Anisotropy‐induced coupling in borehole acoustic modes

Abstract

The guided wave modes of a circular borehole in a weakly anisotropic formation are composed of linear superpositions of the associated modes for an isotropic formation. At moderate frequencies the major modes of concern are the quasi‐Stoneley and quasi‐flexural modes. These guided modes in anisotropic formations can be estimated from a perturbation analysis in terms of the unperturbed solutions for an isotropic formation. When the formation anisotropy is of monoclinic or lower symmetry, the normal and shear stresses become functions of both normal and shear strains through some additional anisotropic constants that are not present in materials with orthorhombic or higher symmetry. These additional elastic constants cause a coupling between the Stoneley and flexural modes. Under these circumstances, an on‐axis monopole or dipole source excites both modes. Coupling coefficients account for the excitation of quasi‐flexural motion by a monopole source, and of the quasi‐Stoneley mode by a dipole. A transversely isotropic (TI) formation with its symmetry axis obliquely inclined with the borehole exhibits monoclinic symmetry in its rotated constants referred to the borehole axis. The monoclinic symmetry of the surrounding formation in such cases causes a coupling between the Stoneley and flexural modes. Computational results show that a borehole inclined at an angle of 60° from the symmetry axis of Austin chalk, a slow TI medium, exhibits coupling between the Stoneley and qSV‐polarized flexural mode acceleration amplitudes of the order of 20 dB or less in the frequency range of interest. A similar obliquely inclined borehole in Bakken shale, a fast TI formation, exhibits a far weaker coupling between the Stoneley and qSV‐polarized flexural modes. The stronger coupling in the case of Austin chalk is a result of relatively large anisotropic constants together with close proximity of the Stoneley and qSV‐polarized flexural dispersions. On the other hand, weaker coupling in Bakken shale is caused by relatively small anisotropic constants and a large separation between the Stoneley and qSV‐polarized flexural dispersions in the moderate frequency range of interest.