Nonlinear estimation of Thomsen anisotropy parameters in TI media

Abstract

Transverse isotropy with the horizontal axis of symmetry (HTI) is the simplest anisotropic model to characterize a geological formation with vertical fractures. We formulate an azimuthally dependent parametric equation for P-wave traveltimes in a layered HTI medium. Also, assuming a known vertical velocity model, we estimate simultaneously the fracture orientation and Thomsen?s anisotropy parameters in a stack of horizontal layers using a modified preconditioning conjugate gradient algorithm. In a numerical example, we show that in the context of weak anisotropy, Thomsen?s anisotropy parameters (delta and epsilon) and fracture orientation can be efficiently estimated using the P-wave traveltimes without a prior information.