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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


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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 2 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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