Page 194 - MATLAB Recipes for Earth Sciences

7.9 Geostatistics (by R. Gebbers) 189

(Xg,Yg) and the observation points (x,y). Then we build the right-hand-
side vector of the kriging system by using the variogram model G_R and add
one to the last row. We next obtain the matrix E with the weights and the
lagrange multiplier. The estimate Zg at each point k is the weighted sum of
the observations z. Finally, the kriging variance s2_k of the grid point is
computed. We plot the results. First we create a grid of the kriging estimate
and the kriging variance:
r = length(R);
Z = reshape(Zg,r,r);
SK = reshape(s2_k,r,r);
A subplot on the right presents the kriged values:

subplot(1,2,1)
pcolor(Xg1,Xg2,Z)
title('Kriging estimate')
xlabel('x-coordinates')
ylabel('y-coordinates')
box on
colorbar('SouthOutside')
The left subplot presents the kriging variance:

subplot(1,2,2)
pcolor(Xg1,Xg2,SK)
title('Kriging variance')
xlabel('x-coordinates')
ylabel('y-coordinates')
box on
colorbar('SouthOutside')
hold on
and we are overlaying the sampling positions:
plot(x,y,'ok')
hold off
The kriged values are shown in Figure 7.16a. The kriging variance depends
only on the distance from the observations and not on the observed values
(Fig. 7.16b). Kriging reproduces the population mean when observations
are beyond the range of the variogram, at the same time kriging variance
increases (lower right corner of the maps in Figure 7.16). The kriging vari-
ance can be used as a criterion to improve sampling design and it is needed
for backtransformation in lognormal kriging. Back-transformation for lo-
gnormal kriging is done by:

(
yx ) exp( z x ) 05– ( . S 2 x ( ) ) N
0 0 0