Borehole Wave Propagation In Isotropic And Anisotropic Media III: Anisotropic Formation

Abstract

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.