Abstract
Large cokriging systems arise in many situations and are difficult to handle in practice. Simplifications such as simple kriging, strictly collocated and multicollocated cokriging are often used and models under which such simplifications are, in fact, equivalent to cokriging have recently received attention. In this paper, a two-dimensional second-order stationary random process with known mean is considered and the redundancy of certain components of the data at certain locations vis-à-vis the solution to the simple cokriging system is examined. Conditions for the simple cokriging weights of these components at these locations are set to zero. The conditions generalise the notion of the autokrigeability coefficient and can, in principle, be applied to any data configuration. In specific sampling situations such as the isotopic and certain heterotropic configurations, models under which simple kriging, strictly collocated, multicollocated and dislocated cokriging are equivalent to simple cokriging are readily identified and results already available in the literature are obtained. These are readily identified and the results are already available in the literature. The advantage of the approach presented here is that it can be applied to any data configuration for analysis of permissible simplifications in simple cokriging.
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References
Chiles JP, Delfiner P (1999) Geostatistics: Modeling spatial uncertainity. Wiley, New York, 659 p
Journel A (1999) Markov models for cross-covariances. Math Geol 31(8):955–964
Matheron G (1979) Recherche de simplification dans une probleme de cokrigage. Technical report N-628, Centre de Geostatistique, Fontainebleau, France, 19 p
Myers DE (1982) Matrix formulation of cokriging. Math Geol 14(3):249–257
Rivoirard J (2001) Which models for collocated cokriging? Math Geol 33(2):117–131
Rivoirard J (2002) On the structural link between variables in kriging with external drift. Math Geol 34(7):797–808
Rivoirard J (2004) On some simplifications of the cokriging neighbourhood. Math Geol 36(8):899–915
Shmaryan LE, Journel A (1999) Two Markov models and their applications. Math Geol 31(8):965–988
Subramanyam A, Pandalai HS (2004) On the equivalence of the cokriging and kriging systems. Math Geol 36(4):507–523
Wackernagel H (1995). Multivariate geostatistics: An introduction with applications, 3rd edn. Springer, Berlin, 256 p
Xu W, Tran TT, Srivastava RM, Journel AG (1992) Integrating seismic data in reservoir modeling: The collocated cokriging alternative. SPE paper 24742, 67th annual technical conference and exhibition, pp 833–842
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Subramanyam, A., Pandalai, H.S. Data Configurations and the Cokriging System: Simplification by Screen Effects. Math Geosci 40, 425–443 (2008). https://doi.org/10.1007/s11004-008-9153-9
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DOI: https://doi.org/10.1007/s11004-008-9153-9