Correlation, Method of Least Squares, Linear Regression and the General Linear Model - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 112

there is a linear relationship between the two variables. However, six olivine
crystals consisting entirely or nearly entirely of forsterite that also were treated
by both methods (chemical analysis and d 174 determination) do not seem to fall on
the best-fitting (%FO

30) straight line. This discrepancy was tested by using the
slightly wider 95 % confidence belt of Type (4). The conclusion of this statistical
analysis was that the best-fitting straight-line relationship could only be used for
olivine crystals with more than 30 % forsterite.
The topic of 95 % confidence belts also will be discussed in Chap. 7 in the
context of trend surface analysis. In that kind of 2-D application the two surfaces
constituting the confidence belt are relatively flat in the area where the observation
points are located but the vertical distance between them increases very rapidly near
the edge of the area with observation points.

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4.2.2 Mineral Resource Estimation Example

Geoscientists are using both facts and concepts to determine the probable
occurrence of ore deposits. Examples of basic facts are age and lithological data
on rock units, chemical determinations and geophysical measurements. There is a
gradual transition from basic facts to conceptual projections of structures and
composition of rock formations. Standard conceptual projections normally made
by geoscientists; e.g., extrapolations to bedrock partially overlain by regolith or
debris, can be taken as facts. A few historical remarks are that, originally, ore was
discovered by prospectors but later economic geologists could narrow their search
by using genetic models. Bateman ( 1919 ) argued convincingly that the old saying
“where ore is, there it is” was to be replaced by answering the question “why ore is
where it is”. He promoted “intelligently directed search for ore or oil”. To-day
much ore is being found by means of advanced geophysical prospecting techniques.
Moreover, as Zhao et al. ( 2008 ) point out, increasingly new deposits are being
discovered at greater depths with the aid of 2-D and 3-D specialized technologies
on the one side (see, e.g., de Kemp 2006 ) and non-linear modeling on the other
(Cheng 2008 ).
Both geomathematics and conceptual thinking are needed to extrapolate data
laterally into less explored areas or vertically from the surface downward into
hidden rock formations at greater depths. Such projections remain subject to
significant uncertainty that has to be quantified in order to allow valid decision-
making. The problem to be considered is how the mineral potential of a region can
be assessed systematically by statistical extrapolation from known facts. Because of
the complexity of the geological framework, many authors have employed a variety
of more subjective methods for mineral potential estimation, often with good
results (see, e.g., Harris et al. 2008 ) but these other, “knowledge-driven” methods
( cf . Bonham-Carter 1994 ; Bardossy and Fodor 2004 ; Carranza 2008 ; Singer and
Menzie 2010 ) are outside the scope of this topic. In this section, some basic