Hi,

I use the kriging algorithm, together with the simple power-model as a variogram, exactly as suggested in chapter 3.7.
I tried the algorithm with random data scattered on a [0,1]x[0,1] square (as x-data) and random y-data. It works really well!
However, in my actual application, my data is highly anisotropic, i.e. I have data scattered on a square [0,10000] x [0,0.1]. This will then cause the algorithm to give nonsensical interpolations and I can only assume that the problem lies in the isotropy assumption of the power-model in the variogram. In this model, it is silently assumed, that the variogram depends only on the distance |r| and not on the direction.
I wonder how I could change that. Did anyone else realize a problem there? and maybe a quick solution?

Thanks a lot,

Stephan

I solved the issue.

Just in case someone wants to know:
The extension to anisotropic models is straight forward. Instead of fitting the model alpha*r^beta, I fit the multidimensional model:

Sqrt(a^2 x^2 + b^2 y^2 + c^2 z^2 + ...)^beta

with fitting parameters a, b, c and a vector {x,y,z,...}.

Clearly, this model reduces to the simple isotropic model in case of a=b=c=...

The fitting can be done with the nonlinear fitting routines in NR, but I did it with mathematica.

Once one has the model parameters a,b,c... for the variogram,the kriging routine works perfectly well.

Regards,

Stephan