Lg波衰减模型中建模误差的定量评估  

Quantitative evaluation of modeling error in Lg-wave attenuation model

作　　者：胡岩松 陈友麟 刘瑞丰[1] 刘伟 Hu Yansong;Chen Youlin;Liu Ruifeng;Liu Wei(Institute of Geophysics,China Earthquake Administration,Beijing 100081,China;Advanced Technology Division,Array Information Technology,Inc.,Greenbelt,Maryland 20770,USA;The Second Monitoring and Application Center,China Earthquake Administration,Xi'an 710054,China)

机构地区：[1]中国地震局地球物理研究所,北京100081 [2]Array信息技术公司先进技术事业部,美国马里兰州格林贝尔特20770 [3]中国地震局第二监测中心,西安710054

出　　处：《地震学报》2022年第6期1019-1034,共16页Acta Seismologica Sinica

基　　金：政府间国际科技创新合作重点专项(2018YFE0100100);中国地震局地球物理研究所基本科研业务费专项(DQJB20K30)共同资助.

摘　　要：对Lg波衰减模型中建模误差的统计特征进行了系统研究,并建立了地壳二维Lg波衰减模型。由于Lg波振幅可能受到几何扩散函数的强烈影响,合理评估反演过程的误差对于能否使用最小二乘意义下的反演非常重要。通过在川滇及其邻近地区收集的建模误差样本,使用K-S数值检验方法、Q-Q图和正态分布图形检验方法对Lg波衰减层析成像反演的输入数据中建模误差的分布特征进行了统计分析。采用奇异值分解(SVD)和反投影方法,分别获得了川滇地区的Q_(Lg)模型,定量计算模型的协方差矩阵和分辨率矩阵,定量评估了Q_(Lg)模型中每个格点的分辨率和误差。结果表明:在一阶近似条件下建模误差服从正态分布;通过开发的数据筛选程序,可以产生一个接近完美正态分布的数据集;与反投影方法相比,利用SVD方法获得的地壳Q值的分辨率更高;在射线覆盖较好的区域,Q_(Lg)模型的分辨率达到100 km,相对误差小于3%。In this study,we performed comprehensive statistical studies for the characteristics of the modeling error in Lg-wave attenuation model and obtained a two-dimensional crustal Lgwave attenuation model.The amplitudes of Lg-wave can be strongly influenced by the geometrical spreading function and it is essential to reasonably evaluate the error of the inversion process if we use the inverted method under the meaning of least squares.Based on the modeling error samples collected in the Sichuan-Yunnan region and its adjacent areas,we use three statistical test methods,namely the K-S test,the Q-Q plot,and the normal distribution plot,to analyze the distribution characteristics of modeling errors in the input data of Lg-wave attenuation tomography inversion.We used both the SVD-based tomographic method and the backprojection method to invert for the Lg Q model of the Sichuan-Yunnan region and its adjacent area respectively.Then,we calculated the covariance matrix and the resolution matrix of the model and evaluated the resolution and error of each grid point in the Lg Q model quantitatively.Our results indicate that the modeling errors in the input data obeyed a normal distribution under first-order approximation.By using the data screening technique,we generated a new dataset with nearly perfect normally distributed for Q tomography.Compared with the result of back-projection,the SVD-based method could allow for obtaining a finer resolution of crustal Q value in the areas with dense ray path coverages,where the model resolution can be resolved within a range of 100 km with a relative error of less than 3%.

关 键 词：Lg波衰减模型 Q值 建模误差 双台法 川滇地区 不确定度估计 

分 类 号：P315.31[天文地球—地震学]