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 densities are necessary. In highly heterogeneous media, even with large numbers of measurements, the resolution may not be sufficient 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. This objective function increases the sensitivity of the parameters and eliminates the skin effect.
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 distribution produced through HT and reduces the computational effort. It also addresses the problems involved in the inverse problem due to including noisy data, the need for many pumping/injection tests and the lack of resolution when the K distribution does not have a Gaussian distribution. 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.