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

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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 1 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

             
        _____ 

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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 2 of 10 , Jul 7, 2005
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        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
        **********************************************************************
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