https://hal-mines-paristech.archives-ouvertes.fr/hal-01524884Emery, XavierXavierEmeryDepartment of Mining Engineering and Advanced Mining Technology Center - Department of Mining Engineering and Advanced Mining Technology Center - UCHILE - Universidad de Chile = University of Chile [Santiago]Lantuéjoul, ChristianChristianLantuéjoulGEOSCIENCES - Centre de Géosciences - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettresCan a Training Image Be a Substitute for a Random Field Model?HAL CCSD2014Multiple-point simulation · Stationarity · Ergodicity · Integral range[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]Lantuéjoul, Christian2017-05-19 09:06:252022-10-22 05:19:512017-05-19 09:06:25enJournal articles10.1007/s11004-013-9492-z1In most multiple-point simulation algorithms, all statistical features areprovided 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, thestochastic nature of multiple-point simulation is questionable. This issue is addressedby considering the case of a sequential simulation algorithm applied to a binary TIthat 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 ofthe random field (supported by the simulation domain) are retrieved as an averageover a large number of outcomes. The results are as follows. It is demonstrated thatmultiple-point simulation performs well whenever the TI is a complete (infinitelylarge) realization of a stationary, ergodic random field. As soon as the TI is restrictedto a limited domain, the statistical features cannot be obtained exactly, but integralrange techniques make it possible to predict how much the TI should be extendedto 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 thealgorithm, which arise when no conditioning template can be found in the TI.