Abstract
The inverse problem of magnetotelluric data is extremely difficult due to its nonlinear and ill-posed nature. The existing gradient-descent approaches for this task surface from the problems of falling into local minima and relying on reliable initial models, while statistical-based methods are computationally expensive. Inspired by the excellent nonlinear mapping ability of deep learning, in this study, we present a novel magnetotelluric inversion method based on fully convolutional networks. This approach directly builds an end-to-end mapping from apparent resistivity and phase data to resistivity anomaly model. The implementation of the proposed method contains two stages: training and testing. During the training stage, the weight sharing mechanism of fully convolutional network is considered, and only the single anomalous body model samples are used for training, which greatly shortens the modeling time and reduces the difficulty of network training. After that, the unknown combinatorial anomaly model can be reconstructed from the magnetotelluric data using the trained network. The proposed method is tested in both synthetic and field data. The results show that the deep learning-based inversion method proposed in this paper is computationally efficient and has high imaging accuracy.
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References
Abubakar A, Habashy TM, Druskin VL, Knizhnerman L, Alumbaugh D (2008) 2.5D forward and inverse modeling for interpreting low frequency electromagnetic measurements. Geophysics 73(4):165–177. https://doi.org/10.1190/1.2937466
Basokur AT, Akca İ (2011) Object-based model verification by a genetic algorithm approach: application to archaeological targets. J Appl Geophys 74:167–174. https://doi.org/10.1016/j.jappgeo.2011.05.004
Chen XB, Zhao GZ, Tang J, Zhan Y, Wang JJ (2005) An adaptive regularized inversion algorithm for magnetotelluric data. Chin J Geophys 48(4):1005–1016. https://doi.org/10.1002/cjg2.742
Constable SC, Parker RL, Constable CG (1987) Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 52(3):289–300. https://doi.org/10.1190/1.1442303
Degroot-Hedlin C, Constable S (2004) Inversion of magnetotelluric data for 2D structure with sharp resistivity contrasts. Geophysics 69(1):78–86. https://doi.org/10.1190/1.1649377
Elwaseif M, Slater L (2013) Reconstruction of discrete resistivity targets using coupled artificial neural networks and watershed algorithms. Near Surf Geophys 11(1988):517–530. https://doi.org/10.3997/1873-0604.2013045
Feng DS, Wang X (2013) Magnetotelluric finite element method forward based on biquadratic interpolation and least squares regularization joint inversion. Chin J Nonfer Metals 23(09):2524–2531
Girshick R, Donahue J, Darrell T (2014) Rich feature hierarchies for accurate object detection and semantic segmentation. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 580–587. https://doi.org/10.1109/CVPR.2014.81
Guo R, Li KM, Yang F, Xu SH, Abubakar A (2020) Application of supervised descent method for 2D magnetotelluric data inversion. Geophysics 85(4):53–65. https://doi.org/10.1190/geo2019-0409.1
Jin KH, McCann M (2017) Deep convolutional neural network for inverse problems in imaging. IEEE Trans Image Process 26(9):4509–4522. https://doi.org/10.1109/TIP.2017.2713099
Kim Y, Nakata N (2018) Geophysical inversion versus machine learning in inverse problems. Lead Edge 37(12):894–901. https://doi.org/10.1190/tle37120894.1
Kingma D, Ba J (2014) Adam: a method for stochastic optimization[EB/OL]. [2014–12–22]. https://arxiv.org/pdf/1412.6980v9.pdf.
Krizhevsky A, Sutskever I, Hinton GE (2012) ImageNet classification with deep convolutional neural networks. In: Proceedings of the 25th international conference on neural information processing systems, pp 1097–1105
Laloy E, Herault R, Lee J, Jacques D, Linde N (2019) Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network. Adv Water Resour 110:387–405. https://doi.org/10.1016/j.advwatres.2017.09.029
Lee SK, Kim HJ, Song Y, Lee CK (2009) MT2DinvMatlab—a program in MATLAB and FORTRAN for two-dimensional magnetotelluric inversion. Comput Geosci 35(8):1722–1734. https://doi.org/10.1016/j.cageo.2008.10.010
Li JF, Liu YH, Yin CC, Ren XY, Su Y (2020a) Fast imaging of time-domain airborne EM data using deep learning technology. Geophysics 85(5):163–170. https://doi.org/10.1190/geo2019-0015.1
Li S, Liu B, Ren Y, Chen YK, Yang SL, Wang YH (2020b) Deep-learning inversion of seismic data. IEEE Trans Geosci Remote Sens 58(3):2135–2149. https://doi.org/10.1109/TGRS.2019.2953473
Liu B, Guo Q, Li SC, Liu BC, Ren YX, Pang YH, Guo X, Liu LB, Jiang P (2020) Deep learning inversion of electrical resistivity data. IEEE Trans Geosci Remote Sens 58(8):5715–5728. https://doi.org/10.1109/TGRS.2020.2969040
Long J, Shelhamer E, Darrell T (2015) Fully convolutional networks for semantic segmentation. In: IEEE conference on computer vision and pattern recognition, pp 3431–3440. https://doi.org/10.1109/CVPR.2015.7298965
Moghadas D (2020) One-dimensional deep learning inversion of electromagnetic induction data using convolutional neural network. Geophys J Int 222(1):247–259. https://doi.org/10.1093/gji/ggaa161
Montahaei M, Oskooi B (2014) Magnetotelluric inversion for azimuthally anisotropic resistivities employing artificial neural networks. Acta Geophys 62:12–43. https://doi.org/10.2478/s11600-013-0164-7
Munoz G (2014) Exploring for geothermal resources with electromagnetic methods. Surv Geophys 35:101–122. https://doi.org/10.1007/s10712-013-9236-0
Nawaz MA, Curtis A (2019) Rapid discriminative variational bayesian inversion of geophysical data for the spatial distribution of geological properties. J Geophys Res 124(6):5867–5887. https://doi.org/10.1029/2018JB016652
Patro PK (2017) Magnetotelluric studies for hydrocarbon and geothermal resources: examples from the Asian region. Surv Geophys 38:1005–1041. https://doi.org/10.1007/s10712-017-9439-x
Rodi W, Mackie RL (2001) Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics 66(1):174–187. https://doi.org/10.1190/1.1444893
Russakovsky O, Deng J, Su H (2015) ImageNet large scale visual recognition challenge. Int J Comput Vision 11:211–252. https://doi.org/10.1007/s11263-015-0816-y
Smith R (2014) Electromagnetic induction methods in mining geophysics from 2008 to 2012. Surv Geophys 35:123–156. https://doi.org/10.1007/s10712-013-9227-1
Smith JT, Boober JR (1991) Rapid inversion of two-and three-dimensional magnetotelluric data. J Geophys Res 96(B3):3905–3922. https://doi.org/10.1029/90JB02416
Sun HY, Demanet L (2020) Extrapolated full waveform inversion with deep learning. Geophysics 85(3):R275–R288. https://doi.org/10.1190/geo2019-0195.1
Vozoff K (1980) Electromagnetic methods in applied geophysics. Geophys Surv 4:9–20. https://doi.org/10.1007/BF01452955
Xiao J, Li J, Chen Y, Han F, Liu QH (2019) Fast Electromagnetic inversion of inhomogeneous scatterers embedded in layered media by born approximation and 3-D U-Net. IEEE Geosci Remote Sens Lett 99:1–5. https://doi.org/10.1109/LGRS.2019.2953708
Zeng SX, Hu J, Li S, Xu S, Fang H, Cai JC (2015) Detection of the deep crustal structure of the qiangtang terrane using magnetotelluric imaging. Tectonophysics 661:180–189. https://doi.org/10.1016/j.tecto.2015.08.038
Zhang ZD, Alkhalifah T (2019) Regularized elastic full-waveform inversion using deep learning. Geophysics 84(5):741–751. https://doi.org/10.1190/geo2018-0685.1
Zhang K, Wei WB, Lu QT, Dong H, Li YQ (2014) Theoretical assessment of 3-D magnetotelluric method for oil and as exploration:synthetic examples. J Appl Geophys 106:23–36. https://doi.org/10.1016/j.jappgeo.2014.04.003
Zhang ZH, Liao XL, Hou CYY, ZL, Fan XT, Xu ZX, (2021) Joint gravity and gravity gradient inversion based on deep learning. Chin J Geophys 64(4):1435–1452. https://doi.org/10.6038/cjg2021O0151
Acknowledgements
The research is sponsored by the National Key Research and Development Program of China (No. 2018YFC1505401), the Research and Development Projects of Sichuan Science and Technology Department (No. 2019YF0460, 2020YGF0303, 2021YJ0031), and the Technology Research and Development Program of China Railway Group Limited (No. CZ01-Key Point-05).
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Edited by Prof. Gabriela Fernández Viejo (CO-EDITOR-IN-CHIEF).
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Liao, X., Shi, Z., Zhang, Z. et al. 2D inversion of magnetotelluric data using deep learning technology. Acta Geophys. 70, 1047–1060 (2022). https://doi.org/10.1007/s11600-022-00773-z
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DOI: https://doi.org/10.1007/s11600-022-00773-z