Geoscience Reference
In-Depth Information
Chapter 10
Fractals
Abstract As illustrated in previous chapters, many geological features display
random characteristics that can be modeled by adopting methods of mathematical
statistics. A question to which new answers are being sought is: Where does the
randomness in Nature come from? Nonlinear process modeling is providing new clues
to answers. Benoit Mandelbrot discovered about 50 years ago that many objects on
Earth can be modeled as fractals with non-Euclidean dimensions. Spatial distribution
of chemical elements in the Earth's crust and features such as the Earth's topography
that traditionally were explained by using deterministic process models, now also are
modeled as fractals or multifractals, which are spatially intertwined fractals. Which
processes have produced phenomena that are random and often characterized by
non-Euclidian dimensions? The physico-chemical processes that have resulted in the
Earth's present configuration were essentially deterministic and “linear” but globally
as well as locally they may display random features that can only be modeled by
adopting a non-linear approach that is increasingly successful in localized prediction.
The situation is analogous to the relation between climate and weather. Longer term
climate change can be modeled deterministically but short-term weather shows
random characteristics that are best modeled by adopting the non-linear approach in
addition to the use of conventional deterministic equations. This chapter reviews
fractal modeling of solid Earth observations and processes with emphasis on topogra-
phy, thickness measurements, geochemistry and hydrothermal processes. There is
some overlap with multifractals that will be discussed in more detail in the next two
chapters. Special attention is paid to improvements in goodness of fit and prediction
obtained by non-linear modeling. The spatial distribution of ore deposits within large
regions or within worldwide permissive tracts often is fractal. Illustrative examples to
be discussed include lode gold deposits on the Canadian Shield and worldwide
podiform Cr deposits, volcanogenic massive sulphide and porphyry copper
deposits. The Pareto distribution is closely associated with fractal modeling of metal
distribution within rocks or surficial cover in large regions. The Concentration-Area
(C-A) method is a useful new tool for geochemical prospecting to help delineate
subareas with anomalously high element concentration values that can be targets for
further exploration with drilling.
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