Self-Healing Sequential Gaussian Simulation for Integration of Secondary Data

Secondary data are important in geostatistical simulation of continuous variables. Seismic data and geological trends are used for porosity modeling. Porosity is used for permeability and residual water saturation modeling. Multiple mineral or contaminant concentrations must often be modeled for mining and environmental applications. Sequential Gaussian simulation (or some other variant of Gaussian simulation) is often used because of its relative simplicity and robustness. The two most common approaches to integrate secondary data in Gaussian simulation are with (1) locally varying mean, or (2) collocated cokriging. A significant problem with both of these techniques is variance inflation, that is, the variance of the resulting simulated values is too high because of an inappropriate decision of stationarity or an artifact of choosing a single secondary data in presence of many. Correction of the simulated results by post-processing or using an ad-hoc variance reduction factor is problematic. Local data are not reproduced at their locations and correction factors must be determined iteratively. We introduce a self-healing procedure for dynamic correction as the simulation proceeds. The dynamic correction is different for the locally varying mean approach and for collocated cokriging since there are different reasons why each of these methods causes variance inflation. The reasons for variance inflation are discussed and the self-healing is applied to a number of data sets. Widespread application is expected; the revised sgsim program is documented.