Loading ...
Sorry, an error occurred while loading the content.

[ai-geostats] kriging with trend

Expand Messages
  • Oriol Falivene
    Dear list, Just a simple question... I m trying to produce a contour map from a structural surface. This surface is highly non-stationary (actuaally dips
    Message 1 of 3 , Jan 5, 2006
    • 0 Attachment
      Dear list,

      Just a simple question...

      I'm trying to produce a contour map from a structural surface. This
      surface is highly non-stationary (actuaally dips towards NW)
      I wolud like to know which could be the best solution for getting a
      reliabel map:

      1) Fit a plyonomial surface to the sample values, which is used as a
      drift. Substract the drift from the observations to get the residuals.
      Estimate the variogram of the residuals (now the residual variable is
      stationary). Perform OK on the residuals. Add the polynomial surface to
      the residuals to get the interpolated surface.

      2) Compute variograms from the observations. Use universal kriging to
      get the interpolated surface.

      Thank you

      Oriol
      --



      ______________________________________

      Oriol Falivene
      ofaliven@...
      http://www.ub.es/ggac

      tel. (+34) 93 4021373
      fax (+34) 93 4021340

      Fac. de Geologia,
      Univ. de Barcelona
    • Gerald van den Boogaart
      Dear Oriol Falivene, If you could assume a linear (or polynomial trend) for the dip, the situation you are talking about, is the classical situation for the
      Message 2 of 3 , Jan 5, 2006
      • 0 Attachment
        Dear Oriol Falivene,

        If you could assume a linear (or polynomial trend) for the dip, the situation
        you are talking about, is the classical situation for the use of intrinsic
        random functions, IRKk-kriging and generalized covariances or generalized
        variograms. The theory is quite good explained in the thick standard books
        on Geostatistics such as that of Cressie or of Chiles and Delfiner. In
        pratice it is quite difficult to actually estimate the generalized variograms
        and to find good software for that.

        Can anyone hint me and Oriol to good software for IRK-k kriging, especially
        regarding the estimation and modelling of the generalised variograms? The
        IRKk/Universal kriging is present everywhere, but the modelling...?

        In case of nonpolynomial trend, the estimation of the variogram gets even more
        tricky.
        > I wolud like to know which could be the best solution for getting a
        > reliabel map:
        > 1) Fit a plyonomial surface to the sample values, which is used as a
        > ...
        1) is wrong, since removing the trend removes the assumption of stationarity,
        which often also results in strange behavior of the variogram (e.g. dropping
        for long distances again)

        2) is not strictly wrong, however whenever a trend is really present, you can
        not fit a ordinary variogram model, due to a quadratic increase in the
        variogramm. You will need a generalized variogram model and than we are back
        at IRFk-kriging.

        Best regards,
        Gerald v.d. Boogaart



        Am Donnerstag, 5. Januar 2006 10:57 schrieb Oriol Falivene:
        > Dear list,
        >
        > Just a simple question...
        >
        > I'm trying to produce a contour map from a structural surface. This
        > surface is highly non-stationary (actuaally dips towards NW)
        > I wolud like to know which could be the best solution for getting a
        > reliabel map:
        >
        > 1) Fit a plyonomial surface to the sample values, which is used as a
        > drift. Substract the drift from the observations to get the residuals.
        > Estimate the variogram of the residuals (now the residual variable is
        > stationary). Perform OK on the residuals. Add the polynomial surface to
        > the residuals to get the interpolated surface.
        >
        > 2) Compute variograms from the observations. Use universal kriging to
        > get the interpolated surface.
        >
        > Thank you
        >
        > Oriol
        > --
        >
        >
        >
        > ______________________________________
        >
        > Oriol Falivene
        > ofaliven@...
        > http://www.ub.es/ggac
        >
        > tel. (+34) 93 4021373
        > fax (+34) 93 4021340
        >
        > Fac. de Geologia,
        > Univ. de Barcelona

        --
        -------------------------------------------------
        Prof. Dr. K. Gerald v.d. Boogaart
        Professor als Juniorprofessor fuer Statistik
        http://www.math-inf.uni-greifswald.de/statistik/

        office: Franz-Mehring-Str. 48, 1.Etage rechts
        e-mail: Gerald.Boogaart@...
        phone: 00+49 (0)3834/86-4621
        fax: 00+49 (0)89-1488-293932 (Faxmail)
        fax: 00+49 (0)3834/86-4615 (Institut)

        paper-mail:
        Ernst-Moritz-Arndt-Universitaet Greifswald
        Institut f�r Mathematik und Informatik
        Jahnstr. 15a
        17487 Greifswald
        Germany
        --------------------------------------------------
      • Isobel Clark
        Oriol If you can get a semi-variogram from the observations which does not contain a parabolic upturn (diagnostic of polynomial type trend) then your trend is
        Message 3 of 3 , Jan 5, 2006
        • 0 Attachment
          Oriol
           
          If you can get a semi-variogram from the observations which does not contain a parabolic upturn (diagnostic of polynomial type trend) then your trend is weak enough to ignore.
           
          You can download a free tutorial on dealing with polynomial type trend at http://geoecosse.bzland.com/softwares
           
          Isobel

          Oriol Falivene <oriolfalivene@...> wrote:
          Dear list,

          Just a simple question...

          I'm trying to produce a contour map from a structural surface. This
          surface is highly non-stationary (actuaally dips towards NW)
          I wolud like to know which could be the best solution for getting a
          reliabel map:

          1) Fit a plyonomial surface to the sample values, which is used as a
          drift. Substract the drift from the observations to get the residuals.
          Estimate the variogram of the residuals (now the residual variable is
          stationary). Perform OK on the residuals. Add the polynomial surface to
          the residuals to get the interpolated surface.

          2) Compute variograms from the observations. Use universal kriging to
          get the interpolated surface.

          Thank you

          Oriol
          --



          ______________________________________

          Oriol Falivene
          ofaliven@...
          http://www.ub.es/ggac

          tel. (+34) 93 4021373
          fax (+34) 93 4021340

          Fac. de Geologia,
          Univ. de Barcelona



          * 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@...

          Signoff ai-geostats

        Your message has been successfully submitted and would be delivered to recipients shortly.