一种三点法求隐伏活动断层产状的计算方法

Three-point Method for Calculation of the Occurrence of Buried Active Fault

求解三点问题的传统方法是作图法。目前缺乏利用初等几何学求解三点问题的完整计算方法。本次研究基于三点法的原理,利用初等几何学知识推导了求断层面倾角、倾向和走向的计算公式。断层面倾角计算公式是以已知三点之间水平距离和三点之间高差为变量的代数表达式。断层面倾向或走向计算公式是以已知三点之间水平距离、三点之间高差和三点连线的方位角为变量的代数表达式。利用这些新公式易于编制计算程序。应用三点法求隐伏活动断层面产状的具体步骤为:①通过改进的钻孔联合地质剖面,取得断层面上已知三点的空间位置数据;②依据已知三点的彼此高度关系条件,选择断层面倾角和辅助角计算公式,计算倾角、辅助角;③依据已知三点的彼此空间位置关系条件,选择断层面倾向和走向计算公式,计算倾向和走向。以扣马断层为例,采用上述新公式计算获得的扣马断层面的倾角、倾向和走向,与采用地质罗盘在探槽中测量的断层面的倾角、倾向和走向结果比较一致。

Graphing method is a traditional method for three-point problem.At present,there is no complete calculation method to solve three-point problem by elementary geometry.Based on the principle of three-point method,a few formulas derived from the knowledge of geometry and trigonometric function are proposed to calculate dip angle,dip,and strike of fault surface.The formulas used to calculate the dip angle of fault surface are the algebraic expressions,within which the horizontal distance and height difference between three known points are used as parameters.The formulas used to calculate dip or strike of fault surface are algebraic expressions that include parameters such as the horizontal distance and height difference as well as the azimuth of the line between the three known points.These new formulas are easy to programme.The steps to obstain the occurrence of buried active fault surface by using the three-point method are presented as follows.First,the spatial location data of the three known points on the fault surface is obtained from improved composite drilling geological section.Secondly,based on the height relationship of the three known points,the formulas are chosen to calculate the dip angle and the auxiliary angle of the fault surface.Thirdly,based on the spatial location relationship of the three known points,the formulas are chosen to calculate the dip and strike of the fault surface.Taking the Kouma fault as an example,the dip angle,dip,and strike of the Kouma fault surface are obtained by using these new formulas.In the prospecting trench,the dip angle,dip,and strike of the Kouma fault surface are measured by using geological compass.Both results of the dip angle,dip,and strike are quite consistent.