Innovative numerical techniques for calculating rock strength characteristics: Leveraging integrated machine learning and geostatistical methods

Accurately predicting rock mechanical properties, such as uniaxial compressive strength (UCS) and internal friction angle (o), is crucial for various subsurface engineering applications. Traditional laboratory testing methods for determining these parameters are often expensive and time-consuming. This research presents a novel methodology that integrates two key techniques, machine learning (ML) and geostatistics, to more efficiently and accurately estimate UCS and o from routinely measured P- and S-wave velocities (VP and VS) based on well-logging operations. The methodology involves training three machine learning models, including multivariate adaptive regression splines (MARS), least absolute shrinkage and selection operator (Lasso), and Ridge regression, on 70% of the data to predict UCS and o. Predictions were validated through cross-validation on the remaining 30% of the data. Next, the Ordinary Kriging (OK) method was employed to evaluate the accuracy and robustness of the applied methods. Finally, all the results were assessed using various metrics, including mean biased prediction error (MBPE), mean absolute prediction error (MAPE), mean squared prediction error (MSPE), and R-squared (R2). The results indicate that the Ridge model delivers the best performance for predicting o, with the lowest MSPE of 2.29 and the highest R2 of 0.98. Additionally, the value of MAPE is the lowest at 0.91, and MBPE has the lowest distance to zero. For UCS, the MARS demonstrates the lowest MSPE and MAPE values, as well as the highest R2, indicating superior performance compared to the other models.