2020/03/22 by Lorenzo Baldassari, Baldassari, Lorenzo, Andrea Scapin +1
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #35B30 #35C20 #35J05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis #Ultrasonics and Acoustic Wave Propagation #math-ph #math.AP #math.MP #msc:35B30 #msc:35C20 #msc:35J05
paper · pdf · doi:10.48550/arxiv.2003.09806
arxiv created 2020/03/22 · openalex publication_date 2020/03/22 · arxiv updated 2020/03/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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.