论文标题
通过时间依赖性极化张量重建小声学包含
Reconstruction of a small acoustic inclusion via Time-dependent Polarization Tensors
论文作者
论文摘要
本文旨在引入与时间依赖性极化张量（TDPTS）的概念，该概念与与直径较小的声学包容相关的波方程，其组成型参数与背景和大小的参数不同于操作波长。首先，考虑了Helmholtz方程的解决方案，并出示了由于包容的存在而导致散射场的完整渐近膨胀的严格系统推导。然后，通过应用傅立叶变换，在截断高频后很容易获得相应的时间域膨胀。 TDPTS的新概念可用于执行成像。驱动数值模拟，表明从嘈杂测量值重建的TDPTS可以对包含的细节进行成像。
This paper aims at introducing the concept of time-dependent polarization tensors (TDPTs) for the wave equation associated to a diametrically small acoustic inclusion, with constitutive parameters different from those of the background and size smaller than the operating wavelength. Firstly, the solution to the Helmholtz equation is considered, and a rigorous systematic derivation of a complete asymptotic expansion of the scattered field due to the presence of the inclusion is presented. Then, by applying the Fourier transform, the corresponding time-domain expansion is readily obtained after truncating the high frequencies. The new concept of TDPTs is shown to be promising for performing imaging. Numerical simulations are driven, showing that the TDPTs reconstructed from noisy measurements allow to image fine shape details of the inclusion.
