“A comparison between Gauss-Newton and Markov-chain Monte Carlo-based methods for inverting spectral induced-polarization data for Cole-Cole parameters,” GEOPHYSICS, 73, no. 6, F247–F259

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. Y7-Y7 ◽  
Author(s):  
Jinsong Chen ◽  
Andreas Kemna ◽  
Susan S. Hubbard
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Induced Polarization ◽  
Polarization Data ◽  
Spectral Induced Polarization

Markov-chain Monte Carlo estimation of distributed Debye relaxations in spectral induced polarization

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. E159-E170 ◽  
Author(s):  
John Keery ◽  
Andrew Binley ◽  
Ahmed Elshenawy ◽  
Jeremy Clifford
Keyword(s):  
Porous Media ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Physical Properties ◽  
Relaxation Times ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Posterior Distributions ◽  
Spectral Induced Polarization

There is growing interest in the link between electrical polarization and physical properties of geologic porous media. In particular, spectral characteristics may be controlled by the same pore geometric properties that influence fluid permeability of such media. Various models have been proposed to describe the spectral-induced-polarization (SIP) response of permeable rocks, and the links between these models and hydraulic properties have been explored, albeit empirically. Computation of the uncertainties in the parameters of such electrical models is essential for effective use of these relationships. The formulation of an electrical dispersion model in terms of a distribution of relaxation times and associated chargeabilities has been demonstrated to be an effective generalized approach; however, thus far, such an approach has only been considered in a deterministic framework. Here, we formulate a spectral model based on a distribution of polarizations. By using a simple polynomial descriptor of such a distribution, we are able to cast the model in a stochastic manner and solve it using a Markov-chain Monte Carlo (McMC) sampler, thus allowing the computation of model-parameter uncertainties. We apply the model to synthetic data and demonstrate that the stochastic method can provide posterior distributions of model parameters with narrow bounds around the true values when little or no noise is added to the synthetic data, with posterior distributions that broaden with increasing noise. We also apply our model to experimental measurements of six sandstone samples and compare physical properties of a number of samples of porous media with stochastic estimates of characteristic relaxation times. We demonstrate the utility of our method on electrical spectra with different response characteristics and show that a single metric of relaxation time for the SIP response is not sufficient to provide clear insight into the physical characteristics of a sample.

scholarly journals A comparison between Gauss-Newton and Markov-chain Monte Carlo–based methods for inverting spectral induced-polarization data for Cole-Cole parameters

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. F247-F259 ◽  
Author(s):  
Jinsong Chen ◽  
Andreas Kemna ◽  
Susan S. Hubbard
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Optimal Solution ◽  
Stochastic Method ◽  
Objective Functions ◽  
Unknown Parameters ◽  
Deterministic Method ◽  
Initial Values ◽  
Spectral Induced Polarization

We have developed a Bayesian model to invert spectral induced-polarization (SIP) data for Cole-Cole parameters using Markov-chain Monte Carlo (MCMC) sampling methods. We compared 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 often is inaccurate or insufficient. In contrast, the MCMC-based inversion method provides extensive globalinformation 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. In addition, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC-based method does not explicitly offer a single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can be used first to obtain the medians of unknown parameters by starting from an arbitrary set of initial values. The deterministic method then can be initiated using the medians as starting values to obtain the optimal estimates of the Cole-Cole parameters.

scholarly journals Time-domain induced polarization – an analysis of Cole–Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion

2017 ◽  
Vol 211 (3) ◽  
pp. 1341-1353 ◽  
Author(s):  
Line Meldgaard Madsen ◽  
Gianluca Fiandaca ◽  
Esben Auken ◽  
Anders Vest Christiansen
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Time Domain ◽  
Induced Polarization

On Markov Chain Monte Carlo Acceleration

1994 ◽  
Author(s):  
Alan E. Gelfand ◽  
Sujit K. Sahu
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo
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