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GEOSTATS: How to compare two surfaces?

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  • Konstantin Malakhanov
    Dear all, I have a geological data set and I d like to compare the interpolation results from different methods (kriging, minimum curvature and IDW). I have an
    Message 1 of 6 , May 18, 1997
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      Dear all,

      I have a geological data set and I'd like to compare the
      interpolation results from different methods (kriging, minimum
      curvature and IDW). I have an "ideal" map from geologists and this
      is the map of isolines. The question is, how to compare grids which
      comes from interpolation methods and this isolines map? I see two
      possibilities here:

      1) to compare grids. Then I need to interpolate the isolines map to
      grid. And this means, I will possibly get some differences due to
      this interpolation., not due to "goodness" (or "badness") of
      interpolation method of interest. Another question, what is a
      criteria to compare two grids? A mean squared difference? And first
      of all, I need an algotithmus to interpolate isolines to grid. I
      found a description of such method (it calls "Profiles" in TNTmips or
      INTERCON in IRDISI), but descriptions are not detailed enough to
      write a code. So, does anyone have such a code (or pointers to that)?

      2) another possibility is to compare two sets of isolines, but I have
      no idea, how.

      If you have ideas about all that, drop a couple of lines, I will
      summarise the responses.

      Thank you in advance,
      Kostantin.
      Konstantin Malakhanov, wiss. Mitarbeiter/research engineer

      IWW, RWTH Aachen
      Tel. 0241-807343
      Fax. 0241-8888348
      E-Mail: kosta@...-aachen.de
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    • Konstantin Malakhanov
      Thanks to Roberto Bruno for his response. To clear my situation: 1) the data is from quarternary stratum with about 390 data
      Message 2 of 6 , May 19, 1997
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        Thanks to Roberto Bruno <roberto.bruno@...> for his
        response.

        To clear my situation:

        1) the data is from quarternary stratum with about 390 data points at
        5km^2 available, so I have no maps from satellite images and no
        "true" grid values.

        2) The isoline map is drawn per hand directly from data points (there
        are wizards among geologists, they can do such things), so there is no
        intermediate grid between data points and isolines map.

        If I understand you right, to get a grid from isolines map, you
        advise to perform kriging of both data set points and isolines(at
        vertex points)? But doesn't that mean loose of information - with isolines I
        know the gradients of surface, with data points- no. Or should one
        rasterize the isolines?

        And what is "test-kriging" ?

        And I'm still looking for detailed description of linear "isolines-to-grid"
        interpolation....

        Thanks,

        Konstantin.
        Konstantin Malakhanov, wiss. Mitarbeiter/research engineer

        IWW, RWTH Aachen
        Tel. 0241-807343
        Fax. 0241-8888348
        E-Mail: kosta@...-aachen.de
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      • SPP USERS
        Re: Konstantin Malakhanov s question: One way would be to contour the map using GEOEAS, for example, (refer the Software FAQ on the AI-GEOSTATS Web server).
        Message 3 of 6 , May 21, 1997
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          Re: Konstantin Malakhanov's question:

          One way would be to contour the map using GEOEAS, for example, (refer the
          Software FAQ on the AI-GEOSTATS Web server). Then compare the map
          with the geological map (it would be better to use the same isocontour interval).
          Nine out of ten times you'd probably get a totally different map, unless the
          interpolated one had "soft" information built in right from the start. I once had
          to contour a distributary channel system from a couple of control wells, and
          then compared that with a kriged map - both looked like it came from two different
          planets.

          Regards, Syed

          PS/- This man versus machine concept is getting pervasive, re Deep Blue
          versus Kasparaov, or a computer versus a geologist.


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        • Gregoire Dubois
          ... I think comparing two sets of isolines doesn t make much sense in general unless you have used the same interpolation method or if you have a high number
          Message 4 of 6 , May 21, 1997
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            Konstantin Malakhanov wrote:
            >
            >
            > 2) another possibility is to compare two sets of isolines, but I have
            > no idea, how.


            I think comparing two sets of isolines doesn't make much sense in general unless you
            have used the same interpolation method or if you have a high number of isoline levels.
            If isolines are handy to use, they also have the magic property to hide unwanted/desired
            information. You never know what is behind the isolines. When drawing your isolines,
            you may have similar general patterns compared to the "ideal" map but you won't know
            how the underlying data behave. Changing the isoline levels may show very different
            patterns compared to those hidden in the "ideal map".

            Converting isolines to a grid rises the same question: how does the data really
            look like ?

            How would you define the mean values between 2 levels ? Nothing can tell you that
            the average is the arithmetic mean. It may be much lower or higher.

            The "ideal" map has been drawn by hand. Therefore the only way to approach the hand
            drawn map would be to convert all assumptions used by the author about the
            spatial variability of the analysed variables, the nature and the scale of
            the variability into an interpolation model. I hope we are not too far in time from
            a geostats version of Deep Blue...


            To be more pragmatic: if you convert your isolines into a grid, you could first convert
            the lines of the isolines into several (depending on the original resolution) points which
            will receive the values defined by the associated levels. Analysing the spatial correlation
            (exploratory variography) of these points may help you to understand the spatial structure
            of the data. The semivariogram can also be compared to the original data. (A problem is that
            you are then working on categorical data and not anymore on supposed continuous data).
            Such approach may help you to recreate the hand drawn map (with kriging)
            but again your information may be strongly different from it if the assumptions are different.

            Gregoire


            --
            Gregoire Dubois (PhD student) Tel. 39-332-78.99.44
            Joint Research Centre Fax. 39-332-78.54.66
            Environment Inst. TP 321 Email: gregoire.dubois@...
            I-21020 Ispra (Va), ITALY URL: http://java.ei.jrc.it/rem/gregoire/
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          • Ali_Alaa@seo.state.nm.us
            I have been reading with interest the responses to the above inquiry. I sent my response directly to Konstantin Malakhanov. I am forwarding it in this
            Message 5 of 6 , May 22, 1997
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              I have been reading with interest the responses to the above inquiry. I
              sent my response directly to Konstantin Malakhanov. I am forwarding it
              in this message.
              That is right! Comparing isolines from different interpolation methods
              may not be a useful thing to do. Gridding may not be useful either..
              Alaa
              _________________________________________________________
              A. Ali, Ph.D., P.E.
              New Mexico State Engineer Office
              P.O.Box 25102, Santa Fe, NM 87504
              e-mails: aali@...; or aali@...
              Web: http://www.engineering.usu.edu/Departments/cee/Faculty/ulall/
              Phone: 505-827-6125 Fax: 505-827-6188
              _________________________________________________________
            • Med Bennett
              ... Would it be use an interpolation method to compute a grid, contour the grid using the same levels as the hand-drawn map, and then compare the contours
              Message 6 of 6 , May 22, 1997
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                >The most suitable way to do it is to use the principle of cross
                >validation. Given n data points, perform the following for each method:
                >1) drop data point i, and use the remaining n-1 data points to provide
                >an estimate at the location of the dropped point.
                >2) compute the err=y_hat_i - yi,
                >where y_hat_i is the estimated value at location i
                > y_i is the value of dropped data at location i
                >3) repeat steps 1 and 2 at all n points, and compute sum of squared
                >error (or the mean square error).
                >4) repeat steps 1,2,3 for all methods; then compare the resulting sum of
                >squared errors (or the mean square error).
                >
                >As you notice, we did not have to create a grid. However, the method
                >with least errors is the one that will give the best estimation grid in
                >terms of this criterion.
                >
                >Regarding the geologist isoline map, another estimation method, is
                >subjective and may or may not be better than the a statistical
                >interpolation method. I am not sure if you can use a statistical method
                >to judge the adequacy of fit of such a map. However, you can select the
                >interpolation method that provides the closest estimate to the isoline
                >map. To do so, select as many points as you can on these isolines, and
                >consider them data points, then perform cross validation as described
                >above. select the interpolation method with the least square error
                >score.
                >
                >Note: I don't recommend the use of grids to solve your problem.
                >if you have any further questions, don't hesitate to contact me.
                >Alaa
                >_________________________________________________________
                >A. Ali, Ph.D., P.E.
                >New Mexico State Engineer Office
                >P.O.Box 25102, Santa Fe, NM 87504
                >e-mails: aali@...; or aali@...
                >Web: http://www.engineering.usu.edu/Departments/cee/Faculty/ulall/
                >Phone: 505-827-6125 Fax: 505-827-6188
                >_________________________________________________________
                >

                Would it be use an interpolation method to compute a grid, contour the grid
                using the same levels as the hand-drawn map, and then compare the contours
                directly, perhaps by calculating the area between corresponding contours in
                each version? We would have to use the map boundaries to close the polygons
                formed by the contour line pairs. This would do away with having to grid
                the hand-contoured map.
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