Publisher Summary Geological genesis of a reservoir causes observations to be correlated in space. While the variogram considers the overall spatial continuity between any two locations, the bi-variate distribution quantifies spatial continuity between specific classes of the property at any two locations. Spatial correlation allows making predictions about the property at un-sampled locations from sample data. A simple visual comparison between the true unknown field and the kriging map shows a smooth pattern in the kriging image and an un-smooth pattern in the true image. Stochastic simulation generates multiple reservoir models, termed realizations, each reproducing the same patterns, each representing alternative representations of the unknown truth. In the same sense as a set of outcomes drawn from a uni-variate distribution model represent the uncertainty about a random variable, a set of stochastically generated reservoir models represent the uncertainty about the unknown true reservoir. The major default of kriging, which leads to its smoothness, lies in the fact that un-sampled locations are estimated independently from one another.