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Using fractals and power laws to predict the location of mineral deposits

WMC Resources - Exploration Division

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WMC The business of mineral exploration is the essential first stage of the mineral supply process. At its most basic, mineral exploration is the process of predicting the spatial location of undiscovered mineral deposits.

It has long been recognised in the exploration industry that the spatial distribution of mineral deposits is not random but in fact clustered on many different scales. Fractal distributions were first used to model ore-deposit spatial distributions by Mandlebrot (1983), however little additional work appears to have been done since and the available literature is very limited. We are aware of the work of Carlson (1991) who looked at the spatial distribution of gold and silver deposits in the south-west USA mineral province, and the work of Blenkinsop (1994, 1995) who considered the spatial distribution of gold deposits in Zimbabwe. Both workers concluded that fractal distributions could be used to model the spatial distribution of deposits in their study areas. Carlson employed the radial density method to measure the fractal distribution whereas Blenkinsop used both this method and the "box-counting" method.

Despite the above work, the current reality is that formal mathematical concepts relating to the spatial distribution of mineral deposits have had very little impact on the practical business of mineral exploration or even on the academic economic geology sector. Nonetheless, the basic implications of the clustering characteristics of mineral deposits are understood intuitively by most explorationists. People know, for example, that a good place to look for a mineral deposit is close to where one has already been found. In many mineral provinces, an empirical relationship is noted concerning an approximately constant spacing (eg 30 km) between major mineral deposits. This is commonly referred to as "periodicity" although in strict mathematical terms it is more likely to be a manifestation of their fractal distribution.

Given the above, it would seem a reasonable possibility that a more rigorous application of mathematical spatial distribution concepts has the potential to aid in the prediction of the location of undiscovered mineral deposits. The proposition that we are particularly interested in is this:

If we can characterise the spatial distribution of known mineral deposits in a particular mineral province in terms of a fractal distribution;

  1. Does this knowledge enable us to make any predictions about the locations of undiscovered mineral deposits in this province? Put another way, can we use this information to model a probability distribution for mineral occurrence in the province that honours the known distribution of deposits but extends into areas that so far may have not been well explored?
  2. A related issue: can we use a fractal distribution defined in Province X, where the spatial distribution of ore deposits is well-known, to model a probability distribution for ore deposit occurrence in some Province Y (with comparable geological, and by inference, deposit spatial distribution characteristics) where there has been little exploration and little is yet known about the distribution of mineral deposits?

References

Blenkinsop, T. G. 1994, The Fractal Distribution of Gold Deposits, in Fractals and Dynamic Systems in Geoscience, edited by J.H. Kruhl, Springer-Verlag, pp. 247-258.

Blenkinsop, T. G. 1995. Fractal Measures for Size and Spatial Distributions of Gold Mines: Economic Applications, Geological Society of Zimbabwe Special Publication No.3., edited by T.G. Blenkinsop and P.L. Tromp, P.L. Balkema, Rotterdam, 177-186.

Carlson, C.A.1991. Spatial distribution of ore deposits, Geology, vol.19, pp. 111-114.

Mandlebrot, B.B.1983, The fractal geometry of nature, W.H. Freeman and Company, New York.