湘西沃溪金锑钨矿床含金石英脉的分形生长动力学

Fractal Growth Dynamics of Auriferous Quartz Veins in the Woxi Au—Sb—W Deposit, Western Hunan Province, China

笔者等对湘西沃溪金锑钨矿床石英脉长度与厚度的分形关系及其厚度的分形分布进行了分析 ,探讨了石英脉分形生长的可能动力学机理。分析结果表明 ,石英脉长度厚度关系的分维值 Dr 在 0 .4 0 70到 1.0 784之间 ,Dr 值与相应石英脉的平均厚度呈明显正相关关系 ,相关系数为 0 .6 6 36。石英脉厚度分布的分维值 DT 在 0 .342 0到1.4 6 6 1之间 ,与相应石英脉平均厚度呈负相关关系 ,相关系数为 - 0 .5 70 6 ,说明厚度分布的分维值 DT 越小 ,脉体连通性越好。研究表明 ,石英脉体生长早期 ,以横向膨胀为主 ,其长度厚度关系分维值 Dr<1.0 ;脉体生长达到一定规模时 ,相邻脉体会通过相互连通而迅速增长 ,总体表现为纵向延长 ,从而导致 Dr>1,Dr随着石英脉的连通生长而增大。模拟结果表明 ,具有稳定的脉体成核率 α和生长速率 β的脉体生长模式将导致脉体厚度的分形分布 ,且厚度分布的分维值 DT 值将随着脉体成核率 α的增大而增大、随着脉体生长速率 β的增大而减小。

The fractal relationships of thicknesses and lengths of quartz veins in the Woxi Au—Sb—W deposit in western Hunan province and the fractal distribution of their thicknesses are analyzed in this paper. Moreover, possible fractal growth dynamic mechanism of quartz veins is also discussed. The results of fractal analysis indicate that the fractal dimension Dr of thickness vs. length varies from 0.4070 to 1.0784 and the values are directly proportional to the average thickness. The correlation coefficient between the fractal dimension Dr and the average thickness is 0.6636. The fractural dimension DT of the thickness distribution of quartz veins varies from 0.3420 to 1.4661 and the values are inversely proportional to the average thickness. The correlation coefficient between fractural dimension DT and average thickness is -0.5706, which indicates that the smaller the fractural dimension DT, the better the fracture connectivity will be. In general, at the early growth stage, the vein grows mainly in a form of lateral expansion and the dimension Dr<1, but when the veins reach a certain size they extend rapidly via vein linking, so that the dimension Dr will be larger than 1. Simulating studies indicate that constant nucleation rate α and growth rate β will bring about fractal distribution of vein thickness and the dimension value DT will increase along with the nucleation rate α and decrease along with the growth rate β. Results of the cellular automation model suggests that the better the fracture connectivity, the smaller the fractal dimension DT will be.