Page 252 - Introduction to Mineral Exploration

10: EVALUATION TECHNIQUES 235

Large errors in estimation of thickness (or hundreds of block values on a complex deposit
grade) can therefore be made when assuming requires the aid of a computer. This method
that the thickness or grade of a block is equal begins to take the spatial distribution of data
to the thickness or grade of a single sample points into account in the calculations.
point about which the block has been drawn. Most of these methods have found applica-
Care should be taken when using the cross- tion in the mining industry, some with con-
sectional method that the appropriate formula siderable success. The results from one method
is used for computing volume between sec- can be cross checked using one of the other
tions, as significant errors in tonnage estima- methods.
tion can be introduced where the area and
shapes on adjacent sections vary considerably. Geostatistical methods
Wire frame modeling, in technical software
packages such as Datamine, offers the user the Semi-variograms
ability to construct a series of sections between The variables in a deposit (grade, thickness,
which the user can link the areas of interest etc.) are a function of the geological envir-
with a wire frame. The package calculates onment. Changing geological and structural
the volume, limiting some of the errors intro- conditions results in variations in grade or
duced by manual methods. Manual contouring quality and thickness between deposits and
methods are less prone to this estimation even within one deposit. However, samples
error by virtue of the fact that contours are that are taken close together tend to reflect the
constructed by linear interpolation, thereby same geological conditions, and have similar
smoothing the data irregularities. thickness and quality. As the sample distance
n
The inverse power of the distance (1/D ) increases, the similarity, or degree of correla-
method can also be used to calculate resources, tion, decreases, until at some distance there
usually using a geological modeling software will be no correlation. Usually the thickness
package. The deposit is divided into a series of variable correlates over a greater distance than
regular blocks within the geologically defined coal quality variables (Whateley 1991, 1992)
boundary, and the available data are used to or grade.
calculate the thickness value for the center Geostatistical methods quantify this con-
of each block. Near sample points are given cept of spatial variability within a deposit
greater weighting than points further away. and display it in the form of a semi-variogram
The weighted average value for each block (Box 10.4). Once a semi-variogram has been
is calculated using the following general calculated, it must be interpreted by fitting
formula: a “model” to it. This model will help to iden-
tify the characteristics of the deposit. An ex-
×
∑ V ( f) ample of a model semi-variogram is shown
Th = in Fig. 10.22. The model fitted to the experi-
∑ f mental data has the mathematical form shown
in the two equations below. It is known as a
where Th = the thickness at any block center, V spherical scheme model and is the most com-
= known thickness value at a sample point, mon type used, although other types do exist
n
f = 1/D weighting function, n = the power to (Journel & Huijbregts 1978, David 1988, Isaaks
which the distance (D) is raised. & Srivastava 1989, Annels 1991).
The geologist has to decide how many of There is often a discontinuity near the
the available data are to be used. This is norm- origin, and this is called the nugget variance
ally decided by choosing a distance factor for or nugget effect (C 0 ). This is generally attribut-
the search area (usually the distance, a, derived able to differences in sample values over very
from the range of a semi-variogram), the power small distances, e.g. two halves of core, and
factor which should be employed (normally can include inaccuracies in sampling and
2
D ), and how many sample points should be assaying, and the associated random errors (see
used to calculate the center point for each section 10.1.2). C 0 is added where a nugget
block. The time needed to calculate many effect exists: