Inversion technique for recovering the elastic constants of transversely isotropic materials

Abstract

A least‐squares iterative inversion technique has been developed for the determination of the elastic parameter δ* of any transversely isotropic modeling material in the laboratory. For most applications in petroleum geophysics, the elastic parameter δ* is very important and is the crucial anisotropic parameter for near‐vertical P‐wave propagation. Despite the potential importance of δ* in seismic exploration and for resolution in an anisotropic medium, the conventional procedures adopted in estimating its value unfortunately are faced with many ambiguities and the reliability of its measurement is doubtful prior to the development of this technique. The anisotropic inverse modeling technique finds the best fitting solution. To optimize the accuracy of the results presented in this paper, analytical rather than numerical differentiations were implemented and the modeling procedures allow for controlled iterative adjustments in resolving the parameter δ*. Inversion of the first‐arrival traveltimes obtained for vertical P‐waves through an anisotropic material known as phenolite yield estimates of the elastic parameter δ* as well as the vertical P‐wave velocity [Formula: see text] of the material. Accurate picking of the first‐arrival traveltimes is essential since δ* is found to be very sensitive to small differences between vertical and oblique traveltime picks. The inversion results have been found to be stable and convergent, and they also highlight the need for good angular coverage to determine the anisotropy parameters in materials suspected of being anisotropic.