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

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.