Mathematical Geology

, Volume 25, Issue 1, pp 41–52 | Cite as

Kriging in a finite domain

  • Clayton V. Deutsch
Articles

Abstract

Adopting a random function model {Z(u),u ε study areaA} and using the normal equations (kriging) for estimation amounts to assume that the study areaA is embedded within a infinite domain. At first glance, this assumption has no inherent limitations since all locations outsideA are of no interest and simply not considered. However, there is an interesting and practically important consequence that is reflected in the kriging weights assigned to data contiguously aligned along finite strings; the weights assigned to the end points of a string are large since the end points inform the infinite half-space beyond the string. These large weights are inappropriate when the finite string has been created by either stratigraphic/geological limits or a finite search neighborhood. This problem will be demonstrated with numerical examples and some partial solutions will be proposed.

Key words

kriging ergodicity stratigraphic limits finite domain 

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References

  1. K. Aki and P. Richards, 1980, Quantitative Seismology: W.H. Freeman and Co., San Francisco, California.Google Scholar
  2. A. Journel and C. J. Huijbregts, 1978, Mining Geostatistics: Academic Press, New York.Google Scholar
  3. G. Matheron, 1971, La Théorie des Variables Régionalisées et Ses Applications: Fasc. 5, Ecole Nat. Sup. des Mines, Paris.Google Scholar

Copyright information

© International Association for Mathematical Geology 1993

Authors and Affiliations

  • Clayton V. Deutsch
    • 1
  1. 1.Department of Applied Earth SciencesStanford UniversityStanford

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