Uncertainty and explainable analysis of machine learning model for reconstruction of sonic slowness logs

Logs are valuable information for oil and gas fields as they help to determine the lithology of the formations surrounding the borehole and the location and reserves of subsurface oil and gas reservoirs. However, important logs are often missing in horizontal or old wells, which poses a challenge in field applications. To address this issue, conventional methods involve supplementing the missing logs by either combining geological experience and referring data from nearby boreholes or reconstructing them directly using the remaining logs in the same borehole. Nevertheless, there is currently no quantitative evaluation for the quality and rationality of the constructed log. In this paper, we utilize data from the 2020 machine learning competition of the Society of Petrophysicists and Logging Analysts (SPWLA), which aims to predict the missing compressional wave slowness (DTC) and shear wave slowness (DTS) logs using other logs in the same borehole. We employ the natural gradient boosting (NGBoost) algorithm to construct an Ensemble Learning model that can predicate the results as well as their uncertainty. Furthermore, we combine the SHAP (SHapley Additive exPlanations) method to investigate the interpretability of the machine learning model. We compare the performance of the NGBosst model with four other commonly used Ensemble Learning methods, including Random Forest, GBDT, XGBoost, LightGBM. The results show that the NGBoost model performs well in the testing set and can provide a probability distribution for the prediction results. This distribution allows petrophysicists to quantitatively analyze the confidence interval of the constructed log. In addition, the variance of the probability distribution of the predicted log can be used to justify the quality of the constructed log. Using the SHAP explainable machine learning model, we calculate the importance of each input log to the predicted results as well as the coupling relationship among input logs. Our findings reveal that the NGBoost model tends to provide greater slowness prediction results when the neutron porosity (CNC) and gamma ray (GR) are large, which is consistent with the cognition of petrophysical models. Furthermore, the machine learning model can capture the influence of the changing borehole caliper on slowness, where the influence of borehole caliper on slowness is complex and not easy to establish a direct relationship. These findings are in line with the physical principle of boreh