GEOSTATS: Summary - Back Transform

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• Here is a summary of the anwers about back transformation. Thanks for all the reply s Ian Hunt 1) A (there are others) correct way to perform the back
Message 1 of 1 , Jun 29, 1998
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Here is a summary of the anwers about back transformation.

Ian Hunt

1)
A (there are others) correct way to perform the back transform is:

z*(u) = exp{y*(u) + [(sigma)^2(u)/2]}

where (sigma)^2(u) = Simple Kriging variance

Note: this back-transform is delicate since any error in the estimation
process
is exponentiated too. Consider kriging with the multi-Gaussian approach
(i.e
normal score transform the data and perform either simple or ordinary
kriging
with the normal score covariance).

If you need to get a feel for uncertainty, then it's better to use a
simulation-type algorithm e.g. sequential gaussian or indicator simulation.

It's impossible to know what the estimation error is since the true value
is
unknown.

A good reference for lognormal kriging is:
A.Journel: The lognormal approach to predicting local distributions of
selective
mining grades. (Math Geology, 12(4):285-303, 1980).

Cheers,

-------
Tony Lolomari
GeoFrame Modeling Commercialization
Schlumberger GeoQuest
5599 San Felipe, Suite 1700; Phone: +1 (713) 513 2478
Houston Texas 77056-2722 Fax: +1 (713) 513 2039

2)
Interpolating grades as suggested in option a will underestimate the
Taking the log of the grades, interpolating, and then back transforming
the resulting
grades will give you the Geometric Mean or the median value.

If you want to do kriging better approach would be to use indicator
kriging.

Most of our reserves are actually prepared using inverse distance
squared
and this has proved to be very adequate.

regards

alan

3)
To give you a better answer, we need to know the following:

What kind of deposit are you working on and what metals are you
interpolating? Why do you transform the data? Is the metal "spikey" and
discontinuous or is it continuous. Is there a known trend?

There are those who still use lognormal variography and kriging, but it is
not popular as it used to be... (see Snowden, Clark etc.)

Variograms of the log transformed data tend to show longer ranges and lower
nuggets than the untransfomed data, and this carries on through the the
continuiity than actually exists in the data. (Try some correlograms of
relative-by-pair variograms...the transformed variograms will give you the
relative shapes and anisotropism however.)

good luck,

keith

4)
A small reminder, the sferical model and the lognormal are theoretically
incompatable under certain conditions, I believe a small note on this was
published by M. Armstrong in the early nineties or late eighties, in Math
Geol. I would also recommend to read the paper by Andre Journel on
lognormal kriging published in 1984 in Math. Geol. However at Stanford we
recommend caution when using this technique as it is not very robust
(exploding variance).

regards,

Jef

_______________________________________________________
Jef Caers

(work)
Stanford University
School of Earth Sciences
Department of Geological and Environmental Sciences
Green Earth Sciences Building, Rm 337,
Stanford, CA 94305-2220, USA

tel (1) 650 723 8064
fax (1) 650 725 2099
e-mail jef@...

(home)
160, Clarendon Rd, #E
Pacifica, CA 94044-2727, USA
tel (1) 650 738 3056
_______________________________________________________

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