Uniform far-field asymptotics of the two-layered Green function in 2D and application to wave scattering in a two-layered medium

TL;DR

This paper derives the sharpest uniform far-field asymptotics for the two-layered Green function in 2D, providing a theoretical basis for imaging buried obstacles in layered media and advancing wave scattering analysis.

Contribution

The paper establishes the most precise uniform far-field asymptotics for the 2D two-layered Green function using steepest descent, with applications to acoustic scattering problems.

Findings

Sharpest uniform far-field asymptotics for 2D two-layered Green function

Derived asymptotics of scattered fields in layered media

Foundation for imaging buried obstacles with phaseless data

Abstract

In this paper, we establish new results for the uniform far-field asymptotics of the two-layered Green function (together with its derivatives) in 2D in the frequency domain. To the best of our knowledge, our results are the sharpest yet obtained. The steepest descent method plays an important role in the proofs of our results. Further, as an application of our new results, we derive the uniform far-field asymptotics of the scattered field to the acoustic scattering problem by buried obstacles in a two-layered medium with a locally rough interface. The results obtained in this paper provide a theoretical foundation for our recent work, where direct imaging methods have been developed to image the locally rough interface from phaseless total-field data or phased far-field data at a fixed frequency. It is believed that the results obtained in this paper will also be useful on its own right.