by Didier Renard » Mon Feb 21, 2022 3:49 pm
Hi Jeffrey
The vmap.auto() has certainly not given you good results in your case. Let me clarify some points:
- the variogram map is NOT calculated on polar grid (as in Isatis). As a matter of fact, although graphically appealing, this representation is not optimal: as matter of fact, the sizes of the polar cells are not equal, which biases the graphical rendition. I finally prefer the square regular grid.
In this square representation, we simply fill each grid cell with the average of half-squared differences values between pairs of points located at a distance/direction which correspond to the location of the grid cell with respect to the center of the plot.
- the variogram map can be calculated in two different ways:
. using vmap.grid when data are located on a regular grid
. using vmap.calc otherwise
Note that you can always use vmap.calc (even when data are on a grid) but calculations take much more time.
- the variogram map, at the end of calculations, stand as a grid whose origin is located in the center of the grid.
This grid can be represented with any graphical module dedicated to a standard grid, such as plot, 3-D block...
THen comes the vmap.auto() module. This module is meant to fit atuomatically the variogram information contained in the variogram map informed on all the cells of the variogram map grid, i.e. in may directions and distances. If you specified nx and ny in the vmapXXX function, the resulting vmap (in 2-D) is automatically dimensioned to (2*nx+1) * (2*ny+1). To give numbers, if you say that nx=ny=10, the vmap grid contains 441 cells. This explains that the fitting procedure may take some time (as when running a traditional variogram fitting procedure with 441 calculated lags!!!).
The fitting procedure uses the same type of arguments as the one performed on a set of traditional variograms: i.e. some recommended structures, the switches to allows/forbid anisotropy, rotation ...
The result is a standard model with possible complex anisotropies.
In order to better understand the fitting, the procedure automatically draw (with the same color scale) the experimental variogram map (left) and the one corresponding to the Model (right).
Usually the fit is rather correct as the amount of experimental information is large. However, one has to pay attention to the cell dimension and the overall grid dimensions for the variogram map grid. If too small, only the small scale structures will be fitted correctly. Another issue comes from the number of pairs. This information is also stored in the variogram map grid. One has to remember that the number of pairs will come as a weight during the fitting procedure: a cell whose weight is small corresponds to a small number of pairs assigned to this cell and it will be disregarded dugin the fitting step.
As I do not have your data in hand, I cannot see which could be the origin for such a mismatch between the left and the right figures resulting from the automatic fit.
