Reconstructing Sonic Well Log Curves based on Machine Learning and Analysis of Model Interpretability

Abstract: (Objective)Well logging technology is a critical means for determining subsurface lithological characteristics and geological structures, playing a pivotal role in the petroleum exploration industry. However, issues such as instrument damage and wellbore conditions frequently lead to data gaps and incomplete curves in well logging. Traditional multivariate linear regression and empirical formula methods fail to construct a reasonable relationship model among well logging curves, resulting in relatively low curve reconstruction accuracy. Although machine learning algorithms are able to find the most appropriate data mapping relationship between a large amount of data and thus improve the model accuracy, the black-box model constructed by them cannot be well explained in comparison. (Methods) In this paper, the Support Vector Regression (SVR), Random Forest (RF), and eXtreme Gradient Boosting (XGBoost) are used to compare with the traditional Multiple Linear Regression (LR) to reconstruct the acoustic logging curve of the NDR well 22-30b-11 and the XGBoost model is interpreted based on the Shapley Additive Explanations (SHAP) algorithm. (Results)The results demonstrate that XGBoost outperforms SVR and RF on the test set, achieving R2 values of 0.996 and MSE of 6.371, surpassing SVR with R2 of 0.990 and MSE of 15.755, and RF with R2 of 0.993 and MSE of 9.871. In contrast, the LR method yields an R2 of 0.969 and MSE of 48.895, indicating that XGBoost exhibits higher accuracy and better generalization performance in reconstructing acoustic time difference curves. This paper innovatively adopts the SHAP algorithm to explain the XGBoost black-box model, showing that when selecting important features for model construction, the XGBoost model adopts formation temperature data as important features significantly more reasonable than the well logging data adopted by the multiple linear regression scheme. Finally the model is interpreted based on SHAP for single point and global feature interactions. (Conclusion)The above results show that the machine learning algorithm is significantly better than the traditional multiple linear regression method in logging curve reconstruction, and prove the feasibility of SHAP algorithm in the interpretation of machine learning model for logging curve reconstruction, which provides a new idea for the subsequent development of machine learning in logging technology.