Regularities of Layering of Basic–Ultrabasic Intrusions as the Result of Self-Organization Processes During the Course of Their Formation

Abstract

A principal feature of stratiform basic-ultrabasic intrusions is alternation of rocks characterized by different proportions of the salic (plagioclase) and mafic (mainly pyroxene) constituents. Owing to considerable density variation of the components, density is attractive for use as a characteristic of the change of rock composition across the section. Five drill holes intersecting the contact of the Critical and Main zones of the intrusion (West Bushveld, South Africa) were analyzed over the depth interval containing deposits of chromium and platinum group minerals (PGM). Several types of density variability over different intervals of the section are identified. There are intervals where density increases and decreases monotonically and ones which are characterized by cyclic (rhythmic), or chaotic changes. Intervals with relatively constant (stable) values of density occur as well. The results of analysis of these regularities suggest a nonlinear oscillator described by a differential equation of the second order to be a workable mathematical model for the process of formation of a layered intrusion. Coefficients of the equation have been estimated for all five drill holes from the empirical series of densities by inverse methods. If it is accepted that crystallisation proceeded from the bottom upwards, the equation is consistent with a point attractor. The average values of coefficients of the equation (that seem to serve as criteria for distinguishing intrusions of different genesis) were calculated, and its stability for various intervals of the section was studied. After terms in the equation with negligibly small coefficients, the dispersion of which exceeds their values, have been omitted, the equation becomes very similar to the one proposed for dynamics of a supercooled melt. It allows certain assumptions to be made about the character of mutual relations of the signal being analyzed (the observed alternation of the rocks) with peculiarities of the petrogenetic process, inverse methods.