Yj. Ren et al., SIMULATION OF MULTIVARIATE GAUSSIAN FIELDS CONDITIONED BY REALIZATIONS OF THE FIELDS AND THEIR DERIVATIVES, Journal of applied mechanics, 63(3), 1996, pp. 758-765
This paper investigates conditional simulation technique of multivaria
te Gaussian random fields by stochastic interpolation technique. For t
he first time in the literature a situation is studied when the random
fields are conditioned not only by a set of realizations of the field
s, but also by a set of realizations of their derivatives. The kriging
estimate of multivariate Gaussian field is proposed, which takes into
account both the random field as well as its derivative. Special cond
itions are imposed on the kriging estimate to determine the kriging we
ights. Basic formulation for simulation of conditioned multivariate ra
ndom fields is established. As a particular case of uncorrelated compo
nents of multivariate field without realizations of the derivative of
the random field, the present formulation includes that of univariate
field given by Hoshiya. Examples of a univariate field and a three com
ponent field are elucidated and some numerical results are discussed.
It is concluded that the information on the derivatives may significan
tly alter the results of the conditional simulation.