Stepwise inversion method using second-order derivatives of elastic impedance for fracture detection in orthorhombic medium

Reservoirs with a group of vertical fractures in a vertical transversely isotropic (VTI) background are considered as orthorhombic (ORT) medium. However, fracture detection in ORT medium using seismic inversion methods remains challenging, as it requires the estimation of more than eight parameters. Assuming the reservoir to be a weakly anisotropic ORT medium with small contrasts in the background elastic parameters, a new azimuthal elastic impedance equation was first derived using parameter combinations and mathematical approximations. This equation exhibited almost the same accuracy as the original equation and contained only six model parameters: the compression modulus, anisotropic shear modulus, anisotropic compression modulus, density, normal fracture weakness, and tangential fracture weakness. Subsequently, a stepwise inversion method using second-order derivatives of the elastic impedance was developed to estimate these parameters. Moreover, the Thomsen anisotropy parameter, epsilon, was estimated from the inversion results using the ratio of the anisotropic compression modulus to the compression modulus. Synthetic examples with moderate noise and field data examples confirm the feasibility and effectiveness of the inversion method. The proposed method exhibited accuracy similar to that of previous inversion strategies and could predict richer vertical fracture information. Ultimately, the method was applied to a three-dimensional work area, and the predictions were consistent with logging and geological a priori information, confirming the effectiveness of this method. Summarily, the proposed stepwise inversion method can alleviate the uncertainty of multi-parameter inversion in ORT medium, thereby improving the reliability of fracture detection.