Image-guided inversion in steady-state hydraulic tomography |
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| Institution: | 1. Université de Rouen, M2C, UMR 6143, CNRS, Morphodynamique Continentale et Côtière, Mont Saint Aignan, France;2. Colorado School of Mines, Dept of Geophysics, Golden, CO, USA;3. ISTerre, CNRS, UMR 5275, Université de Savoie, Equipe Volcan, Le Bourget du Lac, France;1. Chevron Energy Technology Co., 1500 Louisiana St., Houston, TX 77002, USA;2. Dept. of Mathematics, Texas A&M, College Station, TX 77843-3368, USA;3. Dept. of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA;1. Department of Geology and Geological Engineering, Colorado School of Mines, United States;2. Integrated GroundWater Modeling Center, United States;3. Department of Applied Mathematics and Statistics, Colorado School of Mines, United States;4. Climate Change Water and Society (CCWAS), Integrative Graduate Education and Research Traineeship (IGERT), United States;1. Eawag – Swiss Federal Institute of Aquatic Science and Technology, Department of Water Resources and Drinking Water, Dübendorf, Switzerland;2. Centre for Hydrogeology and Geothermics (CHYN), University of Neuchâtel, Neuchâtel, Switzerland;3. Department ICEA and International Center for Hydrology “Dino Tonini”, University of Padova, Padua, Italy;1. Institute of Environmental Assessment and Water Research (IDÆA), Spanish National Research Council (CSIC), 08034 Barcelona, Spain;2. Massachusetts Institute of Technology, 77 Massachusetts Ave, Building 48, Cambridge, MA 02139, USA;3. Université de Rennes 1, CNRS, Geosciences Rennes, UMR 6118, Rennes, France;1. Department of Civil Engineering, University of Ottawa, CBY D216, 161 Louis Pasteur, Ottawa, ON K1N 6N5, Canada;2. Department of Civil Engineering, University of Ottawa, CBY A114, 161 Louis Pasteur, Ottawa, ON K1N 6N5, Canada;3. Department of Civil Engineering, University of Ottawa, CBY A113, 161 Louis Pasteur, Ottawa, ON K1N 6N5, Canada;4. Department of Chemical Engineering, Qatar University, P.O. Box 2713, Doha, Qatar |
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| Abstract: | In steady-state hydraulic tomography, the head data recorded during a series of pumping or/and injection tests can be inverted to determine the transmissivity distributions of an aquifer. This inverse problem is usually under-determined and ill-posed. We propose to use structural information inferred from a guiding image to constrain the inversion process. The guiding image can be drawn from soft data sets such as seismic and ground penetrating radar sections or from geological cross-sections inferred from the wells and some geological expertise. The structural information is extracted from the guiding image through some digital image analysis techniques. Then, it is introduced into the inversion process of the head data as a weighted four direction smoothing matrix used in the regularizer. Such smoothing matrix allows applying the smoothing along the structural features. This helps preserving eventual drops in the hydraulic properties. In addition, we apply a procedure called image-guided interpolation. This technique starts with the tomogram obtained from the image-guided inversion and focus this tomogram. These new approaches are applied on four synthetic toy problems. The hydraulic distributions estimated from the image-guided inversion are closer to the true transmissivity model and have higher resolution than those computed from a classical Gauss–Newton method with uniform isotropic smoothing. |
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| Keywords: | Hydraulic tomography Image-guided-inversion Transmissivity |
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