物理
数学分析
散射
逆散射问题
亥姆霍兹方程
反问题
几何学
积分方程
平面波
声学
出处
期刊:Ultrasonics
[Elsevier]
日期:1987-05-01
卷期号:25 (3): 138-140
被引量:1
标识
DOI:10.1016/0041-624x(87)90019-9
摘要
Abstract The inhomogeneous acoustic wave equation in cylindrically symmetric geometry, is reduced to a one-dimensional Schrodinger equation for time harmonic waves. The scattering potential so formed is uniquely reconstructed by the Gelfand-Levitan theory. In physical terms, the scattering potential is a function of the impedance profile, which is then recovered. If the velocity profile is known (or constant) the density profile, as a function of the radial coordinate, can be deduced. A practical experiment is envisaged whereby the back-scattered time sequence is measured in a pulse-echo mode, and the data are used to reconstruct the density profile.
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