Adaptive, Distribution-Free Uncertainty Quantification for Shear and Stoneley Wave Prediction Using Conformalized Ensemble Learning

The acquisition of shear (DTS) and Stoneley (DTST) wave transit times is indispensable for comprehensive reservoir characterization, yet it is often constrained by significant economic and operational limitations. This data gap has spurred the development of data-driven prediction models; however, a critical "credibility gap" persists. While modern machine learning (ML) models routinely achieve high point-accuracy metrics such as the coefficient of determination (R2), these metrics alone do not guarantee geologically plausible or reliable predictions for high-stakes engineering decisions, including wellbore stability analysis and hydraulic fracture design. This paper directly addresses this credibility gap by introducing and validating a robust and reliable workflow that moves beyond deterministic point estimates to provide rigorous, probabilistic forecasts. The proposed methodology couples high-performance, tree-based ensemble regressors with Conformalized Quantile Regression (CQR), a framework that generates statistically valid, sample-specific prediction intervals without making restrictive distributional assumptions about the data or model errors. Validated using a comprehensive dataset from the geologically complex, heterogeneous carbonate reservoirs of the South Pars gas field, the study reveals nuanced model performance: Random Forest proves optimal for single-well prediction (R2 >0.94), whereas a Stacked Ensemble demonstrates superior robustness for inter-well generalization (R2 >0.92). Crucially, the CQR framework successfully generated adaptive 90% prediction intervals that achieved the target empirical coverage, confirming the method's validity. This work provides a practical, validated methodology to generate trustworthy, probabilistic forecasts of acoustic logs, enabling quantitative risk assessment and bridging the divide between high-accuracy ML and the reliability demands of modern geomechanical, petrophysical, and geophysical analysis and reservoir and drilling engineering.