Geoscience Reference
In-Depth Information
ting lines on the nomograph. Calculate the
error for the size and mass pairs using the
formulae below. If any of the points do not
lie within the nomograph window, modify
the size of the sample so that the point is
within the window. Use a value of 1 for
b
in the calculation of
l
. This is a conservative
value for
b
. Note that the liberation factor
cannot go above 1.0.
Question 3:
Generate a sampling nomograph and check
your results.
References
Aitchison J (1986) The statistical analysis of compositional data:
Monographs on statistics and applied probability. Chapman and
Hall, London, p 416
Aitchison J, Barcelo-Vidal C, Pawlowsky-Glahn V (2002) Some com-
ments on compositional data analysis in archaeometry, in particular
the fallacies in Tangri and Wright's dismissal of logratio analysis.
Archaeometry 44(2):295-304
Chayes F (1962) Numerical correlation and petrographic variation. J
Geol 70(4):440-452
David M (1977) Geostatistical ore reserve estimation. Elsevier,
Amsterdam
Egozcue J, Pawlowsky-Glahn V, Mateu-Figueras G, Barcelo-Vidal C
(2003) Isometric logratio transformations for compositional data
analysis. Math Geol 35(3):279-300
Erickson AJ, Padgett JT (2011) Chapter 4.1: geological data collection.
In: Darling P (ed) SME mining engineering handbook. Society for
Mining Metallurgy & Exploration, pp 145-159
François-Bongarçon DM (1998a) Extensions to the demonstrations of
Gy's formula. In: Valleé M, Sinclair AJ (eds) Quality assurance,
continuous quality improvement and standards in mineral resource
estimation. Exp Min Geol 7(1-2):149-154
François-Bongarçon DM (1998b) Error variance information from
paired data: applications to sampling theory. In: Valleé M, Sin-
clair AJ (eds) Quality assurance, continuous quality improve-
ment and standards in mineral resource estimation. Exp Min Geol
7(1-2):161-168
François-Bongarçon D, Gy P (2001) The most common error in apply-
ing 'Gy's Formula' in the theory of mineral sampling, and the his-
tory of the liberation factor. In: Edwards AC (ed) Mineral resource
and ore reserve estimation—the AusIMM guide to good practice.
The Australasian Institute of Mining and Metallurgy, Melbourne,
pp 67-72
Glacken IM, Snowden DV (2001) Mineral resource estimation. In:
Edwards AC (ed) Mineral resource and ore reserve estimation—the
AusIMM guide to good practice. The Australasian Institute of Min-
ing and Metallurgy, Melbourne, pp 189-198
Gy P (1982) Sampling of particulate materials, theory and practice, 2nd
ed. Elsevier, Amsterdam
Hartmann H (ed) (1992) SME mining engineering handbook, vol 2, 2nd
edn. Society for Mining Metallurgy, and Exploration, Littleton, CO
Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic
Press, New York
b
3
clfgd
†‡
d
σ
2
=
l
=
ˆ
Š‹
l
FE
M
d
S
Alternatively, you may use the following table if needed.
σ
2
(FE)
d (cm)
l
IH
L
size
2.5000
0.9500
0.4750
0.2360
0.1700
0.1000
0.0710
0.0425
0.0250
0.0150
0.0106
5.10.2
Part Two: Nomograph Construction and
Fundamental Error
Question 1:
Plot the size lines calculated above onto a
blank nomograph. The size lines are at a 45°
angle that increases to the left.
Question 2:
Recall the starting sample mass from part 1.
Propose a sampling protocol, including crush-
ing and splitting, such that the total sampling
error,
σ
FE
, is less than 7.5 %. A useful con-
straint is to not introducing more than 5 %
error in a single step. An example is:
Position in
Protocol
Point on
Nomograph
Sample Mass
M
S
(g)
Fragment
Size d (cm)
Fundamental
Error σ
2
Fundamental Sample
Error σ
2
Sample
Error % σ
Primary crushing of core
A
20,000
0.475
Split for first subsample
A-B
2,000
0.475
Secondary crushing
B-C
2,000
0.071
Second split
C-D
50
0.071
Grinding of sample
D-E
50
0.015
Split for lab assay
E-F
1
0.015
Sample FE
Total sample error (2 times
the sample error)
