Reconstruction of density and wave velocity from reflection and transmission data  

利用透射和反射数据反演声波传播的介质密度和波速(英文)

作　　者：苏京勋[1] 刘继军[1] 

机构地区：[1]东南大学数学系,南京210096

出　　处：《Journal of Southeast University(English Edition)》2005年第2期233-238,共6页东南大学学报（英文版）

基　　金：TheNationalNaturalScienceFoundationofChina(No. 10371018)

摘　　要：Consider an inverse problem of reconstructing the coefficient in a linearwave equation on an inhomogeneous slab with density ρ(z) and wave velocity c(z). The inversioninput information is the reflection and transmission data corresponding to a point source. Byapplying the characteristic theory for hyperbolic equations, we establish an integral system fromwhich ρ(z) and c(z) can be recovered simultaneously. In contrast to some known results, our inverseapproach is carried out for depth variable, rather than for travel-time variable. Thereforeinversion results in this paper are more appropriate for the physical interpretation of a mediumslab.研究点源作用下线性波动方程多个系数的反演问题,其中介质密度ρ(z)和波速c(z)为待求量.通过波动方程的特征理论,利用点源产生的反射数据和透射数据,建立了同时反演密度ρ(z)和波速c(z)的封闭积分系统.与已有的结果相比,本文求解反问题是直接在深度变量z而非传输时间变量x下进行的,因此更有助于结果的物理解释.

关 键 词：inverse problem wave equation characteristic theory integral equations 

分 类 号：O175.27[理学—数学]