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

Abstract

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