Computational Geosciences

, Volume 12, Issue 4, pp 573–591 | Cite as

Estimation or simulation? That is the question

  • Jorge Kazuo Yamamoto
Original paper


The issue of smoothing in kriging has been addressed either by estimation or simulation. The solution via estimation calls for postprocessing kriging estimates in order to correct the smoothing effect. Stochastic simulation provides equiprobable images presenting no smoothing and reproducing the covariance model. Consequently, these images reproduce both the sample histogram and the sample semivariogram. However, there is still a problem, which is the lack of local accuracy of simulated images. In this paper, a postprocessing algorithm for correcting the smoothing effect of ordinary kriging estimates is compared with sequential Gaussian simulation realizations. Based on samples drawn from exhaustive data sets, the postprocessing algorithm is shown to be superior to any individual simulation realization yet, at the expense of providing one deterministic estimate of the random function.


Ordinary kriging Smoothing effect Stochastic simulation Sequential Gaussian simulation 


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  1. 1.
    Caers, J.: Adding local accuracy to direct sequential simulation. Math. Geol. 32, 815–850 (2000)CrossRefGoogle Scholar
  2. 2.
    Deutsch, C.V.: Correcting for negative weights in ordinary kriging. Comput. & Geosci. 22, 765–773 (1996)CrossRefGoogle Scholar
  3. 3.
    Deutsch, C.V., Journel, A.G.: GSLIB: Geostatistical Software Library and User’s Guide. Oxford University Press, New York (1992)Google Scholar
  4. 4.
    Goovaerts, P.: Geostatistics for Natural Resource Evaluation. Oxford University Press, New York (1997)Google Scholar
  5. 5.
    Goovaerts, P.: Accounting for estimation optimality criteria in simulated annealing. Math. Geol. 30, 511–534 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Guertin, K.: Correcting conditional bias. In: Verly, G., David, M., Journel, A.G., Marechal, A. (eds.) Geostatistics for Natural Resources Characterization, Part 1: D, pp. 245–260. Reidel, Dordrecht (1984)Google Scholar
  7. 7.
    Journel, A.G., Rao, S.E.: Deriving Conditional Distributions from Ordinary Kriging. Stanford Center for Reservoir Forecasting, Palo Alto (1996)Google Scholar
  8. 8.
    Journel, A., Kyriakidis, P.C., Mao, S.: Correcting the smoothing effect of estimators: a spectral postprocessor. Math. Geol. 32, 787–813 (2000)CrossRefGoogle Scholar
  9. 9.
    Olea, R.: Geostatistics for Engineers and Earth Scientists. Kluwer Academic, Boston (1999)Google Scholar
  10. 10.
    Olea, R., Pawlowsky, V.: Compensating for estimation smoothing in kriging. Math. Geol. 28, 407–417 (1996)CrossRefGoogle Scholar
  11. 11.
    Press, W.H., Falennery, B.P., Tenkolsky, S.A., Vetterling, N.T.: Numerical Recipes in Pascal. Cambridge University Press, New York (1996)Google Scholar
  12. 12.
    Yamamoto, J.K.: Convex_hull—a pascal program for determining the convex hull for planar sets. Comput. & Geosci. 23, 725–738 (1997)CrossRefGoogle Scholar
  13. 13.
    Yamamoto, J.K.: An alternative measure of the reliability of ordinary kriging estimates. Math. Geol. 32, 489–509 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Yamamoto, J.K.: Correcting the smoothing effect of ordinary kriging estimates. Math. Geol. 37, 69–94 (2005)zbMATHCrossRefGoogle Scholar
  15. 15.
    Yamamoto, J.K.: On unbiased backtransform of lognormal kriging estimates. Comput. Geosci. 11, 219–234 (2007)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Environmental and Sedimentary Geology, Institute of GeosciencesUniversity of Sao PauloSao PauloBrazil

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