分形介质与分形地层  

FRACTAL MEDIA AND FRACTAL STRATIGRAPHY

作　　者：李春峰[1] 

机构地区：[1]同济大学海洋地质国家重点实验室,上海200092

出　　处：《地层学杂志》2005年第4期348-354,共7页Journal of Stratigraphy

基　　金：同济大学211工程人才引进启动基金及国家重点基础研究专项经费项目(G2000078501)资助。

摘　　要：由于地层的二元特征,对地层和地下介质有两种不同的认识倾向,即旋回性(准周期性)和随机性。实际的地下介质物性参数的变化以及地层的分布在一般意义上更具有分形和多重分形的特征,而准周期性和随机性只是其中的两种特别情况。与之类似,地层的过渡也不应该是简单的阶梯函数,而应该是由更具有一般意义的启动函数来描述。通过分析一套实际的多重分形碳酸盐岩沉积层序并对其可能指示的古环境和古海平面的变化进行了初步探讨。The applications of nonlinear dynamics and fractal theory to the geosciences have greatly broadened our view, and promoted re-evaluation of our traditional thinking. The complexities of geosystem can be better described using theoretical and numerical models in fractal time-space domain. The concepts of fractal media and fractal stratigraphy are not only true reflections of the fundamental properties of true geological objects, but their introduction can also help to avoid extreme views about stratigraphy. In this paper, the duality of stratigraphy is discussed, at large scales the stratigraphy displays obvious layering, while at small scales, especially in reservoir medium description, macroscopic layering becomes secondary and microscopic variation in physical properties becomes dominant. Because of the differences in geological scales and objectives under consideration, people could have two different tendencies in geological medium descriptions. One would emphasize on the cyclicity and layering in stratigraphy, while someone else may consider that the subsurface media follow random distributions, and thus can be modeled by random processes. But in fact, both views are only special eases when viewed from a fractal perspective. Another natural step forward is bringing in fractional derivatives and using onset functions to extend the geological transitions from traditional step or ramp functions to generalized transition, and thereby to achieve more accurate geological measurement and description. We introduced at the end of the paper an observed multifractal carbonate sequence and demonstrated that fractal and multifractal are not only mathematical concepts, but can be real existence in the nature. Detailed stratigraphy and geochemistry studies on this carbonate sequence could help significantly in our understanding the complexities of paleo-environment or sea level variations.

关 键 词：分形 多重分形 地下介质 地层 碳酸盐岩沉积 古环境 海平面 

分 类 号：P539[天文地球—古生物学与地层学]