Correlation, Method of Least Squares, Linear Regression and the General Linear Model - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 113

principles of quantitative treatment of the geological framework of a region will be
considered and demonstrated on the basis of a simple, 2-D mosaic model. Later, in a
recently performed case history study (Agterberg 2011 ), a multivariate prognosis
made from 1968 data for copper potential of the Abitibi area on the Canadian Shield
will be reviewed and compared with amounts of copper and copper ore discovered
in this area during the past 40 years. It turns out that most newly discovered copper
occurs in the same favorable environments where deposits were already known to
exist closer to the surface of bedrock.
The future of fully automated regional mineral resource estimation is promising
because, increasingly, sophisticated geophysical remote sensing techniques are
becoming available, while rapid progress is being made in the field of 3-D geolo-
gical mapping. It should be kept in mind, however, that the geological framework
generally is highly heterogeneous. ( cf . Chap. 1 ) In addition to continuous spatial
variability observed for geophysical fields, there are numerous discontinuities in
the upper Earth crust, e.g. at contacts between different rock units and where there
are faults. In general, advanced pre-processing techniques are required to produce
realistic 3-D images providing the inputs for mineral potential estimation (de Kemp
et al. 2013 ).
For the purpose of this discussion, it is useful to make a distinction between
mineral exploration and mineral resource estimation. The objective of mineral
exploration is to delineate high-potential target areas. This can be achieved by
ranking cells or pixels in a region by means of a probability index for relative
prospectivity. In mineral resource estimation, the primary objective is to predict
numbers of deposits and their sizes for larger regions. Any probability index has to
be converted into a probability that is unbiased. Early on, mineral resource estima-
tion problems were considered by relatively few authors including Allais ( 1957 )
who used the Poisson model for completely random spatial distribution of large
mineral deposits of any type ( cf . Sect. 3.3.2 ) . Griffiths ( 1966 ) advocating use of
“unit regional value” lumping different types of metal and hydrocarbon deposits
together, and Harris ( 1965 ) who quantified geological maps for cells relating “total
dollar value” based on all metals to bedrock variables by means of multivariate
statistical analysis. A characteristic feature of these early statistical publications
was that natural resources of different types were analyzed simultaneously. Such
lumping can be advantageous if statistical models have the property of additivity
(e.g., a mixture of two spatial Poisson process models is another Poisson process
model) but often it is better to incorporate different genetic models into the mineral
resource estimation. Agterberg ( 1971 , 1974 ) used a commodity-based approach
that can be summarized as follows.
Various sources of uncertainty have to be considered in mineral resource
estimation, and to some extent in exploration. These different types of uncertainty
were considered separately and combined with one another when copper and zinc
mineral potential maps were constructed for the Abitibi area on the Canadian Shield
in the late 1960s and early 1970s (Agterberg et al. 1972 ) to be reviewed in more
detail later in this chapter. To-day, of course, better answers could be obtained than
in the early 1970s, because of both theoretical and computational advances.