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Re: GEOSTATS: Exponential model range

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  • Mohammad J Abedini
    Greetings, With many many thanks to Syed for his illuminating response. Please read the following quote and go ahead with my comment: We possess knowledge
    Message 1 of 7 , Mar 21, 1997
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      Greetings,

      With many many thanks to "Syed" for his illuminating response. Please read
      the following quote and go ahead with my comment:

      "We possess knowledge only by inquiry and cease to have knowledge when we
      cease to question (Ross, 1981)"

      For the past three years or so, part of my PhD research project is to
      investigate the Scale problem that we are facing with in hydrology (in
      particular) and in science (in general). "Syed" response is part of that
      dilemma or perhaps the puzzle that I am struggling with on a continuous
      basis. His response shed some light on me for a better description of my
      recent findings in my own research project which I would like to share it
      with others to gain more.

      I wrote a FORTRAN program which was linked to ARC/INFO in order to map
      depressional storages in a spatial context. In addition, I have DEM data
      set with very high spatial resolution (3 mm) for three micro-plots. When I
      feed DEM with 3mm resolution to the program, I had more than 4000
      depression storages and upon increasing the grid spacing, the number of
      depression will start to decrease dramatically. The total ponded surface
      area as well as total pond volume will increase upon increasing the grid
      spacing which is contrary to my original belief but "Syed" response
      clarified that for me. Interesting enough, when I graphed the potential
      contributing area of each depression in pixel unit against surface area at
      each pour point in the same unit (in log-log space), some systematic
      pattern of change started to develop which did not depend upon:

      o grid spacing
      o data set

      Anyway, thanks again for the illuminating response and thanks to all dear
      colleagues who feel some commitment in themselves to keep this wonderful
      forum active.

      Thanks
      Abedini



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    • Ali_Alaa@seo.state.nm.us
      ... resolution, ... geological ... effect ... however, I ... the ... spatial ... Hi Syed, You are right. I agree with you regarding the nested scales.
      Message 2 of 7 , Mar 21, 1997
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        > You're missing the effect of nested scales. The smaller the
        resolution,
        > the more the number of scales that can be resolved. E.g., to take a
        geological
        > example, I can take samples at very fine resolution and resolve the
        effect
        > of thin laminae on the variogram. Sampling at larger spacings,
        however, I
        > would not be able to see this, but the next larger scale becomes more
        > apparent, i.e., a bedset. Going even higher, I would be able to see
        the
        > effects of a parasequence. And each would indicate some pattern of
        spatial
        > correlation (not necessarily nugget).
        >

        Hi Syed,
        You are right. I agree with you regarding the nested scales.
        However, unless you make something about the data available you will
        still get high nugget if you are considering large grid spacing (scale).
        You may, for example, upscale the measurements to be consistent with the
        scale of your interest (not an easy task though). Unless you do the
        upscaling; you are, in fact, dealing with data reflecting high
        resolution variation and hence, ignoring such a variation if you
        consider higher scales. In this case, you will have a variogram with
        high % of nugget.
        I would like add the following to Syed's comments to Abedini: How did
        you resample the original data?. If you, for example, took a lumped
        average for the data within each 20*20 m. grid cell; you have already
        killed any variation beyond this scale and hence you will not have a bad
        nugget; and may get a decent range. The question is "do we have enough
        of such data to produce a reliable variogram?"

        regards, Alaa
        _________________________________________________________
        Alaa I. 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
        _________________________________________________________
      • Syed.R.Syed@EXXON.sprint.com
        On the problem of scale, some have been adventurous and used statistically self-similar fractals to address the problem of inferring the variation at one scale
        Message 3 of 7 , Mar 22, 1997
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          On the problem of scale, some have been adventurous and used statistically
          self-similar fractals to address the problem of inferring the variation at
          one scale from another (usually bigger scale). E.g. refer Hewett, T.A:
          "Fractal distributions of reservoir heterogeneity and their influence on
          fluid transport," SPE Paper 15386 presented at the 1986 SPE Annual Conference
          and Exhibition, New Orleans (1986). If any have had similar success, I would
          be interested in hearing about them.

          Practically speaking, work only on the scale that matters. E.g., depending
          on the nature of the phenomena, smaller scales may or may not influence the
          dynamic fluid flow simulation results of a hydrocarbon field. Most of the
          time they do, however, so that's why fluid flow engineers have such
          massive migraines trying to history match production using numerical
          simulators.

          There seems to be some confusion over nugget effect and scale (or level of
          support, or sometimes called level of aggregation). The former is
          caused by unresolved variation due to measurements that are taken on some
          minimum spacing (e.g., 10 feet). Variations at spacings less than 10 feet
          therefore cannot be observed, resulting in the apparent nugget. Whether such
          unobserved variation is continuous or not is yet another story. My personal
          experience using cross-validation is that you would have to assume some
          continuity to make realistic predictions at unsampled locations.

          Regards, Syed
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        • Ali_Alaa@seo.state.nm.us
          I don t know who was adventurous and used statistically self-similar fractals to address ....etc. If I was that person, here is my response. Before I
          Message 4 of 7 , Mar 24, 1997
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            I don't know who was "adventurous and used statistically
            self-similar fractals to address ....etc." If I was that person, here is
            my response. Before I respond, I would like to introduce my self (this
            is the second time to post here):
            My name is A. Ali, I work for New Mexico State Engineer office. I have a
            PhD in Geostatstics (Developed new Geostatistical techniques for aquifer
            system characterization and flow and transport simulation in
            non-stationary environments). I have MS in Geotechnical Engineering,
            and completed course work towards MS in Math.&Stat. Beside the above
            areas, my expertise and interests cover other areas such as: the inverse
            problem, Groundwater remediation and management, surface hydrology, and
            Environmental Geotechnical Engineering. For more details about myself
            and about my models, please, visit my homepage at:

            Web: http://www.engineering.usu.edu/Departments/cee/Faculty/ulall/

            Regarding the problem of scale: No, I was not "adventurous", and the
            problem was not "the confusion over nugget effect and scale" either.
            The problem is rather the definition of and, the confusion over, three
            different types of scales; The problem scale, the measurement scale, and
            sampling scale.
            The problem scale is what I am really trying to resolve (e.g., grain
            scale, bed scale, or regional scale).
            The measurement scale is the averaging distance over which an attribute,
            e.g. Hydraulic conductivity (K), is measured at a certain location (In
            other words, we can say that such a value of K is considered a local
            average at such a location within such a scale).
            The sampling scale is how often such measurements are recorded.
            All what I wanted to say is that the range and the nugget will be
            affected by these types of scales.
            For example, we should expect a small nugget effect and a large range if
            the sampling scale is less than the measurement scale; and vice versa.

            Thanks, Alaa

            PS: This is a very good news group with great members.
            _________________________________________________________
            Alaa I. 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
            _________________________________________________________


            > On the problem of scale, some have been adventurous and used
            statistically
            > self-similar fractals to address the problem of inferring the
            variation at
            > one scale from another (usually bigger scale). E.g. refer Hewett, T.A:
            > "Fractal distributions of reservoir heterogeneity and their influence
            on
            > fluid transport," SPE Paper 15386 presented at the 1986 SPE Annual
            Conference
            > and Exhibition, New Orleans (1986). If any have had similar success, I
            would
            > be interested in hearing about them.
            >
            > Practically speaking, work only on the scale that matters. E.g.,
            depending
            > on the nature of the phenomena, smaller scales may or may not
            influence the
            > dynamic fluid flow simulation results of a hydrocarbon field. Most of
            the
            > time they do, however, so that's why fluid flow engineers have such
            > massive migraines trying to history match production using numerical
            > simulators.
            >
            > There seems to be some confusion over nugget effect and scale (or
            level of
            > support, or sometimes called level of aggregation). The former is
            > caused by unresolved variation due to measurements that are taken on
            some
            > minimum spacing (e.g., 10 feet). Variations at spacings less than 10
            feet
            > therefore cannot be observed, resulting in the apparent nugget.
            Whether such
            > unobserved variation is continuous or not is yet another story. My
            personal
            > experience using cross-validation is that you would have to assume
            some
            > continuity to make realistic predictions at unsampled locations.
            >
            > Regards, Syed


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