Abstract
Markov models based on various data screening hypotheses are often used because they reduce the statistical inference burden. In the case of co-located cokriging, the commonly used Markov model results in the cross-covariance being proportional to the primary covariance. Such model is inappropriate in the presence of a smoothly varying secondary variable defined on a much larger volume support than the primary variable. For such cases, an alternative Markov screening hypothesis is proposed that results in a more continuous cross-covariance proportional to the secondary covariance model. A parallel development of both Markov models is presented. A companion paper provides a comparative application to a real data set.
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REFERENCES
Almeida, A. S., 1993, Joint simulation of multiple variables with a Markov-type coregionalization model: Unpublished doctoral dissertation, Stanford University, Stanford, 199 p.
Almeida, A. S., and Journel, A. G., 1996, Joint simulation of multiple variables with a Markov-type coregionalization model: Math. Geology, v. 26, no. 5, p. 565–588.
Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation: Oxford Press, New York, 483 p.
Goulard, M., and Voltz, M., 1992, Linear coregionalization model, Tools for estimation and choice of cross-variogram matrix: Math. Geology, v. 24, no. 3, p. 269–286.
Journel, A. G., and Huijbregts, Ch., 1978, Mining Geostatistics: Academic Press, New York, 600 p.
Shmaryan, L. E., and Journel, A. G., 1999, Two Markov models and their applications: Math. Geology, v. 31, no. 8, p. 965–988.
Yao, T. 1999, Non-parametric crosscovariance modeling as exemplified by soil heavy metal concentrations from the Swiss Jura: Geoderma, v. 88, p. 13–38.
Yao, T., and Journel, A. G., 1998, Automatic modeling of (cross)covariance tables using Fast Fourier Transform: Math. Geology, v. 30, no. 6, p. 589–615.
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Journel, A.G. Markov Models for Cross-Covariances. Mathematical Geology 31, 955–964 (1999). https://doi.org/10.1023/A:1007553013388
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DOI: https://doi.org/10.1023/A:1007553013388