Resolution of four collinear arrays to a 3D prism in multi-electrode resistivity surveys
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Resumen
La Tomografía de Resistividad Eléctrica (TRE) es una técnica geofísica ampliamente usada en diferentes aplicaciones como la hidrogeología, minería, geotermia y arqueología. En este método generalmente se usan arreglos convencionales de electrodos. Aquí examinamos el desempeño de cuatro de estos arreglos (Wenner (WN), dipolo-dipolo (DD), polo-polo (PP) y polo-dipolo (PD)) analizando sus resoluciones a los parámetros de un prisma tri-dimensional (3D) inmerso en un medio huésped homogéneo. Los cinco parámetros del modelo son profundidad, longitud, ancho, espesor y resistividad. Al variar sus cinco parámetros se consideran versiones diferentes de un modelo base. Las sensibilidades, asociadas con las derivadas de la respuesta de resistividad aparente con respecto a los parámetros, son ponderadas con los errores de los datos. Estos errores se estimaron con una ley de potencia de los errores en los voltajes. Las incertidumbres de los parámetros se estiman con una descomposición en valores singulares de las matrices de sensibilidad. Los parámetros mejor resueltos son la profundidad a la cima y la longitud del cuerpo, los peor resueltos son la resistividad, el ancho y el espesor. Los resultados muestran que el número de datos es el factor más importante en la resolución del cuerpo prismático. De los cuatro arreglos, el polo-dipolo fue el mejor porque fue el arreglo con más datos, aún mejor que el Wenner, que tuvo sensibilidades mayores. Otra opción con un número alto de datos es el arreglo Schlumberger con una separación arbitraria entre electrodos de potencial.
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Adeoti, L., Afolabi, O. S., Ojo, O. A., and Ishola, S. K. (2017). Application of three electrical resistivity arrays to evaluate resolution capacity of fractured zones at Apatara Farms, Iwo, Osun State, Nigeria, J. Appl. Sci. Environ. Management, 21(6), 1213-1221. Doi: https://dx.doi.org/10.4314/jasem.v21i6.36
Aguilar Cruz, F. (2019). Parameter resolution of a tri-dimensional body with several electrode arrays in the electrical resistivity technique. [M.Sc. Thesis], CICESE, Ensenada.
Apparao, A., Gangadhara Rao, T., Sivarama Sastry, R., and Subrahmanya Sarma, V. (1992). Depth of detection of buried conductive targets with different electrode arrays in resistivity prospecting, Geophysical Prospecting, 40, 749-760. doi: https://doi.org/10.1111/j.1365-2478.1992.tb00550.x
Apparao, A., Sivarama Sastry, R., and Subrahmanya Sarma, V. (1997). Depth of detection of buried resistive targets with some electrode arrays in resistivity prospecting, Geophysical Prospecting, 45(3), 365-375. doi: https://doi.org/10.1046/j.1365-2478.1997.3360256.x
Barker, R. D. (1979). Signal contribution sections and their use in resistivity studies, Geophysical Journal International, 59(1), 123-129. doi: https://doi.org/10.1111/j.1365-246X.1979.tb02555.x
Beard, L. P., and Tripp, A. C. (1995). Investigating the resolution of IP arrays using inverse theory, Geophysics, 60(5), 1326-1341. doi: https://doi.org/10.1190/1.1443869
Blome, M., Maurer, H., and Greenhalgh, S. (2011), Geoelectrical experimental design–Efficient acquisition and exploitation of complete pole-bipole data sets, Geophysics, 76(6). F15-F26. doi: https://doi.org/10.1190/1.3511350
Brass, G., Flathe, H., and Schulz, R. (1981). Resistivity profiling with different electrode arrays over a graphite deposit. Geophysical Prospecting, 29, 589-600. doi: https://doi.org/10.1111/j.1365-2478.1981.tb00697.x
Chambers, J. E., Kuras, O., Meldrum, P. I., Ogilvy, P. O., and Hollands, J. (2006). Electrical resistivity tomography applied to geologic, hydrogeologic, and engineering investigations at a former waste-disposal site, Geophysics, 71, B231-B239. doi: https://doi.org/10.1190/1.2360184
Coggon, J. H. (1973). A comparison of IP electrode arrays, Geophysics, 38(4), 737-761. https://doi.org/10.1190/1.1440372
Dahlin, T. (2000). Short note on electrode charge-up effects in DC resistivity data acquisition using multi-electrode arrays, Geophysical Prospecting., 48(1), 181-187. doi: https://doi.org/10.1046/j.1365-2478.2000.00172.x
Dahlin, T., and Zhou, B. (2004). A numerical comparison of 2D resistivity imaging with 10 electrode arrays, Geophysical Prospecting, 52(5), 379-398. doi: https://doi.org/10.1111/j.1365-2478.2004.00423.x
Das, U. C., and Parasnis, D. S. (1987). Resistivity and induced polarization responses of arbitrarily shaped 3-D bodies in a two-layered earth, Geophysical Prospecting, 35(1), 98-109. doi: https://doi.org/10.1111/j.1365-2478.1987.tb00805.x
Dey, A., and Morrison, H. F. (1979). Resistivity modelling for arbitrarily shaped two-dimensional structures, Geophysical Prospecting, 27(1), 106-136. doi: https://doi.org/10.1111/j.1365-2478.1979.tb00961.x
Dey, A., Meyer, W. H., Morrison, H. F., and Dolan, W. M. (1975). Electric field response of two-dimensional inhomogeneities to unipolar and bipolar electrode configurations, Geophysics, 40(4), 630-640. doi: https://doi.org/10.1190/1.1440554
Edwards, L. S. (1977). A modified pseudosection for resistivity and induced-polarization, Geophysics, 42(5), 1020-1036. doi: https://doi.org/10.1190/1.1440762
Edwards, R.N., Bailey, R.C., and Garland, G.D. (1981). Conductivity anomalies: lower crust or asthenosphere?, Physics of the Earth and Planetary Interiors, 25(3), 263-272. doi: https://doi.org/10.1016/0031-9201(81)90070-4
Furman, A., Ferré, T. P. A., and Warrick, A. W. (2003). A sensitivity analysis of electrical resistivity tomography array types using analytical element modeling, Vadose Zone Journal, 2(3), 416-423. doi: https://doi.org/10.2136/vzj2003.4160
Gharibi, M., and Bentley, L. R. (2005). Resolution of 3-D electrical resistivity images from inversions of 2-D orthogonal lines, Journal of Environmental and Engineering Geophysics, 10(4), 339-349. doi: https://doi.org/10.2113/JEEG10.4.339
Gómez-Treviño, E., and Esparza, F. J. (2013). What is the depth of investigation of a resistivity measurement? Geophysics, 79(2), W1-W10. doi: https://doi.org/10.1190/geo2013-0261.1
Gūndoğdy, N. Y., Demirci, I., Demirel, C., and Candansayar, M. E. (2020). Characterization of the bridge pillar foundations using 3D focusing inversion of DC resistivity data, Journal of Applied Geophysics, 172, 103875. doi: https://doi.org/10.1016/j.jappgeo.2019.103875
Loke, M. H. (2011). Tutorial: 2-D and 3-D electrical imaging surveys, Geotomo Software, Malaysia.
Loke, M. H., and Barker, R. D. (1995). Least-squares deconvolution of apparent resistivity pseudosections, Geophysics, 60(6), 1682-1690. doi: https://doi.org/10.1190/1.1443900
Militzer, H., Rösler, R., and Losch, W. (1979). Theoretical and experimental investigations for cavity research with geoelectrical resistivity methods, Geophysical Prospecting, 27(3), 640-652. doi: https://doi.org/10.1111/j.1365-2478.1979.tb00991.x
Nyquist, J. E., Peake, J. S., and Roth, M. J. S. (2007). Comparison of an optimized resistivity array with dipole-dipole soundings in karst terrain, Geophysics, 72(4), F139-F144. doi: https://doi.org/10.1190/1.2732994
Okpoli, C. C. (2013). Sensitivity and resolution capacity of electrode configurations, International Journal of Geophysics, ID608037. doi: https://doi.org/10.1155/2013/608037
Oldenburg, D. W., and Li., Y. (1999). Estimating depth of investigation in dc resistivity and IP surveys, Geophysics, 64(2), 403-416. doi: https://doi.org/10.1190/1.1444545
Pridmore, D. F., Hohmann, G. W., Ward, S. H., and Sill, W. R. (1981). An investigation of finite-element modeling for electrical and electromagnetic data in three dimensions, Geophysics, 46(7), 1009-1024. doi: https://doi.org/10.1190/1.1441239
Raiche, A. P., Jupp, D. L. B., Rutter, H., and Vozoff, K. (1985). The joint use of coincident loop transient electromagnetic and Schlumberger sounding to resolve layered structures, Geophysics, 50(10), 1618-1627. doi: https://doi.org/10.1190/1.1441851
Razafindratsima, S., and Lataste, J.-F. (2014). Estimation of the error made in Pole-Dipole Electrical Resistivity Tomography depending on the location of the remote electrode: Modeling and field study, Journal of Applied Geophysics, 100, 44-57. doi: https://doi.org/10.1016/j.jappgeo.2013.10.008
Roy, A., and Apparao, A. (1971). Depth of investigation in direct current methods, Geophysics, 36(5), 943-959. doi: https://doi.org/10.1190/1.1440226
Schulz, R. (1985). The method of integral equation in the direct current resistivity method and its accuracy, Journal of Geophysics-Zeitschrift fur Geophysik, 56(3), 192-200.
Snyder, D. D. (1976). A method for modeling the resistivity and IP response of two-dimensional bodies, Geophysics, 41(5), 997-1015. doi: https://doi.org/10.1190/1.1440677
Spiegel, R. J., Sturdivant, V. R., and Owen, T. E. (1980). Modeling resistivity anomalies from localized voids under irregular terrain, Geophysics, 45(7), 1164-1183. doi: https://doi.org/10.1190/1.1441115
Stummer, P., Maurer, H., and Green, A. G. (2004). Experimental design: Electrical resistivity data sets that provide optimum subsurface information, Geophysics, 69(1), 120-139. doi: https://doi.org/10.1190/1.1649381
Szalai, S., and Szarka, L. (2008). On the classification of surface geoelectric arrays, Geophysical Prospecting, 56(2), 159-175. doi: https://doi.org/10.1111/j.1365-2478.2007.00673.x
Van Nostrand, R. G. (1953). Limitations on resistivity methods as inferred from the buried sphere problem, Geophysics, 18(2), 423-433. doi: https://doi.org/10.1190/1.1437895
Ward, S. H. (1967). Electromagnetic theory for geophysical applications, In Hansen, D.A., et al (Eds.), Mining Geophysics, vol. II, Theory, (pp.10-198), Soc. of Exploration Geophysicists, Tulsa, Oklahoma. doi: https://doi.org/10.1190/1.9781560802716.ch2
Ward, S. H. (1990). Resistivity and Induced Polarization methods, In Ward, S. H. (Ed.), Geotechnical and Environmental Geophysics, vol. I: Review and Tutorial, (pp. 147-189), Soc. of Exploration Geophysicists, Tulsa, Oklahoma. doi: https://doi.org/10.1190/1.9781560802785.ch6
Wilkinson, P. B., Loke, M. H., Meldrum, P. I., Chambers, J. E., Kuras, O., Gunn, D. A., and Ogilvy, R. D. (2012). Practical aspects of applied optimized survey design for electrical resistivity tomography, Geophysical Journal International, 189, 428-440. doi: https://doi.org/10.1111/j.1365-246X.2012.05372.x
Wilkinson, P. B., Meldrum, P. I., Chambers, J. E., Kuras, O., and Ogilvy, R. D. (2006). Improved strategies for the automatic selection of optimized sets of electrical resistivity tomography measurement configuration, Geophysical Journal International, 167(3), 1119-1126. doi: https://doi.org/10.1111/j.1365-246X.2006.03196.x
Xiao, L.-L., Wei, J.-C., Niu, C., Shi, L.-Q., Zhai, P.-H., Yin, H.-Y., and Xie, D.-L. (2015). Study on the distortion of apparent resistivity curves caused by the ¨infinite¨ electrode space of a Pole-Pole array and its correction, Journal of Applied Geophysics, 118, 124-138. doi: https://doi.org/10.1016/j.jappgeo.2015.04.014
Zhou, B., and Dahlin, T. (2003). Properties and effects of measurement errors on 2D resistivity imaging surveying, Near Surface Geophysics, 1(3), 105-117. doi: https://doi.org/10.3997/1873-0604.2003001