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Fuzzy Constrained Inversion of Magnetotelluric Data Using Guided Fuzzy C-Means Clustering

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Abstract

Magnetotelluric (MT) inversion algorithms are an essential tool in exploration geophysics because they provide us with resistivity models of the subsurface. Inverse problems are ill-posed and non-unique. Resistivity models produced by geologically unconstrained MT inversions are typically smooth, which means that the geological interpretations obtained based on the resistivity models will be ambiguous and uncertain. To solve the above problems, geophysicists have made many efforts over the years to introduce any prior information (such as geological structure information and physical property data) into models, which could help to better constrain the inverted model with the inversion algorithms. In the last few years, there has been renewed interest in machine learning techniques. Various machine learning methods have been applied to inversions. Using the fuzzy c-means (FCM) clustering method, geophysicists proposed new inversion algorithms that are capable of building petrophysical information into the inversion. Although the FCM has been used and advanced in previous work, geophysicists concluded that a priori information of the correct number and value of cluster centers is very important for a successful FCM inversion. In fact, it is difficult to obtain the appropriate clustering information in some geophysical survey areas. In this study, we present an effective way to build the petrophysical information for the MT inversion based on FCM clustering algorithm. When the actual petrophysical information is insufficient, considering the characteristics of MT data, we perform a one-dimensional blocky inversion that can clearly identify the interface with distinct electrical property contrast; then, we obtain the number and value of cluster centers from 1D blocky inversion for the further MT inversion with FCM clustering. The algorithm uses guided FCM clustering to improve the model within the iterative minimization during MT inversion. In our MT inversion method, we integrate the geophysical inversion and geological differentiation into a unified scheme, which interact and enhance each other. The resistivity models obtained from the inversion respect the geophysical and petrophysical data and are easy to geologically interpret. We tested the algorithm using two synthetic examples and a field data example.

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References

  • Avdeev D, Avdeeva A (2009) 3D magnetotelluric inversion using a limited-memory quasi-newton optimization. Geophysics 74:F45–F57

    Article  Google Scholar 

  • Ayvaz MT (2007) Simultaneous determination of aquifer parameters and zone structures with fuzzyc-means clustering and meta-heuristic harmony search algorithm. Adv Water Resour 30:2326–2338. https://doi.org/10.1016/j.advwatres.2007.05.009

    Article  Google Scholar 

  • Ayvaz MT, Karahan H, Aral MM (2007) Aquifer parameter and zone structure estimation using kernel-based fuzzy c-means clustering and genetic algorithm. J Hydrol 343:240–253. https://doi.org/10.1016/j.jhydrol.2007.06.018

    Article  Google Scholar 

  • Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York

    Book  Google Scholar 

  • Bezdek JC, Ehrlich R, Full W (1984) FCM: The fuzzy c-means clustering algorithm. Comput Geosci 10:191–203. https://doi.org/10.1016/0098-3004(84)90020-7

    Article  Google Scholar 

  • Bragato G (2004) Fuzzy continuous classification and spatial interpolation in conventional soil survey for soil mapping of the lower Piave plain. Geoderma 118:1–16. https://doi.org/10.1016/S0016-7061(03)00166-6

    Article  Google Scholar 

  • Cao XY, Yin CC, Zhang B, Huang X, Liu YH, Cai J (2018) 3D magnetotelluric inversions with unstructured inite-element and limited-memory quasi-Newton methods. Appl Geophys 15:556–565

    Article  Google Scholar 

  • Carter-McAuslan A, Lelièvre PG, Farquharson CG (2015) A study of fuzzy c-means coupling for joint inversion, using seismic tomography and gravity data test scenarios. Geophysics 80:W1–W15. https://doi.org/10.1190/geo2014-0056.1

    Article  Google Scholar 

  • Chave AD, Jones AG (2012) The magnetotelluric method: theory and practice. Cambridge University, Cambridge

    Book  Google Scholar 

  • Commer M, Newman GA (2009) Three-dimensional controlled-source electromagnetic and magnetotelluric joint inversion. Geophys J Int 178:1305–1316

    Article  Google Scholar 

  • Dekkers MJ, Heslop D, Herrero-Bervera E, Acton G, Krasa D (2014) Insights into magmatic processes and hydrothermal alteration of in situ superfast spreading ocean crust at ODP/IODP site 1256 from a cluster analysis of rock magnetic properties. Geochem Geophys Geosyst 15(8):3430–3447

    Article  Google Scholar 

  • Deng Y, Tang J, Ruan S (2019) Adaptive regularized three-dimensional magnetotelluric inversion based on the LBFGS quasi-Newton method. Chin J Geophys 62(9):3601–3614. https://doi.org/10.6038/cjg2019M0045 (in Chinese)

    Article  Google Scholar 

  • Duda RO, Hart PE (1973) Pattern classiication and scene analysis. Wiley, Hoboken

    Google Scholar 

  • Duda RO, Hart PE, Stork DG (2000) Pattern classiication, 2nd edn. Wiley, Hoboken

    Google Scholar 

  • Dunn JC (1974) Well-separated clusters and optimal fuzzy partitions. J Cybern 4:95–104. https://doi.org/10.1080/01969727408546059

    Article  Google Scholar 

  • Egbert GD, Kelbert A (2012) Computational recipes for electromagnetic inverse problems. Geophys J Int 189:251–267

    Article  Google Scholar 

  • Fan J, Han M, Wang J (2009) Single point iterative weighted fuzzy C-means clustering algorithm for remote sensing image segmentation. Pattern Recognit 42:2527–2540. https://doi.org/10.1016/j.patcog.2009.04.013

    Article  Google Scholar 

  • Farquharson CG, Oldenburg DW (1996) Approximate sensitivities for the electromagnetic inverse problem. Geophys J Int 126:235–252

    Article  Google Scholar 

  • Farquharson CG, Ash MR, Miller HG (2008) Geologically constrained gravity inversion for the Voisey’s Bay ovoid deposit. Lead Edge 27:64–69. https://doi.org/10.1190/1.2831681

    Article  Google Scholar 

  • Fatehi M, Asadi HH (2017) Application of semi-supervised fuzzy c-means method in clustering multivariate geochemical data, a case study from the Dalli Cu-Au porphyry deposit in central Iran. Ore Geol Rev 81:245–255. https://doi.org/10.1016/j.oregeorev.2016.10.002

    Article  Google Scholar 

  • Fontes SL, De Lugao PP, Meju MA, Pinto VR, Flexor JM, Ulugergerli EU, La Terra EF, Gallardo LA (2009) Marine magnetotelluric mapping of basement and salt bodies in the Santos Basin of Brazil. First Break 27:83–87

    Article  Google Scholar 

  • Fontes SL, Meju MA, Maurya VP, La Terra EF, Miquelutti LG (2019) Deep structure of Parecis Basin, Brazil from 3D magnetotelluric imaging. J S Am Earth Sci 96:102381

    Article  Google Scholar 

  • Ghaffarian S, Ghaffarian S (2014) Automatic histogram-based fuzzy C-means clustering for remote sensing imagery. ISPRS J Photogramm Remote Sens 97:46–57. https://doi.org/10.1016/j.isprsjprs.2014.08.006

    Article  Google Scholar 

  • Goktepe AB, Altun S, Sezer A (2005) Soil clustering by fuzzy c-means algorithm. Adv Eng Softw 36:691–698. https://doi.org/10.1016/j.advengsoft.2005.01.008

    Article  Google Scholar 

  • Grayver A (2015) Parallel three-dimensional magnetotelluric inversion using adaptive inite-element method. Part I: Theory and synthetic study. Geophys J Int 202:584–603

    Article  Google Scholar 

  • Güler C, Kurt MA, Alpaslan M, Akbulut C (2012) Assessment of the impact of anthropogenic activities on the groundwater hydrology and chemistry in Tarsus coastal plain (Mersin, SE Turkey) using fuzzy clustering, multivariate statistics and GIS techniques. J Hydrol 414:435–451. https://doi.org/10.1016/j.jhydrol.2011.11.021

    Article  Google Scholar 

  • Haber E, Ascher UM, Oldenburg DW (2004) Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach. Geophysics 69(5):1216–1228

    Article  Google Scholar 

  • Han N, Nam MJ, Kim HJ, Lee TJ, Song Y, Suh JH (2008) Eicient three-dimensional inversion of magnetotelluric data using approximate sensitivities. Geophys J Int 175:477–485

    Article  Google Scholar 

  • Hathaway RJ, Bezdek JC (2001) Fuzzy c-means clustering of incomplete data. IEEE Trans Syst Man Cybern B Cybern 31:735–744. https://doi.org/10.1109/3477.956035

    Article  Google Scholar 

  • Hoppner F, Klawonn F, Kruse R, Runkler T (1999) Fuzzy cluster analysis: methods for classification, data analysis and image recognition. Wiley, Hoboken

    Google Scholar 

  • Jahandari H, Farquharson CG (2017) 3-D minimum-structure inversion of magnetotelluric data using the inite-element method and tetrahedral grids. Geophys J Int 211:1189–1205

    Article  Google Scholar 

  • Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice Hall, New Jersey

    Google Scholar 

  • Karpiah AB, Meju MA, Miller RV, Legrand X, Das PS, Musafarudin RNBR (2020) Crustal structure and basement-cover relationship in the Dangerous Grounds, ofshore North-West Borneo, from 3D joint CSEM and MT imaging. Interpretation SS97–SS111

  • Kaufman L, Rousseeuw PJ (1990) Finding groups in data: an introduction to cluster analysis. Wiley, Hoboken

    Book  Google Scholar 

  • Kieu DT, Kepic A (2015) Incorporating prior information into seismic impedance inversion using fuzzy clustering technique. In: 85th Annual International Meeting, SEG, expanded abstracts: 3451–3455

  • Kieu DT, Kepic A (2020) Seismic-impedance inversion with fuzzy clustering constraints: an example from the Carlin Gold District, Nevada, USA. Geophys Prospect 68:103–128

    Article  Google Scholar 

  • Kieu DT, Kepic A, Pethick AM (2016) Inversion of magnetotelluric data with fuzzy cluster petrophysical and boundary constraints. In: 25th International Geophysical Conference and Exhibition. ASEG, Adelaide, Australia

  • Kordy M, Wannamaker P, Maris V, Cherkaev E, Hill G (2016) 3-dimensional magnetotelluric inversion including topography using deformed hexahedral edge inite elements and direct solvers parallelized on symmetric multiprocessor computers—Part II: direct data-space inverse solution. Geophys J Int 204:94–110

    Article  Google Scholar 

  • Küçükdeniz T, Baray A, Ecerkale K, Esnaf S (2012) Integrated use of fuzzy c-means and convex programming for capacitated multi-facility location problem. Expert Syst Appl 39:4306–4314. https://doi.org/10.1016/j.eswa.2011.09.102

    Article  Google Scholar 

  • Lelièvre PG (2009) Integrating geologic and geophysical data through advanced constrained inversions. Ph.D. thesis, University of British Columbia

  • Lelièvre PG, Farquharson CG, Hurich CA (2012) Joint inversion of seismic traveltimes and gravity data on unstructured grids with application to mineral exploration. Geophysics 77(1):K1–K15. https://doi.org/10.1190/geo2011-0154

    Article  Google Scholar 

  • Li DC, Yang SJ, Hu ZZ, Zhao Z, Li Y, Zhong DK, Sun WB, Ji LS (2012) Integrated interpretation of 3D gravity, magnetic, electromagnetic and seismic data: a case study of conglomerate mass investigation in piedmont area of Kuche Depression. OGP 47(2):353–359 (in Chinese)

  • Lin C, Tan H, Tong T (2008) Three-dimensional conjugate gradient inversion of magnetotelluric sounding data. Appl Geophys 5:314–321

    Article  Google Scholar 

  • Liu S, Jin SG (2020) 3-D gravity anomaly inversion based on improved guided fuzzy C-means clustering algorithm. Pure Appl Geophys 177:1005–1027

    Article  Google Scholar 

  • Maag E, Li YG (2018) Discrete-valued gravity inversion using the guided fuzzy c means clustering technique. Geophysics 83(4):G59–G77. https://doi.org/10.1190/GEO2017-0594.1

    Article  Google Scholar 

  • Mackie RL, Madden TR (1993) Three-dimensional magnetotelluric inversion using conjugate gradients. Geophys J Int 115:215–229

    Article  Google Scholar 

  • Maurya VP, Meju MA, Fontes SL, Padilha AL, La Terra EF, Miquelutti LG (2018) Deep resistivity structure of basalt-covered central part of Parana basin, Brazil, from joint 3-D MT and GDS data imaging: geochemistry. Geophys Geosyst 19:1994–2013

    Article  Google Scholar 

  • Miyamoto S, Ichihashi H, Honda K (2008) Algorithms for fuzzy clustering: methods in c-means clustering with applications. Springer, Berlin

    Google Scholar 

  • Newman GA, Alumbaugh DL (1997) Three-dimensional massively parallel electromagnetic inversion—I. Theory. Geophys J Int 128:345–354

    Article  Google Scholar 

  • Newman GA, Alumbaugh DL (2000) Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophys J Int 140:410–424

    Article  Google Scholar 

  • Newman GA, Boggs PT (2004) Solution accelerators for large-scale three-dimensional electromagnetic inverse problems. Inverse Probl 20:151–170

    Article  Google Scholar 

  • Paasche H, Eberle D (2011) Automated compilation of pseudo-lithology maps from geophysical data sets: a comparison of Gustafson-Kessel and fuzzy c-means cluster algorithms. Explor Geophys 42(4):275–285

    Article  Google Scholar 

  • Paasche H, Tronicke J (2007) Cooperativeinversion of 2D geophysical data sets: a zonal approach based on fuzzy c-means cluster analysis. Geophysics 72(3):A35–A39. https://doi.org/10.1190/1.2670341

    Article  Google Scholar 

  • Paasche H, Tronicke J, Holliger K, Green AG, Maurer H (2006) Integration of diverse physical-property models: subsurface zonation and petrophysical parameter estimation based on fuzzy c-means cluster analyses. Geophysics 71(3):H33–H44. https://doi.org/10.1190/1.2192927

    Article  Google Scholar 

  • Paasche H, Tronicke J, Dietrich P (2010) Automated integration of partially colocated models: subsurface zonation using a modiied fuzzyc-means cluster analysis algorithm. Geophysics 75(3):P11–P22. https://doi.org/10.1190/1.3374411

    Article  Google Scholar 

  • Paasche H, Eberle D, Das S, Cooper A, Debba P, Dietrich P, Dudeni-Thlone N, Gläßer C, Kijko A, Knobloch A, Lausch A, Meyer U, Smit A, Stettler E, Werban U (2014) Are Earth Sciences lagging behind in data integration methodologies? Environ Earth Sci 71(4):1997–2003

    Article  Google Scholar 

  • Phillips ND (2001) Geophysical inversion in an integrated exploration program: examples from the San Nicolas deposit. M.S. thesis, University of British Columbia

  • Portniaguine O, Zhdanov MS (1999) Focusing geophysical inversion images. Geophysics 64:874–888

    Article  Google Scholar 

  • Rodi WL (1976) A technique for improving the accuracy of inite element solutions for magnetotelluric data. Geophys J Intern 44:483–506

    Article  Google Scholar 

  • Rodi WL, Mackie RL (2001) Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics 66(1):174–187

    Article  Google Scholar 

  • Sarkar S, Parihar SM, Dutta A (2016) Fuzzy risk assessment modelling of East Kolkata Wetland area: a remote sensing and GIS based approach. Environ Model Softw 75:105–118. https://doi.org/10.1016/j.envsoft.2015.10.003

    Article  Google Scholar 

  • Sasaki Y (2001) Full 3-D inversion of electromagnetic data on PC. J Appl Geophys 46:45–54

    Article  Google Scholar 

  • Sen M, Stofa PL (1995) Global optimization methods in geophysical inversion. Elsevier, Amsterdam

    Google Scholar 

  • Singh A, Sharma SP et al (2018) Fuzzy constrained Lp-norm inversion of direct current resistivity data. Geophysics 83:E11–E24. https://doi.org/10.1190/GEO2017-0040.1

    Article  Google Scholar 

  • Siripunvaraporn W, Sarakorn W (2011) An efficient data space conjugate gradient Occam’s method for three-dimensional magnetotelluric inversion. Geophys J Int 186:567–579

    Article  Google Scholar 

  • Siripunvaraporn W, Egbert G, Lenbury Y, Uyeshima M (2005) Three-dimensional magnetotelluric inversion: data-space method. Phys Earth Planet Inter 150:3–14

    Article  Google Scholar 

  • Sun JJ, Li YG (2010) Inversion of surface and borehole gravity with thresholding and density constraints. In: 80th Annual International Meeting, SEG, Expanded abstracts: 1798–1803

  • Sun JJ, Li YG (2011) Geophysical inversion using petrophysical constraints with application to lithology differentiation. In: 81th Annual International Meeting, SEG, Expanded Abstracts 2644–2648

  • Sun JJ, Li YG (2015) Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering. Geophysics 80(4):ID1–ID18. https://doi.org/10.1190/geo2014-0049.1

    Article  Google Scholar 

  • Sun JJ, Li YG (2016) Joint inversion of multiple geophysical data using guided fuzzy c-means clustering. Geophysics. 81(3):ID37–ID57

    Article  Google Scholar 

  • Sun JJ, Li YG (2018) Magnetization clustering inversion—part 1: building an automated numerical optimization algorithm. Geophysics 83(5):J61–J73

    Article  Google Scholar 

  • Tietze K, Ritter O, Egbert GD (2015) 3-D joint inversion of the magnetotelluric phase tensor and vertical magnetic transfer functions. Geophys J Int 203:1128–1148

    Article  Google Scholar 

  • Tikhonov AN, Arsenin VY (1977) Solutions of Ill-posed problems. Wiley, New York

    Google Scholar 

  • Usui Y (2015) 3-D inversion of magnetotelluric data using unstructured tetrahedral elements: applicability to data affected by topography. Geophys J Int 202:828–849

    Article  Google Scholar 

  • Usui Y, Ogawa Y, Aizawa K, Kanda W, Hashimoto T, Koyama T, Yamaya Y, Kagiyama T (2017) Three-dimensional resistivity structure of Asama volcano revealed by data-space magnetotelluric inversion using unstructured tetrahedral elements. Geophys J Int 208:1359–1372

    Article  Google Scholar 

  • Wang DC, Zhang GL, Pan XZ, Zhao YG, Zhao MS, Wang GF (2012) Mapping soil texture of a plain area using fuzzy-c-means clustering method based on land surface diurnal temperature diference. Pedosphere 22:394–403. https://doi.org/10.1016/S1002-0160(12)60025-3

    Article  Google Scholar 

  • Ward WOC, Wilkinson PB, Chambers JE, Oxby LS, Bai L (2014) Distribution-based fuzzy clustering of electrical resistivity tomography images for interface detection. Geophys J Int 197(1):310–321

    Article  Google Scholar 

  • Xu KJ, Li YG (2020) Constraining magnetic amplitude inversion with magnetotelluric data to image volcanic units: a case study. Geophysics 85(3):B63–B75

    Article  Google Scholar 

  • Yang B, Liu Z, Xu KJ et al (2019) Fuzzy constrained inversion of magnetotelluric data using guided fuzzy c-means clustering. In: 89th Annual International Meeting, SEG, Expanded Abstracts: 1184–1188

  • Yu H, Deng JZ, Chen H et al (2019) Three-dimensional magnetotelluric inversion under topographic relief based on limited-memory quasi-Newton algorithm (L-BFGS). Chin J Geophys 62(8):3175–3188. https://doi.org/10.6038/cjg2019M0258 (in Chinese)

    Article  Google Scholar 

  • Zevallos I, Assumpcao M, Padilha AL (2009) Inversion of teleseismic receiver function and magnetotelluric sounding to determine basement depth in the Paraná basin. SE Braz J Appl Geophys 68:231–242

    Article  Google Scholar 

  • Zhdanov MS (2002) Geophysical inverse theory and regularization problems. Elsevier, Amsterdam

    Google Scholar 

  • Zhdanov MS (2009) New advances in regularized inversion of gravity and electromagnetic data. Geophys Prospect 57:463–478

    Article  Google Scholar 

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Acknowledgements

We thank Colin Farquharson and another anonymous reviewer for their detailed comments, which helped us to improve this paper. We thank Tarim Oilfield Company for providing the geophysical, well log, and petrophysical data and for their support of the research. And thanks are due to Professor Wang Xuben for his guidance. This paper was financially supported in part by the Key National Research Project of China (2018YFC0603301).

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  1. Department of Geophysics, China University of Petroleum (East China), Qingdao, Shandong, China

    Bo Yang, Kaijun Xu & Zhan Liu

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Yang, B., Xu, K. & Liu, Z. Fuzzy Constrained Inversion of Magnetotelluric Data Using Guided Fuzzy C-Means Clustering. Surv Geophys 42, 399–425 (2021). https://doi.org/10.1007/s10712-020-09628-y

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