Page 115 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

114 Chapter 4

concentration-area method, e.g., a concentration-distance method (Li et al., 2003) and a
summation method (Shen and Cohen, 2005). The concentration-area method and its
variants are appropriate for geochemical data analysis in the spatial domain, in which the
scale-invariant characteristics of geochemical landscapes are related to the empirical
density distributions, spatial variability and geometrical patterns of geochemical data
sets.
Other methods for fractal analysis of geochemical anomalies involve converting
geochemical data into a function of ‘wave numbers’ in the frequency domain, in which
the scale-invariant characteristics of geochemical landscapes are represented by means
of a power spectrum. For details of fractal analysis of geochemical anomalies in the
frequency domain, readers are referred to authoritative explanations by Cheng et al.
(2000). Nevertheless, Cheng et al. (2000) aver that “because the spatial distribution of
power spectrum is determined not only by the wave numbers but also by the power-
spectrum function, it should be characterised by the concentration-area fractal method”.
This means that the concentration-area fractal method is a fundamental technique for
modeling of geochemical anomalies.
The case study on GIS-based application of the concentration-area fractal method
shows the multifractal nature of the geochemical landscape in the Aroroy district
(Philippines) based on stream sediment uni-element data. The results of the case study
illustrate that significant anomalies related to the epithermal Au deposit occurrences are
modeled better when the geochemical landscape is represented as discrete surfaces rather
than as continuous surfaces. Perhaps the application of inverse distance moving average
to derive the continuous geochemical surfaces from the point stream sediment uni-
element data is not optimal in this case, particularly because stream sediments do not
represent continuous geo-objects. The case study demonstrates, nonetheless, that either
continuous or discrete geochemical surfaces can be used in GIS-based concentration-
area multifractal modeling of significant anomalies in stream sediment uni-element data.
As shown in the case study, application of traditional methods of spatial interpolation
to derive continuous geochemical surfaces can undermine multifractal analysis of
geochemical anomalies. However, methods for multifractal interpolation (Cheng, 1999a)
and fractal filtering (Xu and Cheng, 2001) have been developed to take into account the
concentration-area relationship in deriving, from point geochemical data, ‘ready-to-use’
interpolated maps in which background and anomalies are already separated. These
methods have not been demonstrated here, not only because extensive discussion spatial
interpolation and filtering is beyond the scope of this volume but also because they
require specialised software, which is dedicated to such purposes and which is not
available in most commercial or shareware GIS software packages.