Reminders on the Conditioning Kriging

Abstract

Conditioning simulations by using kriging was proposed by G. Matheron at the start of the 70s. The following presentation only recalls results that should be already well-known.

Simulation methods enable us to construct realizations of RF having a fixed covariance K. In practice, the values z (x_α) at the data points x_α are known and we dictate that at these points the RF Z and its simulations must coincide. The conditioning method by kriging makes it possible to carry out a conditional simulation into two steps: construction of a nonconditional simulation, then the conditioning kriging. In the general case, simulations obtained in this way have the specified covariance K and are such that at the data points t(x_α) = z(x_α). In addition, for a RF having multigaussian distribution, the conditional distribution Z(x)|Z(x_α1), …, Z(x_αn) is reproduced.