Geostatistical significance of differences for spatial subsurface phenomenon

A B S T R A C T Optimum subsurface development decision-making depends on uncertainty models that integrate all information, data, and interpretations. Failure to account for the spatial context of subsurface data may lead to naive and overconfident estimations of uncertainty. These assumptions negatively impact the optimality of subsurface development decision-making and, ultimately, the economics of subsurface projects. An essential component is determining the significance of observed local differences in spatial datasets. New and practical methods are required to assess the significance of the difference in local expectation of spatial measures. Then, to determine if the difference is geostatistically significant, we introduce significance measures that account for the spatial context. Demonstrations of applications with geostatistical significance cover three unique spatial applications. The demonstrations use realistic synthetic data to account for stationary (i.e., statistics of interest are invariant under translation) and geological trends of a spatial feature, porosity. All examples utilize random function fields constrained by the histogram, two-point semivariogram, local conditioning data, and expert-mapped secondary information. The proposed workflow performs spatial bootstrap to empirically assess the null distribution and uncertainty in the difference in means based on the spatial context for the locally unconditional and conditional cases. The resulting empirically derived uncertainty distributions are applied to calculate p-values for the spatial version of null hypothesis significance testing. Nevertheless, decisions based solely on p-values suffer from misinterpretation and lack of reproducibility. To address this problem, we propose an alternative workflow that computes the Bayes factor bound and estimation graphics to comprehensively analyze the results and provide evidence to support decision making. The suggested workflow for geostatistical significance supports other subsurface applications such as trend modeling, stress testing decisions of stationarity checking, and model accuracy against input spatial statistics checks. While presented for subsurface porosity modeling, the proposed workflow is compatible with a wide range of spatial/subsurface settings: soil erosion monitoring, groundwater contamination mitigation, sustainable forestry, mining grade control, design of well pads, etcetera. Furthermore, the proposed workflow offers an improved assessment of uncertainty and robust standards to conclude whether an observed difference over spatial sample data is meaningful.