Joint AVO Inversion Based on Adjoint-State Method and Multi-Scale Inversion Strategy

Amplitude variation with offset (AVO) inversion, capable of deriving information on subsurface elastic parameters and fluid properties, represents a pivotal technique in reservoir prediction. Compared to PP-wave AVO inversion, the joint inversion incorporates PS-wave seismic data, enhancing the accuracy and reliability of inversion results, thus providing a more comprehensive portrayal of subsurface geological formations. Both PP-wave and joint inversions can be framed as least-squares optimization problems, with the adjoint-state method serving as an effective tool for computing gradients in optimization problems. We propose a joint inversion method based on the adjoint-state method and a multi-scale inversion strategy for the inversion of three key parameters: fluid factor, shear modulus, and density. Initially, the objective function for joint inversion is constructed based on the Russell approximation, and the adjoint-state equation is derived using the Lagrangian function to compute the gradient of the objective function. Combined with the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, efficient unconstrained optimization is achieved. To further enhance inversion accuracy, a multi-scale inversion strategy is introduced, which progressively optimizes model parameters from coarse to fine scales by utilizing data at different frequencies in stages, thereby improving the accuracy and lateral continuity of the inversion results. Synthetic data tests demonstrate that while the PP-wave inversion based on the adjoint-state method can invert elastic parameters, the joint inversion results are more accurate. The incorporation of the multi-scale inversion strategy further enhances the stability and accuracy of the inversion results, particularly demonstrating strong adaptability in complex geological conditions. Finally, the proposed method is applied to field seismic data, with the inversion results accurately characterizing subsurface media, thereby validating the effectiveness and practicality of the method.