Manifold embedding based on geodesic distance for non-stationary spatial estimation in higher-dimensions

This technical note presents a significant advancement in geostatistical approaches for subsurface characterization by extending the manifold embedding method from two-dimensional to threedimensional space.This development enables the capturing of complex, non-stationary spatial correlations within a higher-dimensional framework.Integrating a fourth dimension, representing varying spatial properties, the method transcends the limitations of conventional two-point geostatistics, particularly in modeling the intricate heterogeneity of subsurface media.Despite its computational intensity and the need for comprehensive secondary data, the manifold embedding approach is invaluable in high-stakes scenarios like geological repository design and contaminant remediation.It stands out as a pivotal tool in hydrogeology and related fields, offering unprecedented precision and detail in subsurface characterizations and modeling.