| Summary: | In this paper we extend the 3-D finite difference method to simulate wave propagations in
an anisotropic medium. The scheme is tested in the homogeneous medium. The finite
difference results agree excellently with the analytic solutions of a point force source
in the transversely isotropic medium. The finite difference synthetics are compared
with ultrasonic lab measurements in a scaled borehole drilled along the X axis in an
orthorhombic phenolite solid. Both monopole and dipole logs agree well.
The 3-D time domain finite difference method is applied to the fluid-filled borehole
wave propagation problems in the anisotropic formation. The following results are
obtained:
1. In a borehole drilled along the Z axis in a phenolite formation, the monopole log
shows the P wave travelling with velocity v[subscript zz]. There are no shear-pseudo-Rayleigh wave arrivals. The dipole log is dominated by the single slow flexural mode.
2. In a borehole drilled along the Y axis in a phenolite formation, the monopole log
shows the P wave travelling with velocity v[subscript yy]. There are shear-pseudo-Rayleigh wave arrivals shown on the monopole seismograms between the P and Stoneley
waves due to the shear wave anisotropy. The anisotropy also causes the shear
wave splitting in the dipole log. The two shear wave arrivals correspond to the
fast and the slow flexural modes.
3. The disagreement between the shear wave velocity from the Stoneley wave inversion
and the direct shear wave log velocity from field data is beyond the errors in
the measurements. It is shown that the formation permeability is not the cause
of the discrepancy. From the estimated "shear/pseudo-Rayleigh" phase velocities
in the array full waveform log and the 3-D finite difference synthetics in the
anisotropic formation, the discrepancy can be explained as shear wave anisotropy.
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