Probability and Statistics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 66

value that may range at random about the line, then the 95 % confidence interval
satisfies:

s

ʦ

zðÞʦ zðÞ

z t 1 : 96

n ˆ

2

zðÞ

If the data come from a normal distribution, a 95 % confidence belt, on the
average, contains about 95 % of the plotted observations. The pattern in Fig. 2.2
suggests several departures from normality notably in the upper tail. It also can be
seen that the absolute value of the largest difference between observed and
expected frequencies is 0.14. This is slightly less than 0.16 representing the 95 %
confidence limit according to the two-tailed Kolmogorov-Smirnov test.

2.5 Sampling

Difficulties of sampling rocks at the surface of the Earth and performing measure-
ments on them were discussed in Chap. 1 . Geophysical measurements generally are
indirect and apply to large volumes of rocks. The determination of rock composi-
tion data is more direct but often there is a problem on how to decide on what larger
rock unit is represented by the piece of rock subjected to chemical analysis. Also, at
the microscopic scale most rocks are heterogeneous and volume of rock sample
matters. The purpose of the examples given in this section is to illustrate some of
the problems often encountered when rock samples are collected for the purpose of
chemical analysis. Normally rocks are crushed before their chemical composition is
determined on a sample taken from the resulting powder. This aspect of rock
sampling has been studied in detail by geochemists, chemists and mineral engineers
(see, e.g., Gy 2004 ). Drill-core samples can be used to produce good results. In this
Section, two examples will be given of a technique called “channel sampling” used
in the mining industry for sampling ore in situ in the past and at present.

2.5.1 Pulacayo Mine Example

De Wijs ( 1951 ) used a series of 118 zinc concentration values (Table 2.4 ) from
samples taken at a regular (2 m) interval along a horizontal drift in the Pulacayo
Mine in Bolivia (Fig. 2.7 ). This series has been used extensively for later study by
many authors including Matheron ( 1962 ), Agterberg ( 1974 , 2012 ), Chen
et al. ( 2007 ), Lovejoy and Schertzer ( 2007 ) and Cheng ( 2014 ). Average zinc
value for Table 2.4 is 15.61 %. This example will again be used later in this
topic. Geological background on the Pulacayo orebody is provided here and
consideration paid to the question of how representative this example is of ore