Markov chain Monte Carlo (McMC) is a technique to sample the posterior distributions in order to quantify the uncertainty and update our knowledge about the model parameters. However, this technique is computationally costly. Therefore, it is frequently combined with a cheap-to-evaluate proxy model. Building an efficient and accurate proxy model using one-shot sampling method (such as Latin-Hypercube) is a challenging task as we do not know a prior the best sample locations and the number of required samples to tune our proxy model. In this paper, we present a novel adaptive sampling techniques using LOLA-Voronoi and Expected Improvement techniques to sequentially update our proxy (here ordinary Kriging model) using best sampling locations and density. This algorithm is used to balance between the exploration and exploitation to create an accurate proxy model for the IC fault model’s misfit function. The results show a large improvement comparing to the one-shot Latin-Hypercube design. The built proxy is then employed to reduce the computational cost of McMC process to find the posterior distributions of the model parameters.


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  1. Christie, M., Demyanov, V., and Erbas, D.
    , 2006, Uncertainty quantification for porous media flows: Journal of Computational Physics, 217(1), p. 143–158. http://dx.doi.org/http://dx.doi.org/10.1016/j.jcp.2006.01.026.
    [Google Scholar]
  2. Crombecq, K., Tommasi, L.D., Gorissen, D., and Dhaene, T.
    , 2009, A novel sequential design strategy for global surrogate modeling, Proceedings of the 2009 Winter Simulation Conference (WSC), p. 731–742. http://dx.doi.org/10.1109/WSC.2009.5429687.
    [Google Scholar]
  3. Gelman, A., and Rubin, D.B.
    , 1992, Inference from Iterative Simulation Using Multiple Sequences: Statistical Science, 7(4), p. 457–472
    [Google Scholar]
  4. Jones, D.
    , 2001, A Taxonomy of Global Optimization Methods Based on Response Surfaces: Journal of Global Optimization, 21(4), p. 345–383. http://dx.doi.org/10.1023/A:1012771025575.
    [Google Scholar]
  5. Mariethoz, P.G., and Caers, P.J.
    , 2014, Multiple-point Geostatistics: Stochastic Modeling with Training Images, Wiley, 376 p
    [Google Scholar]
  6. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E.
    , 1953, Equation of State Calculations by Fast Computing Machines: The Journal of Chemical Physics, 21(6), p. 1087–1092. http://dx.doi.org/ doi: 10.1063/1.1699114.
    https://doi.org/10.1063/1.1699114 [Google Scholar]
  7. Privault, N.
    , 2013, Understanding Markov Chains: Examples and Applications, SpringerSingapore
    [Google Scholar]
  8. Rock Flow Dynamics
    , 2016, tNavigator Reservoir Simulator’s user manual (v.4.2.4)
    [Google Scholar]
  9. Sambridge, M.
    , 1999, Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space: Geophysical Journal International, 138(2), p. 479–494. http://dx.doi.org/10.1046/j.1365-246X.1999.00876.x.
    [Google Scholar]
  10. Santner, T.J., Williams, B.J., and Notz, W.I.
    , 2014, The Design and Analysis of Computer Experiments, Springer, 300 p
    [Google Scholar]
  11. Tavassoli, Z., Carter, J.N., and King, P.R.
    , 2005, An analysis of history matching errors: Computational Geosciences, 9(2), p. 99–123. http://dx.doi.org/10.1007/s10596-005-9001-7.
    [Google Scholar]
  12. van der Herten, J., Couckuyt, I., Deschrijver, D., and Dhaene, T.
    , 2015, A Fuzzy Hybrid Sequential Design Strategy for Global Surrogate Modeling of High-Dimensional Computer Experiments: SIAM Journal on Scientific Computing, 37(2), p. A1020–A1039. http://dx.doi.org/10.1137/140962437.
    [Google Scholar]
  13. Vrugt, J.A.
    , 2016, Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation: Environmental Modelling & Software, 75, p. 273–316. http://dx.doi.org/http://dx.doi.org/10.1016/j.envsoft.2015.08.013.
    [Google Scholar]
  14. Vrugt, J.A., ter Braak, C.J.F., Diks, C.G.H., Robinson, B.A., Hyman, J.M., and Higdon, D.
    , 2009, Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling: nternational Journal of Nonlinear Sciences and Numerical Simulation, 10(3), p. 273–290
    [Google Scholar]
  15. Yang, C., Nghiem, L., Erdle, J., Moinfar, A., Fedutenko, E., Li, H., Mirzabozorg, A., and Card, C.
    , 2015, An Efficient and Practical Workflow for Probabilistic Forecasting of Brown Fields Constrained by Historical Data, paper SPE 175122-MS, presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, USA. http://dx.doi.org/10.2118/175122–MS.
    [Google Scholar]

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