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811Re: AI-GEOSTATS: re CLT and mixtures

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  • Digby Millikan
    Jan 1, 2003
    • 0 Attachment
      Francis,
      Have you looked at indirect lognormal corrections and affine corrections
      for sample
      sizes. Many kriging softwares use diffrent sample sizes for their algorithm
      e.g. a single
      line of zero diameter representing all core sizes, with each block
      discretized to match
      the sample sizes, probably sufficient. Where poor lognormal semivariograms
      are available
      in the past I have used a sichel estimate of the mean of the population then
      cut the grades
      until the arithmetic mean equals the sichel mean and used inverse distance
      modelling
      (White Devil, N.T. Australia). Populations where actually mixed (lognormal
      with a small
      high grade portion) it may have been more useful to provide a mixed
      distribution mean rather
      than a sichel mean which I think a paper has been published on. Unforunately
      it can be
      rare at some undergrounds and such operating environments where several
      mines target
      one mill. However this underground grade modelling was only for financial
      planning,
      as stope design was done entirely from geological interpretation. However at
      open pit
      operations with a single mine and mill operating and more sophisticated
      grade control
      samples are available it is possible to reconcile a resource model to a
      grade control model
      and mill production to within a 0.5% by adjusting variograms and selective
      mining unit
      cut off grades, though I personally have no experience with nugget effect
      adjustments.

      Regards Digby Millikan
      Geolite Mining Systems
      digbym@...




      ----- Original Message -----
      From: "Francis T. Manns" <artesian1@...>
      To: "Isobel Clark" <drisobelclark@...>; "Digby Millikan"
      <digbym@...>
      Cc: <ai-geostats@...>
      Sent: Wednesday, January 01, 2003 8:07 AM
      Subject: RE: AI-GEOSTATS: re CLT and mixtures


      > Dear all,
      >
      > Please excuse my jumping into the dialogue without a proper introduction.
      I
      > just enrolled in the forum in order to search for a collaborator to assist
      > me in understanding what I've done with grade distributions for gold and
      > copper. My recent manuscript on Sadiola was rejected by Canadian
      Institute
      > of Mining Metallurgy and Petroleum [CIM] on the basis that my empirical
      > nugget effect solution needed a mathematical basis. Therefore I would
      like
      > to interest someone, perhaps a grad student somewhere, in pursuing the
      math
      > that eludes me. Would that mathematical proofs be required to have
      > empirical support in earth sciences? How many new mines struggle because
      > the expected grades fall short of predictions, estimates, and
      'calculations'
      > from the geostatistical side?
      >
      > My hypothesis is that in far too many instances, the sample size (weight)
      is
      > too small to represent the end product - the estimate (assay) of the metal
      > content of a tonne of rock or a block of ore. Moreover, the industry
      > standard aliquot of 30 grams is practical for a lab is not practical for
      at
      > least half of the gold deposits in the universe. We're asking 30 grams to
      > represent 1 million grams and then require four or so assays to represent
      > 300 tonnes (e.g., 120 grams to represent to estimate 300 million grams of
      > rock).
      >
      > I use a uniform probability plot to describe the assay distribution. A
      > straight segment on a uniform plot indicates a random number sequence. In
      > most cases, the distributions shows two or more random runs of numbers at
      > the high end of the distribution (these separate runs represent geological
      > loci of crystallization). Though the sample size is small, we at least
      get
      > a collection of random numbers or samples from the deposit. Treating
      these
      > empirically it is possible to correct the arithmetic average of the sample
      > distribution for the sample size limitation.
      >
      > As for conventional geostatistics, it's GIGO. A systematic error or
      errors
      > appear if the sample size is too small for the distribution of metal in
      the
      > rocks. I believe that if we were able to twin all the holes of the garden
      > variety exploration level deposit, we would find that very few holes would
      > actually be twinned, but the mean, standard deviation and standard error
      > would be indistinguishable.
      >
      > I have found that the slope of the straight segment of the uniform
      > probability plot is proportional to the error of the arithmetic average.
      > When one deducts the intercept of the slope at the fiftieth percentile
      from
      > the arithmetic average, one gets a very good estimator of the plant grade
      of
      > the deposit. I would be very happy to correspond with someone who has
      > insight into this phenomenon. It works for a copper distribution that I
      > once had in my possession. The raw data are gone now. I believe the 50th
      > percentile is important on a semi-log plot as it represents the square
      root
      > of the slope "factor", for want of any clearer understanding. I'll add my
      > website, and hope someone could have a glance at what's happening here.
      > It's geologically based, as you can see from my Borneo photograph in the
      > site.
      >
      > http://www.geocities.com/fmanns_artesian/index.html
      >
      > Thank you,
      >
      > Francis Manns, PhD
      > Artesian Geological Research
      > Toronto Ontario
      >
      >
      > -----Original Message-----
      > From: ai-geostats-list@... [mailto:ai-geostats-list@...]On
      > Behalf Of Isobel Clark
      > Sent: December 31, 2002 5:30 AM
      > To: Digby Millikan
      > Cc: ai-geostats@...
      > Subject: Re: AI-GEOSTATS: re CLT and mixtures
      >
      >
      > Digby
      >
      > The original derivation of the kriging equations does
      > not demand any specific distribution. However, it only
      > makes sense if the 'increments' - difference in value
      > - have a fairly stable variance.
      >
      > Kriging works much better IN PRACTICE if those
      > differences are Normal, hence the various
      > transformations offerred such as lognormal kriging,
      > hermitian polynomials, Normal scores, rank transforms
      > and so on.
      >
      > Normalising a mixture of distributions will result in
      > specious answers unless the distributions are mixed in
      > the same proportions all over the study area.
      >
      > Usually a mixed distribution is due to a mixture of
      > real populations. For example, in geology oxide and
      > sulphide samples may show different behaviour. There
      > may be separate phases of deposition.
      >
      > In short, a mixture of distributions generally
      > indicates a violation of the assumption of homogeneity
      > (or, if your prefer, stationarity) which is needed for
      > the proper application of any geostatistics. If
      > possible the populations should be separated and the
      > analysis carried out. If not, you may be able to cope
      > with the data using indicator kriging such as
      > suggested in my 1993 paper. There is also an example
      > in my Cardiff paper of 2000, I think.
      >
      > Isobel
      > http://geocities.com/drisobelclark/resume/Publications.html
      >
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