Enhanced prediction of reservoir porosity and permeability via a Second Spectrum-inspired hybrid framework integrating LSTM, Random Forest, and SHAP

Accurate prediction of reservoir porosity and permeability from wireline well logs remain a central challenge in subsurface characterization, owing to the nonlinear, non-stationary, and spatially autocorrelated nature of petrophysical data. This study presents the Second Spectrum Dual-Pathway Framework, a novel hybrid machine learning architecture conceptually adapted from the NBA Second Spectrum spatiotemporal player-tracking system, which separates macro-level spatial patterns from micro-level sequential dynamics. Applied to 12,101 well-log samples from the Southeastern Sichuan Basin (8 input features: GR, AC, CAL, CNL, DEN, SP, RXO, PE), the framework integrates two complementary learning pathways: Pathway 1 deploys a Random Forest (RF) regressor (n = 200 trees, max_features = √p, min_samples_leaf = 4) as a macro-level, point-wise nonlinear mapper, achieving R 2 = 0.8619, MAE = 0.1772, and RMSE = 0.3003 for porosity, and R 2 = 0.8357, MAE = 0.0728 (log 10 scale) for permeability. Pathway 2 employs a two-layer Bidirectional LSTM (BiLSTM; 64 and 32 units, dropout = 0.25, L2 = 10 -4 , Layer Normalization) trained on RF residuals to model depth-axis sequential autocorrelation — a mechanism physically justified by Durbin–Watson statistics < 1.5 across all logs, confirming strong positive stratigraphic continuity. The hybrid combination (ŷ_hybrid = ŷ_RF + ε_BiLSTM) yields R 2 = 0.8620, MAE = 0.1773, and RMSE = 0.3002 for porosity, demonstrating that the BiLSTM residual pathway captures depth-trending prediction errors unresolved by the spatial model alone. Five-fold cross-validation confirms stable generalization across geological intervals (porosity: mean R 2 = 0.8696 ± 0.0116; permeability: mean R 2 = 0.8440 ± 0.0246). Ensemble-based prediction intervals (RF tree variance) achieve a 90% PI empirical coverage of 98.97%, with higher predictive uncertainty localized in high-permeability zones (mean σ = 0.1103 log 10 mD) relative to tight matrix intervals (mean σ = 0.1857 log 10 mD), consistent with heterogeneous pore network structures beyond wireline log resolution. Explainability is provided via Tree SHAP (RF) and GradientSHAP (BiLSTM): for porosity, the acoustic log (AC; mean |SHAP| = 0.1979) ranks first, followed by GR (0.0985), SP (0.0919), and DEN (0.0909), consistent with established density-porosity and sonic transit time transforms. For permeability, DEN and CNL retain dominance while RXO gains relative importance, reflecting pore connectivity encoded in flushed-zone invasion. Critically, the BiLSTM SHAP profile diverges from the RF profile depth-sensitive logs gain relative attribution in the sequential pathway confirming that the two pathways model complementary and physically distinct geological signals. The total training pipeline executes in approximately 149 seconds (RF: 18 s; BiLSTM: 131 s), with sub-second inference at deployment. The framework is directly integratable into petrophysical evaluation platforms (Techlog, Interactive Petrophysics) and supports uncertainty-aware population of 3D geomodels via P10–P90 permeability realizations.