几种常用应变计算方法的抗差性和适用性对比分析研究  

Comparative analysis of resistance and applicability of several commonly used strain calculation methods

作　　者：陈长云 尧俊凯[1] 占伟 梁经纬[1] 郭南男 唐毅 CHEN ChangYun;YAO JunKai;ZHAN Wei;LIANG JingWei;GUO NanNan;TANG Yi(State Key Laboratory of High-speed Railway Track System,Beijing 100081,China;The First Monitoring and Application Center,CEA,Tianjin 300180,China)

机构地区：[1]高速铁路轨道系统全国重点实验室,北京100081 [2]中国地震局第一监测中心,天津300180

出　　处：《地球物理学进展》2024年第4期1343-1357,共15页Progress in Geophysics

基　　金：高速铁路轨道系统全国重点实验室开放基金课题(2022YJ084)资助。

摘　　要：应变率是描述地壳形变特征的主要参数之一,可用于识别强震前后地壳变形特征,对于认识地震孕育过程以及推进地震预测研究具有重要意义.不同的应变计算方法针对不同的研究目的和数据分布密度有不同的适用性.本文利用模拟数据作为输入,针对不同空间尺度和数据分布特征对比分析了泰森多边形、球面小波、距离加权和最小二乘配置等四种不同应变计算方法的抗差性和适用性.大空间尺度的抗差性分析结果表明,最小二乘配置方法的抗差性最强,其次是距离加权和球面小波方法,泰森多边形方法相关系数衰减速率明显快于其他三种方法.剔除部分采样数据情况下,泰森多边形方法因噪声对解算结果影响较大,其他三种方法的结果具有一致性.中等空间尺度对比分析表明最小二乘配置和距离加权与理论解的残差均方差量值明显小于其他两种方法.泰森多边形方法边缘效应明显,球面小波方法与理论解结果存在一定偏差,最小二乘配置和距离加权方法与理论解有一致性,但前者在变形量值和空间分辨能力与理论解存在偏差,后者在快速变形区与理论解存在偏差.基于实测数据对比分析结果显示泰森多边形方法边缘效应明显;距离加权方法局部存在边缘效应;球面小波方法结果能较好反映断层作用的影响但其存在多处局部高值区;最小二乘配置方法能兼顾断层的近远场变形特征.总之,不同方法对误差的敏感程度、边缘效应、局部奇异分布等方面均存在明显差异,实际应用中需采用可靠性强、结果稳定、边缘效应不明显的方法.Strain rate is one of the main parameters to characterize crustal deformation,which can be used to identify crustal deformation characteristics before and after strong earthquakes and is of great significance to understand the process of seismicity breeding and to advance the research of earthquake prediction.Different strain calculation methods have different applicability for different research purposes and data distribution densities.The robustness and applicability of four different strain calculation methods such as Voronoi,spherical wavelet,distance weighting and least square collocation are analyzed for different spatial scales by using simulation data.The results of resistance analysis on large spatial scale show that the least square collocation method has the strongest resistance,followed by distance weighting and spherical wavelet method,and the attenuation rate of correlation coefficient of Voronoi method is significantly faster than the other three methods.In the case of removing part of the sampled data,the Voronoi method has too much influence on the calculation result because of the noise,and the results of the other three methods are consistent.Comparative analysis of medium spatial scale shows that the residual mean square error of least square collocation and distance weighting is significantly smaller than that of the other two methods.The edge effect of Voronoi method is obvious,the spherical wavelet method has a certain deviation from the theoretical solution,the least square collocation and distance weighting method are consistent with the theoretical solution,but the former has a deviation from the theoretical solution in the deformation magnitude and spatial resolution,and the latter has a deviation from the theoretical solution in the fast deformation region.The results of comparative analysis based on the GNSS observation data from the China Crustal Movement Observation Network show that the edge effect of Voronoi method is obvious.The distance weighting method has local edge effect.The

关 键 词：最小二乘配置 泰森多边形 距离加权 球面小波 抗差性分析 

分 类 号：P315[天文地球—地震学]