- 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

__________________________________

Yahoo! FareChase: Search multiple travel sites in one click.

http://farechase.yahoo.com - 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:abhijitidz_4@...]

Sent: 11 November 2005 21:59

To: ai-geostats@...

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

__________________________________

Yahoo! FareChase: Search multiple travel sites in one click.

http://farechase.yahoo.com - A more elegant solution is to impose additional constraints that require

that the kriging weights are not negative. This can be achieved with

compositional kriging, see Walvoort and De Gruijter, MATHEMATICAL

GEOLOGY 33 (8): 951-966 NOV 2001. I guess that Dennis wrote some nice

software for this too, contact him at: Dennis.Walvoort@....

Gerard

Gerard B.M. Heuvelink

Soil Science Centre

Wageningen University and Research Centre

P.O. Box 47

6700 AA Wageningen

The Netherlands

tel +31 317 474628 / 482420

email gerard.heuvelink@...

http://www.dow.wur.nl/UK/cb/ls/sfi/sfi_alg.htm

-----Original Message-----

From: Gregoire Dubois [mailto:gregoire.dubois@...]

Sent: maandag 14 november 2005 15:12

To: 'Abhijith Titus D'souza'

Cc: ai-geostats@...

Subject: RE: [ai-geostats] why do negative kriging values occur

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:abhijitidz_4@...]

Sent: 11 November 2005 21:59

To: ai-geostats@...

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

__________________________________

Yahoo! FareChase: Search multiple travel sites in one click.

http://farechase.yahoo.com - 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:abhijitidz_4@...]

>Sent: 11 November 2005 21:59

>To: ai-geostats@...

>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

>

>

>

>__________________________________

>Yahoo! FareChase: Search multiple travel sites in one click.

>http://farechase.yahoo.com

>

>

>

>

>

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