基于拟合椭圆的等震线长短轴测量方法  

Measurement method for isoseismal major and minor axes based on ellipse fitting algorithm

作　　者：刘振彪 俞言祥[1] 肖亮[1] 吴清[1] Liu Zhenbiao;Yu Yanxiang;Xiao Liang;Wu Qing(Institute of Geophysics,China Earthquake Administration,Beijing 100081,China)

机构地区：[1]中国地震局地球物理研究所,北京100081

出　　处：《地震学报》2024年第3期458-476,共19页Acta Seismologica Sinica

基　　金：中国地震局地球物理研究所基本科研业务费(DQJB22Z03)资助。

摘　　要：提出了一种改进的拟合椭圆算法用于测量等震线长短轴,即将等震线测量的模式和直接测量算法的概念以约束的形式加入拟合椭圆算法,并使用最小二乘法求解椭圆系数,在与传统等震线测量方法保持一致的基础上,减少了直接测量方法的主观不确定性。在此基础上讨论了拟合椭圆算法的适用性和鲁棒性,将等震线长短轴的测量结果与前人的结果进行了对比。结果表明:拟合椭圆算法的适用性较好,可用于等震线的拟合;拟合椭圆算法的鲁棒性较好,计算结果较为稳定;对于未闭合且形状复杂的等震线,计算结果相对离散,要单独验证结果是否合理;利用拟合椭圆算法得到的等震线长短轴结果与前人的结果较为一致,可用于建立烈度衰减关系。As the fundamental data for establishing the seismic intensity attenuation relationship,the reliability of isoseismal data directly affects the accuracy and reliability of the intensity attenuation relationship.The acquisition of traditional isoseismal parameters is based on direct measurement,which inevitably introduces a degree of subjectivity.A more objective approach to measuring the parameters of isoseismals has been proposed.However,it is inevitable that conceptual differences will exist due to algorithmic differences and the lack of links between the novel algorithm and commonly used direct measurement methods.In view of this,this paper introduces a novel approach to measuring the major and minor axes of isoseismals.The mode of isoseismal measurement and the concepts from the direct measurement method are incorporated into the ellipse fitting algorithm as mathematical constraints,thereby providing a systematic method for measuring the radii of isoseismal major and minor axes.In order to reduce the subjective influence of isoseismal major and minor-axis measurements,the radii of isoseismal major and minor axes are measured using the best-fitting ellipse of the isoseismal.This approach is based on the consistency and inheritance of the methods and concepts of the direct measurements.The resulting data provide the basic data for the establishment of intensity attenuation relationship.The measurement modes of isoseismals are classified into two types according to whether the major-axis strike is fixed or not.In order to accommodate this distinction,the strike of major axis is also incorporated into the algorithm as a constraint.Additionally,the area of isoseismal is incorporated into the algorithm as a constraint.This leads to the proposal of four ellipse fitting algorithms in total:(1) An unconstrained fitting algorithm,which implies that no additional constraints are imposed during the model fitting process.(2) A fitting algorithm with major-axis strike constrained,which involves the addition of a priori maj

关 键 词：等震线长短轴测量方法 拟合椭圆算法 最小二乘拟合 算法测试 

分 类 号：P315.9[天文地球—地震学]