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RE: [ai-geostats] modelling trend and kriging type

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  • ABREU Carlos Eduardo
    Dear Els A good reference on geostats in the oil industry is the excelent book from Olivier Dubrule Geostatistics for Seismic Data Integration in Earth
    Message 1 of 10 , Jul 1, 2005
    • 0 Attachment
      Dear Els

      A good reference on geostats in the oil industry is the excelent book from
      Olivier Dubrule "Geostatistics for Seismic Data Integration in Earth
      Models", where you will also find KDE aplications.

      Actually, it is the reference book of a 1 day course offered by SEG (Society
      of Exploration GEophysicists)/EAGE (European Association og Geoscientists
      and Engineers).
      http://www.eage.org/index.php?Menu_Code=DISCDetails&EVS_Id=45&ActiveMenu=57&
      Opendivs=s13,s15


      Sincerely

      Carlos Eduardo ABreu

      -----Message d'origine-----
      De : Els Verfaillie [mailto:els.verfaillie@...]
      Envoyé : vendredi 1 juillet 2005 10:55
      À : Pierre Goovaerts; Recep kantarci; ai-geostats@...
      Objet : RE: [ai-geostats] modelling trend and kriging type


      Dear AI-list,

      in which context KED is mostly used? I have found examples of this
      methodology in the context of soil science and climatology:


      Bourennane, H., King, D. and Couturier, A., 2000. Comparison of kriging with
      external drift and simple linear regression for predicting soil horizon
      thickness with different sample densities: Geoderma, v. 97, p. 255-271.

      Bourennane, H. and King, D., 2003. Using multiple external drifts to
      estimate a soil variable: Geoderma, v. 114, p. 1-18.

      Goovaerts, P., 1999. Using elevation to aid the geostatistical mapping of
      rainfall erosivity: Catena, v. 34, p. 227-242.

      Hudson, G. and Wackernagel, H., 1994. Mapping temperature using kriging with
      external drift: theory and an example from Scotland: International Journal
      of Climatology, v. 14, p. 77-91.

      Martinez-Cob, A. and Cuenca, R.H., 1992. Influence of elevation on regional
      evapotranspiration using multivariate geostatistics for various climatic
      regimes in Oregon. Journal of Hydrology 136, 353–380.


      Are there other interesting references for this methodology in the same or
      other application fields?

      Best wishes,
      ___________________________________________________

      Els Verfaillie, PhD student
      Renard Centre of Marine Geology - Ghent University
      Krijgslaan 281-S8
      B-9000 Gent - Belgium
      tel: +32-9-2644573 fax: +32-9-2644967
      e-mail: Els.Verfaillie@...
      http://www.rcmg.ugent.be/
      ___________________________________________________


      -----Original Message-----
      From: Pierre Goovaerts [mailto:Goovaerts@...]
      Sent: donderdag 30 juni 2005 16:54
      To: Recep kantarci; ai-geostats@...
      Subject: RE: [ai-geostats] modelling trend and kriging type


      To add to the excellent comments by Edzer and Gregoire,

      1. Universal kriging = kriging with a trend. The second terminology has been
      proposed by Andre
      Journel who felt that the term "universal" was vague and misleadingly
      "ambitious".

      2. Kriging with an external drift (KED) is mathematically the same as
      universal kriging (UK). Secondary variables
      are simply replacing the spatial coordinates used in UK.

      3. Regression kriging denotes all the techniques where the trend is modeled
      outside the kriging algorithm.
      There are various methods that can be used to model that trend, ranging from
      linear regression
      to neural networks. Kriging is used to interpolate the residuals. In
      practice these techniques have more
      flexibility than universal kriging in term of modeling the trend: multiple
      variables either categorical or
      continuous can be incorporated easily and many sofwtare are available for
      this trend modeling.
      The only limitation is that the trend is modeled globally (i.e. the
      regression coefficients are constant
      in space) while in KED the coefficients are reestimated within each search
      window.

      Cheers,

      Pierre


      Pierre Goovaerts

      Chief Scientist at Biomedware

      516 North State Street

      Ann Arbor, MI 48104

      Voice: (734) 913-1098
      Fax: (734) 913-2201

      http://home.comcast.net/~goovaerts/

      -----Original Message-----
      From: Recep kantarci [mailto:recep_kantarci_1978@...]
      Sent: Thu 6/30/2005 9:38 AM
      To: ai-geostats@...
      Cc:
      Subject: [ai-geostats] modelling trend and kriging type


      Dear ai-geostats members

      When the data used has a trend, it is needed to model trend and in
      this case there exists various types of kriging to apply (universal kriging,
      kriging with a trend, regression kriging etc).
      If this is the case, does one should use the same type of kriging or
      different depending on modeling the trend using coordinates of target
      variable or using other (namely, secondary or auxillary) variables such as
      elevation or topography ? That is , are there a dinstinction depending on
      the type of variables to model the trend while kriging?

      Best regards
      Recep


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    • PCollier@xstrata.com.au
      Hi all I may know this already, but what are the symptoms of data with a trend? What is the difference between a dataset with a trend and a non-stationary
      Message 2 of 10 , Jul 6, 2005
      • 0 Attachment
        RE: [ai-geostats] modelling trend and kriging type

        Hi all

        I may know this already, but what are the symptoms of data with a trend?  What is the difference between a dataset with a trend and a non-stationary dataset?

        Cheers


        Perry Collier

        Senior Mine Geologist
        Ernest Henry Mine  
        Xstrata Copper Australia
        Ph (07) 4769 4527
        Fx (07) 4769 4555
        E-mail PCollier@...
        Web http://www.xstrata.com
         
        PO Box 527
        Cloncurry QLD 4824
        Australia
         
        "Light travels faster than sound. That is why some people appear bright
        until you hear them speak"




        -----Original Message-----
        From: Pierre Goovaerts [mailto:Goovaerts@...]
        Sent: Friday, 1 July 2005 12:54 AM
        To: Recep kantarci; ai-geostats@...
        Subject: RE: [ai-geostats] modelling trend and kriging type


        To add to the excellent comments by Edzer and Gregoire,
         
        1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre
        Journel who felt that the term "universal" was vague and misleadingly "ambitious".
         
        2. Kriging with an external drift (KED) is mathematically the same as universal kriging (UK). Secondary variables
        are simply replacing the spatial coordinates used in UK.
         
        3. Regression kriging denotes all the techniques where the trend is modeled outside the kriging algorithm.
        There are various methods that can be used to model that trend, ranging from linear regression
        to neural networks. Kriging is used to interpolate the residuals. In practice these techniques have more
        flexibility than universal kriging in term of modeling the trend: multiple variables either categorical or
        continuous can be incorporated  easily and many sofwtare are available for this trend modeling.
        The only limitation is that the trend is modeled globally (i.e. the regression coefficients are constant
        in space) while in KED the coefficients are reestimated within each search window.
         
        Cheers,
         
        Pierre
         

        Pierre Goovaerts

        Chief Scientist at Biomedware

        516 North State Street

        Ann Arbor, MI 48104

        Voice: (734) 913-1098
        Fax: (734) 913-2201

        http://home.comcast.net/~goovaerts/

                -----Original Message-----
                From: Recep kantarci [mailto:recep_kantarci_1978@...]
                Sent: Thu 6/30/2005 9:38 AM
                To: ai-geostats@...
                Cc:
                Subject: [ai-geostats] modelling trend and kriging type
               
               
                Dear ai-geostats members
                
                When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc).

                If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging?

                
                Best regards
                Recep

               
          _____ 

                Yahoo! kullaniyor musunuz?
                Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma Yahoo! Posta’da
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      • Isobel Clark
        Perry Your basic semi-variogram graph has a parabola added to it. Shoots off upwards (usually) at some distance. If the distance is large (past the range of
        Message 3 of 10 , Jul 7, 2005
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          Perry
           
          Your basic semi-variogram graph has a parabola added to it. Shoots off upwards (usually) at some distance. If the distance is large (past the range of influence) you can ignore it. See some of our  mid-80s papers on the Wolfcamp data which lots of people use as a teaching set now. Or read my free tutorial at http://geoecosse.bizland.com/softwares (kriging with trend).
           
          Isobel

          PCollier@... wrote:

          Hi all

          I may know this already, but what are the symptoms of data with a trend?  What is the difference between a dataset with a trend and a non-stationary dataset?

          Cheers


          Perry Collier

          Senior Mine Geologist
          Ernest Henry Mine  
          Xstrata Copper Australia
          Ph (07) 4769 4527
          Fx (07) 4769 4555
          E-mail PCollier@...
          Web http://www.xstrata.com
           
          PO Box 527
          Cloncurry QLD 4824
          Australia
           
          "Light travels faster than sound. That is why some people appear bright
          until you hear them speak"




          -----Original Message-----
          From: Pierre Goovaerts [mailto:Goovaerts@...]
          Sent: Friday, 1 July 2005 12:54 AM
          To: Recep kantarci; ai-geostats@...
          Subject: RE: [ai-geostats] modelling trend and kriging type


          To add to the excellent comments by Edzer and Gregoire,
           
          1. Universal kriging = kriging with a trend. The second terminology has been proposed by Andre
          Journel who felt that the term "universal" was vague and misleadingly "ambitious".
           
          2. Kriging with an external drift (KED) is mathematically the same as universal kriging (UK). Secondary variables
          are simply replacing the spatial coordinates used in UK.
           
          3. Regression kriging denotes all the techniques where the trend is modeled outside the kriging algorithm.
          There are various methods that can be used to model that trend, ranging from linear regression
          to neural networks. Kriging is used to interpolate the residuals. In practice these techniques have more
          flexibility than universal kriging in term of modeling the trend: multiple variables either categorical or
          continuous can be incorporated  easily and many sofwtare are available for this trend modeling.
          The only limitation is that the trend is modeled globally (i.e. the regression coefficients are constant
          in space) while in KED the coefficients are reestimated within each search window.
           
          Cheers,
           
          Pierre
           

          Pierre Goovaerts

          Chief Scientist at Biomedware

          516 North State Street

          Ann Arbor, MI 48104

          Voice: (734) 913-1098
          Fax: (734) 913-2201

          http://home.comcast.net/~goovaerts/

                  -----Original Message-----
                  From: Recep kantarci [mailto:recep_kantarci_1978@...]
                  Sent: Thu 6/30/2005 9:38 AM
                  To: ai-geostats@...
                  Cc:
                  Subject: [ai-geostats] modelling trend and kriging type
                 
                 
                  Dear ai-geostats members
                  
                  When the data used has a trend, it is needed to model trend and in this case there exists various types of kriging to apply (universal kriging, kriging with a trend, regression kriging etc).

                  If this is the case, does one should use the same type of kriging or different depending on modeling the trend using coordinates of target variable or using other (namely, secondary or auxillary) variables such as elevation or topography ? That is , are there a dinstinction depending on the type of variables to model the trend while kriging?

                  
                  Best regards
                  Recep

                 
            _____ 

                  Yahoo! kullaniyor musunuz?
                  Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma Yahoo! Posta’da
                  http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

          **********************************************************************

          The information contained in this e-mail is confidential and is

          intended only for the use of the addressee(s).

          If you receive this e-mail in error, any use, distribution or

          copying of this e-mail is not permitted. You are requested to

          forward unwanted e-mail and address any problems to the

          Xstrata Queensland Support Centre.

          Support Centre e-mail: supportcentre@...

          Support Centre phone: Australia 1800 500 646

          International +61 2 9034 3710

          **********************************************************************

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        • Gregoire Dubois
          Hi Perry, I am curious to see how others will reply to your second question on the difference between a dataset with a trend and one that is non-stationary! My
          Message 4 of 10 , Jul 7, 2005
          • 0 Attachment
            Hi Perry,

            I am curious to see how others will reply to your second question on the
            difference between a dataset with a trend and one that is
            non-stationary! My reply may sound provocative: you can always remove a
            trend when you recognize that there is one. Moving from non-stationarity
            to stationarity, on the other hand, can be infinitely more complex (e.g.
            moving to non-Euclidean space)

            :)


            For what concerns the detection of trends, have a look at the variogram:
            a quadratic/exp. increase usually means that there is a trend. Get rid
            of the presumed trend and check the variogram of the residuals which
            should clearly show a change of structure (if you had a trend
            obviously). Quicker might be to use a moving windows strategy to plot
            local averages and check if you see any structure (be careful that the
            "structure" is not simply an anisotropy of your variable). You could
            have a look into the old archives of AI-GEOSTATS. There have been very
            nice replies from Donald Myers (see his publications) in the past on
            these issues. see http://groups.yahoo.com/group/ai-geostats/

            Regards

            GD



            -----Original Message-----
            From: PCollier@... [mailto:PCollier@...]
            Sent: 07 July 2005 03:49
            To: ai-geostats@...
            Subject: RE: [ai-geostats] modelling trend and kriging type


            Hi all
            I may know this already, but what are the symptoms of data with a trend?
            What is the difference between a dataset with a trend and a
            non-stationary dataset?
            Cheers


            Perry Collier
            Senior Mine Geologist
            Ernest Henry Mine
            Xstrata Copper Australia
            Ph (07) 4769 4527
            Fx (07) 4769 4555
            E-mail PCollier@...
            Web http://www.xstrata.com

            PO Box 527
            Cloncurry QLD 4824
            Australia

            "Light travels faster than sound. That is why some people appear bright
            until you hear them speak"




            -----Original Message-----
            From: Pierre Goovaerts [mailto:Goovaerts@...]
            Sent: Friday, 1 July 2005 12:54 AM
            To: Recep kantarci; ai-geostats@...
            Subject: RE: [ai-geostats] modelling trend and kriging type


            To add to the excellent comments by Edzer and Gregoire,

            1. Universal kriging = kriging with a trend. The second terminology has
            been proposed by Andre
            Journel who felt that the term "universal" was vague and misleadingly
            "ambitious".

            2. Kriging with an external drift (KED) is mathematically the same as
            universal kriging (UK). Secondary variables
            are simply replacing the spatial coordinates used in UK.

            3. Regression kriging denotes all the techniques where the trend is
            modeled outside the kriging algorithm.
            There are various methods that can be used to model that trend, ranging
            from linear regression
            to neural networks. Kriging is used to interpolate the residuals. In
            practice these techniques have more
            flexibility than universal kriging in term of modeling the trend:
            multiple variables either categorical or
            continuous can be incorporated easily and many sofwtare are available
            for this trend modeling.
            The only limitation is that the trend is modeled globally (i.e. the
            regression coefficients are constant
            in space) while in KED the coefficients are reestimated within each
            search window.

            Cheers,

            Pierre

            Pierre Goovaerts
            Chief Scientist at Biomedware
            516 North State Street
            Ann Arbor, MI 48104
            Voice: (734) 913-1098
            Fax: (734) 913-2201
            http://home.comcast.net/~goovaerts/
            -----Original Message-----
            From: Recep kantarci [mailto:recep_kantarci_1978@...]
            Sent: Thu 6/30/2005 9:38 AM
            To: ai-geostats@...
            Cc:
            Subject: [ai-geostats] modelling trend and kriging type


            Dear ai-geostats members

            When the data used has a trend, it is needed to model trend and
            in this case there exists various types of kriging to apply (universal
            kriging, kriging with a trend, regression kriging etc).
            If this is the case, does one should use the same type of
            kriging or different depending on modeling the trend using coordinates
            of target variable or using other (namely, secondary or auxillary)
            variables such as elevation or topography ? That is , are there a
            dinstinction depending on the type of variables to model the trend while
            kriging?

            Best regards
            Recep

            _____
            Yahoo! kullaniyor musunuz?
            Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi
            korunma Yahoo! Posta'da
            http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>
            **********************************************************************
            The information contained in this e-mail is confidential and is
            intended only for the use of the addressee(s).
            If you receive this e-mail in error, any use, distribution or
            copying of this e-mail is not permitted. You are requested to
            forward unwanted e-mail and address any problems to the
            Xstrata Queensland Support Centre.
            Support Centre e-mail: supportcentre@...
            Support Centre phone: Australia 1800 500 646
            International +61 2 9034 3710
            **********************************************************************
          • sebastiano.trevisani@unipd.it
            Dear Perry Collier I`m interested in the second question: what is the difference between a dataset with a trend and a non-stationary dataset? Without clearly
            Message 5 of 10 , Jul 8, 2005
            • 0 Attachment
              Dear Perry Collier
              I`m interested in the second question: what is the difference between a dataset
              with a trend and a non-stationary dataset?
              Without clearly pointing out about which kind of stationarity we are talking
              (second order, intrinsic or generalized intrinsic), we need stationarity
              (well !!! togheter with ergodicity) for some statistical index (in this case a
              index about spatial variability) to perform inference. From my perspective the
              dualism trend-residual makes possible always (or not?) to explain non
              stationarity in spatial variability in term of presence of a trend: this trend
              could be global as well as local: it is only a matter of scale.The point is: we
              have reasons or so many data to use a complex trend model?

              In particular this question makes me to think to a point. Very often people who
              use Universal Kriging do this:
              1) detrend data globally (same trend coefficients for all spatial domain)
              2) calculate a residual variogram
              3) perfom Uk with local search windows (inside which the trend coefficients are
              calculated i.e. the trend is filtered locally)
              This doesen`t seem to me correct: I think (maybe, if you have many data IRF-K
              approach works better) that you can not
              one time calculate trend globally and the other time locally: it could happen
              that globally you need a quadratic trend while locally a linear trend model is
              enough. What about that?

              Sincerely,
              Sebastiano Trevisani



              At 03.48 07/07/2005, PCollier@... wrote:

              Hi all

              I may know this already, but what are the symptoms of data with a trend? What
              is the difference between a dataset with a trend and a non-stationary dataset?

              Cheers

              Perry Collier

              Senior Mine Geologist
              Ernest Henry Mine
              Xstrata Copper Australia
              Ph (07) 4769 4527
              Fx (07) 4769 4555
              E-mail PCollier@...
              Web http://www.xstrata.com

              PO Box 527
              Cloncurry QLD 4824
              Australia

              "Light travels faster than sound. That is why some people appear bright
              until you hear them speak"



              -----Original Message-----
              From: Pierre Goovaerts [mailto:Goovaerts@...]
              Sent: Friday, 1 July 2005 12:54 AM
              To: Recep kantarci; ai-geostats@...
              Subject: RE: [ai-geostats] modelling trend and kriging type

              To add to the excellent comments by Edzer and Gregoire,

              1. Universal kriging = kriging with a trend. The second terminology has been
              proposed by Andre
              Journel who felt that the term "universal" was vague and
              misleadingly "ambitious".

              2. Kriging with an external drift (KED) is mathematically the same as universal
              kriging (UK). Secondary variables
              are simply replacing the spatial coordinates used in UK.

              3. Regression kriging denotes all the techniques where the trend is modeled
              outside the kriging algorithm.
              There are various methods that can be used to model that trend, ranging from
              linear regression
              to neural networks. Kriging is used to interpolate the residuals. In practice
              these techniques have more
              flexibility than universal kriging in term of modeling the trend: multiple
              variables either categorical or
              continuous can be incorporated easily and many sofwtare are available for this
              trend modeling.
              The only limitation is that the trend is modeled globally (i.e. the regression
              coefficients are constant
              in space) while in KED the coefficients are reestimated within each search
              window.

              Cheers,

              Pierre


              Pierre Goovaerts

              Chief Scientist at Biomedware

              516 North State Street

              Ann Arbor, MI 48104

              Voice: (734) 913-1098
              Fax: (734) 913-2201

              http://home.comcast.net/~goovaerts/

              -----Original Message-----
              From: Recep kantarci [mailto:recep_kantarci_1978@...]
              Sent: Thu 6/30/2005 9:38 AM
              To: ai-geostats@...
              Cc:
              Subject: [ai-geostats] modelling trend and kriging type


              Dear ai-geostats members

              When the data used has a trend, it is needed to model trend and in this
              case there exists various types of kriging to apply (universal kriging, kriging
              with a trend, regression kriging etc).

              If this is the case, does one should use the same type of kriging or
              different depending on modeling the trend using coordinates of target variable
              or using other (namely, secondary or auxillary) variables such as elevation or
              topography ? That is , are there a dinstinction depending on the type of
              variables to model the trend while kriging?


              Best regards
              Recep


              _____

              Yahoo! kullaniyor musunuz?
              Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma
              Yahoo! Posta’da
              http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

              **********************************************************************

              The information contained in this e-mail is confidential and is

              intended only for the use of the addressee(s).

              If you receive this e-mail in error, any use, distribution or

              copying of this e-mail is not permitted. You are requested to

              forward unwanted e-mail and address any problems to the

              Xstrata Queensland Support Centre.

              Support Centre e-mail: supportcentre@...

              Support Centre phone: Australia 1800 500 646

              International +61 2 9034 3710

              **********************************************************************
              * By using the ai-geostats mailing list you agree to follow its rules
              ( see http://www.ai-geostats.org/help_ai-geostats.htm )

              * To unsubscribe to ai-geostats, send the following in the subject or in the
              body (plain text format) of an email message to sympa@...

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