Nonlinear amplitude variation with offset and azimuthal inversion for HTI media based on the elastic stiffness matrix

Abstract

Transverse isotropy with a horizontal axis of symmetry (HTI) is generally considered as parallel vertical cracks embedded in an isotropic matrix or vertically dipping shale sequences and is widely used in unconventional hydrocarbon exploration. Inversion of anisotropy parameters for HTI media is important for characterizing fractures and filled fluids. However, owing to the added azimuthal dimension and small contribution of anisotropic parameters, achieving stable inversion of anisotropy parameters from azimuthal seismic data is challenging. A nonlinear amplitude variation with offset and azimuthal inversion is proposed to address this issue, indirectly predicting the anisotropy using the stiffness matrix. First, P-, SV- and SH-exact elastic impedance matrices for HTI media characterized by the stiffness matrix are derived from Hooke’s law and used to construct a new exact reflection coefficient. Subsequently, a PP reflectivity approximation is obtained in the weak-contrast half-space of the stiffness matrix. Numerical experiments with the symmetry-axis perpendicular to the crack plane show that the PP reflectivity with an azimuth of 90° is only related to C33, C44, and density, whereas C11, C13, and C55 contribute the most to the PP reflectivity with an azimuth of 0°. Therefore, the six-parameter simultaneous inversion can be decomposed into a three-parameter inversion within two azimuths to ensure the accuracy of the stiffness matrix inversion. Finally, to overcome the ill-posedness of the indirect calculation of the anisotropy parameters, a nonlinear inversion algorithm constrained by the relationship between the stiffness matrix and anisotropy parameters is developed. Applications of the model and field seismic data prove that the proposed method performs better in terms of stability and accuracy than conventional azimuthal amplitude difference methods.