Nonparametric transformations for data correlation and integration: From theory to practice
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The purpose of this paper is two-fold. First, we introduce the use of nonparametric transformations for correlating petrophysical data during reservoir characterization. Such transformations are completely data driven and do not require an a priori functional relationship between response and predictor variables, which is the case with traditional multiple regression. The transformations are very general, computationally efficient, and can easily handle mixed data types; for example, continuous variables such as porosity, and permeability, and categorical variables such as rock type and lithofacies. The power of the nonparametric transformation techniques for data correlation has been illustrated through synthetic and field examples. Second, we use these transformations to propose a two-stage approach for data integration during heterogeneity characterization. The principal advantages of our approach over traditional cokriging or cosimulation methods are: (1) it does not require a linear relationship between primary and secondary data, (2) it exploits the secondary information to its full potential by maximizing the correlation between the primary and secondary data, (3) it can be easily applied to cases where several types of secondary or soft data are involved, and (4) it significantly reduces variance function calculations and thus greatly facilitates non-Gaussian cosimulation. We demonstrate the data integration procedure using synthetic and field examples. The field example involves estimation of pore-footage distribution using well data and multiple seismic attributes.