Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Saturday, January 7, 2012

Gold, part 2: Is there a maximum size for gold deposits?

In our last installment, I presented a graph showing the size distribution for global gold deposits of greater than one million ounces. In it I tried to estimate the slope of the relationship between the size of deposits and their ranking, in terms of size,  in the hopes that the slope had some predictive power for the deposits that are yet to be found.

Two suggested scaling laws for the size-distribution of gold deposits (global).

Once again, the interpretation of these graphs is the rank, (in size, less one) of any deposit is the abscissa, and size is the ordinate. The reason for subtracting one from the rank number is that the largest deposit shown on the graph is actually the second-largest deposit in the state--and there is one deposit larger.

In our last installment, we assumed that the blue line was the better representation of the scaling law for gold deposits. Today we explain why the yellow line may be the correct answer, and that it does not mean we can expect to find multi-billion ounce deposits of gold (at least nowhere near the Earth's surface).

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The Earth system consists of myriads of local interacting subsystems. Intuitively, we might not expect the overall effects of these to merge into a background of white noise, we find instead that highly ordered structure arises on a variety of scales ranging up to that of the globe.

A simple scaling law for the size-distribution of gold is an example of red noise (or pink noise, depending on the slope). The observed power-law is a characteristic of a system at a state of self-organized criticality (SOC), as is nicely outlined here. In essence, the scaling law we observe in the size-distribution of gold deposits due to self-organization in the geological processes which control the reservoir size of crustal fluids which contained the gold, and possibly also the fracturing process which preceded the emplacement of the gold in the rocks.

Today we look at the size-distribution of gold deposits in Nevada.

The above graph was plotted using the data from the Nevada Bureau of Mines and Geology review of its mineral industry for 2009. There were 191 (unambiguous) significant deposits of precious metals for which I have combined the most recent mineral resources (all categories) plus any pre-existing historical production. I only counted gold ounces--and freely acknowledge that some of the mines in the above chart were probably better described as copper or silver mines--and treated all categories (proven and probable reserves, measured and indicated resources, and inferred resources) equally. If you feel the methodology is flawed you are invited to use your own.

We can compare the current size-distribution of gold deposits to the size-distribution of gold deposits in the Carlin Trend in 1989 (Rendu and Guzman, 1991).

Remarkably, both sets of data appear to be described by a straight line of constant slope, at least between for deposits between about 100,000 ounces and 10 million ounces in size.

During Nevada's "maturation" as a gold province, the scaling law describing the size-distribution of gold deposits remained constant over two orders of magnitude in size. The slope of these lines is about 1.5, placing the scaling law exponent between pink noise and red noise.

When we look at the figure on the top of the page, the blue line has a slope < 1, whereas the yellow line has a slope of about 1.5. For this reason, I propose the yellow line to be a better representation of the scaling law for the global deposits. The reason I first leaned towards the blue line was due to insufficiency of observations.

For comparison, if I only looked at deposits in Nevada greater than 1 million ounces, I would not be as confident describing the size-distribution with the yellow line.

SOC theory would seem to tell us the entire distribution should be characterized by a power law. Why not gold deposits?

In nature, there are limits. Infinity is not an option. Earthquakes are recognized as SOC processes, yet they have a maximum size, as the capacity for earth materials to store and transmit strain is finite. Similarly, we would expect there to be an upper limit for the size of crustal reservoirs of gold-bearing fluids. The result is that the largest gold deposit we find is much less than we would predict on the basis of our observed power law.

This explanation does not explain why there also appears to be a deficit in small deposits. For this the reason is economic. Under the current reporting regime (NI 43-101), gold in the ground cannot be considered a "deposit" unless it is reasonable to expect it to be exploited profitably. The requirement for economic exploitability will exclude many small--well, since they are not deposits, let's call them "collections"--of gold. Additionally, many company geologists will ignore such collections as soon as it becomes clear they are unlikely to become a deposit.

So it's up to these guys! (sorry about the quality--this is a point-and-shoot photo scanned way back in the '90s). He's using a rubber cut-out from an inner tube as a pan. This site is a thrilling walk north of Asanta village, western Ghana, on land almost certainly on a concession held by Endeavour.


Hronsky, J. M. A., 2011. Self-organized critical systems and ore formation: The key to spatial targeting? SEG Newsletter, 84, 3p.

Nevada Bureau of Mines, 2010. The Nevada Mineral Industry 2009. Special Publication MI-2009. http://www.nbmg.unr.edu/dox/mi/09.pdf, accessed today.

Rendu, J. M. and Guzman, J., 1991. Study of the size distribution of the Carlin Trend gold deposits. Mining Engineering, 43: 139-140.

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