Estimating a Shear Modulus of a Transversely Isotropic Formation

A method to estimate C66, which is a shear modulus of a transversely isotropic formation (with its symmetry axis parallel to the borehole), is developed and tested. The inversion for C66 is based upon a cost function which has three terms: a measure of the misfit between the observed and predicted wavenumbers, a measure of the misfit between the current estimate for CBB and the initial guess of its value, and penalty functions which constrain the estimate for C66 to physically acceptable values. The inversion is applied to synthetic data for fast and slow formations, and the estimates for CBB are within 5% of their correct values and are well resolved. The inversion is applied to field data from a formation which consists mostly of siltstone. All estimates for C66 are significantly higher than for C44, and the S-wave anisotropy generally ranges from 19 to 24%.