Page 12 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Predictive Modeling of Mineral Exploration Targets 7

predictive modeling – mechanistic and empirical – and hybrids of these two types can be
distinguished (cf. Harbaugh and Bonham-Carter, 1970).
Mechanistic modeling applies fundamental or theoretical knowledge of individual
predictor variables (i.e., processes) and their interactions in order to predict or
understand the target variable of interest. Mechanistic modeling is therefore equivalent
to theoretical modeling. Mechanistic modeling relies on mathematical equations to
describe the interactions of processes that control the behaviour of system of interest. It
applies relevant physical laws and is often based on laboratory studies, field experiments
and physical models. Solving the theoretical equations in mechanistic modeling can be
complex and require application of generalising or simplifying assumptions (e.g.,
simplified geometry, homogeneity, idealised initial conditions and boundary conditions).
Mechanistic modeling therefore invariably follows a deductive approach. The predictive
capability of a mechanistic model can be determined and then improved via probabilistic
uncertainty analyses to investigate sensitivity of prediction to one or more predictor
variables or assumptions.
There are two sub-types of mechanistic modeling – deterministic and stochastic.
Deterministic modeling applies mathematical representations (e.g., differential
equations) of the processes that control the behaviour of system of interest. It makes
definite predictions of quantities (e.g., metal concentrations) without considering any
randomness in the distributions of the variables in the mathematical equations.
Stochastic modeling also applies mathematical representations of the processes that
control the behaviour of system of interest, but it considers the presence of some random
distribution in one or more predictor variables and in the target variable. Stochastic
modeling therefore does not result in single estimates of the target variable but a
probability distribution of estimates, which is derived from a large number of
simulations (stochastic projections), reflecting random distributions in the predictor and
target variables. Purely deterministic modeling has been rarely, if not never, used in
mineral exploration, except in laboratory studies of mineral deposit formation (e.g.,
L’Heureux and Katsev, 2006). Purely stochastic modeling is seldom used in the target
generation phase of mineral exploration, but it has been applied, however, in the
resource estimation and reserve definition phases of mineral exploration (e.g., Sahu,
1982; Harris, 1984; Sahu and Raiker, 1985).
An interesting application of stochastic modeling is where the target variable sought
represents fractal geo-objects as a result of stochastic rather than deterministic processes.
A fractal geo-object is one which can be fragmented into various parts, and each
fragment has similar geometry as the whole geo-object (Mandelbrot, 1983).
Geochemical dispersion patterns and spatial distributions of mineral deposits are
postulated to be fractals (Bölviken et al., 1992; Agterberg et al., 1993b). Agterberg
(2001) and Rantitsch (2001) have demonstrated the utility of stochastic modeling to
examine the fractal geometry of geochemical landscapes, as conventional geostatistical
methods are not able to do so when the spatial variability of geochemical anomalies
exceeds the spatial resolution (i.e., sampling density) of geochemical data sets. Hybrids
of stochastic modeling (not based on assumption of fractals) and quantitative empirical