On the lognormal distribution of oxides in igneous rocks, using magnetic susceptibility as a proxy for oxide mineral concentration

Abstract

Trace element concentrations in igneous rocks are frequently lognormally distributed, and Shaw (1961) suggested that minor minerals in igneous rocks might also be lognormally distributed. There is accumulating evidence to show that bulk magnetic susceptibility (BMS) often closely follows a lognormal distribution in fresh igneous rocks but, because BMS is dependent upon oxide-grain size and mineralogy, it is not obvious why this should be so. We have adopted Shaw's simple theoretical model as an argument to account for the lognormal distribution of BMS. The obvious prevailing conditions must be that the original melt was uniform, that pressure, temperature and oxygen fugacity were constant and that the minerals were formed at equilibrium. In addition, because BMS is also a function of grain size and mineralogy, the distribution of these latter parameters must be insensitive to changes in P , T , etc. at equilibrium. It appears that there must be a limit to the lognormal law in trying to apply it to minerals of greater concentration. However, BMS proxies for oxide content, and because it does closely follow the lognormal distribution it thus appears that, in crystalline igneous rocks, the lognormal law is obeyed by minerals of concentrations at least up to a few percent. Knowledge of the mean and variance of such distributions can be useful in a variety of petrological applications, especially in drillcore logging; a simple example is presented.

Magnetic classification of stony meteorites: 3. Achondrites

“…For each measured specimen, the decimal logarithm of apparent mass specific susceptibility χ is tabulated (in 10 −9 m 3 /kg). The use of log units is justified for presentation reasons (as the data vary by 3 orders of magnitude) and also by the fact that χ is expected to follow a log normal distribution for a given formation or parent body (Latham et al 1989). Therefore, it is more representative to average the data in terms of logχ rather than χ.…”

Mass and magnetic properties for 3D geological and geophysical modelling of the southern Agnew–Wiluna Greenstone Belt and Leinster nickel deposits, Western Australia

“…All histograms in this study use bin widths defined by the data range and number of samples (Freedman & Diaconis 1981). Magnetic properties typically follow a log-normal (base 10) distribution (Latham et al 1989;Puranen 1989) and so are presented on logarithmic axes. The arithmetic mean consistently overestimates the most likely value for log-normal distributions, so the median is provided to give a better estimate of the most likely value for skewed data, and the geometric mean is provided to indicate the most likely value associated with log-normal properties (Kirkwood 1979;Borradaile 2003).…”

Magnetic classification of stony meteorites: 2. Non‐ordinary chondrites

“…For each measured specimen, the decimal logarithm of apparent mass specific susceptibility χ is tabulated (in 10 −9 m 3 /kg). The use of log units is justified for presentation reasons (as data varies on 3 orders of magnitude) and also by the fact that χ is expected for a given formation or parent body to follow a log normal distribution (Latham et al 1989). Therefore it is more representative to average data as logχ rather than as χ.…”