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Task 1.2: Fully Coupled Hydrogeophysical Inversion of Salt-Tracer Experiments RECORD PhD Retreat 9 th -10 th June 2009 Davina Pollock, Center for Applied.

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1 Task 1.2: Fully Coupled Hydrogeophysical Inversion of Salt-Tracer Experiments RECORD PhD Retreat 9 th -10 th June 2009 Davina Pollock, Center for Applied Geoscience, University of Tübingen / ETH Zürich

2 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Introduction  Hydraulic conductivity (K) = key groundwater parameter  Measurements:  Wells  expensive  low resolution  Geophysics  does not measure directly hydraulic conductivity  petrophysical relationships  Use geophysics to monitor hydraulic tests  Relate change in geophysical properties to hydraulic stress  Electrical Resistivity Tomography (ERT) during salt-tracer tests  Various previous studies (e.g. Binley et al., 1996; Slater et al., 2000; Binley et al., 2002; Kemna et al., 2002; Vanderborght et al., 2005; Singha and Gorelick, 2005, Cassiani, 2006)

3 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie General Approach  Standard: classical geophysical inversion followed by hydraulic interpretation of concentration distribution  decoupled  risk of non-physical results (e.g., loss of mass)  no direct inference of hydraulic conductivity  Approach in which hydraulics and geophysics are considered as a coupled system:  physics of groundwater flow, transport, and geoelectrics satisfied by definition  efficient and stable inversion strategy?

4 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Governing Equations  Groundwater Flow Equation  Advection Dispersion Equation  Archie‘s Law  Poisson Equation FORWARD INVERSE

5 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Our Approach  Time-lapse ERT during tracer test  Analyse temporal moments of electrical-potential perturbations  Relate mean arrival time of electrical signal to hydraulic conductivity  Temporal moment generating equations  Incorporation into geostatistical inversion

6 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Temporal Moments of Concentration  Definition of zeroth and first moments:  Advection Dispersion Equation:  Moment generating equation:  Already used in inversion (e.g. Harvey and Gorelick, 1995; Cirpka and Kitanidis 2000; James et al., 2000; Nowak and Cirpka, 2006)

7 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Temporal Moments of Potential Perturbations  Definition  Poisson equation  Initial distribution φ 0  Linearisation  perturbation φ‘  Moment generating equation (Pollock & Cirpka, 2008) Valid if κc<<σ 0 and for m 1 /m 0

8 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Setup  Quasi two-dimensional sandbox  Injection of salt tracer  ERT monitoring using different electrode configurations  Results shown are for a hypothetical test case Electrodes Fixed head

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11 Measurements t c =m 1 /m 0 m0m0

12 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Sensitivities depends on electrode configuration resistance with respect to concentration Mean arrival time of potential perturbation with respect to log-hydraulic conductivity

13 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Geostatistical Inversion  Geostatistical regularisation (Kitanidis, 1995)  parameters considered spatially correlated random variables  deterministic trend Xβ plus random deviation Y′ :  maximise posterior likelihood of parameters  minimise objective function: Penalise not meeting the measurements Deviation from prior mean value Penalise spatial fluctuations

14 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie depends on electrode configuration

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16 Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie Final Remarks  Encouraging results:  larger features in ln(K) resolved  physical behaviour guaranteed  Not all details resolved  in ln(K) field  but also in time curves of electrical signals  include higher order moments as data?  Starting experiments in 2-D sandbox  application to real lab data  Necessary extensions for field applications:  3-D  different boundary conditions

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19 Acknowledgement  Funded by Swiss National Science Foundation under the grant

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