The Theory of Kriging

This chapter presents the theory of kriging. Kriging is an estimation method that gives the best unbiased linear estimates of point values or of block averages. Here “best” means minimum variance. Three types of kriging estimators are discussed: ordinary kriging (OK) used when the mean is unknown, kriging the unknown mean value and simple kriging (SK) used when the mean is known.The equations for these three estimators are derived for the stationary case, and are extended to the case of intrinsic variables for ordinary kriging. The additivity theorem which gives the links between the OK and SK estimators is proved. For ordinary kriging, the formula for the slope of the linear regression of the true grade on its estimate is given, and its importance in relation to conditional unbiasedness is discussed. Lastly, kriging is shown to be an exact interpolator.