一种用于弹性介质逆散射的非解耦时域直接采样方法
A Non-Decoupled Time-Domain Direct Sampling Method for Inverse Elastic Medium Scattering
AI总结：
该研究针对弹性波逆介质问题，提出一种时域直接采样方法，通过时移相关策略和传播时间对齐机制，从单个入射源定位散射体，经理论分析和数值实验验证了该方法的有效性、性能及适用性。
摘要：
本文研究弹性波的逆介质问题，即从时间分辨的边界测量中重建未知不均匀性。我们提出一种新颖的时域直接采样方法，用于从单个入射源定位散射体，且不对激励的时间轮廓作特定假设。成像泛函引入时移相关策略，用传播时间对齐机制取代传统的P - S波分解，实现从耦合弹性波场直接成像。通过傅里叶 - 拉普拉斯变换的帕塞瓦尔恒等式在频域重新表述成像泛函，利用修正贝塞尔函数性质表征其渐近行为，证明在目标位置达到最大值，能可靠识别散射体。提供了严格理论依据并进行数值实验验证其性能和适用性。
英文摘要：
This work is concerned with an inverse medium problem for elastic waves, in which unknown inhomogeneities are reconstructed from time-resolved boundary measurements. We propose a novel time-domain direct sampling method for locating scatterers from a single incident source, without imposing specific assumptions on the temporal profile of the excitation. In particular, the imaging functional introduces a time-shifted correlation strategy that replaces the traditional $P$-$S$ wave decomposition with a travel-time alignment mechanism, thereby enabling direct imaging from the coupled elastic wave field. To analyze the proposed time-domain imaging functional, we employ Parseval's identity for the Fourier--Laplace transform and reformulate the functional in the frequency domain. By exploiting properties of modified Bessel functions, we characterize the asymptotic behavior of the imaging functional and show that it attains its maximum at the target location, which enables reliable identification of the scatterer. Rigorous theoretical justifications are provided to substantiate the effectiveness of the proposed method. Numerical experiments are also presented to demonstrate its performance and applicability.
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