Abstract
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.
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References
Carr, J., Myers, D. E., and Glass, C., 1985, Co-Kriging: A Computer Program: Computers and Geosciences, v. 11, p. 111–127.
Clark, I., Basinger, K., and Harper, W., 1989, MUCK—A Novel Approach to Co-Kriging.in 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.
Myers, D. E., 1982, Matrix Formulation of Cokriging: Math. Geol., v. 14, p. 249–257.
Myers, D. E., 1983, Estimation of Linear Combinations and Cokriging: Math. Geol., v. 15, p. 633–637.
Myers, D. E., 1984, Cokriging: New Developments,in G. Verly et al., (Eds.), Geostatistics for Natural Resource Characterization: D. Reidel, Dordrecht.
Myers, D. E., 1985, Co-Kriging: Methods and Alternatives.in P. Glaeser, (Ed.), The Role of Data in Scientific Progress: Elsevier, New York.
Myers, D. E., 1988a, Some Aspects of Multivariate Analysis.in C. F. Chung et al. (Eds.), Quantitative Analysis of Mineral and Energy Resources: D. Reidel, Dordrecht, p. 669–687.
Myers, D. E., 1988b, Multivariate Geostatistics for Environmental Monitoring: Sciences de la Terre, v. 27, p. 411–428.
Myers, D. E., 1988c, Interpolation with Positive Definite Functions: Sciences de la Terre, v. 28, p. 251–265.
Myers, D. E., 1989, Vector Conditional Simulation.in M. Armstrong (Ed.), Geostatistics: D. Reidel, Dordrecht, p. 283–293.
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Myers, D.E. Pseudo-cross variograms, positive-definiteness, and cokriging. Math Geol 23, 805–816 (1991). https://doi.org/10.1007/BF02068776
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DOI: https://doi.org/10.1007/BF02068776