Abstract
An extension of an artificial neural network (ANN) approach to solve the magnetotelluric (MT) inverse problem for azimuthally anisotropic resistivities is presented and applied for a real dataset. Three different model classes, containing general 1-D and 2-D azimuthally anisotropic features, have been considered. For each model class, characteristics of three-layer feed forward ANNs trained through an error back propagation algorithm have been adjusted to approximate the inverse modeling function. It appears that, at least for synthetic models, reasonable results would be obtained by applying the amplitudes of the complex impedance tensor elements as inputs. Furthermore, the Levenberg-Marquart algorithm possesses optimal performance as a learning paradigm for this problem.
The evaluation of applicability of the trained ANNs for unknown data sets excluded from the learning procedure reveals that the trained ANNs possess acceptable interpolation and extrapolation abilities to estimate model parameters accurately. This method was also successfully used for a field dataset wherein anisotropy had been previously recognized.
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References
Berdichevsky, M.N., and V.I. Dmitriev (2008), Models and Methods of Magnetotellurics, Springer, Berlin Heidelberg.
Brasse, H., G. Kapinos, Y. Li, L. Mütschard, W. Soyer, and D. Eydam (2009), Structural electrical anisotropy in the crust at the South-Central Chilean continental margin as inferred from geomagnetic transfer functions, Phys. Earth Planet. In. 173,1–2, 7–16, DOI: 10.1016/j.pepi.2008.10.017.
Calderón-Macias, C., M.K. Sen, and P.L. Stoffa (2000), Artificial neural networks for parameter estimation in geophysics, Geophys. Prospect. 48,1, 21–47, DOI: 10.1046/j.1365-2478.2000.00171.x.
Cooley, J.W., and J.W. Tukey (1965), An algorithm for the machine calculation of complex Fourier series, Math. Comput. 19,90, 297–301, DOI: 10.1090/S0025-5718-1965-0178586-1.
Gatzemeier, A., and M. Moorkamp (2005), 3-D modelling of electrical anisotropy from electromagnetic array data: hypothesis testing for different upper mantle conduction mechanisms, Phys. Earth Planet. In. 149,3–4, 225–242, DOI: 10.1016/j.pepi.2004.10.004.
Haykin, S. (1999), Neural Networks: A Comprehensive Foundation, 2nd ed., Prentice-Hall Int., New Jersey, 842 pp.
Heise, W., and J. Pous (2001), Effects of anisotropy on the two-dimensional inversion procedure, Geophys. J. Int. 147,3, 610–621, DOI: 10.1046/j.0956-540x.2001.01560.x.
Heise, W., and J. Pous (2003), Anomalous phases exceeding 90° in magnetotellurics: anisotropic model studies and a field example, Geophys. J. Int. 155,1, 308–318, DOI: 10.1046/j.1365-246X.2003.02050.x.
Heise, W., T.G. Caldwell, H.M. Bibby, and C. Brown (2006), Anisotropy and phase splits in magnetotellurics, Phys. Earth Planet. In. 158,2–4, 107–121, DOI: 10.1016/j.pepi.2006.03.021.
Irie, B., and S. Miyake (1988), Capabilities of three-layered perceptrons. In: M. Caudill and C. Butler (eds.), Proc. IEEE Int. Conference on Neural Networks, 24–27 July 1988, San Diego, USA, Vol. 1, SOS Printing, 641–648, DOI: 10.1109/ICNN.1988.23901.
Kapinos, G. (2010), Amphibious magnetotellurics at the South-Central Chilean continental margin, Ph.D. Thesis, FU Berlin.
Lippmann, R.P. (1987), An introduction to computing with neural nets, IEEE Trans. Acoust. Speech Signal Process. 4,2, 4–22, DOI: 10.1109/MASSP.1987.1165576.
López-Escobar, L., J. Cembrano, and H. Moreno (1995), Geochemistry and tectonics of the Chilean Southern Andes basaltic Quaternary volcanism (37-46δS), Andean Geol. 22,2, 219–234, DOI: 10.5027/andgeoV22n2-a06.
Melnick, D. (2007), Neogene seismotectonics of the south-central Chile margin, Ph.D. Thesis, Institut für Geowissenschaften, Mathematisch-Naturwissenschaftliche Fakultät, Universität Potsdam.
Nakamura, K. (1977), Volcanoes as possible indicators of tectonic stress orientation — principle and proposal, J. Volcanol. Geoth. Res. 2,1, 1–16, DOI: 10.1016/0377-0273(77)90012-9.
Neyamadpour, A., S. Taib, and W.A.T. Wan Abdullah (2009), Using artificial neural networks to invert 2D DC resistivity imaging data for high resistivity contrast regions: A MATLAB application, Comput. Geosci. 35,11, 2268–2274, DOI: 10.1016/j.cageo.2009.04.004.
Neyamadpour, A., W.A.T. Wan Abdullah, S. Taib, and D. Niamadpour (2010), 3D inversion of DC data using artificial neural networks, Stud. Geophys. Geod. 54,3, 465–485, DOI: 10.1007/s11200-010-0027-5.
Pek, J., and F.A.M. Santos (2006), Magnetotelluric inversion for anisotropic conductivities in layered media, Phys. Earth Planet. In. 158,2–4, 139–158, DOI: 10.1016/j.pepi.2006.03.023.
Pek, J., and T. Verner (1997), Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media, Geophys. J. Int. 128,3, 505–521, DOI: 10.1111/j.1365-246X.1997.tb05314.x.
Poulton, M.M. (2002), Neural networks as an intelligence amplification tool: A review of applications, Geophysics 67,3, 979–993, DOI: 10.1190/1.1484539.
Poulton, M.M., and R.A. Birken (1998), Estimating one-dimensional models from frequency-domain electromagnetic data using modular neural networks, IEEE Trans. Geosci. Remote Sens. 36,2, 547–555, DOI: 10.1109/36.662737.
Rodi, W., and R.L. Mackie (2001), Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion, Geophysics 66,1, 174–187, DOI: 10.1190/1.1444893.
Röth, G., and A. Tarantola (1994), Neural networks and inversion of seismic data, J. Geophys. Res. 99,B4, 6753–6768, DOI: 10.1029/93JB01563.
Roux, E., M. Moorkamp, A.G. Jones, M. Bischoff, B. Endrun, S. Lebedev, and T. Meier (2011), Joint inversion of long-period magnetotelluric data and surface-wave dispersion curves for anisotropic structure: Application to data from Central Germany, Geophys. Res. Lett. 38,5, L05304, DOI: 10.1029/2010GL046358.
Roy, K.K. (2010), Inversion of potential field data. In: K.K. Roy, Potential Theory in Applied Geophysics, Springer, Berlin Heidelberg, 561–570.
Scherwath, M., E. Flueh, I. Grevemeyer, F. Tillman, E. Contreras-Reyes, and W. Weinrebe (2006), Investigating subduction zone processes in Chile, EOS Trans. AGU 87,27, 265–269, DOI: 10.1029/2006EO270001.
Shimelevich, M.I., and E.A. Obornev (2009), An approximation method for solving the inverse MTS problem with the use of neural networks, Phys. Solid Earth. 45,12, 1055–1071, DOI: 10.1134/S1069351309120039.
Singh, U.K., R.K. Tiwari, and S.B. Singh (2005), One-dimensional inversion of geoelectrical resistivity sounding data using artificial neural networks — A case study, Comput. Geosci. 31,1, 99–108, DOI: 10.1016/j.cageo.2004.09.014.
Soyer, W. (2002), Analysis of geomagnetic variations in the Central and Southern Andes, Ph.D. Thesis, FreieUniversität, Berlin.
Spichak, V., and I. Popova (2000), Artificial neural network inversion of magnetotelluric data in terms of three-dimensional Earth macroparameters, Geophys. J. Int. 142,1, 15–26, DOI: 10.1046/j.1365-246x.2000.00065.x.
Spichak, V., K. Fukuoka, T. Kobayashi, T. Mogi, I. Popova, and H. Shima (2002), ANN reconstruction of geoelectrical parameters of the Minou fault zone by scalar CSAMT data, J. Appl. Geophys. 49,1–2, 75–90, DOI: 10.1016/S0926-9851(01)00100-8.
Van der Baan, M., and C. Jutten (2000), Neural networks in geophysical applications, Geophysics 65,4, 1032–1047, DOI: 10.1190/1.1444797.
Wannamaker, P.E. (2005), Anisotropy versus heterogeneity in continental solid Earth electromagnetic studies: fundamental response characteristics and implications for physicochemical state, Surv. Geophys. 26,6, 733–765, DOI: 10.1007/s10712-005-1832-1.
Wiese, H. (1962), GeomagnetischeTiefentellurik. Teil II: Die Streichrichtung der Untergrundstrukturen des elektrischen Widerstandes, erschlossen aus geomagnetischen Variationen, Geofis. Pura Appl. 52,1, 83–103, DOI: 10.1007/BF01996002 (in German).
Yin, C. (2003), Inherent nonuniqueness in magnetotelluric inversion for 1D anisotropic models, Geophysics 68,1, 138–146, DOI: 10.1190/1.1543201.
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Montahaei, M., Oskooi, B. Magnetotelluric inversion for azimuthally anisotropic resistivities employing artificial neural networks. Acta Geophys. 62, 12–43 (2014). https://doi.org/10.2478/s11600-013-0164-7
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DOI: https://doi.org/10.2478/s11600-013-0164-7