An algorithm for hydraulic tomography based on a mixture model Carlos Minutti 1 , Walter A. Illman 2 , Susana Gomez 1 1 Institute of Research in Applied Mathematics and Systems, National University of Mexico, Mexico City, Mexico 2 Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario, Canada carlos.minutti@iimas.unam.mx Abstract. Hydraulic Tomography (HT) has become one of the most robust methods to char- acterize 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 pre- dicting contaminant transport behavior. In addition, during inverse modeling, the groundwater flow equation is solved numerous times, thus the computational burden could be large, espe- cially 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. Keywords: Hydraulic Tomography · Gaussian Mixture · Aquifer heterogeneity. 1 Introduction During a hydraulic tomography experiment, water is sequentially pumped from or injected into an aquifer at different intervals of the aquifer. During each pumping/injection event, hydraulic head responses of the aquifer at different intervals are monitored, yielding a set of head/discharge (or recharge) data. By sequentially pumping/injecting water at one interval and monitoring the steady state head responses at others, many head/discharge (recharge) data sets are obtained (Yeh and Liu [11]). These head values can be compared with results given by the groundwater flow equation (the forward model) that describes the head response taking into account the hydraulic conductivity (K) values and the pumping/injection rate. The goal of hydraulic tomography (HT) is to find the K values throughout the aquifer that minimizes the difference between observed and simulated head values and this process is also known as the inverse problem. ICCS Camera Ready Version 2019 To cite this paper please use the final published version: DOI: 10.1007/978-3-030-22744-9_37