Optimal One-Dimensional Subsurface Sampling via Effective Sample Size and Latin Hypercube Integration

Abstract Appraising geological formations using well logs is critical for detailed subsurface description, cost-effective data acquisition, and obtaining high-resolution information essential for accurate geological, petrophysical, and geomechanical analysis. The primary challenge in spatial sampling of well logs is the optimum selection of the sample frequency and locations that provide the most precise spatial domain representation, considering inherent variability and spatial autocorrelation. Traditional sampling methods, such as random, systematic, and K-means clustering sampling, often fail to account for these factors, leading to redundant or deficient information due to autocorrelation between spatial samples. To address these challenges, we develop a new sampling technique that integrates the principles of effective number of samples and Latin hypercube sampling (LHS) specifically for one-dimensional sequences, such as those used during well-logging operations for subsurface characterization. The developed spatially effective Latin hypercube sampling (SE-LHS) workflow calculates the effective sample size as the optimum sampling frequency and then identifies the locations that maximize coverage over spatial and feature extents. For nonstationary data, a preliminary segmentation is necessary, followed by applying SE-LHS to each segment to obtain the total number of samples and their locations. SE-LHS outperforms traditional sampling techniques by accurately reproducing the original dataset's distribution and reducing spatial autocorrelation between samples. Additionally, SE-LHS samples give rise to statistics that more closely match those of the original data and provide narrower confidence intervals for estimating statistical properties than traditional sampling methods. This enhanced performance is particularly beneficial for maximizing the value of costly data collection campaigns for subsurface modeling to support optimum resource development and decision-making.