Continuous and Discrete Inverse‐Scattering Problems in a Stratified Elastic Medium. I. Plane Waves at Normal Incidence
Continuous and Discrete Inverse‐Scattering Problems in a Stratified Elastic Medium. I. Plane Waves at Normal Incidence
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分层弹性介质中的连续和离散逆散射问题 I. 法向入射的平面波。
DOI：
10.1121/1.1911568
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发表时间：
1969
影响因子：
2.4
通讯作者：
K. Aki
中科院分区：
文献类型：
--
作者：
J. A. Ware;K. Aki
本文研究了获得解析解和实际计算程序的问题，以从已被介质反射或传输的波中恢复未知弹性介质的特性。该介质由两个与异质区域接触的同质半空间组成。解析解是通过将平面波在分层弹性介质中垂直入射传播的运动方程转化为一维薛定谔方程而获得的，该方程的逆散射问题已经得到解决。实际的计算过程是通过解决相应的离散逆散射问题来获得的，该问题是通过用一系列同质层近似异质区域而产生的，使得通过每层的传播时间相同。在连续和离散逆散射问题中，介质的阻抗作为传播时间的函数是从介质的脉冲响应中恢复的。还开发了连续解决方案的离散类比。对于由自由表面界定的分层弹性半空间也获得了类似的结果。
This paper investigates the problem of obtaining an analytic solution and practical computational procedures for recovering the properties of an unknown elastic medium from waves that have been reflected by or transmitted through the medium. The medium consists of two homogeneous half‐spaces in contact with a heterogeneous region. The analytic solution is obtained by transforming the equation of motion for the propagation of plane waves at normal incidence in a stratified elastic medium into a one‐dimensional Schrodinger equation for which the inverse‐scattering problem has already been solved. The practical computational procedures are obtained by solving the corresponding discrete inverse‐scattering problem resulting from approximating the heterogeneous region with a sequence of homogeneous layers such that the travel time through each layer is the same. In both the continuous and discrete inverse scattering problems, the impedance of the medium as a function of travel time is recovered from the impulse response of the medium. A discrete analogy of the continuous solution is also developed. Similar results are obtained for a stratified elastic half space bounded by a free surface.