A Geostatistical Evolution Strategy for Subsurface Characterization: Theory and Validation Through Hypothetical Two-Dimensional Hydraulic Conductivity Fields

A novel approach that uses the covariance matrix adaptation evolution strategy in conjunction with geostatistical covariance functions and simultaneous ensemble Kalman filters is introduced to characterize the hydraulic conductivity fields of aquifers. To verify the performance, several similarity measures between the target and estimated fields are used, including the correlation coefficient, least absolute deviation, least squares, and cross-variance ratio. Three different cases are synthesized through validation with a small-scale domain (40 x 40), in which the hydraulic conductivity fields are stationary, nonstationary, and stationary with reduced prior information. According to these applications, the developed approach produces excellent estimations whether the field is stationary or nonstationary when the conditioning information is sufficient. With limited conditioning information, the performance of the estimation is slightly but not significantly lower. To validate the scalability, the developed approach is applied to larger domains (100 x 100, 150 x 150, and 200 x 200), and a modified approach based on principal components is used. According to this analysis, the developed approach requires low computational cost by making predictions with a limited number of forward-model runs and internal computations. Furthermore, the approach requires a small amount of prior information for the estimation. Based on these applications, this approach shows high potential to create cost-effective estimates that can be used as a reference for the current state-of-the-art geostatistical inversion approaches to improve subsurface characterization.