More Detail, Less Certainty: Conditional Simulation

Abstract

Conditional simulation deserves to be used more in analysis and mapping of regionalized variables. An important advantage to the geostatistical approach to mapping lies in the modeling of spatial covariance that precedes interpolation; semivariogram models derived from this step can make the final estimates sensitive to directional anisotropics present in the data. On the other hand, the smoothing property of kriging can also mean that one throws away detail at the mapping stage. I have argued above that when the geologist wants to estimate reserves, the smoothing property of kriged estimates in the presence of a large nugget effect is desirable. In some cases, the geologist may want to enhance extreme values, emphasize directional anisotropics, and in other ways exploit the fine-scale variation in data. In the place of local estimates with minimal estimation variance, the geologist wants a map that honors observed values of the regionalized variable, has the same degree of fine-scale variability as the observed data, and obeys the same spatial law. By relaxing the requirement of minimal squared error, conditional simulation sacrifices some certainty for more detail.