at various distances. This type of information is needed in our evaluation of kriging as a technique for estimating Pu and Am spatial distribution and inventory in soil in NTS. Delfiner and Gilbert (1978) use kriging to estimate average Pu concentrations and inventory in soil for unit areas of size 100- x 100-ft at the Area 13 (Project 57) site on NTS. Barnes @t al. (1977) discuss some basic concepts of kriging and illustrate the technique using Area 13 data. An advantage of kriging over other moving average methods is that it gives the "proper" weight to spatial observations to estimate a concentration at a nonsampled location (see Figure 6). "Proper" has to be qualified; it means optimum if the correlation structure (called the variograms) of the data is known with some assurance. The variogram is the basis of kriging. It expresses the variability of the difference of two observations as a function of their distance from each other. Referring to Figure 6, let the concentration at each dot be given by a random variable Z(x), where x represents the location of the point and Z(x) the concentrations at point x. When there are no trends or “drift in concentrations over distance, the experimental (estimated variogram) is computed using N ¢(h) = oS h h YS tz +h) - 2Qxyl’ , i=l (17) where h is the distance between two points and N, is the number of pairs of observations that are distance h apart. At each distance h, ¢(h) is the average squared difference between two observations. Therefore, ¥(h) is a measure of variability between two observations as a function of their distance h from each other. KRIGING ADVANTAGE: ‘’PROPER’’* WEIGHT TO SPATIAL OBSERVATIONS ® PuCONC. 5 | © ESTIMATED-58% HERE e @ @. OBSERVED e e Pu “ CONC. *WITH RESPECT TO CORRELATION STRUCTURE (VARIOGRAM) OF DATA Figure 6. Estimation of Concentration at a Nonsampled Location Using Kriging. 424