Sequential Bayesian seismic inversion for fracture parameters and fluid indicator in tilted transversely isotropic media

Abstract

A rock permeated by tilted aligned fractures, which is common in the earth, can be considered as a tilted transversely isotropic (TTI) medium under the assumption of the long wavelength. We develop a feasible method to predict fracture parameters (namely weakness parameters and dip angle) and fluid type in TTI rock using azimuthal seismic data. Based on an approximate stiffness matrix, we first deduce a linear reflection coefficient of the gas-bearing TTI medium in terms of the new fluid indicator and fracture parameters. The reflection coefficient is then rewritten in the form of the Fourier series to decouple the fracture and skeleton-fluid information. Next, the sequential Bayesian inversion method is proposed, which consists of three steps. The first two steps conquer inversion instability owing to coupling of the fracture parameters by constructing a linear relationship between the second- and fourth-order Fourier coefficients. The last step aims at estimating the skeleton-fluid parameters. The sequential Bayesian inversion method alleviates the inversion ill-posedness that is caused by large differences in contributions of the fracture and skeleton-fluid parameters to the reflection coefficient. Synthetic and field cases prove our method is stable and rational in fracture and fluid detections. Finally, we draw the following conclusions from numerical experiments. The approximate stiffness coefficients and derived reflection coefficient are of satisfactory accuracy for the gas-bearing reservoir with low fracture density. The new fluid indicator is sensitive to fluid type but very weakly dependent on mineral composition and porosity. Deconvolution processing can improve the accuracies of different seismic components calculated using the discrete Fourier transformation.