Integrating ensemble learning with empirical rock-physics equations for sonic-log reconstruction and geomechanical property estimation: a case study from the Williston basin

Abstract Accurate prediction of geomechanical properties is important for reliable hydrocarbon reservoir exploration and development, but conventional well logging and core analysis can be costly, time-consuming, and limited by incomplete sonic-log coverage. This study develops a two-stage hybrid framework that integrates ensemble machine learning with empirical rock-physics relationships to predict geomechanical properties from readily available conventional well logs. Deep resistivity (AT90), gamma ray (GR), caliper (HCAL), neutron porosity (NPHI), and bulk density (RHOZ) logs were used as input features for model training and prediction of compressional-wave transit time (DTCO) and shear-wave transit time (DTSM). Four ensemble learning algorithms—Random Forest, Light Gradient Boosting Machine, Extra Trees, and Extreme Gradient Boosting—were evaluated, and the predicted sonic responses were subsequently incorporated into established rock-physics equations to estimate Poisson’s ratio, Young’s modulus, and shear modulus. SHapley Additive exPlanations (SHAP) were further employed to quantify feature contributions and interpret the relationship between model predictions and petrophysical controls. Extra Trees produced the best predictions, with coefficients of determination (R-squared) of 0.97 for both targets; root mean squared error and mean absolute error were 10 and 6.1 for DTSM and 3.7 and 2.1 for DTCO, respectively. Measured DTSM showed poor agreement with the Castagna correlation, whereas elastic properties calculated from machine-learning predictions agreed well with those derived from measured logs. The scientific contribution is an interpretable, formation-specific framework that connects conventional-log prediction of missing sonic curves to physics-based estimation of multiple elastic properties, providing a practical basis for reservoir characterization where complete sonic coverage is unavailable.