A FAST AND EXACT METHOD FOR MULTIDIMENSIONAL GAUSSIAN STOCHASTIC SIMULATIONS - EXTENSION TO REALIZATIONS CONDITIONED ON DIRECT AND INDIRECTMEASUREMENTS

Recently Dietrich and Newsam [1993] derived a fast and exact method fo r generating unconditional realizations of a stationary, multidimensio nal Gaussian random field on a rectangular sampling grid. The method i s based on embedding the random field covariance matrix in a larger po sitive definite matrix with circulant/block circulant structure. The c irculant structure of the embedding matrix means that a square root of this matrix can be efficiently computed by the fast Fourier transform ; realizations are then generated by multiplying vectors of white nois e by this square root. This paper extends the method to generating rea lizations conditioned on direct and/or indirect measurements of the fi eld collected at an arbitrary set of scattered data points.