Prediction variance in gstat

[rifortie@ggl.ulaval.ca]

Dear Sir:

I am using gstat to interpolate the Bouguer anomaly on a regular grid. The
size of my study area is 34 km x 26 km. 545 observations of Bouguer anomaly
are available and the station density is fairly constant over the study
area. The population variance is 81. I used gstat to fit a model on the
omnidirectional variogram (nugget effect of 2.6, sill of 102.6 and scale of
6.4 km). Afterwards, I used again gstat to interpolate the Bouguer anomaly
on a grid interval of 1 km based on the former model. gstat calculated also
the prediction variance. I plotted then the results in Surfer. I am quite
happy with the results but I have some trouble in interpreting the map of
prediction variance. I find that the values of prediction variance are quite
low (around 3). From my understanding of the ordinary kriging after reading
the text book of Isaaks and Srivastava, the prediction variance is
calculated from the population variance, the weights and covariances of
observations, and the Lagrange parameter. In an example given by Isaaks and
Srivastava, they found a prediction variance of 7.15 (after a error
correction that I found in their development) fairly close to the population
variance of 10 (the sill). They used only 7 observations to make the
interpolation. Should the prediction variance be close to the population
variance? Does the prediction variance decrease with the increase of
observations? Could you help me in this interpretation? Are the results correct?

Accept my best regards,

Richard
______________________________________________
Richard Fortier, Ph. D., ing.
Professeur adjoint
Departement de geologie et de genie geologique
Pavillon Pouliot
Cite universitaire
Universite Laval
Sainte-Foy (Quebec)
Canada
G1K 7P4
Telephone (phone): (418) 656-2746
Telecopieur (fax): (418) 656-7339