electrical resistivity tomography; time-lapse; prediction-focused approach; direct forecast; inversion
Abstract :
[en] Time-lapse applications of electrical methods have grown significantly over the last decade. However, the quantitative interpretation of tomograms in terms of physical properties, such as salinity, temperature or saturation, remains difficult. In many applications, geophysical models are transformed into hydrological models, but this transformation suffers from spatially and temporally varying resolution resulting from the regularization used by the deterministic inversion. In this study, we investigate a prediction-focused approach (PFA) to directly estimate subsurface physical properties with electrical resistance data, circumventing the need for classic tomographic inversions. First, we generate a prior set of resistance data and physical property forecast through hydrogeological and geophysical simulations mimicking the field experiment. We reduce the dimension of both the data and the forecast through principal component analysis in order to keep the most informative part of both sets in a reduced dimension space. Then, we apply canonical correlation analysis to explore the relationship between the data and the forecast in their reduced dimension space. If a linear relationship can be established, the posterior distribution of the forecast can be directly sampled using a Gaussian process regression where the field data scores are the conditioning data. In this paper, we demonstrate PFA for various physical property distributions. We also develop a framework to propagate the estimated noise level in the reduced dimension space. We validate the results by a Monte Carlo study on the posterior distribution and demonstrate that PFA yields accurate uncertainty for the cases studied.
Disciplines :
Geological, petroleum & mining engineering
Author, co-author :
Hermans, Thomas ; Université de Liège > Département ArGEnCo > Géophysique appliquée
Oware, Erasmus
Caers, Jef
Language :
English
Title :
Direct prediction of spatially and temporally varying physical properties from time-lapse electrical resistance data
Publication date :
2016
Journal title :
Water Resources Research
ISSN :
0043-1397
eISSN :
1944-7973
Publisher :
American Geophysical Union, Washington, United States - District of Columbia
Arato, A., J. Boaga, C. Comina, M. De Seta, E. Di Sipio, A. Galgaro, N. Giordano, and G. Mandrone (2015), Geophysical monitoring for shallow geothermal applications—Two Italian case histories, First Break, 33(8), 75–79.
Audebert, M., R. Cl�ment, N. Touze-Foltz, T. G�nther, S. Moreau, and C. Duquennoi (2014), Time-lapse ERT interpretation methodology for leachate injection monitoring based on multiple inversions and a clustering strategy (MICS), J. Appl. Geophys., 111, 320–333, doi:10.1016/j.jappgeo.2014.09.024.
Auken, E., J. Doetsch, G. Fiandaca, A. V. Christiansen, A. Gazoty, A. G. Cahill, and R. Jakobsen (2014), Imaging subsurface migration of dissolved CO2 in a shallow aquifer using 3-D time-lapse electrical resistivity tomography, J. Appl. Geophys., 101, 31–41, doi:10.1016/j.jappgeo.2013.11.011.
Beaujean, J., F. Nguyen, A. Kemna, A. Antonsson, and P. Engesgaard (2014), Calibration of seawater intrusion models: Inverse parameter estimation using surface electrical resistivity tomography and borehole data, Water Resour. Res., 50, 6828–6849, doi:10.1002/2013WR014020.
Ben Hadj Miled, M. K., and E. L. Miller (2007), A projection-based level-set approach to enhance conductivity anomaly reconstruction in electrical resistance tomography, Inverse Probl., 23(6), 2375–2400, doi:10.1088/0266-5611/23/6/007.
Binley, A., P. Winship, L. J. West, M. Pokar, and R. Middleton (2002), Seasonal variation of moisture content in unsaturated sandstone inferred from borehole radar and resistivity profiles, J. Hydrol., 267(3), 160–172.
Binley, A., S. S. Hubbard, J. A. Huisman, A. Revil, D. A. Robinson, K. Singha, and L. D. Slater (2015), The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales, Water Resour. Res., 51, 3837–3866, doi:10.1002/2015WR017016.
Briggs, M. A., F. D. Day-Lewis, J. B. T. Ong, G. P. Curtis, and J. W. Lane (2013), Simultaneous estimation of local-scale and flow path-scale dual-domain mass transfer parameters using geoelectrical monitoring, Water Resour. Res., 49, 5615–5630, doi:10.1002/wrcr.20397.
Campbell, R., C. Bower, and L. Richards (1948), Change of electrical conductivity with temperature and the relation of osmotic pressure to electrical conductivity and ion concentration in soil extracts, Soil Sci. Soc. Am. Proc., 13, 66–69.
Carrigan, C. R., et al. (2013), Electrical resistance tomographic monitoring of CO2 movement in deep geologic reservoirs, Int. J. Greenhouse Gas Control, 18, 401–408, doi:10.1016/j.ijggc.2013.04.016.
Caterina, D., J. Beaujean, T. Robert, and F. Nguyen (2013), A comparison study of different image appraisal tools for electrical resistivity tomography, Near Surf. Geophys., 11, 639–657, doi:10.3997/1873-0604.2013022.
Caterina, D., T. Hermans, and F. Nguyen (2014), Case studies of incorporation of prior information in electrical resistivity tomography: Comparison of different approaches, Near Surf. Geophys., 12, 451–465, doi:10.3997/1873-0604.2013070.
Chen, X., H. Murakami, M. S. Hahn, G. E. Hammond, M. L. Rockhold, J. M. Zachara, and Y. Rubin (2012), Three-dimensional Bayesian geostatistical aquifer characterization at the Hanford 300 Area using tracer test data, Water Resour. Res., 48, W06501, doi:10.1029/2011WR010675.
Chr�tien, M., J. F. Lataste, R. Fabre, and A. Denis (2014), Electrical resistivity tomography to understand clay behavior during seasonal water content variations, Eng. Geol., 169, 112–123, doi:10.1016/j.enggeo.2013.11.019.
Christensen, N.K., S. Christensen, and T.P.A. Ferre (2016), Testing alternative uses of electromagnetic data to reduce the prediction error of groundwater models, Hydrol. Earth Syst. Sci., 20(5), 1925–1946, doi:10.5194/hess-20-1925-2016.
Day-Lewis, F. D., K. Singha, and A. Binley (2005), Applying petrophysical models to radar travel time and electrical resistivity tomograms: Resolution-dependent limitations, J. Geophys. Res., 110, B08206, doi:10.1029/2004JB003569.
Day-Lewis, F. D., Y. Chen, and K. Singha (2007), Moment inference from tomograms, Geophys. Res. Lett., 34, L22404, doi:10.1029/2007GL031621.
Doetsch, J., N. Linde, and A. Binley (2010), Structural joint inversion of time-lapse crosshole ERT and GPR traveltime data, Geophys. Res. Lett., 37, L24404, doi:10.1029/2010GL045482.
Doetsch, J., N. Linde, T. Vogt, A. Binley, and A. G. Green (2012), Imaging and quantifying salt-tracer transport in a riparian groundwater system by means of 3D ERT monitoring, Geophysics, 77(5), B207–B218, doi:10.1190/geo2012-0046.1.
Fiandaca, G., J. Doetsch, G. Vignoli, and E. Auken (2015), Generalized focusing of time-lapse changes with applications to direct current and time-domain induced polarization inversions, Geophys. J. Int., 203(2), 1101–1112.
Flores Orozco, A., A. Kemna, and E. Zimmermann (2012), Data error quantification in spectral induced polarization imaging, Geophysics, 77(3), E227–E237, doi:10.1190/GEO2010-0194.1.
Hansen, T. M., K. S. Cordua, B. H. Jacobsen, and K. Mosegaard (2014), Accounting for imperfect forward modeling in geophysical inverse problems — Exemplified for crosshole tomography, Geophysics, 79(3), H1–H21, doi:10.1190/geo2013-0215.1.
Hermans, T., A. Vandenbohede, L. Lebbe, and F. Nguyen (2012), A shallow geothermal experiment in a sandy aquifer monitored using electric resistivity tomography, Geophysics, 77(1), B11–B21, doi:10.1190/geo2011-0199.1.
Hermans, T., F. Nguyen, T. Robert, and A. Revil (2014), Geophysical methods for monitoring temperature changes in shallow low enthalpy geothermal systems, Energies, 7(8), 5083–5118, doi:10.3390/en7085083.
Hermans, T., S. Wildemeersch, P. Jamin, P. Orban, S. Brouy�re, A. Dassargues, and F. Nguyen (2015), Quantitative temperature monitoring of a heat tracing experiment using cross-borehole ERT, Geothermics, 53, 14–26, doi:10.1016/j.geothermics.2014.03.013.
Hermans, T., A. Kemna, and F. Nguyen (2016), Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data, Geophysics, 81(5), E311–E322.
Hinnell, A. C., T. P. Ferr�, J. A. Vrugt, J. A. Huisman, S. Moysey, J. Rings, and M. B. Kowalsky (2010), Improved extraction of hydrologic information from geophysical data through coupled hydrogeophysical inversion, Water Resour. Res., 46, W00D40, doi:10.1029/2008WR007060.
Irving, J., and K. Singha (2010), Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities, Water Resour. Res., 46, W11514, doi:10.1029/2009WR008340.
Johnson, T. C., L. D. Slater, D. Ntarlagiannis, F. D. Day-Lewis, and M. Elwaseif (2012), Monitoring groundwater-surface water interaction using time-series and time-frequency analysis of transient three-dimensional electrical resistivity changes, Water Resour. Res., 48, W07506, doi:10.1029/2012WR011893.
Johnson, T. C., R. J. Versteeg, F. D. Day-Lewis, W. Major, and J. W. Lane (2015), Time-lapse electrical geophysical monitoring of amendment-based biostimulation, Ground Water, 53(6), 920–932, doi:10.1111/gwat.12291.
Karaoulis, M., J. H. Kim, and P. Tsourlos (2011), 4D active time constrained resistivity inversion, J. Appl. Geophys., 73, 25–34.
Kemna, A., B. Kulessa, and H. Vereecken (2002), Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models, J. Hydrol., 267(3-4), 125–146.
Kim, J. H., M. J. Yi, S. G. Park, and J. G. Kim (2009), 4-D inversion of DC resistivity monitoring data acquired over a dynamically changing earth model, J. Appl. Geophys., 68(4), 522–532.
Koestel, J., A. Kemna, M. Javaux, A. Binley, and H. Vereecken (2008), Quantitative imaging of solute transport in an unsaturated and undisturbed soil monolith with 3-D ERT and TDR, Water Resour. Res., 44, W12411, doi:10.1029/2007WR006755.
Krzanowski, W. J. (2000), Principles of Multivariate Analysis: A User's Perspective, Oxford Stat. Ser. 22, revised ed., Oxford Univ. Press, N. Y.
LaBrecque, D. J., M. Miletto, W. Daily, A. Ramirez, and E. Owen (1996), The effects of noise on Occam's inversion of resistivity tomography data, Geophysics, 61(2), 538–548.
Laloy, E., N. Linde, and J. A. Vrugt (2012), Mass conservative three-dimensional water tracer distribution from Markov chain Monte Carlo inversion of time-lapse ground-penetrating radar data, Water Resour. Res., 48, W07510, doi:10.1029/2011WR011238.
Linde, N., P. Renard, T. Mukerji, and J. Caers (2015), Geological realism in hydrogeological and geophysical inverse modeling: A review, Adv. Water Resour., 86, 86–101, doi:10.1016/j.advwatres.2015.09.019.
Lochb�hler, T., G. Pirot, J. Straubhaar, and N. Linde (2014), Conditioning of multiple-point statistics facies simulations to tomographic images, Math. Geosci., 46(5), 625–645, doi:10.1007/s11004-013-9484-z.
Masy, T., D. Caterina, O. Tromme, B. Lavigne, P. Thonart, S. Hiligsmann, and F. Nguyen (2016), Electrical resistivity tomography to monitor enhanced biodegradation of hydrocarbons with Rhodococcus erythropolis T902.1 at a pilot scale, J. Contam. Hydrol., 184, 1–13, doi:10.1016/j.jconhyd.2015.11.001.
Moysey, S., K. Singha, and R. Knight (2005), A framework for inferring field-scale rock physics relationships through numerical simulation, Geophys. Res. Lett., 32, L08304, doi:10.1029/2004GL022152.
M�ller, K., J. Vanderborght, A. Englert, A. Kemna, J. A. Huisman, J. Rings, and H. Vereecken (2010), Imaging and characterization of solute transport during two tracer tests in a shallow aquifer using electrical resistivity tomography and multilevel groundwater samplers, Water Resour. Res., 46, W03502, doi:10.1029/2008WR007595.
Murakami, H., X. Chen, M. S. Hahn, Y. Liu, M. L. Rockhold, V. R. Vermeul, J. M. Zachara, and Y. Rubin (2010), Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area, Hydrol. Earth Syst. Sci., 14(10), 1989–2001, doi:10.5194/hess-14-1989-2010.
Nguyen, F., A. Kemna, T. Robert, and T. Hermans (2016), Data-driven selection of the minimum-gradient support parameter in time-lapse focused electric imaging, Geophysics, 81(1), A1–A5, doi:10.1190/GEO2015-0226.1.
Oware, E. K., and S. M. J. Moysey (2014), Geophysical evaluation of solute plume spatial moments using an adaptive POD algorithm for electrical resistivity imaging, J. Hydrol., 517, 471–480, doi:10.1016/j.jhydrol.2014.05.054.
Oware, E. K., S. M. J. Moysey, and T. Khan (2013), Physically based regularization of hydrogeophysical inverse problems for improved imaging of process-driven systems, Water Resour. Res., 49, 6238–6247, doi:10.1002/wrcr.20462.
Pidlisecky, A., K. Singha, and F. D. Day-Lewis (2011), A distribution-based parametrization for improved tomographic imaging of solute plumes, Geophys. J. Int., 187(1), 214–224, doi:10.1111/j.1365-246X.2011.05131.x.
Robert, T., D. Caterina, J. Deceuster, O. Kaufmann, and F. Nguyen (2012), A salt tracer test monitored with surface ERT to detect preferential flow and transport paths in fractured/karstified limestones, Geophysics, 77, B55–B67.
Rubin, Y., and S. Hubbard (2005), Hydrogeophysics, Water Sci. and Technol. Libr., Springer, Dordrecht, Netherlands.
Rubin, Y., X. Chen, H. Murakami, and M. Hahn (2010), A Bayesian approach for inverse modeling, data assimilation, and conditional simulation of spatial random fields, Water Resour. Res., 46, W10523, doi:10.1029/2009WR008799.
Satija, A., and J. Caers (2015), Direct forecasting of subsurface flow response from non-linear dynamic data by linear least-squares in canonical functional principal component space, Adv. Water Resour., 77, 69–81, doi:10.1016/j.advwatres.2015.01.002.
Scheidt, C., P. Renard, and J. Caers (2015), Prediction-focused subsurface modeling: Investigating the need for accuracy in flow-based inverse modeling, Math. Geosci., 47(2), 173–191, doi:10.1007/s11004-014-9521-6.
Singha, K., and S. M. Gorelick (2005), Saline tracer visualized with three-dimensional electrical resistivity tomography: Field-scale spatial moment analysis, Water Resour. Res., 41, W05023, doi:10.1029/2004WR003460.
Singha, K., and S. Moysey (2006), Accounting for spatially variable resolution in electrical resistivity tomography through field-scale rock-physics relations, Geophysics, 71(4), A25–A28, doi:10.1190/1.2209753.
Singha, K., F. D. Day-Lewis, T. Johnson, and L. Slater (2015), Advances in interpretation of subsurface processes with time-lapse electrical imagin, Hydrol. Processes, 29(6), 1549–1576.
Strebelle, S. (2002), Conditional simulation of complex geological structures using multiple-point statistics, Math. Geol., 34(1), 1–21.
Tarantola, A. (2005), Inverse Problem Theory and Methods for Model Parameter Estimation, Soc. for Ind. and Appl. Math., Philadelphia, Penn.
Therrien, R., R. McLaren, E. Sudicky, and S. Panday (2010), HydroGeoSphere: A Three-Dimensional Numerical Model Describing Fully-Integrated Subsurface and Surface Flow and Solute Transport, Groundwater Simul. Group, Waterloo, Ont., Canada.
Tonkin, M. J., and J. Doherty (2005), A hybrid regularized inversion methodology for highly parameterized environmental models, Water Resour. Res., 41, W10412, doi:10.1029/2005WR003995.
Truex, M. J., T. C. Johnson, C. E. Strickland, J. E. Peterson, and S. S. Hubbard (2013), Monitoring Vadose Zone Desiccation with Geophysical Methods, Vadose Zone J., 12(2), 14, doi:10.2136/vzj2012.0147.
Vanderborght, J., A. Kemna, H. Hardelauf, and H. Vereecken (2005), Potential of electrical resistivity tomography to infer aquifer transport characteristics from tracer studies: A synthetic case study, Water Resour. Res., 41, W06013, doi:10.1029/2004WR003774.
Vereecken, H., A. Binley, G. Cassiani, A. Revil, and K. Titov (2007), Applied Hydrogeophysics, NATO Sci. Ser. IV. Earth Environ. Sci., Springer, Dordrecht, Netherlands.
Wallin, E. L., T. C. Johnson, W. J. Greenwood, and J. M. Zachara (2013), Imaging high stage river-water intrusion into a contaminated aquifer along a major river corridor using 2-D time-lapse surface electrical resistivity tomography, Water Resour. Res., 49, 1693–1708, doi:10.1002/wrcr.20119.
Zhou, B., and S. A. Greenhalgh (2000), Cross-hole resistivity tomography using different electrode configurations, Geophys. Prospect., 48(5), 887–912.
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