a consequence
of the Chebyshev operator, the mesh is stretched in the vertical
direction. As a large benefit, the Chebyshev operator allows for
an explicit treatment of interfaces. Boundary conditions can be implemented
with a characteristics approach. The characteristic variables are
evaluated at zero viscosity. We use this approach to model seismic
wave propagation at the interface between a fluid and a porous medium.
Each medium is represented by a different mesh and the two meshes
are connected through the above described characteristics domain-decomposition
method. We show an experiment for sealed pore boundary conditions,
where we first compare the numerical solution to an analytical solution.
We then show the influence of heterogeneity and viscosity of the
pore fluid on the propagation of the Stoneley wave and surface waves
in general.