A 2.5-D velocity-stress finite-difference code is described that models acoustic propagation in a borehole penetrating a generally anisotropic formation. The excitation may be a dilatation (monopole), or a point force (dipole) in an arbitrary direction. The anisotropic formation is homogeneous along the axis of the borehole but may be inhomogeneous in the transverse plane. The borehole cross section and location of the source in the borehole are arbitrary. Synthetic time-domain waveforms are displayed for arrays of monopole and dipole receivers deployed along the borehole axis in both fast and slow anisotropic formations. The specific anisotropy model employed for the numerical results is a transversely isotropic (TI) formation with its axis of symmetry inclined with respect to the borehole axis by an arbitrary angle. Flexural/shear and Stoneley wave slowness and attenuation estimates are extracted from the synthetic waveforms using a variant of Prony’s method for a range of borehole inclinations relative to the formation axis of symmetry. In a fast formation, with borehole and formation symmetry axes perpendicular, flexural mode dispersion curves for quasi-SV and SH polarizations separate only at low frequency where moderate attenuation is also observed. In a slow formation, distinct dispersion curves are obtained for quasi-SV and SH polarizations over the entire frequency range. Moderate attenuation is again observed at low frequency. Scaled laboratory experiments confirm the numerical procedure. Experimental and numerical waveforms for monopole and several polarizations of dipole excitation in a transversely isotropic model formation overlay with excellent agreement.
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Leslie et al. (1992) studied this question.