Effects of spatially variable resolution on field-scale estimates of tracer concentration from electrical inversions using Archie’s law

Two important mechanisms affect our ability to estimate solute concentrations quantitatively from the inversion of field-scale electrical resistivity tomography ERT data: 1 the spatially variable physical processes that govern the flow of current as well as the variation of physical properties in space and 2 the overparameterization of inverse models, which requires the imposition of a smoothing constraint regularization to facilitate convergence of the inverse solution. Based on analyses of field and synthetic data, we find that the ability of ERT to recover the 3D shape and magnitudes of a migrating conductive target is spatially variable. Additionally, the application of Archie’s law to tomograms from field ERT data produced solute concentrations that are consistently less than 10% of point measurements collected in the field and estimated from transport modeling. Estimates of concentration from ERT using Archie’s law only fit measured solute concentrations if the apparent formation factor is varied with space and time and allowed to take on unreasonably high values. Our analysis suggests that the inability to find a single petrophysical relation in space and time between concentration and electrical resistivity is largely an effect of two properties of ERT surveys: 1 decreased sensitivity of ERT to detect the target plume with increasing distance from the electrodes and 2 the smoothing imprint of regularization used in inversion.

[1]  A. Sato,et al.  Three‐dimensional spatial and temporal monitoring of soil water content using electrical resistivity tomography , 2001 .

[2]  R. Knight,et al.  3. An Introduction to Rock Physics Principles for Near-Surface Geophysics , 2005 .

[3]  W. Daily,et al.  The effects of noise on Occam's inversion of resistivity tomography data , 1996 .

[4]  Robin Newmark,et al.  Monitoring Carbon Dioxide Floods Using Electrical Resistance Tomography (ERT): Sensitivity Studies , 2003 .

[5]  Douglas LaBrecque,et al.  Monitoring an underground steam injection process using electrical resistance tomography , 1993 .

[6]  M. H. Waxman,et al.  Electrical Conductivities in Oil-Bearing Shaly Sands , 1968 .

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

[8]  Paul P. Wang,et al.  MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems; Documentation and User's Guide , 1999 .

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

[10]  S.P. Garabedian,et al.  Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts. 2. Analysis of spatial moments for a nonreactive tracer , 1991 .

[11]  Stephen K. Park.  Fluid migration in the vadose zone from 3-D inversion of resistivity monitoring data , 1998 .

[12]  Andrew Binley,et al.  Electrical imaging of saline tracer migration for the investigation of unsaturated zone transport mechanisms. , 1997 .

[13]  David L. Alumbaugh,et al.  A geostatistically based inverse model for electrical resistivity surveys and its applications to vadose zone hydrology , 2002 .

[14]  C. Welty,et al.  A Critical Review of Data on Field-Scale Dispersion in Aquifers , 1992 .

[15]  Arlen W. Harbaugh,et al.  User's documentation for MODFLOW-96, an update to the U.S. Geological Survey modular finite-difference ground-water flow model , 1996 .

[16]  Kamini Singha,et al.  A framework for inferring field‐scale rock physics relationships through numerical simulation , 2005 .

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

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

[19]  W. M. McCardell,et al.  Ionic Double-Layer Conductivity in Reservoir Rock , 1953 .

[20]  Roelof Versteeg,et al.  Object-Based Inversion of Crosswell Radar Tomography Data to Monitor Vegetable Oil Injection Experiments , 2004 .

[21]  M.R.J. Wyllie,et al.  The Presence of Conductive Solids in Reservoir Rocks as a Factor in Electric Log Interpretation , 1950 .

[22]  Retardation of ammonium and potassium transport through a contaminated sand and gravel aquifer: the role of cation exchange , 1989 .

[23]  R. Knight,et al.  Modeling the field‐scale relationship between dielectric constant and water content in heterogeneous systems , 2004 .

[24]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[25]  P. Glover,et al.  Theory of ionic-surface electrical conduction in porous media , 1997 .

[26]  Abelardo Ramirez,et al.  Electrical imaging at the large block test—Yucca Mountain, Nevada , 2001 .

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

[28]  F. Day‐Lewis,et al.  Assessing the resolution‐dependent utility of tomograms for geostatistics , 2004 .

[29]  Douglas W. Oldenburg,et al.  Applied geophysical inversion , 1994 .

[30]  Abelardo Ramirez,et al.  Electrical resistance tomography during in-situ trichloroethylene remediation at the Savannah River Site , 1995 .

[31]  Andrew Binley,et al.  Applying petrophysical models to radar travel time and electrical resistivity tomograms: Resolution‐dependent limitations , 2005 .

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

[33]  A. L. Ramirez,et al.  Stochastic inversion of electrical resistivity changes using a Markov Chain Monte Carlo approach , 2005 .