Conditioning Geostatistical Operations to Nonlinear Volume Averages

The all-important process of data integration calls for algorithms that can handle secondary data often defined as nonlinear averages of the primary (hard) data over specific areas or volumes. It is suggested to approximate these nonlinear averages by linear averages of a nonlinear transform of the primary variable. Kriging of such nonlinear transforms, followed by the inverse transform, allows exact reproduction of all original data, both of point support and nonlinear volume averages. In a simulation mode, the previous cokriging provides the mean and variance of a conditional distribution from which to draw a simulated value, which is then backtransformed into a simulated value of the primary variable. The nonlinear averaged data values are then reproduced exactly. The direct sequential simulation algorithm adopted does not call for using any Gaussian distribution.