基于奇异值分解的空间变异地震动模拟  

Simulation of spatially varying ground motions based on singular value decomposition

作　　者：姚二雷 苗雨[1] 陈超[1] 

机构地区：[1]华中科技大学土木工程与力学学院,湖北武汉430074

出　　处：《华中科技大学学报（自然科学版）》2016年第10期22-25,40,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51378234);华中科技大学自主创新基金优青培育资助项目(2015MS060)

摘　　要：提出一种新的基于奇异值分解的地震动合成方法.该方法在合成多点地震动时采用复功率谱矩阵的奇异值分解,将复功率谱矩阵分解为一个埃尔米特矩阵与其共轭转置矩阵的乘积.该埃尔米特矩阵及其共轭转置矩阵分别由低阶的左、右特征值矩阵及奇异值平方根组成的矩阵近似表示,这一过程极大地降低了复功率谱矩阵的分解难度.算例验证表明:奇异值分解法既能避免科列斯基分解法及特征正交分解法中不合理元素的出现,又可通过分解矩阵的降维节省大量的存储空间,在保证精度的前提下提高合成效率.地震动合成实例计算分析表明使用该方法可快速高效地生成大量模拟点处的地震动时程.A new approach was developed to generate ground motions by using the singular value de- composition. In this method, singular value decomposition was performed on the complex power spectral matrix, and then the matrix could be expressed as the product of one Hermite matrix and its conjugate transposed matrix. The Hermite matrix and its conjugate transposed matrix could be approxi- mately replaced by left eigenvector matrix, right eigenvector matrix and singular value matrix, respec- tively, reducing the difficulty of decomposition of complex power spectral matrix greatly. The results of a simple example demonstrate that by employing the singular value decomposition, invalid elements resulted from previous decomposition methods can be avoided and a large amount of storage space can be saved so that the decomposition efficiency can be increased without influencing the precision basically. The results of examples for synthesizing ground motions verify that this method can be used to efficiently generate a large number of ground motions at different simulated points.

关 键 词：地震动合成 功率谱矩阵 奇异值分解 科列斯基分解 特征正交分解 合成效率 

分 类 号：P315.9[天文地球—地震学]