刘振彪,俞言祥,肖亮,吴清. 2024. 基于拟合椭圆的等震线长短轴测量方法. 地震学报,46(3):1−19. doi: 10.11939/jass.20220160
引用本文: 刘振彪,俞言祥,肖亮,吴清. 2024. 基于拟合椭圆的等震线长短轴测量方法. 地震学报,46(3):1−19. doi: 10.11939/jass.20220160
Liu Z B,Yu Y X,Xiao L,Wu Q. 2024. Isoseismal major and minor axes measurements based on fitted ellipses. Acta Seismologica Sinica46(3):1−19. doi: 10.11939/jass.20220160
Citation: Liu Z B,Yu Y X,Xiao L,Wu Q. 2024. Isoseismal major and minor axes measurements based on fitted ellipses. Acta Seismologica Sinica46(3):1−19. doi: 10.11939/jass.20220160

基于拟合椭圆的等震线长短轴测量方法

Isoseismal major and minor axes measurements based on fitted ellipses

  • 摘要: 提出了一种改进的拟合椭圆算法用于测量等震线的长短轴,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和继承的基础上,减少了直接测量算法的主观不确定性。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。

     

    Abstract:
    As the fundamental data for establishing the relationship seismic intensity attenuation, the reliability of isoseismal line data directly affects the accuracy and reliability of the intensity attenuation relationship. The acquisition of traditional isoseismal line parameters is based on direct measurement, which inevitably introduces a degree of subjectivity. A more objective approach to measuring the parameters of isoseismal maps has been proposed. However, it is inevitable that conceptual differences will exist due to algorithmic differences and the lack of links to commonly used direct measurement methods. In view of this, this paper introduces a novel approach to measuring the major and minor axes of isoseismal lines. The model of isoseismal line measurement and the concepts from the direct measurement method are incorporated into the fitted ellipse 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-fit ellipse of the isoseismal line. This approach is based on the consistency and inheritance of the methods and concepts of the direct measurements. The resulting data provides the basic data for the establishment of intensity attenuation relationship.
    The measurement modes of isoseismal lines 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 incorporated into the algorithm as a constraint. Additionally, the area of isoseismal line 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 constrained major-axis strike, which involves the addition of a priori major-axis strike information to the model fitting process. ③ A fitting algorithm with constrained area and major-axis strike, which incorporates both the a priori major-axis strike and the model area into the model fitting process. ④ A fitting algorithm with constrained area, which entails the addition of a priori model area to the model fitting process.
    It should be noted that the results of the algorithm will degrade from an ellipse to a circle when the isoseismal shape is circular (i.e. a special ellipse). Therefore, it is necessary to construct circular isoseismal line and simulate different levels of sampling noise so as to test the applicability of the algorithm. The results of the algorithm test demonstrate that all four algorithms yield satisfactory outcomes when the noise is minimal. However, the algorithm with area constraints exhibits a significantly superior performance compared with the algorithm without area constraints when the noise is elevated. Nevertheless, the applicability of the algorithms for degradation to a circle is deemed acceptable, given that extreme noise cases are unlikely to occur in practical scenarios.
    The isoseismal data used by the ellipse fitting algorithm is subject to sampling bias, which may affect the output of algorithm. Therefore, it is necessary to analyze the impact of data sampling differences on the results of algorithm. The robustness of the algorithm was evaluated by randomly sampling sampling points of isoseismal line to simulate different sampling scenarios. The results indicate that the parameter values are normally distributed, with the majority of results falling within one standard deviation of the mean value. Furthermore, the algorithm is robust. For the unclosed isoseismal line with complex shapes, the calculation results are relatively discrete, and thus require separate verification. Furthermore, the measurements obtained by the ellipse fitting algorithm are consistent with previous results and can be used to establish the intensity attenuation relationship.

     

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