In this paper we present a finite difference scheme for seismic wave propagation ina fluid-filled borehole in a transversely isotropic formation. The first-order hyperbolicdifferential equations are approximated explicitly on a staggered grid using an algorithmthat is fourth-order accurate in space and second-order accurate in time. The griddispersion and grid anisotropy are analyzed. Grid dispersion and anisotropy are wellsuppressed by a grid size of 10 points per wavelength. The stability condition is alsoobtained from the dispersion analysis. This finite difference scheme is implementedon the nCUBE2 parallel computer with a grid decomposition algorithm. The finitedifference synthetic waveforms are compared with those generated using the discretewavenumber method. They are in good agreement. The damping layers effectivelyabsorbed the boundary reflections. Four vertically heterogeneous borehole models: ahorizontal layered formation, a borehole with a radius change, a semi-infinite borehole,and a semi-infinite borehole with a layer, are studied using the finite difference method. Snapshots from the finite difference results provide pictures of the radiating wavefields.
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