数学地质的主要进展和发展趋势

数学地质是地质学的一个重要的新分支。本文涉及数学地质在几个领域的主要进展,分形、耗散结构、灰色系统模型和模糊数学在地质学中的应用。分形已成功地应用于准晶体微粒结构、断层系统和地质构造分布、多孔介质、地质体表面粗糙度和其他问题研究。耗散结构已应用于矿物离解过程、热液成矿作用动力学、混合岩成因以及地壳地幔的结构和运动等的研究。灰色系统理论在水文地质、工程地质、环境地质和矿床预测的很多问题中得到应用。模糊数学是解决很多地质问题的有用的定量工具。最后,讨论了数学地质的进一步发展趋势。

MAIN ADVANCES AND DEVELOPMENT TRENDS IN MATHEMATICAL GEOLOGY

Mathematical geology is a new and important branch of geological sciences. This paper deals with the main advances of mathematical geology in the following fields; applications of fractal, dissipative structure, grey system models and fuzzy mathematics in geology. Fractal has been used successfully in the study of impalpable structure of metacrystals, fault systems and geological structure distribution, porous medium, surface roughness of geological bodies and other problems. Dissipative structure has been applied in the study of dissociation of minerals, dynamics of hydrothermal mineralization, genesis of migmatite, structure and motions of the earth' s crust and mantle and so on. Grey system models have been used in many problems of hydrogeology, engineering geology, environmental geology and mineral deposit predictions. Fuzzy mathematics is a widely usd quantitative tool for solving many geological problems. Finally, trends of development of mathematical geology are discussed.