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Mathematical Geology

, Volume 26, Issue 6, pp 733–752 | Cite as

Robustness of noise filtering by kriging analysis

  • G. Bourgault
Articles

Abstract

In geostatistics, factorial kriging is often proposed to filter noise. This filter is built from a linear model which is ideally suited to a Gaussian signal with additive independent noise. Robustness of the performance of factorial kriging is evaluated in less congenial situations. Three different types of noise are considered all perturbing a lognormally distributed signal. The first noise model is independent of the signal. The second noise model is heteroscedastic; its variance depends on the signal, yet noise and signal are uncorrelated. The third noise model is both heteroscedastic and linearly correlated with the signal. In ideal conditions, exhaustive sampling and additive independent noise, factorial kriging succeeds to reproduce the spatial patterns of high signal values. This score remains good in presence of heteroscedastic noise variance but falls quickly in presence of noise-to-signal correlation as soon as the sample becomes sparser.

Key words

noise filtering signal heteroscedasticity factorial kriging data sparsity 

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References

  1. Carr, J. R., 1990, Application of Spatial Filter Theory to Kriging: Math. Geol., v. 22, n. 8, p. 1063–1079.Google Scholar
  2. Deutsch, C. V., and Journel, A. G., 1992,GSLIB Geostatistical Software Library and User's Guide: Oxford Press, 340 p.Google Scholar
  3. Galli, A., Gerdil-Neuillet, F., and Dadou, C., 1984, Factorial Kriging Analysis: A Substitute to Spectral Analysis of Magnetic Data,in G. Verly et al. (Eds.),Geostatistics for Natural Resources Characterization: p. 543–557.Google Scholar
  4. Journel, A. G., and Huijbregts, Ch. J., 1978,Mining Geostatistics: Academic Press, New York, 600 p.Google Scholar
  5. Koch, G. S., and Link, R. F., 1970,Statistical Analysis of Geological Data: Wiley and Sons, 375 p.Google Scholar
  6. Ma, Y. Z., and Royer, J. J., 1988, Local Geostatistical Filtering Application to Remote Sensing,in Geomathematics and Geostatistics Analysis Applied to Space and Time Dependent Data (Vol. 27): Sciences de la Terre, Série Informatique, Nancy, p. 17–36.Google Scholar
  7. Matheron, G., 1982,Pour une Analyse Krigeante des Données Régionalisées, N-732: Centre de Géostatistique et de Morphologie Mathématique, Fontainebleau, 22 p.Google Scholar
  8. Sandjivy, L., and Galli, A., 1985,Analyse Krigeante et Analyse Spectrale (Vol. 21): Sciences de la Terre, Série Informatique Géologique, p. 115–124.Google Scholar

Copyright information

© International Association for Mathematical Geology 1994

Authors and Affiliations

  • G. Bourgault
    • 1
  1. 1.Department of Geology and Environmental SciencesStanford UniversityUSA

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