Oscillatory zoning in agate: Qualitative analysis of the Wang-Merino dynamic model and quantitative estimates of trace-element distribution in a sample from Arc-Bogdo (Mongolia)

Zoning in agate crystallizing in a medium enriched with silica, water, and trace elements may be caused by successive precipitation of the latter on t he crystallization front. The Wang-Merino mathematical model of this proces s involves periodic solutions. We investigate the bifurcational values of t he parameters of this model and make up a complete list of their phase port raits, 51 in total. For some of the physical parameters, we constructed a p hase portrait and estimated the duration of a limit cycle, the variation ra nge of trace-element contents, and the width of the zone crystallized durin g one cycle. Ion microprobe analysis of Fe, Sr, and Zn abundances in a samp le of agate from Arc-Bogdo (Mongolia) yielded statistical characteristics o f its oscillatory zoning. The distribution of trace elements showed a numbe r of specific features, namely, (1) a regular trend indicating gradual accu mulation of elements across the zoning pattern, (2) the presence of two ove rlapped cycles superposed with unstable oscillations ("noise"), and (3) "an tipersistent" behavior within each interval of estimation.