2D and 3D data sets, partial and total horizontal variograms

[Daniele Iannuzzo]

Thank you, Edzer, for your answers. You were very useful and accurate in your letter, and you solved all problems I had.   Well, actually, you solved the problems I had then, but now I have new problems, I can't understand exactly if I have them with geostatistical theory or with GSTAT, so I would be very happy if someone could help me again.   I have a 3D data set, but while x,y coordinates are very scattered, there are only few z values, i.e. all samples are collected at only three or four different height (z) values. When I calculated with GSTAT the variograms layer by layer (i.e., a 2D data set) I obtained an expected result: the sample variogram  e.g. 90� +/- 90� (i.e. total) was composed by the same number of point pairs (or quite the same) as the 90� +/- 89� one. When I used the 3D data set, i calculated the partial variogram with this GSTAT notation (as it appears on the left side of the GNUPLOT screen): <x,y> 0�+/- 90�, <z> 0�+/- 0� (I will call this sample variogram the 'horizontal total' from here on). Again as expected, the number of point pairs contributing to this sample variogram was equal to the sum of the single layers total variograms point pairs (of course cutoff and width were the same). But if I try, in the 3D data set, to calculate the sample variogram: <x,y> 0�+/- 89�, <z> 0�+/- 0�, I find it is composed by a number of point pairs smaller then the previous one, i.e. one half, more or less, with respect to the horizontal total. Moreover, the number of point pairs of the partial horizontal, is different from the sum of the single layers partial sample variograms point pairs (again with the same cutoff, width and angular tolerance).   I didn't expect these last results, and I was not able to find an explanation. Is there something I don't now about geostatistics that could explain this or am I wrong in handling GSTAT?   Thank you in advance for everyone could help me and best regards.   Daniele.