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