Statistical Tapers for Correlation-Based Localization in Ensemble Data Assimilation
This study addresses the limitations of conventional distance-based localization in subsurface reservoir data assimilation, which often introduces spurious updates and excessively damps ensemble variance by neglecting flow dynamics, nonlinear observation operators, or prior structural information. The authors reformulate localization as a shrinkage problem in correlation space and, for the first time, incorporate statistical reliability into taper function design. They propose three novel approaches: a generalized power-law taper, a Bayesian spike-and-slab logistic taper, and a discrepancy-based taper derived from Morozov’s discrepancy principle. Numerical experiments demonstrate that the proposed correlation-based localization effectively suppresses spurious correlations while preserving genuine parameter–data relationships. Among the methods, the logistic taper best maintains posterior ensemble variance and consistently outperforms traditional distance-based localization, particularly in scenarios where spatial distance is ineffective or misleading.