Deriving constraints on small-scale variograms due to variograms of large-scale data

The application of kriging-based geostatistical algorithms to integrate large-scale seismic data calls for direct and cross variograms of the seismic variable and primary variable (e.g., porosity) at the modeling scale, which is typically much smaller than the seismic data resolution. In order to ensure positive definiteness of the cokriging matrix, a licit small-scale coregionalization model has to be built. Since there are no small-scale secondary data, an analytical method is presented to infer small-scale seismic variograms. The method is applied to estimate the 3-D porosity distribution of a West Texas oil field given seismic data and porosity data at 62 wells.