An inverse kinematic problem with internal sources
An inverse kinematic problem with internal sources
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具有内部源的逆运动学问题
DOI：
10.1088/0266-5611/31/5/055006
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发表时间：
2014
期刊：
影响因子：
2.1
通讯作者：
Hanming Zhou
中科院分区：
文献类型：
--
作者：
L. Pestov;G. Uhlmann;Hanming Zhou
给定R n中的有界域M？>与共形欧氏度量g = dx 2？>，我们考虑了恢复区域Γ M？>的半测邻域的反问题，以及来自行进时间数据（下面定义）和Γ的笛卡尔坐标的邻域中的共形因子ρ。我们开发了一个明确的重建程序，这个问题。关键成分是重建过程和共形Killing方程的柯西问题之间的关系。
Given a bounded domain M in R n ?> with a conformally Euclidean metric g = &rgr; dx 2 ?> , we consider the inverse problem of recovering a semigeodesic neighborhood of a domain Γ ⊂ ∂ M ?> and the conformal factor ρ in the neighborhood from the travel time data (defined below) and the Cartesian coordinates of Γ. We develop an explicit reconstruction procedure for this problem. The key ingredient is the relation between the reconstruction procedure and a Cauchy problem of the conformal Killing equation.