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Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion |
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| Authors: | A F?Hernandez |
| Institution: | (1) Department of Hydrology and Water Resources, University of Arizona, Tucson Arizona, 85721, USA;(2) Dipartimento Ingegneria Idraulica, Ambientale, Infrastrutture Viarie, Rilevamento (D.I.I.A.R.) Politecnico di Milano, Piazza L. Da Vinci, 32 I-20133 Milano, Italy;(3) Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, Barcelona, E-08034, Spain |
| Abstract: | Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.This work is supported in part by NSF/ITR Grant EAR-0110289. The first author was additionally supported by scholarships from CONACYT and Instituto de Investigaciones Electricas of Mexico. Additional support was provided by the European Commission under Contract EVK1-CT-1999-00041 (W-SAHaRA-Stochastic Analysis of Well Head Protection and Risk Assessment). |
| Keywords: | Aquifer characteristics Groundwater flow Inverse problem Regression analysis Uncertainty Steady-state conditions Stochastic processes Geostatistics |
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