A Plausible Explanation for Common Fractal Temporal-Spectral Slopes of Drainage Flows and Chemistries at Full-Scale Mining Operations

Where full-scale minesite-drainage monitoring has been carried out at sufficiently high sampling frequencies and long durations, interesting and intriguing patterns have been seen in the time series.  Some observations include: flow rates and aqueous concentrations of minesite drainages are not simple or steady; they are not stochastic, but also not deterministic; they are not random or chaotic. They display periodicity in complex ways.

Based on spectral analyses of time series for minesite drainages as well as for non-mining-related rivers and catchments, the typical trend is decreasing spectral power of the peaks with decreasing wavelength.  The resulting slopes are commonly fractal, typically ranging between zero (random) to 2 (random walk).  The slope of 1 ("1-over-f") is the most complex and yet has been documented in many sciences and arts.  These fractal slopes are “ubiquitous” in some non-mining catchments.

Consistent with Earth-System Science, electrical fields in the Earth are inevitably linked to other processes like large and small physical movements, magnetic variations in the earth, weather systems, and cosmic radiation.  For example, the movement of natural water through a porous or fractured medium can create an electrical field that in turn affects the distribution of ions in that water.  Small changes in ground electrical potential, considered minor background electrical "noise" by some, can significantly affect aqueous chemistry.

This study asks the question, “Why?”  Why are fractal spectral slopes so common in drainage flows and chemistries whenever data have been sufficient to search for them?

A plausible answer begins with the fact that many minesite components are open systems in the surficial environment, well grounded to the earth which behaves like an electrical capacitor.  Thus, relatively large minesite components can act as first-order low-pass signal filters.  These filters cause the spectral powers of individual periodicities entering them to (1) decrease along a fractal slope of 2 at wavelengths shorter than the "cutoff wavelength" and (2) remain unfiltered at longer wavelengths.  When several mechanisms are simultaneously acting and overlapping as low-pass filters, fractal slopes including 1-over-f slopes can appear.  Based on this rationale, periodic processes grounded to the Earth can show fractal temporal slopes when sufficient data are collected.