Estimating A Shear Modulus Of A Transversely Isotropic Formation

Abstract

A method to estimate c[subscript 66], 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 c[subscript 66] 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 c[subscript 66] and the initial guess of its value, and penalty functions which constrain the estimate for c[subscript 66] to physically acceptable values. The inversion is applied to synthetic data for fast and slow formations, and the estimates for c[subscript 66] 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 c[subscript 66] are significantly higher than for c[subscript 44] , and the S-wave anisotropy generally ranges from 19 to 24%.