Mathematical Description And Application Of Faults

Faults,as one of the main causes of earthquakes,tend to have a direct impact on stratigraphic distribution in geological formations.In mineral mining,encountering faults will increase safety risk and mining difficulty,then reduce mining efficiency.In order to fully understand the specific form of fault,combining with the characteristics of fault itself,we have developed a mature industrial curve surface fitting technology applied to fault research work,which can not only solve the practical difficulties encountered in mining engineering,but also complement the study of the fault.It is crucial to select fitting methods and analysis of fault parameters for fault fitting description.The better applied maturation methods include the least squares method,the Lagrangian interpolation method and the Hermite interpolation method.In this study,it was characterized by high precision and high smoothness to meet the complex curve surface.Based on the analysis of the advantages and disadvantages of each method,we proposed to use the spline function to study the fitting under the fault condition,and expounded the concrete solution of the cubic spline function i in detail,then performed the study on curve fitting by using the spline function.Based on the spline function theory,using F19 fault as the research object,we applied the numerical modeling experiment and studied the relativity between fault throw and strike length through explaining the theory,structural elements and styles of fault.Finnally,the obtained datas were incorporated to perform fault simulation and practical application analyses,then further confirmed the feasibility of describing the fault strike by using spline function.The results showed that the drilling data were compensated and pretreated by the actual datas of the fault in the engineering section.According to the datas obtained from the three-dimensional simulation,we got the specific existence form of the fault direction in the three-dimensional space,and had a completely understanding of fault from the three-dimensional sense.And to a certain extent,it can provide theoretical guidance for engineering applicationsin mineral mining and mining design.