Mathematical Geology

, Volume 23, Issue 6, pp 805–816 | Cite as

Pseudo-cross variograms, positive-definiteness, and cokriging

  • Donald E. Myers


Cokriging allows the use of data on correlated variables to be used to enhance the estimation of a primary variable or more generally to enhance the estimation of all variables. In the first case, known as the undersampled case, it allows data on an auxiliary variable to be used to make up for an insufficient amount of data. Original formulations required that there be sufficiently many locations where data is available for both variables. The pseudo-cross-variogram, introduced by Clark et al. (1989), allows computing a related empirical spatial function in order to model the function, which can then be used in the cokriging equations in lieu of the cross-variogram. A number of questions left unanswered by Clark et al. are resolved, such as the availability of valid models, an appropriate definition of positive-definiteness, and the relationship of the pseudo-cross-variogram to the usual cross-variogram. The latter is important for modeling this function.

Key words

cokriging cross-variograms positive-definiteness undersampled 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Carr, J., Myers, D. E., and Glass, C., 1985, Co-Kriging: A Computer Program: Computers and Geosciences, v. 11, p. 111–127.Google Scholar
  2. Clark, I., Basinger, K., and Harper, W., 1989, MUCK—A Novel Approach to B. E. Buxton (Ed.), Proceedings of the Conference on Geostatistical, Sensitivity, and Uncertainty: Methods for Ground-Water Flow and Radionuclide Transport Modeling: Batelle Press, Columbus, p. 473–494.Google Scholar
  3. Myers, D. E., 1982, Matrix Formulation of Cokriging: Math. Geol., v. 14, p. 249–257.Google Scholar
  4. Myers, D. E., 1983, Estimation of Linear Combinations and Cokriging: Math. Geol., v. 15, p. 633–637.Google Scholar
  5. Myers, D. E., 1984, Cokriging: New Developments,in G. Verly et al., (Eds.), Geostatistics for Natural Resource Characterization: D. Reidel, Dordrecht.Google Scholar
  6. Myers, D. E., 1985, Co-Kriging: Methods and P. Glaeser, (Ed.), The Role of Data in Scientific Progress: Elsevier, New York.Google Scholar
  7. Myers, D. E., 1988a, Some Aspects of Multivariate C. F. Chung et al. (Eds.), Quantitative Analysis of Mineral and Energy Resources: D. Reidel, Dordrecht, p. 669–687.Google Scholar
  8. Myers, D. E., 1988b, Multivariate Geostatistics for Environmental Monitoring: Sciences de la Terre, v. 27, p. 411–428.Google Scholar
  9. Myers, D. E., 1988c, Interpolation with Positive Definite Functions: Sciences de la Terre, v. 28, p. 251–265.Google Scholar
  10. Myers, D. E., 1989, Vector Conditional M. Armstrong (Ed.), Geostatistics: D. Reidel, Dordrecht, p. 283–293.Google Scholar

Copyright information

© International Association for Mathematical Geology 1991

Authors and Affiliations

  • Donald E. Myers
    • 1
  1. 1.Department of MathematicsUniversity of ArizonaTucson

Personalised recommendations