Estimating a shear modulus of a transversely isotropic rock

Abstract

We have developed a method of estimating c66, one of the shear moduli of a transversely isotropic rock, using a guided wave generated during acoustic logging. (The symmetry axis of the anisotropy is assumed to parallel to the borehole.) The inversion for c66 is based on a cost function which has three terms: a measure of the misfit between the observed and predicted wavenumbers of the guided wave (tube wave), a measure of the misfit between the current estimate for and its most-likely value, and penalty functions which constrain the estimate for c66 to physically acceptable values. Estimates for c6e from synthetic data are almost always within 1% of their correct value. Estimates for '266 from field data that was collected in a formation with a high clay content are typical of transversely isotropic rocks.