We present a novel numerical approach for the comprehensive, flexible,
and accurate simulation of poro-elastic wave propagation in 2D polar
coordinates. An important application of this method and its extensions
will be the modeling of complex seismic wave phenomena in fluid-filled
boreholes, which represents a major, and as of yet largely unresolved,
computational problem in exploration geophysics. In view of this,
we consider a numerical mesh, which can be arbitrarily heterogeneous,
consisting of two or more concentric rings representing the fluid
in the center and the surrounding porous medium. The spatial discretization
is based on a Chebyshev expansion in the radial direction and a Fourier
expansion in the azimuthal direction and a Runge-Kutta integration
scheme for the time evolution. A domain decomposition method is used
to match the fluid-solid boundary conditions based on the method
of characteristics. This multi-domain approach allows for significant
reductions of the number of grid points in the azimuthal direction
for the inner grid domain and thus for corresponding increases of
the time step and enhancements of computational efficiency. The viability
and accuracy of the proposed method has been rigorously tested and
verified through comparisons with analytical solutions as well as
with the results obtained with a corresponding, previously published,
and independently bench-marked solution for 2D Cartesian coordinates.
Finally, the proposed numerical solution also satisfies the reciprocity
theorem, which indicates that the inherent singularity associated
with the origin of the polar coordinate system is adequately handled.