An Algorithm for Hydraulic Tomography Based on a Mixture Model

摘要

Hydraulic Tomography (HT) has become one of the most robust methods to characterize the heterogeneity in hydraulic parameters such as hydraulic conductivity and specific storage. However, in order to obtain high resolution hydraulic parameter estimates, several pumping/injection tests with sufficient monitoring data are necessary. In highly heterogeneous media, even with large numbers of measurements, the resolution may not be enough for predicting contaminant transport behavior. In addition, during inverse modeling, the groundwater flow equation is solved numerous times, thus the computational burden could be large, especially for a large, three-dimensional, transient model. In this work we present a new approach to model aquifer heterogeneity, based on a Gaussian Mixture Model (GMM) to parameterize the K field, which significantly reduces the number of parameters to be estimated during the inversion process. In addition, a new objective function based on the spatial derivatives of hydraulic heads is introduced. The developed approach is tested with synthetic data and data from a previously conducted sandbox experiments. Results indicate that the new approach improves the accuracy of the K heterogeneity map produced through HT and reduces the computational effort. For two dimensional synthetic experiments, this approach was able to achieve a significant reduction in the error for K field estimation as well as computational time compared to a geostatistical inversion approach. Similar results were also achieved when the approach was tested using pumping test data conducted in a synthetic aquifer constructed in the laboratory.