Magnetotelluric Bayesian trans-dimensional inversion improved by parallel tempering algorithm

Yin Bin1,2 Hu Xiangyun1,2

(1.Institute of Geophysics and Geomatics, China University of Geosciences (Wuhan) , Wuhan, Hubei, China 430074)
(2.Hubei Key Laboratory of Subsurface Multi-scale Imaging, Wuhan, Hubei, China 430074)

【Abstract】Conventional linearized gradient inversions have been widely used in magnetotelluric (MT) data processing. However, these inversions have several problems. For example, inversion results are closely dependent on the initial model, and solution uncertainty cannot be analyzed. To overcome these problems, we propose MT Bayesian trans-dimensional inversion optimized by parallel tempering algorithm. First we apply the trans-dimensional inversion to inverse MT data and analyze the uncertainty based on the stochastic inversion theory. Then, we bring in the parallel tempering algorithm in order to accelerate the inversion convergence. Finally, we simultaneously run several Markov Chains and make them swap in different temperatures. Tests on synthetic model with noise prove that the proposed inversion is obviously improved by the parallel tempering algorithm, and it is better than conventional ones.

【Keywords】 magnetotelluric (MT) ; nonlinear Bayesian; trans-dimensional inversion; parallel tempering;


【Funds】 National Natural Science Foundation of China (41274077 and 41474055) Program of China Geological Survey (12120113101800)

Download this article


    [1] Li Jinming. Geoelectric field and electrical exploration. Beijing: Geological Publishing House, 2005 (in Chinese).

    [2]Shi Xueming, Wang Jiaying. One dimensional magnetotelluric sounding inversion using simulated annealing. Earth Science, 1998, 23(5): 108–111 (in Chinese).

    [3]Liu Yunfeng, Cao Chunlei. Inversion of onedimensional MT data using genetic algorithm.Journal of Zhejiang University (Natural Science Edition), 1997, 31(3): 300–305 (in Chinese).

    [4]Xu Yixian, Wang Jiaying. A multiresolution inversion of one dimensional magnetotelluric data. Chinese Journal of Geophysics, 1998, 41(5): 704–711 (in Chinese).

    [5]Wang Jiaying.Lecture on nonlinear inverse methods in geophysical data (5): The artificial neural network method. Chinese Journal of Engineering Geophysics, 2008, 5(3): 255–265 (in Chinese).

    [6]Wang Shuming, Liu Yulan, Wang Jiaying. Lecture on nonlinear inverse methods in geophysical data (9): Ant colony optimization. Chinese Journal of Engineering Geophysics, 2009, 6(2): 131–136 (in Chinese).

    [7]Tarantola A. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, 1987.

    [8]Yin Bin, Hu Xiangyun. Overview of nonlinear inversion using Bayesian method. Progress in Geophysics, 2016, 31(3): 1027–1032 (in Chinese).

    [9]Tarits P, Jouanne V, Menvielle M, et al. Bayesian statistics of nonlinear inverse problems: example of the magnetotelluric 1D inverse problem. Geophysical Journal International, 1994, 119(2): 353–368.

    [10]Sen M, Stoffa P. Bayesian inference, Gibbs’ sampler and uncertainty estimation in geophysical inversion. Geophysical Prospecting, 1996, 44(2): 313–350.

    [11]Grandis H, Menvielle M, Roussignol M. Bayesian inversion with Markov chains-I.The magnetotelluric onedimensional case. Geophysical Journal International, 1999, 138(3): 757–768.

    [12]Sambridge M, Mosegaard K. Monte Carlo methods in geophysical inverse problems. Reviews of Geophysics, 2002, 40(3): 1–3.

    [13]Yang Dikun, Hu Xiangyun. Inversion of noisy data by probabilistic methodology. Chinese Journal of Geophysics, 2008, 51(3): 901–907 (in Chinese).

    [14]Guo Rongwen, Dosso S, Liu Jianxin, et al. Non-linearity in Bayesian 1-D magnetotelluric inversion. Geophysical Journal International, 2011, 185(2): 663–675.

    [15]Wang Baoli, Sun Ruiying, Yin Xingyao, et al. Nonlinear inversion based on Metropolis sampling algorithm. OGP, 2015, 50(1): 111–117 (in Chinese).

    [16]Zhang Fanchang, Xiao Zhangbo, Yin Xingyao. Bayesian stochastic inversion constrained by seismic data. OGP, 2014, 49(1): 176–182 (in Chinese).

    [17]Zhang Guangzhi, Wang Danyang, Yin Xingyao. Seismic parameter estimation using Markov Chain Monte Carlo Method. OGP, 2011, 46(4): 605–609 (in Chinese).

    [18]Sambridge M. A parallel tempering algorithm for probabilistic sampling and multimodal optimization. Geophysical Journal International, 2014, 196(1): 357–374.

    [19]Luo Xiaolin. Constraining the shape of a gravity anomalous body using reversible jump Markov Chain Monte Carlo. Geophysical Journal International, 2010, 180(3): 1067–1079.

    [20]Minsley B. A trans–dimensional Bayesian Markov Chain Monte Carlo algorithm for model assessment using frequency–domain electromagnetic data. Geophysical Journal International, 2011, 187 (1): 252–272.

    [21]Ray A, Alumbaugh D, Hoversten G, et al. Robust and accelerated Bayesian inversion of marine controlled–source electromagnetic data using parallel tempering. Geophysics, 2013, 78 (6): E271–E280.

    [22]Yin Changchun, Qi Yanfu, Liu Yunhe, et al. Transdimensional Bayesian inversion of frequency–domain airborne EM data. Chinese Journal of Geophysics, 2014, 57 (9): 2971–2980 (in Chinese).

    [23]Ray A, Key Kerry. Bayesian inversion of marine CSEM data with a trans–dimensional self parametrizing algorithm. Geophysical Journal International, 2012, 191 (3): 1135–1151.

    [24]Green P J. Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika, 1995, 82 (4): 711–732.

    [25]Malinverno A. Parsimonious Bayesian Markov Chain Monte Carlo inversion in a nonlinear geophysical problem. Geophysical Journal International, 2002, 151 (3): 675–688.

    [26]Xu Shun, Zhou Xin, Ou-Yang Zhongcan. Parallel tempering simulation on generalized canonical ensemble. Communications in Computational Physics, 2012, 12(5): 1293–1306.

    [27]Rosas-Carbajal Marina, Linde Niklas, Kalscheuer Thomas et al. Twodimensional probabilistic inversion of plane-wave electromagnetic data: methodology, model constraints and joint inversion with electrical resistivity data. Geophysical Journal International, 2014, 196 (3): 1508–1524.

    [28]Ray A, Key Kerry, Bodin Thomas, et al. Bayesian inversion of marine CSEM data from the Scarborough gas field using a transdimensional 2-D parametrization. Geophysical Journal International, 2014, 199 (3): 1847–1860.

    [29]Chen Jinsong, Hoversten G, Key K, et al. Stochastic inversion of magnetotelluric data using a sharp boundary parameterization and application to a geothermal site. Geophysics, 2012, 77 (4): E265–E279.

This Article


CN: 13-1095/TE

Vol 51, No. 06, Pages 1212-1218+1053

December 2016


Article Outline


  • 1 Introduction
  • 2 Method principle
  • 3 Non-linear numerical sampling algorithm
  • 4 Parallel tempering
  • 5 Numerical tests of theoretical model inversion
  • 6 Conclusions
  • References