Negative weights is a consequence of continuity, thus part of physical
and mathematical solution.
As point by Gregoire .. when de geometry of points is enough good some
points are "masked" .
The negative value in the estimator happens when high values receive
negative weigths ... and the others are low... !
Negative weights are familiar for filter´s users (seismic, geophysics
and image)
Remember that variogram is a expectation for all the domain thus doesn´t
have the responsability to solve local problems. If you have some
"rapport" with your data you know that this kind of problem appears in
the contact of low values sometimes surround by high values.
The king of the negative weights is gaussian model!
The solution cited by Gregoire is old for mining users and work very well.
Thanks for your attention
Armando
Gregoire Dubois wrote:
Negative kriging weights can occur when you have a so-called "screening
effect", that is points close to the location at which an estimation is
needed "mask" points that are further appart. The problem is thus the
topology of your sampling locations.
Solution: reduce the neighborhood of your estimator (e.g. use 1 or 2
points in each sector of your serch ellipse to avoid searching too far)
A reference explaining the maths behind the weights is: Clayton V.
Deutsch, (1996) Correcting for negative weights in ordinary kriging,
Computers & Geosciences, Volume 22, Issue 7,Pages 765-773.
An excellent (free!) tool for visualising this problem is E{Z}-Kriging
(see FAQ section of AI-GEOSTATS) written by Denis Walvoort.
Hope this helps,
Gregoire
__________________________________________
Gregoire Dubois (Ph.D.)
European Commission
Tel. +39 (0)332 78 6360
Fax. +39 (0)332 78 5466
WWW: http://rem.jrc.cec.eu.int
WWW: http://www.ai-geostats.org
-----Original Message-----
From: Abhijith Titus D'souza [mailto:[EMAIL PROTECTED]
Sent: 11 November 2005 21:59
To: ai-geostats@unil.ch
Subject: [ai-geostats] why do negative kriging values occur
Hello List:
I'm new to this list and just beginning to get into geostatistics. I
tried searching for possible answers on the mailing list, but had no
luck. So here I am with my question:
My dataset consists of 149 samples(too less ???, but
that is all I have !!) from an offshore area and I am
trying to estimate the grade of a mineral. I used the
software ISATIS for my work. 40% of my data is between
0 to 5% with the maximum being 99 %. The data displays
a uniform distribution if we ignore the 40% low
values.I tried using gaussian transformation, but to
no avail and so stuck with the original data. The
variogram model did fit well (at least globally)and as
I proceeded towards ordinary kriging I got quite a few percentages of
negative values (3% of the estimated values were negative), with the
lowest being -6%. I contacted the ISATIS technical support team and they
told me to play around with the neighbourhood distance and number of
samples in the neighbourhood etc. After many trial and error runs I
finally got a nice kriging map but it sill had some negative values
(less than 1% of the estimated values) with the lowest being -0.02.I'm
curious as to what could be the reasons behind the negative values. I do
get some negative weights, but is that only reason. Could someone give
me a mathematical and/or intuitive meaning to the negative estimates?
Thank you
Titus
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