Machine learning assisted Kriging to capture spatial variability in petrophysical property modelling

Machine learning (ML) models have been widely used for estimating formation geophysical properties. While ML models excel at capturing non-linear correlations among parameters, incorporating the impact of spatial variability into the training and testing process remains challenging. On the other hand, deterministic geostatistical models such as Kriging are capable of capturing spatial variability to a great extent but often rely on the assumption of linearity, making them less suitable for non-linear relations. In this study, a machine learning (Least Squared Support Vector Regression, LSSVR) model is integrated into Kriging interpolation to estimate the sonic compressional wave velocity with high spatial variability over a geological setting. This new methodology consists of two steps: (1) constructing an initial machine learning model using LSSVR and calculating the residuals, and (2) applying Kriging interpolation and gradually modifying the training data using Kriging estimation to optimize the machine learning model. The proposed model effectively captures the non-linear relation between auxiliary and target variables along with the spatial autocorrelation of data. To evaluate the performance of proposed hybrid model, a dataset comprising geophysical downhole logging measurements including density, gamma ray, depth and sonic velocity were extracted from 122 boreholes in a mine site located at the Bowen basin in Queensland, Australia. The data was averaged over a sandstone interval and divided into training and testing sets. Four models, namely linear regression, regression Kriging, LSSVR and the hybrid model were developed and compared with each other based on their R 2 and RMSE values. The results demonstrate that the hybrid model outperforms the other models highlighting the effectiveness of employing a hybrid approach in capturing the spatial variability in petrophysical data over geological formations.