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## 524Re: AI-GEOSTATS: hole effect

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• Jan 30, 2002
Fernando,

I'm not sure what variogram you were given that works only in 1d
I can think of two -- gamma(h) = 1 -cos(h) and gamma(h)=exp(-ah)*cos(h)

The problem with higher dimensions is that the 'size' of the hole, defined
as |min(C(h))|/ C(0) which takes the value 1.0 for the first of these
variograms , has to less dramatic in higher dimensions. The higher the
number of dimensions, the less important the hole size can be.

So ideally you would like a variogram that is legitimate in 2d but not in
3d. I can't remember any of those off hand - although they do exist.

The next best thing is one that works in 3d (and therefore also in 1d and
2d). This will have a smaller hole effect size than is theoretically
possible for 2d data. The one I'm giving you does attain the maximum hole
size allowed for 3d data. It is

gamma(h) = 1 - sin(r)/r

The problem is that it has quadratic behavior at the origin - so you might
need to add a small spherical or exponential variogram as suggested by
Isobel to ensure that your resultant random function model is not
differentiable.

Bye

Colin Daly

----- Original Message -----
From: <ft.maestre@...>
To: <ai-geostats@...>
Sent: Friday, January 25, 2002 12:29 PM
Subject: AI-GEOSTATS: hole effect

Dear list,

I am working with vegetation data, and I have got some variograms
that are characterized by the presence of a "hole effect" that I
would like to model. I have found in the manual of GSLIB (2nd
edition) a model with a periodical component that can be fitted to
such data, but the authors remark that this model valid only in one
direction. Since I am working with omnidirectional variograms in a
two-dimensional grid, I would be very grateful if somebody could give
me any indication about where I can find conditional negative semi-
definite (CNSD) models that incorporate a periodic component and that
are valid for two-dimensional data.

Many thanks in advance for your attention.

Best Regards,

Fernando T. Maestre
Departamento de EcologĂ­a
Apdo correos 99
03080 Alicante
SPAIN

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