The application of cokriging using an improved Markov model

Normally cokriging, which is extended by kriging to take into account extra information and viewed as an unbiased prediction method with minimum prediction variance, integrates the information carried by a secondary variable related to the primary variable being estimated. The linear model of coregionalization (LMC) and the Markov model 1 (MM1) are proposed for cokriging to fulfill the integration of the primary variable and the secondary one. The main limitation of LMC is the requirement of modeling a positive definite cross covariance matrix for both primary and secondary variables, which cannot be solved by original cokriging. Although MM1 is a reasonable model if the primary variable is defined on the same or a larger volume support than the secondary one, allowing it to screen the influence of further away data of the primary variable; consider the case of a secondary variable defined on a much larger support than the primary variable, the MM1 is not appropriate. Then an improved Markov model 2 (MM2) for such a case is presented to meet the above condition. The MM2 screening hypothesis indicates that the secondary datum screens the influence of all further away secondary data on primary datum. Experimental results show that cokriging under the MM2 is practical when a secondary variable is defined on a much larger support than the primary variable.