2023/05/10 by Long Li, Yang Jian-sheng, Li, Long +5
Engineering · Mathematics · #FOS: Mathematics #Geophysical Methods and Applications #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2305.05941
openalex publication_date 2023/05/10 · openalex created_date 2023/05/12 · openalex updated_date 2026/07/28
This paper is concerned with the problem of inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in 2D. A direct imaging method is proposed to reconstruct the locally rough interface from the phaseless total-field data measured on the upper half of the circle with a large radius at a fixed frequency or from the phased far-field data measured on the upper half of the unit circle at a fixed frequency. The presence of the locally rough interface poses challenges in the theoretical analysis of the imaging methods. To address these challenges, a technically involved asymptotic analysis is provided for the relevant oscillatory integrals involved in the imaging methods, based mainly on the techniques and results in our recent work [L. Li, J. Yang, B. Zhang and H. Zhang, arXiv:2208.00456] on the uniform far-field asymptotics of the scattered field for acoustic scattering in a two-layered medium. Finally, extensive numerical experiments are conducted to demonstrate the feasibility and robustness of our imaging algorithms.