Page 13 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

8 Chapter 1

modeling (see below) have been applied, however, in mapping of significant
geochemical anomalies (e.g., Singer and Kouda, 2001; Agterberg, 2007) and prospective
areas (e.g., Agterberg, 1974; Pan et al., 1992; Grunsky et al., 1994).
In contrast to mechanistic modeling, empirical modeling is appropriate when the
underlying geochemical and/or physical processes that control the behaviour of the
system of interest are insufficiently or indirectly known. Methods for empirical modeling
do not take into account interactions of such processes in a mathematical sense as in
mechanistic modeling. Instead, they characterise or quantify the influence of one or more
of such processes on the behaviour of the system of interest via empirical model
equations. Empirical modeling is therefore equivalent to symbolic modeling and
generally follows an inductive approach. The equations in empirical modeling are
constructed to define relationships between the target variable and a number of predictor
variables representing processes in order to describe or symbolise the observed or
predicted behaviour of the system of interest. Empirical modeling requires substantial
amounts of data of both the target and predictor variables in order to quantify accurately
their relationships. In terms of sufficiency of data of the target variable, there are two
sub-types of empirical modeling – quantitative and qualitative.
Quantitative empirical modeling is appropriate when data of the target variable are
sufficient to obtain, say, statistically significant results. Data of the target variable are
usually divided into a training set and a testing set. Based on a training set, relationships
between the target and predictor variables are quantified and then used for prediction.
Methods for quantitative empirical modeling can be statistical, probabilistic or
mathematical. The quality of a quantitative empirical model is described by its
goodness-of-fit to data in a training set and its predictive ability against data in a testing
set. In mapping of prospective areas, quantitative empirical modeling is also known as
data-driven modeling. In contrast, qualitative or heuristic modeling is appropriate when
data of the target variable are insufficient or absent. In qualitative modeling,
relationships between the target and predictor variables are defined based on expert
opinion. Qualitative modeling thus seems to follow a deductive approach. The quality of
a qualitative empirical model can be described by its predictive ability against available
(albeit insufficient) data of the target variable. In mapping of prospective areas,
qualitative empirical modeling is also known as knowledge-driven modeling.
Based on the preceding discussion, further distinctions between mechanistic
modeling and empirical modeling can be made as follows. Whereas mechanistic
modeling attempts to characterise and understand the fundamental or theoretical
processes that control the behaviour of the system of interest, empirical modeling
attempts to depict quantitatively the influence of well-understood processes on the
behaviour of the system of interest. Therefore, mechanistic modeling strives to derive
realistic predictive models, whereas empirical modeling endeavours to derive
approximate yet plausible predictive models. Furthermore, mechanistic modeling is
dynamic, because it can contain the time variable in the mathematical equations
especially in deterministic modeling; whereas empirical modeling usually ignores the
time variable and is therefore static. Predictive modeling of geochemical anomalies,