[en] Several techniques are available to estimate the depth of investigation or to identify possible artifacts in dc resistivity surveys. Commonly, the depth of investigation (DOI) is mainly estimated by using an arbitrarily chosen cut-off value on a selected indicator (resolution, sensitivity or DOI index). Ranges of cut-off values are recommended in the literature for the different indicators. However, small changes in threshold values may induce strong variations in the estimated depths of investigation. To overcome this problem, we developed a new statistical method to estimate the DOI of dc resistivity surveys based on a modified DOI index approach. This method is composed of 5 successive steps. First, two inversions are performed by using different resistivity reference models for the inversion (0.1 and 10 times the arithmetic mean of the logarithm of the observed apparent resistivity values). Inversion models are extended to the edges of the survey line and to a depth range of three times the pseudodepth of investigation of the largest array spacing used. In step 2, we compute the histogram of a newly defined scaled DOI index. Step 3 consists of the fitting of the mixture of two Gaussian distributions (G1 and G2) to the cumulative distribution function of the scaled DOI index values. Based on this fitting, step 4 focuses on the computation of an interpretation index (II) defined for every cell j of the model as the relative probability density that the cell j belongs to G1, which describes the Gaussian distribution of the cells with a scaled DOI index close to 0.0. In step 5, a new inversion is performed by using a third resistivity reference model (the arithmetic mean of the logarithm of the observed apparent resistivity values). The final electrical resistivity image is produced by using II as alpha blending values allowing the visual discrimination between well-constrained areas and poorly-constrained cells. The efficiency of the proposed methodology is assessed on synthetic and field data. By using synthetic benchmark analysis, we demonstrate that the selected well-constrained cells are well-reconstructed in size and shape as well as in resistivity contrasts. Compared to the existing image appraisal tools, the proposed statistical method allows the identification of the statistically well-constrained cells of the model without using any arbitrary cut-off value. Using this statistical method in combination with the resolution, when interpreting dc resistivity surveys, provides the geophysicist valuable information to avoid over- or misinterpretation of ERT images.
Disciplines :
Geological, petroleum & mining engineering
Author, co-author :
Deceuster, John; University of Mons
Etienne, Adélaïde; University of Mons
Robert, Tanguy ; Université de Liège - ULiège > Département ArGEnCo > Hydrogéologie & Géologie de l'environnement
Nguyen, Frédéric ; Université de Liège - ULiège > Département ArGEnCo > Géophysique appliquée
Kaufmann, O.
Language :
English
Title :
A modified DOI-based method to statistically estimate the depth of investigation of dc resistivity surveys
Alumbaugh D.L., Newman G.A. Image appraisal for 2-D and 3-D electromagnetic inversion. Geophysics 2000, 65:1455-1467.
Ashman K.M., Bird C.M., Zepf S.E. Detecting bimodality in astronomical datasets. Astron. J. 1994, 108:2348-2361.
Caterina D., Beaujean J., Robert T., Nguyen F. Image appraisal tools for electrical resistivity tomography. SAGEEP 2011, 24:7. 10.4133/1.3614283.
Caterina D., Beaujean J., Robert T., Nguyen F. A comparison study of different image appraisal tools for electrical resistivity tomography. Near Surf. Geophys. 2013, 11:639-657.
Christiansen A.V., Auken E. A global measure for depth of investigation. Geophysics 2012, 77(4):WB171-WB177.
Constable S.C., Parker R.L., Constable C.G. Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 1987, 52:289-300.
Dahlin T., Zhou B. A numerical comparison of 2D resistivity imaging with 10 electrode arrays. Geophys. Prospect. 2004, 52:379-398.
Day-Lewis F.D., Singha K., Binley A. Applying petrophysical models to radar travel time and electrical resistivity tomograms: resolution-dependent limitations. J. Geophys. Res. 2005, 110:B08206. (17 pp.).
Deceuster J., Kaufmann O. Improving the delineation of hydrocarbon-impacted soils and water through IP tomographies: a field study at an industrial waste land. J. Contam. Hydrol. 2012, 136-137:25-42.
deGroot-Hedlin C., Constable S. Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics 1990, 55:1613-1624.
Edwards L.S. A modified pseudosection for resistivity and induced polarization. Geophysics 1977, 42:1020-1036.
Farquharson C.G., Oldenburg D.W. Non-linear inversion using general measures of data misfit and model structure. Geophys. J. Int. 1998, 134:213-227.
Friedel S. Resolution, stability and efficiency of resistivity tomography estimated from a generalized inverse approach. Geophys. J. Int. 2003, 153:305-316.
Hilbich C., Marescot L., Hauck C., Loke M.H., Mäusbacher R. Applicability of electrical resistivity tomography monitoring to coarse blocky and ice-rich permafrost landforms. Permafr. Periglac. Process. 2009, 20:269-284.
Kaufmann O., Deceuster J., Quinif Y. An electrical resistivity imaging-based strategy to enable site-scaled planning over covered palaeokarst features in the Tournaisis area (Belgium). Eng. Geol. 2012, 133-134:49-65.
Kemna A. Tomographic inversion of complex resistivity: theory and application 2000, (PhD thesis), Ruhr-University of Bochum.
LaBrecque D.J., Miletto M., Daily W., Ramirez A., Owen E. The effects of noise on Occam's Inversion of resistivity tomography data. Geophysics 1996, 61:538-548.
Lines L.R., Treitel S. Tutorial: a review of least-squares inversion and its application to geophysical problems. Geophys. Prospect. 1984, 32:159-186.
Loke M.H., Barker R.D. Rapid least-squares inversion of apparent resistivity pseudosections using a quasi-Newton method. Geophys. Prospect. 1996, 44:131-152.
Loke M.H., Dahlin T. A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion. J. Appl. Geophys. 2002, 49:149-162.
Loke M.H., Acworth I., Dahlin T. A comparison of smooth and blocky inversion methods in 2D electrical imaging surveys. Explor. Geophys. 2003, 34:182-187.
Marescot L., Loke M.H., Chapellier D., Delaloye R., Lambiel C., Reynard E. Assessing reliability of 2D resistivity imaging in mountain permafrost studies using the Depth of Investigation index method. Near Surf. Geophys. 2003, 1:57-67.
Meju M. Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice 1994, Society of Exploration Geophysicists.
Menke W. Geophysical Data Analysis: Discrete Inverse Theory 2012, MATLAB edition, Academic Press, Inc., New York, (330 pp.). 3rd Edition.
Nguyen F., Kemna A., Antonsson A., Engesgaard P., Kuras O., Ogilvy R., Gisbert J., Jorreto S., Pulido-Bosch A. Characterization of seawater intrusion using 2D electrical imaging. Near Surf. Geophys. 2009, 7:377-390.
Oldenborger G.A., Routh P.S. The point-spread function measure of resolution for the 3-D electrical resistivity experiment. Geophys. J. Int. 2009, 176:405-414.
Oldenborger G.A., Routh P.S., Knoll M.D. Model reliability for 3D electrical resistivity tomography: application of the volume of investigation index to a time-lapse monitoring experiment. Geophysics 2007, 72:F167-F175.
Oldenburg D.W., Li Y. Estimating depth of investigation in dc resistivity and IP surveys. Geophysics 1999, 64:403-416.
Park S.K., Van G.P. Inversion of pole-pole data for 3-D resistivity structure beneath arrays of electrodes. Geophysics 1991, 56:951-960.
Pearson K. Editorial note. Biometrika 1929, 21:370-375.
Ramirez A.L., Daily W.D., Newmark R.L. Electrical resistance tomography for steam injection monitoring and process control. J. Environ. Eng. Geophys. 1995, 1:39-51.
Robert T., Dassargues A., Brouyère S., Kaufmann O., Hallet V., Nguyen F. Assessing the contribution of electrical resistivity tomography (ERT) and self-potential (SP) methods for a water well drilling program in fractured/karstified limestones. J. Appl. Geophys. 2011, 75(1):42-53.
Robert T., Caterina D., Deceuster J., Kaufmann O., Nguyen F. A salt tracer test monitored with surface ERT to detect preferential flow and transport paths in fractured/karstified limestones. Geophysics 2012, 77(2):B55-B67.
Stummer P., Maurer H., Green A.G. Experimental design: electrical resistivity data sets that provide optimum subsurface information. Geophysics 2004, 69(1):120-139.
Wolke R., Schwetlick H. Iteratively reweighted least squares algorithms, convergence analysis and numerical comparisons. SIAM J. Sci. Stat. Comput. 1988, 9:907-921.