Global Optimizing Prestack Seismic Inversion Approach Using an Accurate Hessian Matrix Based on Exact Zoeppritz Equations

To increase the accuracy and vertical resolution of seismic inversion for exploratory purposes, a new method was developed for P-wave velocity, S-wave velocity, and density inversion using prestack seismic data based on the mayfly optimization algorithm (MA), exact Zoeppritz equations, and Bayesian framework. A new form of an accurate Hessian matrix was successfully derived. We innovatively used the MA nonlinear amplitude variation with angle (AVA) inversion based on the accurate Hessian matrix (MANAI-Hessian) method for prestack seismic inversion and highlighted two main challenges for the first time. The popular and recent whale optimization algorithm (WOA) and a conventional Levenberg–Marquardt (LM) method were introduced to demonstrate the existence of these two challenges. Comprehensive partial derivative tests were well designed to verify the existence of the second-order partial derivatives of the P-wave reflection coefficients. A 3-D special wedge model was introduced to test the accuracy and vertical resolution of the new method. Next, we applied the proposed method to the field data of deep carbonate rock from a study area in China. Compared with the conventional LM method and the accurate Jacobian matrix-based nonlinear AVA inversion method, which provides foundational approaches to address the two main challenges, the proposed approach shows superior performance in terms of accuracy and vertical resolution.