Full-waveform inversion of pure quasi-P waves in titled transversely isotropic media based on different parameterization

Abstract

Full-waveform inversion (FWI) builds subsurface parameter models by minimizing the residuals between the modeled and observed data. Accounting for the effects of anisotropy is critical for high-resolution imaging of complex structures. We develop an acoustic anisotropic FWI method based on a pure quasi P-wave (qP-wave) equation. The equation coefficients and their derivatives with respect to the Thomsen’s anisotropy parameters ([Formula: see text] and [Formula: see text]) are estimated by least-squares (LS) optimization. We derive the functional gradients and analyze the radiation patterns for six parameter classes: the velocity along the symmetry axis [Formula: see text], [Formula: see text] and [Formula: see text], the normal moveout velocity [Formula: see text], anisotropy parameters [Formula: see text] and [Formula: see text], the horizontal velocity [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], and [Formula: see text], [Formula: see text] and [Formula: see text]. The parameterization [Formula: see text] has significant tradeoff between [Formula: see text] and [Formula: see text] at the intermediate and wide scattering angles. The anisotropy parameters [Formula: see text] and [Formula: see text] are resolvable at the short scattering angles for the parameterizations [Formula: see text] and [Formula: see text], respectively. The parameter crosstalk for the parameterizations [Formula: see text] and [Formula: see text] is more serious than that for other types of parameterizations. We perform FWI of pure qP-waves in vertical and titled transversely isotropic (VTI and TTI) media. Inversion results on the Overthrust VTI model and the modified BP TTI model show that the velocity, anisotropy parameters and tilt angle can be individually reconstructed when other parameters are sufficiently accurate. The multi-parameter FWI cannot obtain reliable tilt angles for each type of parameterization. The inversion with the parameterization [Formula: see text] produces [Formula: see text], [Formula: see text] and [Formula: see text] models with modest accuracy, whereas the parameterization [Formula: see text] helps to improve the accuracy of [Formula: see text] and [Formula: see text] models.