by **Didier Renard** » Tue May 15, 2018 3:20 pm

Hi Mathias,

You rmethodology is the usual one. However let us mention that, when you run Gibbs (iterative method), you essentially generate several simulations (different trajectories) which will give several sets of simulated outcomes at each site where some inequality is defined.

Then we usually average them out in order to produce a mean value that is called a conditional expectation.

Then, if your aim is to produce an estimation over the field, it is OK to use this average as a hard data for the kriging step (this is what is done in Isatis for example). However, note that this operation generates a strange result: the variance os estimation error will zero at those inequality point, although the data is not as hard.

Morever, I warn you that using this conditional expectation would not be correct if you wanted to run simulations conditioned by hard data and inequality data, as reducing the set of simulated values (at inequalities) to a conditional expectation dramatically reduces the variability. Instead, you should use each set of simulated values at inequalities to condition the simulation over the field.

Hope my explanations are clear enough.