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.
Type de document :
Article dans une revue
Mathematical Geosciences, Springer Verlag, 2014, 46, pp.133-147. 〈10.1007/s11004-013-9492-z〉
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Contributeur : Christian Lantuéjoul <>
Soumis le : vendredi 19 mai 2017 - 09:06:25
Dernière modification le : vendredi 27 juillet 2018 - 12:12:59




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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