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Re: GEOSTATS: How to compare two surfaces?

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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 1 of 6 , May 19, 1997
      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 2 of 6 , May 21, 1997
        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 3 of 6 , May 21, 1997
          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 4 of 6 , May 22, 1997
            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 5 of 6 , May 22, 1997
              >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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