Fractals - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 372

Fig. 10.3 Spherical harmonic development of the Earth's topography (after Vening Meinesz
1964 ). T¼ total topography; S¼ocean floor topography; L¼ continental topography. Horizontal
scale is for order n (¼1 to 31) of spherical harmonics; vertical scale is root mean square of
elevation multiplied by n ½ ·( n +1) ½ . Hatched curve represents inverse values of Rayleigh numbers
for hypothetical mantle currents (not discussed here) distributed according the corresponding
spherical harmonics (Source: Vening Meinesz 1964 , Fig. IV.2)

10.1.2 Chemical Element Concentration
Values: Mitchell-Sulphurets Example

Cheng ( 1994 ) has studied the spatial distribution of 1,030 concentration values of
gold and associated elements in partially altered volcanic rocks in the Mitchell-
Sulphurets area, northwestern British Columbia (Fig. 10.4a ). Plots of Au content in
surface samples (Fig. 10.4b ) from altered and unaltered rocks using logarithmic
probability paper ( lognormal Q - Q plot) suggest that the gold concentration values

satisfy a single, positively skewed frequency distribution that is approximately
lognormal (Fig. 10.4c ). On the other hand, when geochemical isopleths are
constructed (isolines or contours for concentration values in ppb Au) and log-log
paper is used to plot the cumulative area of surface rocks with larger concentration
values against the contour value, the altered and unaltered rocks show entirely
different power-law relations (Fig. 10.4d ). This indicates that a power-law-based
approach can be useful for the delineation of geo-chemical anomalies in addition to
commonly used approaches directly based on element frequency distributions and
contour maps (see, e.g., Sinclair 1991 ).
Figure 10.5 shows Au and Cu maps employing single contours to divide the data
set into two parts, above and below the contour's value. It can be seen that the
shapes of the areas enclosed by successive contours are changing gradually; total
enclosed area decreases as the value of the contour increases. From these contours
an optimum threshold for separating anomalies from background areas can be
selected by means of a log-log plot for the element concentration-area relation.
This threshold coincides with a sudden change in the rate of decrease of the area
enclosed by higher value contours on the log-log plot.

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