碎裂岩的分数维分析:理论、方法及地质意义

FRACTAL ANALYSIS OF CATACLASTIC ROCKS:THEORY,TECHNIQUES AND APPLICATIONS

理论研究表明具有自相似性的几何分裂体可以用分数维描述,其分数维值 D 的大小取决于碎裂模式。碎裂岩粒度分布具有自相似性,可以用 D 值定量描述。D 值的求法有三种,即粒径法、面积法和体积法。对天然变形的断层岩分数维分析表明,D 值随断层岩形成的地质环境(温度、压力和应变量等)变化,如围压增加,D 值增大;应变量增加,D 值增大,并趋向定值。

Theoritical study shows that self-slmilar cataclastic processes produce cataclastic rocks with characteristic fractal dimension,which depends on the modes of deformation.A mode of deformation is defined by base'B'and number of fragile elements as a parent cell each time is broken into next order elements.Fractal dimension D of cataclasite can be expressed in terms of particle size(diameter,sectional area and volume)and their distribution frequency:D= -slope(diameter-frequency),D=-2 slope(area-frequency),D=-3 slope(volume-frequ- ency),where slope is the slope of regression line for particle size vs frequency in a log-log co- ordinates. Three techniques can be used in particle distribution analysis,namely Sammis'technique image analysis and sieving technique. Study on naturally deformed catalclasites suggests that fractal dimension D increases with increasing strain and reaches a constant for a specific mode of deformation.D also increases with increasing depth of deformation.It is pointed out that strain,confining pressure and strain rate are probably the main factors that contribute to D value.