Combining Regression Kriging With Machine Learning Mapping for Spatial Variable Estimation

Spatial variable estimation is a basic application of geostatistics. In general, this task is performed based on observations of limited points. For some cases, intensive observed data obtained from other sources are also available as the auxiliary variables. To utilize the auxiliary information in these data, methods such as regression kriging (RK) or cokriging are proposed. However, these methods all assume that the auxiliary variables keep linear correlation with the target variable implicitly, which is not satisfied in most cases. In this letter, through the combination of nonlinear machine learning mapping (MLM), we propose a novel hybrid method to relax the linear assumption of RK. The proposed method is applied to a real-world subsurface shale volume estimation task for demonstration. Compared with existing methods such as ordinary kriging, RK, and MLM, the relative estimation error reduction of the proposed method is larger than 10%. Meanwhile, the estimation resolution is also improved. This indicates that the proposed method provides an alternative way for further spatial variable estimation practices.