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GEOSTATS: modeling zonal anisotropy

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  • Chaosheng Zhang
    Dear colleagues, Question: How to model the variograms of a zonal anisotropy? I m dealing with an area of 75km*75km, with heavy metal contents in 747 samples.
    Message 1 of 3 , Jul 16, 1997
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      Dear colleagues,

      Question: How to model the variograms of a zonal anisotropy?

      I'm dealing with an area of 75km*75km, with heavy metal contents in 747
      samples. The samples are quite evenly distributed, and high contents of
      heavy metals are distributed from NW corner along to SE corner, just like a
      belt. Taking element Cobalt as an example, I have calculated the
      omnivariogram and directional variograms. They can be satisfactorily fitted
      by Gausion model (thanks to so many samples), and the specific parameters
      are (the variance= 0.12):

      ---------------------------------------------------------
      Direction Model Nugget Sill Range(km)
      ---------------------------------------------------------
      Omni Gaussion 0.03 0.13 40
      5 (E-W) Gaussion 0.03 0.10 40
      50 (NE-SW) Gaussion 0.03 0.21 40
      95 (N-S) Gaussion 0.03 0.14 40
      140(NW-SE) Gaussion 0.03 0.07 40
      ---------------------------------------------------------

      The results are very good, and the only differences are the sill values.
      However, for Kriging, I don't know how to input the model. It seems very
      difficult to model it with nested models: When one direction is OK, the
      others will become worse. I'm familiar with isotropy and geometrical
      anisotropy, but puzzled by zonal anisotropy. I am using the softwares of
      VARIOWIN (V2.2) and GEO-EAS (V1.2.1).

      Any help are appreciated, and thanks in advance!

      Chaosheng Zhang


      +===============================================+
      |_____|_____|_____|_____|_____|_____|_____|_____|
      |__|_____|_____|_____|_____|_____|_____|__|__|__|
      |_____| |_____|
      |__|__| Dr. Chaosheng Zhang |__|__|
      |_____| Geological Survey of Sweden, SGU |_____|
      |_____| P.O. Box 670 |_____|
      |__|__| S-751 28 Uppsala |__|__|
      |__|__| SWEDEN |__|__|
      |_____| Tel: +46 18 179000/179290 |_____|
      |_____| Fax: +46 18 179210 |_____|
      |_____| E-mail: chaosheng.zhang@... |_____|
      |__|__|___________________________________|__|__|
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      +===============================================+

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    • Mohammad J Abedini
      Greetings ... A while ago, I raised the same question on this forum. Based on the responses that I received from my dear colleagues, I realized that I should
      Message 2 of 3 , Jul 16, 1997
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        Greetings

        On Wed, 16 Jul 1997, Chaosheng Zhang wrote:

        >
        > Question: How to model the variograms of a zonal anisotropy?

        > others will become worse. I'm familiar with isotropy and geometrical
        > anisotropy, but puzzled by zonal anisotropy. I am using the softwares of
        > VARIOWIN (V2.2) and GEO-EAS (V1.2.1).

        A while ago, I raised the same question on this forum. Based on the
        responses that I received from my dear colleagues, I realized that I
        should be on my own in that regard.

        One of our dear colleagues at that time provided some input which more or
        less geared toward preventing that situation to happen as opposed to
        remediating the problem.

        Hope this helps

        Regards
        Abedini



        >
        > Any help are appreciated, and thanks in advance!
        >
        > Chaosheng Zhang
        >
        >
        > +===============================================+
        > |_____|_____|_____|_____|_____|_____|_____|_____|
        > |__|_____|_____|_____|_____|_____|_____|__|__|__|
        > |_____| |_____|
        > |__|__| Dr. Chaosheng Zhang |__|__|
        > |_____| Geological Survey of Sweden, SGU |_____|
        > |_____| P.O. Box 670 |_____|
        > |__|__| S-751 28 Uppsala |__|__|
        > |__|__| SWEDEN |__|__|
        > |_____| Tel: +46 18 179000/179290 |_____|
        > |_____| Fax: +46 18 179210 |_____|
        > |_____| E-mail: chaosheng.zhang@... |_____|
        > |__|__|___________________________________|__|__|
        > |_____|_____|_____|_____|_____|_____|_____|_____|
        > +===============================================+
        >
        > --
        > *To post a message to the list, send it to ai-geostats@....
        > *As a general service to list users, please remember to post a summary
        > of any useful responses to your questions.
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        >

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      • Edzer J. Pebesma
        ... You can ``fake zonal anisotropy by geometric anisotropy. I think both Isaaks&Srivastava (Applied Geostatistics) and Deutsch&Journel (GSLIB) write about
        Message 3 of 3 , Jul 17, 1997
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          Chaosheng Zhang wrote:
          >
          > Dear colleagues,
          >
          > Question: How to model the variograms of a zonal anisotropy?
          >
          > I'm dealing with an area of 75km*75km, with heavy metal contents in 747
          > samples. The samples are quite evenly distributed, and high
          ...
          > ---------------------------------------------------------
          > Direction Model Nugget Sill Range(km)
          > ---------------------------------------------------------
          > Omni Gaussion 0.03 0.13 40
          > 5 (E-W) Gaussion 0.03 0.10 40
          > 50 (NE-SW) Gaussion 0.03 0.21 40
          > 95 (N-S) Gaussion 0.03 0.14 40
          > 140(NW-SE) Gaussion 0.03 0.07 40
          > ---------------------------------------------------------
          You can ``fake'' zonal anisotropy by geometric anisotropy.
          I think both Isaaks&Srivastava (Applied Geostatistics) and
          Deutsch&Journel (GSLIB) write about this.

          In your example: model the variogram as the sum of:
          1. a nugget (.03)
          2. a Gaussian model (partial sill 0.04 to fit NW-SE, range 40)
          3. some model with geometric anisotropy with:
          a. the principal direction in NW-SE
          b. a long range in this direction (e.g. 40000 km.)
          c. an anisotropy ratio that will give it a range of 40 km
          in the NE-SW direction (e.g. 0.001)
          d. a partial sill, equal to 0.21-(0.03+0.04)=0.14
          Note that steps b and c are related: range * anis.ratio should
          equal 40, in your case.

          You will not exactly reproduce both the 0.10 and 0.14, but
          hopefully end up with a reasonable average. Tweeking with
          different variogram models in 3. might help.

          Good luck,
          --
          Edzer
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