A nonlinear inversion method for Young’s modulus and shear modulus based on the exact Zoeppritz equations

Introduction Young’s modulus and shear modulus are essential mechanical parameters for evaluating subsurface rocks, playing a pivotal role in the exploration and development of unconventional resources. Young’s modulus indicates the brittleness of the reservoir, while shear modulus determines the ease of fracturing rock layers. Methods Traditional methods estimate these moduli through indirect calculations and approximate expressions, which are prone to cumulative errors and rely on multiple assumptions, reducing inversion accuracy. This paper presents a direct inversion method for acquiring of Young’s modulus and shear modulus using the exact Zoeppritz equations, integrated within a Bayesian framework for pre-stack inversion. The quantum particle swarm optimization (QPSO) algorithm is introduced to achieve a nonlinear solution to the objective function. Results Tests on synthetic and actual field data demonstrate the feasibility and effectiveness of the proposed method, yielding more accurate inversion results compared to traditional methods. Discussion These findings provide valuable insights for predicting reservoir brittleness and characterizing reservoirs in unconventional shale gas exploration and development.