Kriging: The Best Estimate

Filling the Gaps

With facies and per-facies statistics in hand, we still have to put a value in every cell from only a handful of wells. Kriging does this as a weighted average of the wells, giving nearby and less redundant wells more weight, with the weights chosen from the variogram so the estimate is unbiased and has the smallest possible error. At a well it returns the measured value exactly.

The Kriging Variance

Kriging also reports its own uncertainty, the kriging variance: zero at the wells and rising with distance from them. The variance map is the honesty check, showing where the model rests on data and where it is extrapolating into the unknown. It depends only on the data layout and the variogram, not on the measured values themselves.

Smooth by Design

Because kriging minimizes error it averages, and averaging smooths. The kriged map is the best single estimate but it is smoother than the real rock, the central limitation we confront next. Even so, kriging is the workhorse for a best estimate and the engine that sits inside simulation.