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

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)

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?

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

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

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)

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

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

Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie

Measurements t c =m 1 /m 0 m0m0

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

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

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

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

Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie

Acknowledgement  Funded by Swiss National Science Foundation under the grant

Zentrum für Angewandte Geowissenschaften (ZAG) Hydrogeologie