Scaling Laws for the Distribution of Gold, Geothermal, and Gas Resources

Mass dimensions of natural resources have important implications for ore-forming processes and resource estimation and exploration. The mass dimension is established from a power law scaling relationship between numbers of resources and distance from an origin. The relation between the total quantity of resource and distance, measured by the mass-radius scaling exponent, may be even more useful. Lode gold deposits, geothermal wells and volcanoes, and conventional and unconventional gas wells are examined in this study. Mass dimensions and scaling exponents generally increase from the lode gold through geothermal wells to gas data sets, reflecting decreasing degrees of clustering. Mass dimensions are similar to or slightly less than the mass-radius scaling exponents, and could be used as estimates of the minimum scaling exponent in the common case that data are not available for the latter. All the resources in this study are formed by fluid fluxes in the crust, and, therefore, percolation theory is an appropriate unifying framework to understand their significance. The mass dimensions indicate that none of the percolation networks that formed the deposits reached the percolation threshold.