Nonlinear Inversion Method of Russell’s Fluid Factor Based on Exact-Zoeppritz Equation

Russell’s fluid factor plays a crucial role in predicting hydrocarbon reservoirs. Numerous studies have been conducted on the inversion of Russell’s fluid factor. However, most of these studies exploit the approximate formulas of Zoeppritz as the forward equation. The approximate formulas affect the accuracy of the estimated Russell’s fluid factor, particularly in the moderate to large incidence angle range. To address this issue, we propose a nonlinear inversion scheme for Russell’s fluid factor based on the exact-Zoeppritz equation. Initially, we derive a new form of the Zoeppritz equation that incorporates Russell’s fluid factor and Poisson’s ratio. Then, in the Bayesian framework, we establish a joint P-wave and S-wave (PP–PS) objective function that represents by Russell’s fluid factor. To solve the nonlinear objective function, we enhance the traditional whale optimization algorithm (WOA) by incorporating the Lévy flight strategy and stochastic learning theory, resulting in an optimized version named Lévy flight and stochastic learning whale optimization algorithm (LSWOA). Russell’s fluid factor estimated by the new inversion method could provide a theoretical basis for the identification of oil and gas reservoirs, and also provide a new way for unconventional reservoir prediction and sweet spot identification. To validate the accuracy of our method, we test it using both synthetic and actual field seismic data. Our test results demonstrate that the PP–PS wave joint inversion method of Russell’s fluid factor based on the LSWOA algorithm exhibits high inversion accuracy and can be effectively applied in production.