Abstract:
Zoning in agate crystallizing in a medium enriched with silica, water, and trace elements may be caused by successive precipitation of the latter on the crystallization front. The Wang-Merino mathematical model of this process involves periodic solutions. We investigate the bifurcational values of the parameters of this model and make up a complete list of their phase portraits, 51 in total. For some of the physical parameters, we constructed a phase portrait and estimated the duration of a limit cycle, the variation range of trace-element contents, and the width of the zone crystallized during one cycle. Ion microprobe analysis of Fe, Sr, and Zn abundances in a sample of agate from Arc-Bogdo (Mongolia) yielded statistical characteristics of its oscillatory zoning. The distribution of trace elements showed a number of specific features, namely, (1) a regular trend indicating gradual accumulation of elements across the zoning pattern, (2) the presence of two overlapped cycles superposed with unstable oscillations ("noise"), and (3) "antipersistent" behavior within each interval of estimation.