Borehole seismic experiments are very sensitive to the source and
receiver geometry, the presence or absence of a casing, and to heterogeneities
in the formation surrounding the borehole. For applications that
go beyond the use of first-arrival times, analytical solutions are
generally not sufficient and numerical methods are needed. Here,
we present a novel numerical approach for the comprehensive, flexible,
and accurate simulation of poro-elastic wave propagation in cylindrical
coordinates. An important application of this method is 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. We consider a numerical mesh consisting
of three concentric domains representing the borehole fluid in the
center followed by the casing and the surrounding porous formation.
The spatial discretization is based on a Chebyshev expansion in the
radial direction and Fourier expansions in the other directions.
Time stepping is performed through a Runge-Kutta integration scheme.
A domain decomposition method based on the method of characteristics
is used to match the boundary conditions at fluid/porous-solid and
porous-solid/porous-solid interfaces. The viability and accuracy
of the proposed method has been tested and verified in polar coordinates
through comparisons with analytical solutions as well as with the
results obtained with a corresponding, previously published, and
independently benchmarked solution for 2D Cartesian coordinates.
For the cylindrical case, the equations of motion can be solved by
using spectral operators in all dimensions, thus allowing for 3D
heterogeneity and arbitrary receiver and source geometries, or by
applying a Fourier decomposition in the azimuthal direction assuming
rotational symmetry of the model.