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

Abstract

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.