Mathematical Geology

, Volume 34, Issue 7, pp 797–808

# On the Structural Link Between Variables in Kriging with External Drift

• Jacques Rivoirard
Article

## Abstract

Kriging with external drift allows one to estimate a target variable, accounting for a densely sampled auxiliary variable. Contrary to cokriging, kriging with external drift does not make explicit the structural link between target variable and auxiliary variable, for the latter is considered to be deterministic. In this paper, we show that kriging with external drift assumes implicitly an absence of spatial dependence between the auxiliary variable and the residual of the linear regression of target variable on auxiliary variable at same point. This is the simple model with orthogonal residual, where cokriging is collocated and coincides with kriging of the residual. In this model, the cross-structure is proportional to the structure of the auxiliary variable, and the linear regression of target variable on auxiliary variable does not depend on the support.

cokriging Markov models regression residual

## REFERENCES

1. Almeida, A., and Journel, A., 1994, Joint simulation of multiple variables with a Markov-type coregionalization model: Math. Geol., v. 26, no. 5, p. 565–588.Google Scholar
2. Bordessoule, J. L., Demange, C., and Rivoirard, J., 1989, Using an orthogonal residual between ore and metal to estimate in-situ resources, inArmstrong, M., ed., Geostatistics: Kluwer, Dordrecht, v. 2, p. 923–934.Google Scholar
3. Chilès, J.-P., and Delfiner, P., 1999, Geostatistics: Modeling spatial uncertainty, Wiley, New York, 695 p.Google Scholar
4. Goovaerts, P., 1997, Geostatistics for natural resources evaluation, Oxford University Press, New York, 483 p.Google Scholar
5. Journel, A., 1999, Markov models for cross-covariances: Math. Geol., v. 31, no. 8, p. 955–964.Google Scholar
6. Rivoirard, J., 2001, Which models for collocated cokriging?: Math. Geol., v. 33, no. 2, p. 117–131.Google Scholar
7. Shmaryan, L. E., and Journel, A., 1999, Two Markov models and their application: Math. Geol., v. 31, no. 8, p. 965–988.Google Scholar
8. Wackernagel, H., 1995, Multivariate geostatistics: An introduction with applications, Springer, Berlin, 256 p.Google Scholar
9. Xu, W., Tran, T. T., Srivastava, R. M., and Journel, A. G., 1992, Integrating seismic data in reservoir modeling: The collocated cokriging alternative. 67th Annual Technical Conference and exhibition, SPE paper 24742, p. 833-884.Google Scholar