关键词: 模糊聚类分析, 灰色聚类, 诱发地震

Abstract: A method of predicting the upper-limit of the potential magnitude of reservoir induced earthquakes is proposed by using fuzzy cluster and grey cluster analyses.The applicability of the method has been discussed by taking Xinfengjiang reservoir area as an example.Fuzzy cluster analysis:A fuzzy subset should be set up at first.The fuzzy subset is defined by the function μ=A(u),where μ is called the subordination function of A.If its image is to be demonstrated,the threshold value λ which is between 0 and 1 must be chosen.If A(u)≥λ,then it is the case of u∈A or otherwise u∈A.In fuzzy cluster analyses, if R_λ is in fuzzy equivalence relation to U,then R_λ is in common equivalence relation to U for any 0≤λ≤1.According to this equivalence relation,the elements in U can be classified.When λ declines from 1 to 0, the classifications change from detailed to sketch,and then merge gradually,forming a dynamic image of cluster.In grey cluster analysis,prediction is made by using the grey target of the cluster.The object of the cluster is classified according to the grey type of different target, i.e.to take the weight of the collected samples by using statistic method,and to determine the value characteristic of the state of the predicted object on the weight function.The type then can be decided according to the magnitude of the value.Reservoir induced earthquake is a function of various factors.In the prediction,the depth and volume of the reservoir,the state of regional stress, fault activity, lithology and seisimicity background are taken as cluster factors, while the magnitude of reservoir induced earthquakes is taken as type and the predicted resevoir as the object.The results show that the predicted upper-limit magnitude is coincident with the actual case of earthquake occurrence.

Key words: Fuzzy cluster analysis, Grey cluster, Induced earthquake