Prediction of Occurrence of Discrete Events - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 144

If a binary map layer is used as an indicator variable, the probability of
occurrence of a deposit is greater when it is present than when it is absent, and
W + is positive whereas W is negative. Consequently, C generally is positive.
However, in a practical application, it may turn out that C is negative. This would
mean that the map layer considered is not an indicator variable. In a situation of this
type, one could switch presence of the map layer with its absence, so that W + and
C both become positive (and W negative). An excellent strategy often applied in
practice is to create corridors of variable width x around linear map features that are
either lineaments as in Fig. 5.1 or contacts between different rock types (e.g.,
boundaries of intrusive bodies) and to maximize C ( x ). From d dα ¼

2
αþ 1

2 being
positive it follows that Q ( x ) and C ( x ) reach their maximum value at the same value
of x ( cf . Agterberg et al. 1990 ).

ð Þ

5.1.2 Meguma Terrane Gold Deposits Example

The first application of WofE was concerned with Meguma Terrane gold deposits in
Nova Scotia (Wright 1988 ; Bonham-Carter et al. 1988 ). The study area of
2,591 km 2 is shown in Fig. 5.3 . In total, there were 68 gold deposits. Gold
production and reserves figures were available for 32 gold mines. If unit cell area
is made sufficiently small, maps of posterior probabilities become similar in
appearance except that, like the prior probability, all posterior probabilities are
directly proportional to unit cell area selected. In this application, unit cell area
arbitrarily was set at 1 km 2 .
Three examples of map patterns considered are shown in Figs. 5.4 , 5.5 , and 5.6 .
Figure 5.4 is a ternary pattern for geochemical signature for Au. This pattern has
three states instead of two because it is based on information from lake sediments
that are missing in parts of the area close to rivers or the coastline. Each lake is
surrounded by a catchment basin. In order to avoid strong violations of conditional
independence of map layers, the 16 chemical elements for with measurements were
available were combined into a single index or signature by multiple regression.
If data are missing, the weight is set equal to 0. The positive weight for the
geochemical signature is relatively large but the negative weight is small. Multiple
regression is one way to combine variables with similar map patterns into a single
index; another good method for accomplishing this is to perform principal component
analysis on all variables and then use scores for the first principal component to create
a single new map layer (Agterberg and Bonham-Carter 2005 ;Wangetal. 2012 ).
Figure 5.5 shows corridors constructed around Acadian anticlines. Both positive and
negative weights are significant. Figure 5.6 is for a corridor constructed around
contacts of Devonian granite. Some gold deposits could be genetically related
with these granites. This hypothesis can be tested statistically by application of the
following procedure.