三角形形状因子对地壳形变计算精度的影响

EFFECTS OF TRIANGLE SHAPE FACTOR ON PRECISION OF CRUSTAL DEFORMATION CALCULATED

引入三角形内切圆半径与外接圆半径之比值作为三角形形状因子 ,讨论利用三角形法计算应变分量的精度与三角形形状因子之间的关系。设计一种涵盖所有三角形形状的方法 ,计算分析了用三角形法计算应变分量精度的分布。研究表明 :当三角形形状因子达到 0 .36时 ,计算得到的应变分量均方差 ,一般不会超过位移数据均方差的 3倍 ;而当三角形形状因子小于 0 .1时 ,计算得到的应变分量均方差会陡然增大 ,这样的三角形一般不适合用于应变分量的计算。在利用GPS观测站组成三角形计算地应变时 ,建议所组成的三角形形状因子的阈值应取为0 .1～ 0 .36。

In this paper, the shape factor of a triangle is defined as the ratio of interior radius to exterior radius of the triangle. The relationship between the precisions of strain components calculated by the triangular method and the shape factor are studied. A method covering all of different triangle shapes is designed and the distributions of the precisions of strain components are obtained in the cases of different triangle shapes. The study shows that if the shape factor larger than 0.36, the standard deviations of strain components obtained will be less than three times of the standard deviation of displacement ; if the shape factor less than 0.1, the standard deviations of strain components obtained will increase considerably and then these triangles are not suitable for calculating the strain components. When the strains are calculated by the triangle composed of GPS stations, the threshold of the shape factor is suggested to be 0.1 to 0.36.