Amplitude variation with offset inversion for the effective stress parameter based on an exact Zoeppritz equation

Abstract Effective stress is a key indicator for guiding hydraulic fracturing, predicting pore pressure, and identifying reservoir fluids. Accurate prediction of effective stress holds substantial practical importance for reservoir characterization. Currently, two primary methods are employed for effective stress prediction: indirect calculation and inversion based on linear approximation equations. However, indirect calculation introduces cumulative errors and fails to fully use the information in seismic data, whereas inversion based on linear approximation equations suffers from low resolution and limited accuracy. To address these limitations and obtain high-quality reservoir characterization parameters, we propose a novel approach by integrating the rock physics model with the Zoeppritz equation under the assumption of isotropic media. This integration yields a new mathematical expression for effective stress prediction. An objective function is constructed based on Bayesian theory, incorporating the modified Cauchy constraint as a regularization term to enhance stability and accuracy. The Gauss–Newton method is then applied to optimize the objective function, yielding inversion results. Both synthetic and real data tests demonstrate that the proposed method significantly improves precision and resolution compared to traditional approaches while maintaining robust stability. This advancement provides more reliable and effective information for reservoir characterization, offering valuable insights for future exploration and development efforts.