| If scaling laws can be established for the distribution of natural resources, they would have
important economic consequences. For example, they can be used to estimate total resources,
they can dictate exploration strategies, and they can also point to processes by which natural
resources form. A scaling law for the spatial distribution of natural resources can be proposed
as:
M(r) ~ r-D
where M(r) is the mass of resource within a circle of radius r. If the mass of individual
occurrences of resources is unity, this law describes the Mass Dimension D of the
resource, commonly analysed by the number-in-circle method. In this case D is simply
interpreted as a measure of the clustering of the resource distribution. Space filling or
random distributions have D = 2: lower values indicate a decrease in density with
distance. If the mass of resource varies at each occurrence (as typical in nature), then
M(r) ~ r-D is a general scaling law, with an exponent that is referred to here as
the Mass-Radius scaling exponent. This exponent can have values greater than
2.
Mass Dimensions and Mass-Radius scaling exponents have been determined in this study
for Archean gold deposits in Zimbabwe, direct use of geothermal energy in Oregon,
geothermal energy use in New Zealand and conventional and unconventional gas production
in Pennsylvania. Mass Dimensions vary between 0.4 and 2, reflecting the variable clustering
of the data sets. The highest values are from conventional gas production, while
unconventional gas production and geothermal energy have lower values. In general Mass
Dimensions and Mass-Radius scaling exponents are similar in any data sets. An
interesting consequence is that an approximate value for the Mass-Radius scaling
exponent can be given by the Mass Dimension. It is commonly hard to measure
the Mass-Radius scaling exponent because accurate data for mass is difficult to
obtain. The similarity of the two exponents suggests that substituting the Mass
Dimension for the Mass-Radius scaling exponent can solve this problem to some limit of
accuracy, but the generality of this relationship needs testing on more data sets. |