An Interpolation Method Using an Improved Markov Model

Reconstruction always uses some kinds of interpolation methods and its accuracy can be improved by using multiple data with different dimensions, resolutions or types. COSGSIM (sequential Gaussian co-simulation) has been a widely used geostatistical interpolation method and is introduced into other fields for prediction and reconstruction in recent years because it can estimate unknown values by multiple known data including known primary data (hard data) and some auxiliary data (soft data). The LMC (linear model of coregionalization) and the original MM1 (Markov model 1) are proposed for COSGSIM to fulfill the integration of the primary data and auxiliary data. The main limitation of LMC is the requirement of modeling a positive definite cross covariance matrix for different variables. MM1 is a reasonable model only when the primary data are defined on the larger volume support than the auxiliary data. Then MM2 (Markov model 2) for such a case is presented to meet the above condition in an improved Markov model. MM2 screening hypothesis indicates that an auxiliary datum screens the influence of any other auxiliary datum on its primary collocated datum. Experimental results show that the interpolated results of COSGSIM under MM2 are much better than those of COSGSIM under MM1 if the primary data are defined on a larger volume support.