Fully coupled hydrogeophysical inversion of synthetic salt tracer experiments

[1] We present a method for the determination of hydraulic conductivity from monitoring of salt tracer tests by electrical resistivity tomography (ERT). To ensure that the underlying principles of flow, transport, and geoelectrics are obeyed in the inversion, we perform a fully coupled hydrogeophysical analysis using temporal moments of electrical potential perturbations. In the predictive mode, we use moment-generating equations with corresponding adjoint equations for the evaluation of sensitivities. For inversion, we apply the quasi-linear geostatistical inversion approach. The method is tested in a synthetic case study mimicking a laboratory-scale quasi two-dimensional sandbox, in which 48 electrodes and 8 piezometers are used. The hydraulic conductivity field is estimated from the mean arrival times of electrical potential perturbations and hydraulic heads. The estimated hydraulic conductivity field reproduces most features with, however, a loss of variability. Even though only the temporal moments of the electrical signals are used for inversion, the transient behavior is satisfactorily recovered. Also, the spatial patterns of concentration arrival times in the true and estimated cases are in good agreement, so that the propagation of the tracer plume can be followed fairly accurately. We test the effects of large measurement errors and erroneous prior information on the performance of the inversion. While prior statistical parameters are of minor importance in detecting the major pattern of hydraulic conductivity, a large measurement error could have an important impact on the solution. Also, the choice of electrode configurations appears to be important. In particular, strictly surface-based geoelectrical surveys do not seem to be very suitable for identifying spatial patterns of hydraulic conductivity by ERT monitoring of salt tracer tests within aquifers.

[1]  C. R. Dietrich,et al.  A fast and exact method for multidimensional gaussian stochastic simulations , 1993 .

[2]  Wei Li,et al.  Efficient geostatistical inverse methods for structured and unstructured grids , 2006 .

[3]  G. E. Archie.  The electrical resistivity log as an aid in determining some reservoir characteristics , 1942 .

[4]  A. Binley,et al.  Cross-hole electrical imaging of a controlled saline tracer injection , 2000 .

[5]  Zhou Bing,et al.  Cross‐hole resistivity tomography using different electrode configurations , 2000 .

[6]  Georgios P. Tsoflias,et al.  Shallow seismic AVO variations related to partial water saturation during a pumping test , 2007 .

[7]  J. Nitao,et al.  Electrical resistivity tomography of vadose water movement , 1992 .

[8]  Salvatore Straface,et al.  Self‐potential signals associated with pumping tests experiments , 2004 .

[9]  Wolfgang Nowak,et al.  Efficient Computation of Linearized Cross-Covariance and Auto-Covariance Matrices of Interdependent Quantities , 2003 .

[10]  A. Binley,et al.  Examination of Solute Transport in an Undisturbed Soil Column Using Electrical Resistance Tomography , 1996 .

[11]  Peter K. Kitanidis,et al.  Sensitivity of temporal moments calculated by the adjoint-state method and joint inversing of head and tracer data , 2000 .

[12]  H. Vereecken,et al.  Potential of electrical resistivity tomography to infer aquifer transport characteristics from tracer studies: A synthetic case study , 2005 .

[13]  P. Kitanidis.  Quasi‐Linear Geostatistical Theory for Inversing , 1995 .

[14]  E. G. Vomvoris,et al.  A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one‐dimensional simulations , 1983 .

[15]  W. Nowak.  Geostatistical methods for the identification of flow and transport parameters in the subsurface , 2005 .

[16]  S. Gorelick,et al.  Saline tracer visualized with three‐dimensional electrical resistivity tomography: Field‐scale spatial moment analysis , 2005 .

[17]  Timothy A. Davis,et al.  Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method , 2004, TOMS.

[18]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[19]  P. Kitanidis.  On the geostatistical approach to the inverse problem , 1996 .

[20]  Wei Li,et al.  Three‐Dimensional Geostatistical Inversion of Flowmeter and Pumping Test Data , 2008, Ground water.

[21]  W. Nowak,et al.  Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data , 2006 .

[22]  Olaf A. Cirpka,et al.  Temporal moments in geoelectrical monitoring of salt tracer experiments , 2008 .

[23]  H. Vereecken,et al.  Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models , 2002 .

[24]  Jan W. Hopmans,et al.  Soil water flux density measurements near 1 cm d−1 using an improved heat pulse probe design , 2008 .

[25]  Stefan Finsterle,et al.  Estimation of field‐scale soil hydraulic and dielectric parameters through joint inversion of GPR and hydrological data , 2005 .

[26]  A. Binley,et al.  Improved hydrogeophysical characterization using joint inversion of cross‐hole electrical resistance and ground‐penetrating radar traveltime data , 2006 .

[27]  T. Dahlin,et al.  A numerical comparison of 2D resistivity imaging with 10 electrode arrays , 2004 .

[28]  Charles F. Harvey,et al.  Temporal Moment‐Generating Equations: Modeling Transport and Mass Transfer in Heterogeneous Aquifers , 1995 .

[29]  Alan G. Green,et al.  Experimental design: Electrical resistivity data sets that provide optimum subsurface information , 2004 .

[30]  William W.-G. Yeh,et al.  Coupled inverse problems in groundwater modeling - 1. Sensitivity analysis and parameter identification. , 1990 .

[31]  S. Finsterle,et al.  Estimating flow parameter distributions using ground-penetrating radar and hydrological measurements , 2004 .

[32]  W. Li,et al.  Two‐dimensional characterization of hydraulic heterogeneity by multiple pumping tests , 2007 .

[33]  Kamini Singha,et al.  Geoelectrical inference of mass transfer parameters using temporal moments , 2008 .

[34]  A. Binley,et al.  Vadose zone flow model parameterisation using cross-borehole radar and resistivity imaging , 2001 .

[35]  T. Hansen,et al.  Identifying Unsaturated Hydraulic Parameters Using an Integrated Data Fusion Approach on Cross‐Borehole Geophysical Data , 2006 .