GEOSTATS: modeling zonal anisotropy

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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.
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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• ... 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

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

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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