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## 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
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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|__|__| Dr. Chaosheng Zhang |__|__|
|_____| Geological Survey of Sweden, SGU |_____|
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• 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
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
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>

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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 3 of 3 , Jul 17, 1997
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
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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