Prediction of Occurrence of Discrete Events

Many geological bodies or events including various types of mineral deposits, earthquakes and landslides can be represented as points on small-scale maps. Various methods exist to express probability of occurrence of such events in terms of various map patterns based on geological, geophysical and geochemical data (Agterberg 1989a). The machine-based approach was greatly facilitated by the development of Geographic Information systems (GIS, cf. Bonham-Carter 1994). Weights-of-Evidence modeling and weighted logistic regression are two powerful methods useful for estimating probabilities of occurrence of an event within a small unit area. Weights-of-Evidence (WofE) consists of first assuming that the event can occur anywhere within the study area according to a completely random Poisson distribution model. This equiprobability assumption provides the prior probability that only depends on size of an arbitrarily small unit area. Various indicator map patterns commonly reduced to binary (presence-absence) or ternary (presence-absence-unknown) form are used to update this prior probability by means of Bayes’ rule in order to create a map of posterior probabilities that is useful for selecting target areas for further exploration for undiscovered mineral deposits or for the prediction of occurrence of other discrete events such as earthquakes or landslides. If probabilities are transformed into logits, Bayes’ rule is simplified: the posterior logit simply is equal to the sum of the prior logit and the weights of which there is only one for each map layer at the same point. These weights are either positive (W+) or negative (W−) depending on presence or absence of the indicator, or zero for missing data. An important consideration in WofE applications is that the indicator patterns should be approximately conditionally independent (CI). WofE will be illustrated by applications to gold deposits in Meguma Terrain, Nova Scotia, and to flowing wells in the Greater Toronto area. Weighted logistic regression (WLR) also can be used to estimate probabilities of occurrence of discrete events. Both WofE and WLR are applied to gold occurrences in the Gowganda area on the Canadian Shield, northern Ontario, and to occurrences of hydrothermal vents on the East Pacific Rise. Indicator patterns used include favorable rock types, proximity to anticlinal structures or contacts between rock units, indices representing various geochemical elements, proximity to lineaments and igneous intrusives, aeromagnetic data, relative age, and topographic elevation. The Kolmogorov-Smirnov test is used for testing goodness of fit.