Stochastic inversion of 2D magnetotelluric data using sharp boundary parameterization (original) (raw)
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A fully non-linear inversion scheme based on bayesian Markov Chain Monte Carlo (MCMC) algorithm has been developed for magnetotelluric (MT) 1-D and thin-sheet models. Application for both synthetic and field data from various scale showed satisfying results with reference to synthetic models and local geology. The paper describes an attempt to apply the MT inversion algorithm to 3-D cases. We incorporate existing 3-D MT forward modelling algorithm based on staggered grid finite-difference technique. Tests using simple conductivity models showed that there are problems remain to be studied further : (i) equivalence or ambiguity, (ii) sensitivity or resolution in terms of "a priori" conductivity values. Additionally, efficient and faster forward modelling algorithm is needed since MCMC based inversion is a slow and computer intensive method. Partially resolving the forward modelling due to conductivity change of only one grid or cell might improve the algorithm. However, the fact that the algorithm showed decreasing error or misfit is encouraging.
A fully non-linear inversion scheme based on bayesian Markov Chain Monte Carlo (MCMC) algorithm has been developed for magnetotelluric (MT) 1 D and thin-sheet models. Application for both synthetic and field data from various scale showed satisfying results with reference to synthetic models and local geology. The paper describes an attempt to apply the MT inversion algorithm to 3 D cases. We incorporate existing 3 D MT forward modelling algorithm based on staggered grid finite-difference technique. Tests using simple conductivity models showed that there are problems remain to be studied further : (i) equivalence or ambiguity, (ii) sensitivity or resolution in terms of "a priori" conductivity values. Additionally, efficient and faster forward modelling algorithm is needed since MCMC based inversion is a slow and computer intensive method. Partially resolving the forward modelling due to conductivity change of only one grid or cell might improve the algorithm. However, the fact that the algorithm showed decreasing error or misfit is encouraging.
MCMC Algorithm for Inversion of Magnetotelluric Data in 3D: A Synthetic Case
The Markov Chain Monte Carlo (MCMC) algorithm has been successfully applied for inversion of 1D MT and VES data and also 3D EM (impedance tensor and tipper) data using thin-sheet approximation. This paper presents preliminary results of the MCMC inversion algorithm incorporating the full 3D MT modeling. In the MCMC inversion algorithm, a large number of samples of the model space is stochastically generated by using a Markov Chain’s transition probability that is a function of the misfit. The generated samples converge to the optimal model. The method was tested by inverting synthetic data associated with a simple block model similar to the COMMEMI test model. Due to intensive and time consuming calculation to perform the 3D forward modeling, we used a limited number of periods (in the interval from 0.1 to 1000 sec.) and the number of possible "a priori" resistivity values. The inverse model from a few iterations recovered the synthetic model relatively well, where the low (1 Ohm.m) and high (100 Ohm.m) resistivity blocks can be distinguished. Possible improvement of the algorithm includes (i) use more efficient 3D MT forward modeling program to calculate or to approximate the misfit and (ii) use of more powerful computer combined with the compiler capable of using multi-cores and / or multi-processors.
3-D MAGNETOTELLURIC INVERSION USING MARKOV CHAIN ALGORITHM
In the Bayesian inference, the solution of a geophysical inverse problem is defined by the posterior probability density function of earth model given the observed data. By discretizing the model space, the posterior probability density function is evaluated using samples drawn from the multi-dimensional model space. The sequence of models follows a Markov chain with the transition probability serving as the sampling probability. The algorithm is used to resolve a 3-D magnetotelluric inverse problem. The 3-D heterogeneity is approximated by a thin sheet model with variable conductances. Inversions of synthetic data demonstrate the effectiveness of the proposed method in recovering the true structure.