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.

翻译：本文研究二维局部粗糙界面分层介质中时谐声学平面波的反散射问题。提出了一种直接成像方法，通过固定频率下在大半径上半圆测量的无相位总场数据，或固定频率下在单位上半圆测量的相位远场数据，重建局部粗糙界面。局部粗糙界面的存在给成像方法的理论分析带来挑战。为应对这些挑战，基于我们近期工作[李.L.、杨.J.、张.B.、张.H., arXiv:2208.00456]中关于分层介质声散射均匀远场渐近分析的技术与结果，对成像方法中涉及的振荡积分进行了技术性渐近分析。最后，通过大量数值实验验证了成像算法的可行性与鲁棒性。