Abstract
In this paper, we investigate the applicability of artificial neural networks in inverting three-dimensional DC resistivity imaging data. The model used to produce synthetic data for training the artificial neural network (ANN) system was a homogeneous medium of resistivity 100 Ωm with an embedded anomalous body of resistivity 1000 Ωm. The different sizes for anomalous body were selected and their location was changed to different positions within the homogeneous model mesh elements. The 3D data set was generated using a finite element forward modeling code through standard 3D modeling software. We investigated different learning paradigms in the training process of the neural network. Resilient propagation was more efficient than any other paradigm. We studied the effect of the data type used on neural network inversion and found that the use of location and the apparent resistivity of data points as the input and corresponding true resistivity as the output of networks produces satisfactory results. We also investigated the effect of the training data pool volume on the inversion properties. We created several synthetic data sets to study the interpolation and extrapolation properties of the ANN. The range of 100–1000 Ωm was divided into six resistivity values as the background resistivity and different resistivity values were also used for the anomalous body. Results from numerous neural network tests indicate that the neural network possesses sufficient interpolation and extrapolation abilities with the selected volume of training data. The trained network was also applied on a real field dataset, collected by a pole-pole array using a square grid (8 ×8) with a 2-m electrode spacing. The inversion results demonstrate that the trained network was able to invert three-dimensional electrical resistivity imaging data. The interpreted results of neural network also agree with the known information about the investigation area.
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Aristodemou E., Pain C., De Oliveira C., Goddard T. and Harris C., 2005. Inversion of nuclear well-logging data using neural networks. Geophys. Prospect., 53, 103–120.
Baum E. and Haussler D., 1989. What size net gives valid generalization? In: Touretzky D. (Ed.), Advances in Neural Information Processing Systems I. Morgan Kaufman, San Mateo, CA, 80–90.
Battiti R., 1992. First and second order methods for learning: between steepest descent and Newton’s method. Neural Comput., 4(2), 141–166.
Calderon-Macias C., Sen M. and Stoffa P., 2000. Artificial neural networks for parameter estimation in geophysics. Geophys. Prospect., 48, 21–47.
Chambers J.E., Ogilvy R.D., Kuras O., Cripps J.C. and Meldrum P.I., 2002. 3D electrical imaging of known targets at a controlled environmental test site. Environ. Geol., 41, 690–704.
Claerbout J.F. and Muir F., 1973. Robust modeling with erratic data. Geophysics, 38, 826–844.
Cranganu C., 2007. Using artificial neural networks to predict the presence of overpressured zones in the Anadarko Basin, Oklahoma. Pure Appl. Geophys., 164, 2067–2081.
Edwards L.S., 1977. A modified pseudosection for resistivity and induced-polarization. Geophysics, 42, 1020–1036.
El-Qady G., Monteiro Santos F.A., Hassaneen A.Gh. and Trindade L., 2005. 3D inversion of VES data from Saqqara archaeological area Egypt. Near Surf. Geophys., 3, 227–233.
El-Qady G. and Ushijima K., 2001. Inversion of DC resistivity data using neural networks. Geophys. Prospect., 49, 417–430.
Hagan M.T., Demuth H.B. and Beale M.H., 1996. Neural Network Design. PWS Publishing, Boston, MA.
Hagan M.T. and Menhaj M., 1994. Training feed forward networks with the Marquardt algorithms. IEEE Trans. Neural Netw., 5, 989–993.
Haykin S., 1994. Neural Networks: A Comprehensive Foundation. Macmilan, New York, ISBN: 0-02-352761-7.
Ho T.L., 2009. 3-D inversion of borehole-to-surface electrical data using a back-propagation neural network. J. Appl. Geophys., 68, 489–499, doi: 10.1016/j.jappgeo.2008.06.002.
Irie B. and Miyake S., 1988. Capabilities of three-layered perceptrons. In: Caudill M. and Butler C. (Eds.), IEEE Conference on Neural Networks, Vol. 1. SOS Printing, San Diego, CA., 641–648.
Lippman R., 1987. An introduction to computing with neural nets. IEEE Trans. Acoust. Speech Signal Process., 4, 4–22.
Loke M.H. and Barker R.D., 1996a. Practical techniques for 3D resistivity surveys and data Inversion. Geophys. Prospect., 44, 499–523.
Loke M.H. and Barker R.D., 1996b. Rapid least-squares inversion of apparent resistivity pseudo-sections using quasi-Newton method. Geophys. Prospect., 44, 131–152.
Loke M.H., 2000. Electrical Imaging Surveys for Environmental and Engineering Studies. A Practical Guide to 2D and 3D Surveys. http://www.terrajp.co.jp/lokenote.pdf.
Loke M.H., 2007. Res3Dinv Software, Version 2.14. Geoelectrical imaging 2D&3D, Pinang, Malaysia.
McGillivray P.R. and Oldenburg D.W., 1990. Methods for calculating Frechet derivatives and sensitivities for the non-linear inverse problem: A comparative study. Geophys. Prospect., 38, 499–524.
Mehrotra K., Mohan C. and Ranka S., 1991. Bounds on the number of samples needed for learning. IEEE Trans. Neural Netw., 2, 548–558.
Poulton M. and El-Fouly A., 1991. Preprocessing GPR signatures for cascading neural network classification. SEG Expanded Abstracts, 10, 507–509, doi: 10.1190/1.1888789.
Poulton M., Sternberg K. and Glass C., 1992. Neural network pattern recognition of subsurface EM images. J. Appl. Geophys., 29, 21–36.
Powell M.J.D., 1977. Restart procedures for the conjugate gradient method. Math. Program., 12, 241–254.
Rajavelu A., Musavi M. and Shirvaikar M., 1989. A neural network approach to character recognition. Neural Netw., 2, 387–393.
Riedmiller M. and Braun H., 1993. A direct adaptive method for faster backpropagation learning: the RPROP algorithm. IEEE International Conference on Neural Networks (ICNN’93), 586–591, ISBN: 978-0780309999.
Sasaki Y., 1989. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data. Geophysics, 54, 254–262.
Scales L.E., 1985. Introduction to Non-Linear Optimization. Springer-Verlag, New York.
Singh U.K., Tiwari R.K. and Singh S.B., 2005. One-dimensional inversion of geoelectrical resistivity sounding data using artificial neural networks — a case study. Comput. Geosci., 31, 99–108.
Slater L. and Binley A., 2003. Evaluation of permeable reactive barrier (PRB) integrity using electrical imaging methods. Geophysics, 68, 911–921.
Soupios P.M., Georgakopoulos P., Papadopoulos N., Saltas V., Andeadakis A., Vallianatos F., Sarris A. and Makris J.P., 2007. Use of engineering geophysics to investigate a site for a building foundation. J. Geophys. Eng., 4, 94–103.
Spichak V.V., 2007. Neural network reconstruction of macro-parameters of 3-D geoelectric structures. In: Spichak V. (Ed.), Electromagnetic Sounding of the Earth’s Interior. Elsevier, Amsterdam, The Netherlands, 223–260.
Spichak V.V., Fukuoka K., Kobayashi T., Mogi T., Popova I. and Shima H., 1999. Neural network based interpretation of insufficient and noisy MT data in terms of the target macro — parameters. In: Zhdanov M. and Wannamaker P. (Eds.), Extended Abstracts of 2nd Symposium on 3D Electromagnetics, Salt-Lake City, USA, 297–300 (http://www.igemi.troitsk.ru/~spichak/Spichak-pdf/EM3D99.PDF).
Spichak V.V., Fukuoka K., Kobayashi T., Mogi T., Popova I. and Shima H., 2002. Artificial neural network reconstruction of geoelectrical parameters of the Minou fault zone by scalar CSAMT data. J. Appl. Geophys., 49, 75–90.
Spichak V.V. and Popova I.V., 2000. Artificial neural network inversion of MT — data in terms of 3D earth macro-parameters. Geophys. J. Int., 42, 15–26.
Spitzer K., 1998. The three-dimensional DC sensitivity for surface and subsurface sources. Geophys. J. Int., 134, 736–746.
Sultan S.A., Monteiro-Santos F.A. and Helal A., 2006. A study of the groundwater seepage at Hibis Temple using geoelectrical data, Kharga Oasis, Egypt. Near Surf. Geophys., 4, 347–354.
Tsourlos P. and Ogilvy R., 1999. An algorithm for the 3-D Inversion of Topographic Resistivity and Induced Polarization data: Preliminary Results. J. Balkan Geophys. Soc., 2(2), 30–45.
Werbos P.J., 1994. The Roots of Back-Propagation. From Order Derivatives to Neural Networks and Political Forecasting. John Wiley &Sons, New York.
Wiener J.M., Rogers J.A., Rogers J.F. and Moll R.F., 1991. Predicting carbonate permeabilities from wireline logs using a back-propagation neural network. SEG Expanded Abstracts, 10, 285–288.
Winkler E., 1994. Inversion of electromagnetic data using neural networks. Extended Abstracts of 56th EAEG Meeting, P124.
Zhao S. and Yedlin M.J., 1996. Some refinements on the finite-difference method for 3-D dc resistivity modeling. Geophysics, 61, 1301–1307.
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Neyamadpour, A., Wan Abdullah, W.A.T., Taib, S. et al. 3D inversion of DC data using artificial neural networks. Stud Geophys Geod 54, 465–485 (2010). https://doi.org/10.1007/s11200-010-0027-5
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DOI: https://doi.org/10.1007/s11200-010-0027-5