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

Abstract

Abstract:Mass dimensions of natural resources, established from power law scaling relationships between numbers of resources and distance from an origin, have important implications for ore-forming processes, resource estimation and exploration. 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. The 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 the mass-radius scaling exponents, and could be used as substitutes in the common case that data are not available for the latter. All of these resources 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. 2 AbstractMass dimensions of natural resources, established from power law scaling relationships between numbers of resources and distance from an origin, have important implications for oreforming processes, resource estimation and exploration. 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. The 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 the mass-radius scaling exponents, and could be used as substitutes in the common case that data are not available for the latter. All of these resources 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.

Chapter 1: Structural Geology Applied to the Evaluation of Hydrothermal Gold Deposits

“…This type of analysis, developed in three dimensions, would seem highly suited to evaluating the resource potential of stockworks. Network analysis is closely aligned to percolation theory (Stauffer and Aharony, 1994), which has interesting potential for understanding hydrothermal mineralization (Blenkinsop, 2014). Networks are also useful to describe 3D model topologies (Thiele et al, 2016a(Thiele et al, , 2016b.…”

Cloud Extraction Scheme for Multi-Spectral Images Using Landsat-8 OLI Images With High Brightness Reflectivity Covered

“…is the fractal dimension, and C is a proportionality constant. Each dimension corresponds to one scale-free (linear) segment and reflects the number of pixels or the summation of the pixel values that are equal to and greater than the corresponding r [36]. Taking the logarithms of the above formula, we obtain the following:…”

A new method for extraction of alteration information using the Landsat 8 imagery in a heavily vegetated and sediments‐covered region: A case study from Zhejiang Province, E. China

“…Generally, this model can be represented as follows: where r is the characteristic linear measure; in this case, it is the logarithmic pixel values; C is the constant of proportionality (prefactor parameter); D is well known as the fractal dimension; N( r ) is equal to the number or summation of pixel values greater than or equal to r , namely, N( r ) = N (≥ r ). This formula always has a scale invariant property (Blenkinsop, ).…”