Advertisement

Mathematical Geology

, Volume 25, Issue 8, pp 1015–1026 | Cite as

On the pseudo cross-variogram

  • A. Papritz
  • H. R. Künsch
  • R. Webster
Articles

Abstract

Normal cross-variograms cannot be estimated from data in the usual way when there are only a few points where both variables have been measured. But the experimental pseudo cross-variogram can be computed even where there are no matching sampling points, and this appears as its principal advantage. The pseudo cross-variogram may be unbounded, though for its existence the intrinsic hypothesis alone is not a sufficient stationarity condition. In addition the differences between the two random processes must be second order stationary. Modeling the function by linear coregionalization reflects the more restrictive stationarity condition: the pseudo cross-variogram can be unbounded only if the unbounded correlation structures are the same in all variograms. As an alternative to using the pseudo cross-variogram a new method is presented that allows estimating the normal cross variogram from data where only one variable has been measured at a point.

Key words

cokriging coregionalization cross-correlation temporal change undersampling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atkinson, P. M., Webster, R., and Curran, P. J., 1992, Cokriging with Ground-Based Radiometry: Remote Sensing of Environment, v. 41, p. 45–60.Google Scholar
  2. Clark, I., Basinger, K. L., and Harper, W. V., 1989, MUCK—a Novel Approach to Cokriging.in B. E. Buxton (Ed.),Proceedings of the Conference on Geostatistical, Sensitivity, and Uncertainty Methods for Ground-Water Flow and Radionuclide Transport Modeling: Battelle Press, Columbus, p. 473–493.Google Scholar
  3. Delfiner, P., 1976, Linear Estimation of Non Stationary Spatial Phenomena.in M. Guarascio, M. David, and C. Huijbregts (Eds.),Advanced Geostatistics in the Mining Industry: D. Reidel Publishing Company, Dordrecht, p. 49–68.Google Scholar
  4. Goulard, M., and Voltz, M., 1992, Linear Coregionalization Model: Tools for Estimation and Choice of Cross-Variogram Matrix: Math. Geol., v. 24, p. 269–286.Google Scholar
  5. Journel, A. G., and Huijbregts, C. J., 1978,Mining Geostatistics: Academic Press, London, 600 p.Google Scholar
  6. Matheron, G., 1979, Recherche de Simplification dans un Problème de Cokrigeage: Publication N-628, Centre de Géostatistique, Ecole des Mines de Paris, Fontainebleau. 19 p.Google Scholar
  7. Myers, D. E., 1982, Matrix Formulation of Co-Kriging: Math. Geol., v. 14, p. 249–257.Google Scholar
  8. Myers, D. E., 1983, Estimation of Linear Combinations and Co-Kriging: Math. Geol., v. 15, p. 633–637.Google Scholar
  9. Myers, D. E., 1991, Pseudo-Cross Variograms, Positive-Definiteness, and Cokriging: Math. Geol., v. 23, p. 805–816.Google Scholar
  10. Papritz, A., and Flühler, H., in press, Temporal Change of Spatially Autocorrelated Soil Properties: Optimal Estimation by Cokriging: Geoderma.Google Scholar
  11. Priestley, M. B., 1981,Spectral Analysis and Time Series: Academic Press, London, 890 p.Google Scholar
  12. Wackernagel, H., 1988, Geostatistical Techniques for Interpreting Multivariate Spatial Information.in C. F. Chung, A. G. Fabbri, and R. Sinding-Larsen (Eds.),Quantitative Analysis of Mineral and Energy Resources: D. Reidel Publishing Company, Dordrecht, p. 393–409.Google Scholar
  13. Wackernagel, H., in press, Cokriging vs. Kriging in Regionalized Multivariate Data Analysis: Geoderma.Google Scholar

Copyright information

© International Association for Mathematical Geology 1993

Authors and Affiliations

  • A. Papritz
    • 1
  • H. R. Künsch
    • 2
  • R. Webster
    • 1
  1. 1.Institute of Terrestrial EcologyETH Zürich, Soil PhysicsSchlierenSwitzerland
  2. 2.Seminar for StatisticsETH ZürichZürichSwitzerland

Personalised recommendations