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A fast and exact method for multidimensional Gaussian stochastic simulations: Extension to realizations conditioned on direct and indirect measurements
Author(s) -
Dietrich C. R.,
Newsam G. N.
Publication year - 1996
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/94wr02977
Subject(s) - circulant matrix , mathematics , random field , covariance matrix , matrix (chemical analysis) , covariance function , white noise , gaussian , square root , gaussian random field , gaussian process , mathematical analysis , algorithm , statistics , geometry , physics , materials science , quantum mechanics , composite material
Recently Dietnch and Newsam [1993] derived a fast and exact method for generating unconditional realizations of a stationary, multidimensional Gaussian random field on a rectangular sampling grid. The method is based on embedding the random field covariance matrix in a larger positive definite matrix with circulant/block circulant structure. The circulant 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 noise by this square root. This paper extends the method to generating realizations conditioned on direct and/or indirect measurements of the field collected at an arbitrary set of scattered data points.