A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

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We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive global ... continued below

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Chen, Jinsong; Kemna, Andreas & Hubbard, Susan S. May 15, 2008.

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We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive global information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.

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  • Journal Name: Geothermics

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  • Report No.: LBNL-766E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 940562
  • Archival Resource Key: ark:/67531/metadc897531

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  • May 15, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Sept. 29, 2017, 4:20 p.m.

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Chen, Jinsong; Kemna, Andreas & Hubbard, Susan S. A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters, article, May 15, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc897531/: accessed October 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.