Estimation of transversely isotropic formation parameters using flexural and quadrupole dispersion data in the fast formation

Abstract

Borehole acoustic logging plays an important role in inverting the five Thomsen parameters of many formations characterized as a transversely isotropic medium with a vertical axis of symmetry (VTI). In general, these parameters are obtained under certain assumptions, and the formation type defined by the relation of Thomsen parameters is not taken into consideration. We have developed a method to determine the Thomsen parameters of all kinds of fast VTI formations from the first-order flexural and first-order quadrupole dispersion data by dividing the Thomsen parameters inversion process into two parts: low-frequency asymptotic slowness inversion of the flexural or quadrupole dispersion and Thomsen anisotropy parameter inversion by a constrained evolutionary optimization algorithm. Compared with traditional approaches, the new method is not only independent of any assumed correlation among the Thomsen anisotropy parameters but it also provides a more accurate result than the inversion of either of them alone for both kinds of fast VTI formations. The inversion results obtained from either the flexural or quadrupole dispersion data alone are incorrect if the formation type is incorrectly identified, such as misidentifying an isotropic formation as a special VTI formation. The new method can not only identify the type of fast VTI formation, but it also obtains the shear slowness in a special VTI formation, which cannot be obtained by existing methods. Accordingly, the application to synthetic examples validates the significance and necessity of the proposed joint method in inversion of the Thomsen parameters.