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.