Reconstruction of the electromagnetic field in layered media using the concept of approximate transmission conditions

We propose a fast and stable method to reconstruct the electromagnetic field in layered media from overdetermined data on the outer boundary. This procedure can be used for instance as a data pre-processing in inversion algorithms to accurately image buried objects under known stratified structures. Our method is based on successive use of so-called approximate transmission conditions that provide accurate reconstructions for layers with sufficiently small width. The feasibility and efficiency of the proposed method are demonstrated by numerical experiments.