断层的数学描述及应用

发布时间：2018-04-18 10:26

本文选题：断层 + 描述　；参考：《贵州民族大学》2017年硕士论文

【摘要】：断层作为地震产生的主要原因之一,在地质构造中往往对地层分布具有直接影响。在矿产开采中,遇到断层将会增加安全风险和采掘难度,同时降低开采效率。为了充分认识断层的具体存在形式,结合断层自身特性,将已经发展成熟的工业曲线曲面拟合技术应用于断层研究工作。不仅对解决采矿工程中遇到的实际困难进行了理论探索,而且对断层的研究进行了补充。断层的拟合描述问题,关键在于选取拟合方法和进行断层参数解析。较为成熟的拟合方法有最小二乘法、拉格朗日插值法和埃尔米特插值法等,为满足复杂曲线曲面要求高精度、高平滑等特点。本文以描述断层走向为主线,在分析各方法优缺点的基础上,提出在断层条件下利用样条函数进行拟合研究。并详细阐述了三次样条函数具体求解过程,得出分段函数的具体存在形式,进而确定断层走向的线性特征。将米箩煤矿揭露的F19断层作为研究对象,通过介绍断层的定义、构造要素及类型。基于样条函数理论,应用数值模拟实验,从定量分析角度研究断层落差与走向长度之间的相关关系。结合所得数据对断层进行模拟及实际应用分析,验证了样条函数描述断层走向的可行性。研究结果表明,利用工程剖面中揭露断层的实际数据对钻孔数据进行弥补,并对数据进行预处理。根据所得数据进行三维模拟,得出断层走向在三维空间条件下的具体存在形式,从立体感观上对断层实际有了全新的认识。不仅在一定程度上可以为地质分析工作提供理论指导,而且在矿产开采与回采设计等工程应用中具有实践意义。
[Abstract]:As one of the main causes of earthquakes, faults often have direct influence on stratigraphic distribution in geological structures.In mining, the fault will increase the safety risk and mining difficulty, and reduce the mining efficiency.In order to fully understand the concrete forms of faults and combine the characteristics of faults, the mature fitting technology of industrial curves and surfaces is applied to fault research.It not only makes theoretical exploration to solve the practical difficulties in mining engineering, but also complements the study of faults.The key problem of fault fitting is selecting fitting method and analyzing fault parameters.The more mature fitting methods include least square method, Lagrangian interpolation method and Hermite interpolation method, etc. In order to meet the needs of complex curves and surfaces, high accuracy and high smoothness are required.On the basis of analyzing the advantages and disadvantages of each method, this paper puts forward to use spline function to fit the fault under the condition of fault, taking describing fault strike as the main line and analyzing the advantages and disadvantages of each method.The concrete solution process of cubic spline function is described in detail, the concrete existence form of piecewise function is obtained, and the linear characteristic of fault strike is determined.The F19 fault exposed by Milo Coal Mine is taken as the research object, and the definition, structural elements and types of fault are introduced.Based on spline function theory and numerical simulation experiment, the correlation between fault drop and strike length is studied from the angle of quantitative analysis.Combined with the obtained data, the fault is simulated and analyzed in practice, and the feasibility of describing fault strike by spline function is verified.The results show that the borehole data can be compensated and preprocessed by using the actual data of the disclosing faults in the engineering section.According to the 3D simulation of the obtained data, the concrete existing form of fault strike under the condition of three-dimensional space is obtained, and a new understanding of the fault is obtained from the perspective of three-dimensional perception.It can not only provide theoretical guidance for geological analysis to a certain extent, but also have practical significance in engineering applications such as mineral mining and mining design.
【学位授予单位】：贵州民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TD311

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