Estimating the Elastic Moduli of Transversely Isotropic Formations

Using acoustic logging data, we develop a method of estimating the horizontal shear modulus C66) of a transversely isotropic formation with its axis of symmetry parallel to that of the borehole. The data for the inversion are the wavenumbers, at every frequency, of the guided waves. The inversion minimizes the difference between these observed wavenumbers and those calculated by a forward model. The final estimates of the elastic moduli are constrained by the a priori estimates of their values and by the requirement to keep the stiffness tensor positive definite. The inversion produced similar results when it was applied to synthetic data from hard and soft formations. The estimate for the shear modulus, C66, was fairly accurate because this parameter is moderately well resolved. The estimates for Cll and C13 are inaccurate because they are poorly resolved by the data. Tight constraints on the fluid modulus prevent this parameter from changing. much. The inversion did not attempt to estimate either C33 or C44 because they can be determined from the refracted P and S-waves or the flexural wave.