地统计内插方法 克里金插值(Kriging).pptVIP

8.2 Random Field Real Example 式中：C0为块金值；C0+w为基台值；h为样本点的空间距离；α为变程。 8.2 Random Field Insight to Variogram Anisotropic Variogram Isotropic Variogram 8.2 Random Field Insight to Variogram First Law of Geography: “All things are related, but nearby things are more related than distant things” h=20 0 0.15 0.3 0.45 0 0.15 0.3 0.45 h=10 0 0.15 0.3 0.45 0 0.15 0.3 0.45 h=2 0 0.15 0.3 0.45 0 0.15 0.3 0.45 8.2 Random Field Insight to Variogram Isotropic Variogram If h=0 And we have Covariance function 8.2 Random Field Practical Rules for Selecting Variogram The number of sample values used in estimating the variogram must not be 30; The variogram model should not be fitted to variogram data at separation distances greater than ? of the largest dimension of the study area. One should pay more attention to sample variogram values at short lags. Eye fitting (with experiences) usually gives a good start to select a model. 8.3 Simple Kriging Kriging is an optimal estimation method. ?Often called “BLUE”, best linear unbiased estimator–Best, because it aims at minimizing the estimation variance –Linear, because its estimates are weighted linear combinations of the available data –Unbiased as it tries to have zero mean estimation error 8.3 Simple Kriging Suppose Z(x) is a stationary field with The estimator of simple Kriging is as follows 8.3 Simple Kriging is often referred to as the bias The difference between the estimated value u*(xo) and the unknown true value u(xo) The expectation of estimation error, This (simple kriging) estimator is unbiased even without any condition on the weighting coefficients wi 8.3 Simple Kriging The variance of estimation error is 8.3 Simple Kriging The variance of estimation error is (Kriging variance) 8.3 Simple Kriging The variance of estimation error is = + + + … Minimize the Kriging variance, 8.3 Simple Kriging The simplified form is The matrix form is (Kriging variance) 8.3 Simple Kriging Classwork Deriv