[ai-geostats] Re: Kriging Small Blocks
I was talking about kriging before cutoff is applied.
If the cutoff is applied to the block estimates my
comments stand. If you aply the cutoff to your data
first and then krige, you get the opposite problem,
because you will over-estimate every value and
under-estimate the tonnage.
My point (1) is that, if you wish to avoid conditional
bias in your kriging, you could consider using a
non-linear kriging method such as those mentioned. I
have no experience with either, since I follow a
different route in the correction of conditional bias
in mineral resource estimation.
--- nicolau.barros@... wrote: > Isobel,
> So for mining purposes can't we just krige before
> applying the cut-off
> criteria? I mean, for most mining applications one
> will prefer to have a
> more realistic geologic block model and will always
> have the chance to
> evaluate his/her panels under the appropriate
> cut-off criteria, but applying
> that criteria after estimating small blocks, right?
> Could you please explain your point in solution (1)
> below? Thanks for
> indicating the literature.
> Nicolau Barros
> Mine Planning and Production Control Department
> Mineração Rio do Norte S.A.
> +55 (93) 549 8215
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> -----Mensagem original-----
> De: Isobel Clark [mailto:drisobelclark@...]
> Enviada em: segunda-feira, 19 de julho de 2004 05:23
> Para: Julhendra_Solin@...
> Cc: ai-geostats@...
> Assunto: [ai-geostats] Re: Kriging Small Blocks
> The warning about kriging small blocks is about
> "small" relative to the sampling density. For
> less than about one-third of the grid spacing.
> The warning is the same as the one about 'point'
> kriging (mapping) The map is too smooth - or, at
> least, a lot smoother than the real surface would
> High value areas will be under-estimated and low
> areas will be over-estimated.
> If your objective in kriging is to obtain general
> of an area with an idea of where the highs and lows
> are, then ordinary kriging is sufficient. The over-
> and under- estimations cancel out on average.
> In mining applications, where block kriging
> originated, most applications require a 'cutoff',
> where values below a certain value are not included
> the 'plan'. In this case, mapping or estimating
> blocks will result in an over-estimation of
> ground and an under-estimation in average value.
> In pollution or environmental applications, the
> at risk will be under-estimated as will the true
> toxicity or risk factors.
> There are two major ways round this problem:
> (1) use a non-linear kriging approach such as
> disjunctive kriging or the multivariate gaussian. Ed
> Isaacs and Mohan Srivastava's book is th ebest
> reference for the latter. Rivoirard's book for DK.
> (2) simulation. There are lots of simulation methods
> around, which allow you to 'put back the roughness'
> and get an idea how bad the problem might be. GSLib
> pretty good on this.
> If, as in mining, you wish to apply some sort
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- Hi Isabel
If you go to www.isaaks.com and click on "Otherstuff", you will find an
example where the block estimates are conditionally biased (rather
severely), but the grade tonnage curves are right on the money. Perhaps this
will help clear the confusion. Ed
From: Isobel Clark [mailto:drisobelclark@...]
Sent: Monday, July 19, 2004 10:47 AM
To: Edward Isaaks
Subject: [ai-geostats] Re: Kriging Small Blocks
I would differ from your explanation on one point.
If you are merely declaring a mineral resource, i.e.
mineral in the ground, then the conditional bias may
not be relevant at the "pre feasibility" stage.
However, as soon as you introduce any economic or
technical parameters which entail selection, the
conditional bias makes its appearance.
In every project I have worked on, from
pre-feasibility onwards, I have been asked for a
grade/tonnage calculation - no matter how hand-waving
it may be. The grade/tonnage curve will be affected by
the conditional bias. By how much has to be assessed
at the time. Most of Chapter 3 in Practical
Geostatistics 1979 is devoted to working out what the
(theoretical) global grade tonnage curve looks like
when you adjust for the variance reduction. Even this
will differ from the curve derived from the kriged
estimates, no matter what size the block.
The problem is even greater for environmental
applications, especially toxic level risks. A 'global
view' - i.e. a map - will not identify the true peaks
because of the conditional bias. The fact that the
overall average is unbiassed is irrelevant when trying
to identify an area which is likely to be lethal.
So, there is no contradiction. Conditional bias is
unimportant (or irrelevant) until you apply some
selection criterion. Yes, we agree. However, selection
criteria can be relevant at very early stages of a
project. It depends on your objective.
free downloads of Practical Geostatistics 1979
PS: sorry I mis-spelled your name, I know it drives me
nuts when people call me 'Clarke' ;-)
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