Simulation by Empirical Orthogonal Functions

Three dimensional Simulation by Empirical Orthogonal Functions

Nils-Otto Kitterød and Lars Gottschalk

Last updated March 20. 2015.
On these pages we have evaluated a simulation method based on Karhunen-Loéve expansion also called simulation by Empirical Orthogonal Functions (EOF). Our experiences so far are summarized in the conclusions. You can look at some three dimensional realizations based on 1. and 2.order exponetial covariance functions, and some of the associated three dimensional eigenfunctions, if you want to!

'Gaussian' realizations - derived from a 2.order exponential covariance funciton.

'Exponential' realizations - derived from a 1.order exponential covariance function.

Directly derived eigenfunctions - based on high density sampling of the covariance function.

Interpolated eigenfunctions - derived from spatially sparse sampling of the covariance funciton.

This case study is a part of 'The Gardermoen project, the Environment of the Subsurface' funded by the Research Council of Norway and the Norwegian Civil Aviation Authorities. We are also indebted to the Norwegian Water Resources and Energy Administration for financial support.

Nils-Otto Kitterød

key-words: Karhunen-Loéve expansion, Eigenfunctions, Empirical Orthogonal Functions, Geostatistics, Kriging