Full cokriging of Z1 accounting for secondary variables Z2,..., ZNv requires the inference of all covariance functions (,) Ci, j(,) between variables i and j. This very difficult task can be eased by considering only the colocated secondary variables. The underlying hypotheses is that the colocated value screens out the influence of further away data. In this situation, only the covariances C1, j need be inferred. The MM1 approximation alleviate the modeling effort further with the following approximation:
where Ci, j(0) = Ci, j(,) = Ci, j(,)
This approximation is acceptable if the support of the secondary variables is not larger than the support of the primary variable Z1. For example, if Z1 is rock porosity and Z2 rock permeability, MM1 approximation is acceptable. It would not be if Z2 were seismic amplitude, because seismic amplitude is generally defined on a much larger scale than porosity.
|covariance||is a model of Covariance|
|matrix||is an object that represents a matrix. Expression mat(i,j) must be valid and return element (i,j) of the matrix (i and j are greater than or equal to 1), and the matrix must have a copy constructor. The elements of matrix are of type convertible to double.|