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RE: GEOSTATS: How to compare two surfaces?

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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 1 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 2 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 3 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 4 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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