AI-GEOSTATS: Re: Samples in a Block
- Hi, Mark, Donald
Donald Myers final sentence opened a door for me:
"There is no definitive answer to the question since it
depends on the question, i.e., what is the data to be
In this perspective, I would line to raise several issues.
My background and experience is mainly that of a mining
geologist who is familiar with geostatistics, and has had
the opportunity to work with several geostatisticians.
Forgive me for broadening the problem, but such are geology
In my opinion, the final purpose of aampling is
estimation leading to mining extraction that achieves
optimal metal recovery and minimal dilution. Estimating/
modeling of the variogram and kriging are interim
objectives. Geological mapping, interpretation and modeling
are also essential steps with whom sampling methods,
sampling grid dimensions and geostatistical aspects should
be integrated in the determination of global and local
continuity (Sinclair and Vallée, 1994).
The basic problem of sampling grid size should be viewed in
three dimensions. Our usual sampling grids are planned for
efficiency, using a stratified drilling pattern
perpendicular to the plane of apparent structural /
geological continuity. So far, so good!
However, once we have achieved a first delineation and can
calculate a semivariogram along the drill hole axis,
too often we neglect or forget to verify if these
continuity parameters apply are present in the other two
This problem has been detected by Michel David and described
in a sampling paper titled "What happens if?" given at a
sampling symposium in Australia in 1976 where he describes
the problem and recommends sampling specifically designed
to verify continuity parameters in the second and third
dimensions. Sadly, there is only one sentence in
"Geostatistical Ore Reserve Estimation (which was already
in print at the time this paper was prepared and presented)
that refers to this problem (around page 200).
Journel and Huijbregts in "Mining Geostatistics" also
describe this problem (1978) and recommend a few simple
tools, for instance to lay out a cross of more closely
spaced drill holes within the main grid.
I consider, based on my mining experience, that sampling
of rock in place should be targeted stratified sampling,
not random sampling. Regionalized variables require
When the exploration or mining geologist halves the sampling
grid dimension, he/she is basically using a similar
strategy. I know the results of this effort are viewed by
geostatisticians as the "clustering" problem! For the mining
geologist, the objective is local estimation and close
determination of ore limits, whether they are grade contacts
or sharp contacts both for planning and extraction.
What is the ideal sampling grid dimension for the mining
geologist and the mining engineer? My answer: the one
that allows to plan and develop and extract the ore (from
stopes or open pit) efficiently as described above. I
understand the student/researcher cannot rely on similar
amounts of funds for drilling.
Another important consideration in the Davil paper and in
Geosatistical Ore Estimaion is that of sample preparation
and assaying quality control. Quoting from the paper"
" ... (frequently) it is the sanple preparation procedure
whick generates the nugget effect rather than the real
mineralization which generates the nugget effect"
[underlined in the text]. This subject makes up almost a
chapter of Geostatistical Ore Reserve Estimation.
A higher "induced" nugget effect, that is a higher sampling/
assaying variance of the values used for a selectin decision
will reduce the accuracy of LOCAL estimation and mine
What is the final grid dimension (the one we call measured
resource, proven reserve). This will vary depending on
orebody configuration and mining method selected. In a open
pit, with a fairly sizeable, not too complex and not too
nuggetty ore body, you generally can get away with a wider
grid for proven ore than yo can in the majority of cases
In an open pit you can sample more systematically,
from bench to bench than you can in most underground mine.
Also one has more flexibility for selection by adjusting
blast limits based on test drilling on the pit floor and
sampling of blast holes.
For those this may interest, here are references of papers,
including some I was involved in that deal with these
Marcel Vallée Eng. Geol.
Géoconseil Marcel Vallée Inc.
706 Routhier St
Sainte-Foy, Québec G1X 3J9
Tel: (1) 418 652 3497
Fax: (1) 418 652 9148
David M., 1976, What Happens If? A few remarks on Useful
Geostatistical Concepts for the Design of Sampling Patterns.
The Aus. I.M.M Melbourne Branch, Sampling Symposium, Sept.
1976, preprint of proceedings, 16 p. (A major sampling
Postolski, T. A., Sinclair, A. J. (1998) Geology as a
Basis for Refining Semivariogram Models for Porphyry-Type
Deposits. Exploration and Mining Geology, Vol. 7, Nº 1-2,
Vallée, M, Dagbert, M, & Côte, D. (1993) Quality control
requirements for more reliable mineral deposit and reserve
estimates. CIM Bulletin, vol. 86. No 969, p. 65-74.
(the ideas presented in this note have been developed here)
Sinclair, A.J. and Vallée, M. (1994) Reviewing continuity:
An essential element of quality control for deposit and
reserve estimation. Exploration and Mining Geology, Vol.3,
Nº 2, pp. 95-108. (Determination of continuity is at the
core of estimation!)
Vallée, M. (1998) Sampling Quality Control. Exploration and
Mining Geology, Vol, 7, Nº 1-2, p. 107-116. (Some material
on sampling strategy; sampling and assay variance work
against good semivariograms and good estimation)
Vallée, M. (1992) Guide to the evaluation of gold deposits.
CIM Special Volume 45, Canadian Institute of Mining,
Metallurgy and Petroleum, Montréal, Canada, 299 p.
(A general perspective of the work of the geologist in
estimation and mining. It was consdidered by Canadian
at the time of publication, to be oriented too much toward
the use of geostatistics!)
Vallée M. Draft Standards for Exploration and
Resource/Reserve Estimation. Developed and expanded
by the author from a report sponsored by the
Québec Department of Natural Resources following
the Bre-X affair, 110 pages, 800 k WordPerfect file.
(This on-going work presents an ISO-9000:2000 compatible
Quality Management and Continuous Improvement system
that intends to integrate the geological, geostatistical
and minng characteristics and constraints of mineral
The Volume 7, No 1-2 issue of Exploration and Mining Geology
is a special issue on "Quality Assurance, Continuous
Improvement and Standards in Resource Estimation.
Abstracts of the papers can be viewed on the CIM web site
(www.cim.org) at the Geological Society and/or Publications
pages. Eight of the nineteen papers deal with sampling and
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