SIMULATION OF NORMAL DISTRIBUTED SMOOTH FIELDS BY KARHUNEN-LOEVE EXPANSION IN COMBINATION WITH KRIGING

Simulation of multigaussian stochastic fields can be made after a Karh unen-Loeve expansion of a given covariance function. This method is al so called simulation by Empirical Orthogonal Functions. The simulation s are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues deri ved from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined var iance error, turns out to be a cardinal question. Some ordinary analyt ical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extreme ly quick convergence to 99.5% of total variance for the 2nd order expo nential ('gaussian') covariance function, while the opposite is true f or the Ist order exponential covariance function. Due to these converg ence characteristics, the Karhunen-Loeve method is most suitable for s imulating smooth fields with 'gaussian' shaped covariance functions. P ractical applications of Karhunen-Loeve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we sugges t interpolation by kriging and limits for reproduction of the predefin ed covariance functions are evaluated.