A New Inverse Modeling Approach for Hydraulic Conductivity Estimation Based on Gaussian Mixtures

Abstract

AbstractThis study proposes a new inverse algorithm to estimate the hydraulic conductivity (K) distribution based on a Gaussian Mixture Model that significantly reduces the number of parameters to be estimated during the inversion process. Moreover, a new objective function that increases the sensitivity of parameters using the spatial derivatives of hydraulic heads is introduced, and the algorithm is further improved by including a Bayes estimator that takes advantage of different possible solutions. The developed approach is tested through multiple synthetic experiments consisting of 250 randomly generated K fields resulting in different levels of heterogeneity and the use of different number of pumping tests, with a total of 1,000 cases of two‐dimensional configuration. A large number of cases are considered to ensure that our findings and conclusions are not based on a single realization. Results revealed significant improvements to K estimates, computational time, and predictions of independently conducted tests not used in the calibration effort when compared to a geostatistical inverse approach. Overall, our results reveal that the Gaussian Mixture inversion approach is able to achieve similar or higher levels of accuracy using half of the pumping tests and 20% of the computational time compared to a geostatistical inversion approach.