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Multi-criteria analysis in GIS environment for natural resource development - a case study on gold exploration
Independence
N different pieces of evidences are assumed to be
conditionally independent and the posterior
odds O(H/E) are obtained as
O(H/E1, E2
.En) = O(H) εLEi.
Where, LE is the likelihood of
estimate.
Likelihood of estimate, LE is calculated on the basis of the
importance of the presence or absence of a criteria on the presence of
hypothesis (presence of mineral occurrence). Details on this has been discussed
in Bonham-Carter et al.(1990).
Conjunction
The evidence is
true only if all the contributing pieces of evidences are true, i.e.,
if
E = E1 and E2,and
and En, the joint probability is calculated using fuzzy set
theory as
P(E/E') = Mini(P(Ei/H).
Disjunction
The
evidence is true if any of the pieces of evidence is true, that is
if E1 or
E2
.or En,
the joint probability is calculated using fuzzy set theory
as
P(E/E') = Maxi(P(Ei/H)).
When p indicator patterns are considered
simultaneously, each unit cell is assigned a posterior probability derived from
the prior logits as
logit(d/1,2
.p) = W(1)+
.+ W(p)+ logit(d),
and
the posterior probability is calculated as
1/(1+exp(logit(d/1,2
p))).
Mineral potential mapping at the
Hutti-Maski schist belt - A case study
The Archaean Hutti-Maski
greenstone belt consists predominantly of metavolcanics and subordinate
metasediments. This association of rock is surrounded by multiple phases of
intrusive diapiric granitoids. Vescicular metabasalt is the host rock for these
auriferous lodes. These lodes are localized along shear zones,
granite-metabasalt contacts, granophyre-metabasalt contacts and fold axes. The
geometry and orientation of the lodes is affected by shear zone. Groundwater and
weathered bedrock were most suitable media for detecting the dispersion halos
related to mineralization. The generated pedogeochemical, hydrogeochemical,
lineament proximity and lithological data were closely associated with the known
gold occurrences (Sahoo and Pandalai, 1999; 2000, Sahoo et al., 2000).
Developing the Decision-tree
The data sets that would suffice
in targeting potential zones for gold exploration were put to a raster GIS
(IDRISI) and analysed empirically the spatial relationship of the factors with
the known gold occurrences. The datasets include the lithological map, lineament
maps, water chemistry data, trace element concentrations in soil and known
deposit map. These maps were rasterised at 30m resolution and all of them were
coregistered with a base map. A series of binary maps, i.e. a map showing
whether a characteristic is present or not were prepared. During processing, the
operations performed were generation of required map classes and selection of
lineaments between map classes using vector-raster and introduction of dilation
(buffering) to produce proximity maps. The maps used as predictors (evidence)
such as proximity of lineament, proximity of favorable geochemical signature and
presence/absence of rock-type were modelled with the hypothesis, known mineral
occurrences. The optimization is carried out through a decision tree analysis,
which partitions the dataset, using the predictor variable at a time, to produce
mutually exclusive subsets.
In decision tree approach, integration of
pieces of evidences, given hypotheses are combined and updated by propagation of
probability for each pixel in a raster GIS. The primary evidence maps are either
true-false type with probability values of 1 or 0 respectively or the proximity
to feature type with uncertain values 0 and 1. In this paper, the uncertainties
associated with the evidence maps are efficiently propagated with the use of
fuzzy-logic and Bayesian probabilities while integrating the maps. The
predictive modelling strategy for mapping favorable areas for gold targeting
involves a decision tree containing few levels of decisions (Fig. 1). The decision model uses boolean operations
and Bayesian probability functions to evaluate hypotheses in terms of one or
more pieces of evidences. As hypotheses are evaluated, the prior probability is
reevaluated to produce posterior probability. The inference engine program was
external to the GIS and was interfaced with it. Where geological data was
uncertain, the model used fuzzy-logic. The maps were then combined using weights
to evaluate how important the presence or absence of a characteristic is, based
on the mineral occurrence present in the area.
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