The inverse medium problem in 1D PML-truncated heterogeneous semi-infinite domains
The inverse medium problem in 1D PML-truncated heterogeneous semi-infinite domains
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DOI：
10.1080/17415977.2010.492510
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发表时间：
2010-01-01
影响因子：
1.3
通讯作者：
Kallivokas, Loukas F.
中科院分区：
文献类型：
--
作者：
Kang, Jun Won;Kallivokas, Loukas F.
我们讨论了一种基于全波场的反演方法，用于直接在时域内重建非均质半无限畴的材料剖面，该方法基于对该畴对规定波照明的响应的表面测量。恢复模速度/波速深度剖面的能力通常与岩土工程现场特征应用相关，这是特别感兴趣的。我们解决了与波场反演相关的四个关键问题：(a)为了限制异构物理域的半无限范围，在截断界面引入了完美匹配层（PML）；(b)考虑到PML的引入，我们对耦合PML-正则域问题使用了混合非分域PML公式；(c)为了解决反演问题，我们采用了一个偏微分方程（PDE）约束优化框架，该框架正式导致一个经典的Karush-Kuhn-Tucker （KKT）系统，该系统包括初始值状态、终值伴随和时间无关的控制问题；(d)为了缩小可行性空间和减轻固有的解的多重性，我们讨论了Tikhonov和全变分正则化方案，并赋予正则化因子连续算法。我们还限制了总观测时间，以最优地考虑反演迭代期间域的异质性。我们报告的理论和结果，导致有效地重建尖锐和光滑的轮廓在一维。
We discuss a total wavefield-based inversion approach for the reconstruction of the material profile of heterogeneous semi-infinite domains, directly in the time domain, based on surficial measurements of the domain's response to prescribed wave illumination. The ability to recover the in-depth profile of moduli/wave velocities typically associated with geotechnical site characterization applications is of particular interest. We address four key issues associated with the wavefield-based inversion: (a) to limit the semi-infinite extent of the heterogeneous physical domain, a perfectly-matched-layer (PML) is introduced at the truncation interface; (b) to account for the introduction of the PML, we use a mixed unsplit-field PML formulation for the coupled PML-regular-domain problem; (c) to tackle the inversion, we adopt a partial-differential-equation (PDE)-constrained optimization framework that formally leads to a classic Karush-Kuhn-Tucker (KKT) system comprising the initial-value state, final-value adjoint and time-independent control problems; and (d) to narrow the feasibility space and alleviate the inherent solution multiplicity, we discuss Tikhonov and Total Variation regularization schemes, endowed with a regularization factor continuation algorithm. We also limit the total observation time to optimally account for the domain's heterogeneity during inversion iterations. We report on the theory and results that lead efficiently to the reconstruction of both sharp and smooth profiles in one dimension.