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Can a Training Image Be a Substitute for a Random Field Model?

Abstract : In most multiple-point simulation algorithms, all statistical features are provided by one or several training images (TI) that serve as a substitute for a ran- dom field model. However, because in practice the TI is always of finite size, the stochastic nature of multiple-point simulation is questionable. This issue is addressed by considering the case of a sequential simulation algorithm applied to a binary TI that is a genuine realization of an underlying random field. At each step, the algo- rithm uses templates containing the current target point as well as all previously sim- ulated points. The simulation is validated by checking that all statistical features of the random field (supported by the simulation domain) are retrieved as an average over a large number of outcomes. The results are as follows. It is demonstrated that multiple-point simulation performs well whenever the TI is a complete (infinitely large) realization of a stationary, ergodic random field. As soon as the TI is restricted to a limited domain, the statistical features cannot be obtained exactly, but integral range techniques make it possible to predict how much the TI should be extended to approximate them up to a prespecified precision. Moreover, one can take advan- tage of extending the TI to reduce the number of disruptions in the execution of the algorithm, which arise when no conditioning template can be found in the TI.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01524884
Contributor : Christian Lantuéjoul <>
Submitted on : Friday, May 19, 2017 - 9:06:25 AM
Last modification on : Wednesday, October 14, 2020 - 3:52:18 AM

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Xavier Emery, Christian Lantuéjoul. Can a Training Image Be a Substitute for a Random Field Model?. Mathematical Geosciences, Springer Verlag, 2014, 46, pp.133-147. ⟨10.1007/s11004-013-9492-z⟩. ⟨hal-01524884⟩

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