Prestack Seismic Inversion via Global Optimization With an Accurate Hessian Matrix and the Three-Variable Cauchy Distribution for Exact Zoeppritz Equations

Prestack inversion is typically based on the Zoeppritz equation combined with gradient-based optimization of objective functions. To address the limitations of traditional gradient-based algorithms that heavily rely on initial models, researchers have introduced intelligent optimization algorithms, such as particle swarm optimization (PSO), into prestack inversion to improve inversion accuracy. However, these global optimization algorithms often exhibit low computational efficiency due to insufficient consideration of gradients and the Hessian matrix. In this study, we introduce the exact Zoeppritz gradient-based global optimization (EZGBO) method, which integrates an accurate gradient and the Hessian matrix under a Bayesian framework with a three-variable Cauchy prior into the gradient-based global optimizer (GBO) to enhance inversion accuracy and efficiency. The proposed method combines the advantages of traditional Newton-like algorithms and global intelligent optimization algorithms by incorporating the accurate gradient and the Hessian matrix of the objective function into the global optimization process. This approach achieves better inversion results with fewer particles and iterations, thus enhancing computational efficiency. To ensure the stability of the stochastic global inversion, we employ adaptive edge-preserving smoothing (Ad-EPS) to facilitate optimal positioning of the population particles. Finally, we validate the proposed method using both synthetic and field data. Specifically, we compared the proposed method with quantum PSO (Q) and traditional approaches. The results show that our method excels in accuracy, stability, efficiency, and resolution, offering a novel solution to global optimization in prestack inversion.