Probability and Statistics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 70

Table 2.5 Example of 61 gold assays (inch-dwt values) taken at 5-ft intervals along a drive in the
Virginia Mine
414, 362, 155, 621, 1034, 827, 1034, 1603, 621, 672, 569, 1189, 362, 2741, 776, 6671, 465, 155, 259,
310, 465, 362, 414, 414, 465, 103, 1344, 2637, 155, 569, 155, 52, 52, 155, 2172, 414, 1138, 310, 982,
724, 259, 465, 569, 310, 543, 440, 621, 414, 207, 3051, 2586, 776, 6050, 1086, 362, 517, 776, 621, 827,
724, 362, 284, 259
1 in.-dwt ¼ 3.95 cm-g; digitized from Krige and Ueckermann ( 1963 , Fig. 2)

2.5.2 Virginia Mine Example

Another set of chemical analyses for channel samples (digitized from Krige and
Ueckermann 1963 , Fig. 2) is shown in Table 2.5 . These are 61 gold assays taken at
5-ft intervals along a drive in the Virginia Mine, Witwatersrand gold field,
South Africa. Each number is the product of a gold concentration value and
thickness of the vein (or gold “reef”) reported as an inch-pennyweight value
(1 in.-dwt ¼3.95 cm-g). Because they were digitized from a graph these values
are approximations only. A striking difference between the values in Tables 2.4 and
2.5 is that the gold measures are much more erratic than the zinc values. A measure
often used to express degree of variability in a data set is the coefficient of variation
(CV) which is the standard deviation divided by the mean. For Table 2.4 ,
CV 0.51; for Table 2.5 , it is 1.33. Nevertheless, one can also see in Table 2.5

that neighboring values in the series tend to be similar. Such autocorrelation is
common in chemical element concentration values in rocks, especially for metals.
Witwatersrand gold assays also will be used in other examples later in this topic.
The spatial autocorrelation of the series shown in Tables 2.4 and 2.5 is similar to
that shown in many time series. However, it should be kept in mind that geoche-
mical space series are linear samples taken from 3-D rock bodies that usually
display similar or other autocorrelation in other places and directions as well.
This fact led Matheron ( 1962 , 1965 ) to formalize the concept of “regionalized
random variable” with properties different from the independent and identically
distributed (iid) random variables commonly used in other applications of statistics
such as populations of plants and in socio-economic surveys.

¼

References

Agterberg FP (1961) The skew frequency curve of some ore minerals. Geol Mijnb 40:149-162
Agterberg FP (1974) Geomathematics. Elsevier, Amsterdam
Agterberg FP (1990) Automated stratigraphic correlation. Elsevier, Amsterdam
Agterberg FP (2012) Sampling and analysis of element concentration distribution in rock units and
orebodies. Nonlinear Process Geophys 19:23-44
Agterberg FP (2013) At the interface between mathematical geoscience and classical statistics.
In: Pardo-Ig ´ zquiza E, Guardiola-Albert C, Heredia J, Moreno-Merino L, Dur ´ n JJ, Vargas-
Guzm ´ n JA (eds) Mathematics of planet earth. Springer, Heidelberg, pp 19-22