Re: AI-GEOSTATS: Ore Reserves Classification
Thanks for the clear exposition on the limitation of
the kriging variance as a measure of reliability for
It should, perhaps, be pointed out that the kriging
variance is what we minimise and hence, surely, some
measure of reliability? The whole geometry versus
variability thing has been at issue since Philips and
Watson provided their seminal (sic) paper in 1986.
Given consistent data quality and a Normal (gaussian)
distribution, geometry is what determines likely
error. Under those circumstances, 1000 simulations
will yield an average of the kriged value and a
standard deviation equal to the kriging standard
If the data quality is not consistent and the
distribution of values is not Gaussian, then your
comments hold particular force. Since these are the
circumstances under which I labour daily, I would
appreciate any and all suggestions as to what we use
instead. Simulation is not an option when you have
hundreds of thousands of blocks and a limited time to
produce a reserve.
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- Dear list members,
I wish to make a remark on the discussion started on the kriging variance.
In my opinion the SD of the solution obtained by kriging is determined by
two effects. One is the (geometrical) distribution of the data, the other
one is the (a priori) standard deviation of the data. Richards remark is
right if the data has equal weights or standard deviations (SD). However if
the data is all weighted equally (by say 1.0) we will get a scaled 'SD'. If
you like studentized statistics, you can get a estimate for the SD of the
solution by multiplying with the a posteriori variance factor.
In our problems (cross validation of bathymetry data) we have a estimate for
the SD, which we use in the covariance function for the kriging problem. The
resulting SD of the solution will depend on the chosen a priori SD for the
Just my 2 cents,
Quality Positioning Services bv, Huis ter Heideweg 16, 3705 LZ
Zeist, the Netherlands
Tel +31 (0)30 6925825, Fax +31 (0)30 6923663, Web http://www.qps.nl
From: Richard Hague [mailto:richardh@...]
Sent: woensdag 3 april 2002 6:48
Subject: Re: AI-GEOSTATS: Ore Reserves Classification
The use of the kriging variance to categorise/classify Mineral (Ore)
Resources and/or Ore Reserves is an old chestnut that periodically raises
it's ugly head. The kriging variance is related, pure and simply, to the
data configuration and has nothing to do with the sample grades/variables
being used for interpolation. As an example say a grade was being
interpolated into a block which has been sampled on each corner, regardless
of what the individual sample grades are, the kriging variance for that
block is going to be the same. Example: if all four samples have the same
grade of (say) 2.35g/t Au you will get the same kriging variance as the case
where the four samples grades are (say) 0.01, 102.9, 0.88 and 3.60 g/t Au.
Naturally I would have more confidence in the interpolated grade in the
former scenario than the latter; thus the use of the kriging variance to
determine confidence (or classification) of an estimate is misleading.
One method of obtaining some feel for the possible error range would be to
run a large number of grade simulations into the block, the variance of all
simulated grades would give an indication of error - again in the example
given above, the variance of the simulated grades using the former case
would be much smaller than in the latter case.
Of course classification of Mineral (Ore) Resources and/or Ore Reserves
needs to take into account a lot more items (as expounded by the JORC
(1999) code) - than just some objective measure of estimation error, it
needs to take into consideration, amongst other things, data quality - if
you have poor quality data (eg biased/inaccurate), regardless of how good
any statistical measure of the estimation error is, you will always have
JORC; 1999: Australasian code for reporting of mineral resources and ore
reserves (the JORC Code). Prepared by the Joint Ore Reserves Committee of
the Australasian Institute of Mining and Metallurgy, Australian Institute of
Geoscientists and Minerals Council of Australia (JORC).
Hellman & Schofield Pty Ltd
p&f: +61 (0)7 3217 7355
e: richardh@... <mailto:richardh@...>
w: http://www.hellscho.com.au <http://www.hellscho.com.au>
----- Original Message -----
From: José <mailto:cuador@...> Quintín Cuador Gil
To: ai-geostats@... <mailto:ai-geostats@...>
Sent: Wednesday, March 27, 2002 4:27 AM
Subject: AI-GEOSTATS: Ore Reserves Classification
Dear list members
The Kriging variance has some uses. In mining, it can be used in the Ore
What is the opinion about this in the Geostatistical community?
It is possible to use the Kriging variance for ores reserves
classification?, (Yes or No).
Thanks in advances for any opinion.
José Quintín Cuador Gil
Department of Informática
University of Pinar del Río
< cuador@... <mailto:cuador@...> >
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