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[ai-geostats] why do negative kriging values occur

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  • Abhijith Titus D'souza
    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
    Message 1 of 4 , Nov 11, 2005
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      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
    • Gregoire Dubois
      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
      Message 2 of 4 , Nov 14, 2005
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        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
      • Heuvelink, Gerard
        A more elegant solution is to impose additional constraints that require that the kriging weights are not negative. This can be achieved with compositional
        Message 3 of 4 , Nov 14, 2005
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          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
        • Armando
          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
          Message 4 of 4 , Nov 14, 2005
          • 0 Attachment
            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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