Abstract
In this paper, the problem of simulating a 3-dimensional stationary, isotropic multigaussian random function with covariance C is considered. On the basis of the Central Limit Theorem, a possible procedure consists of simulating a large number of independent stationary random functions (not necessarily multigaussian) with covariance C. This procedure raises two questions:
-
i)
how to simulate a random function of covariance C? Several algorithms are possible (spectral, dilution, turning bands, tessellation, migration …). These algorithms are briefly presented and compared from various standpoints such as their range of validity and their efficiency.
-
ii)
what is the number of random functions that have to be simulated? Even if no magic number can be recommended, a helpful tool to answer this question is the Berry-Esséen theorem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alabert, F.G. (1987) “Stochastic imaging of spatial distributions using hard and soft data”, Master’s thesis, Stanford University.
Alfaro Sironvalle, M. (1979) “Etude de la robustesse des simulations de fonctions aléatoires”, Geostatistics Doctoral Thesis, School of Mines of Paris.
Bouleau, N. (1986) Probab tés de L’ingénieur, Hermann, Paris.
Feller, W. (1971) An introduction to Probability Theory and its Applications, Vol. 2, Wiley, New-York.
Freulon, X. and de Fouquet, C. (1991) “Remarques sur la pratique des bandes tournantes à 3 dimensions” , Cahiers de Géostatistique N° 1, pp. 101,117.
Freulon, X. (1992) “Conditionnement du modèle gaussien par des inégalités ou des randomisées”, Geostatistics Doctoral Thesis, School of Mines of Paris.
Jeulin, D. (1991) “Modèles morphologiques de structures aléatoires et de changement d’échelle”, Doctoral Thesis, University of Caen.
Journel, A.G. and Huijbregts, C.J. (1978) Mining Geostatistics, Academic Press, London.
Lantuéjoul, Ch. (1991) “Ergodicity and Integral Range”, Journal of Microscopy, Vol. 161–3, pp. 387–404.
Mantoglou, A. and Wilson, J.L. (1982) “The Turning Bands Method for Simulation of Random Fields Using Line Generation by A Spectral Method”, Water Res. Res., Vol. 18–5, pp. 1379–1394f.
Matérn, B. (1986) Spatial Variation, Lecture Notes in Statistics Vol. 36, Springer-Verlag, Berlin (2nd edition).
Matheron, G. (1968a) “Schéma Booléen séquentiel de partition aléatoire”, Internal Report
N-83, Centre de Morphologie Mathématique, Fontainebleau.
Matheron, G. (1968b) “Processus de renouvellement et pseudo-périodicités”, Internal Report N-71, Centre de Morphologie Mathématique, Fontainebleau.
Matheron, G. (1971) “Les polyèdres Poissonniens isotropes”, 3ème Symposium Européen sur la Fragmentation, Cannes, 5–8 octobre 1971.
Matheron, G. (1973) “The intrinsic random functions and their applications”, Adv. Appl. Prob., Vol. 5, pp. 439–468.
Matheron, G. (1984) The selectivity of the distributions and “the second principle of geostatistics”. In Verly, G. et al. (eds.) Geostatistics for natural ressources characterization, pp. 421–423, NATO ASI Series C, Vol 122, Reidel, Dordrecht.
Matheron, G. (1987) “Simulation de fonctions aléatoires admettant un variogramme concave donné”, Internal Report N-11/87, Centre de Géostatistique, Fontainebleau.
Matheron, G. (1988) Estimating and Choosing, Springer-Verlag, Berlin.
Miles, R.E. (1972) “The random division of space”, special supplement to Adv. in Applied Prob., pp. 243–266.
Rao, M.M. (1984) Probab ty Theory with Applications, Academic Press, Orlando.
Serra, J. (1968) “Fonctions aléatoires de Dilution”, Internal Report C-12, Centre de Morphologie Mathématique, Fontainebleau.
Shinozuka, M. and Jan, C.M. (1972) “Digital simulation of random processes and its applications”, J. of Sound and Vib., Vol. 25–1, pp. 111–128.
Yaglom, A.M. (1986) Correlation Theory of Stationary and related Random Functions, Springer Series in Statistics, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Lantuéjoul, C. (1994). Non Conditional Simulation of Stationary Isotropic Multigaussian Random Functions. In: Armstrong, M., Dowd, P.A. (eds) Geostatistical Simulations. Quantitative Geology and Geostatistics, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8267-4_13
Download citation
DOI: https://doi.org/10.1007/978-94-015-8267-4_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4372-6
Online ISBN: 978-94-015-8267-4
eBook Packages: Springer Book Archive