Data Configurations and the Cokriging System: Simplification by Screen Effects
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Data Configurations and the Cokriging System: Simplification by Screen Effects A. Subramanyam · H.S. Pandalai
Received: 28 January 2006 / Accepted: 25 January 2008 / Published online: 14 March 2008 © International Association for Mathematical Geology 2008
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 twodimensional 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. Keywords Simple cokriging · Data configuration · Screen effect · Cokriging neighbourhood · Markov models
1 Introduction Theoretical models that permit simplification of large cokriging systems have received attention in recent literature (Chiles and Delfiner 1999; Journel 1999; A. Subramanyam · H.S. Pandalai () Department of Earth Sciences, Indian Institute of Technology (Bombay), Powai, Mumbai 400076, India e-mail: [email protected]
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Math Geosci (2008) 40: 425–443
Shmaryan and Journel 1999; Rivoirard 2001, 2002, 2004; Subramanyam and Pandalai 2004). Simplifications of cokriging systems occur as a result of the covariance structure and the configuration of the multivariate data. For example, in the case of isotopic data, simple cokriging reduces to simple kriging under the autokrigeability criterion (Matheron 1979; Wackernagel 1995; Subramanyam and Pandalai 2004). Other examples of simplifications in the cokriging neighbourhood that are found in the literature include the collocated or strictly collocated, multicollocated and dislocated cokriging (Xu et al. 1992; Chiles and Delfiner 1999; Rivoirard 2001, 2004). A closely related technique used to incorporate information from auxiliary variables is kriging with external drift (Chiles and Delfiner 1999; Rivoirard 2002). The term “cokriging neighbourhood” is used here as in Rivoirard (2004) to mean the data available for prediction and the term “simplified cokriging configurati
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