Fracture parameters estimation from azimuthal seismic data in orthorhombic medium

At present, approaches based on the AVAaz (P-wave amplitude versus the incident angle and azimuth) inversion are highly pivotal for estimating fracture parameters (namely fracture density and orientation) in vertically transverse isotropic background with parallel vertical fractures (namely VFTI medium, which is a common kind of orthorhombic rock). Nevertheless, these approaches involve solving a multi-parameter nonlinear inverse problem and the azimuthal variation of P-wave amplitude induced by fractures is easily concealed by noise and strong background information. Besides, unknown relationships of the fracture density with weakness parameters in the general VFTI medium will produce the uncertainty of predicting the fracture density by the weakness parameters or their related combinations. To solve these problems, we demonstrate the relationships of the weakness parameters of the VFTI medium with the fracture density and infill by a numerical experiment and conclude the tangential weakness parameters and their related combinations are preferable fracture density indicators. On this basis, we present a method integrating an azimuthally anisotropic elastic impedance (azimuthal AEI) equation and K-L (Karhunen-Loeve) transform to robustly and reasonably estimate fracture density and orientation. The azimuthal AEI equation incorporating the prior fracture orientation and Fourier series weakens the 90 degrees ambiguity of fracture orientation estimation and decouples weak fracture information from strong background information to enhance prediction stability. And the K-L transform improves the azimuthal variation of the P-wave amplitude induced by the fractures. Moreover, another simpler indicator of the fracture density, the standard deviation of the natural logarithm of the azimuthal AEI, is given to simplify the estimation process. The synthetic model and field data confirm the feasibility and stability of these proposed mechanisms and techniques.