2013/11/17 by Manas Kar, Kar, Manas, Mourad Sini +1
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1311.4137
openalex publication_date 2013/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we are concerned with the inverse scattering by interfaces for\nthe linearized and isotropic elastic model at a fixed frequency. First, we\nderive complex geometrical optic solutions with linear or spherical phases\nhaving a computable dominant part and an H^\α-decaying remainder term\nwith \α <3, where H\α is the classical Sobolev space. Second,\nbased on these properties, we estimate the convex hull as well as non convex\nparts of the interface using the farfields of only one of the two reflected\nbody waves (pressure waves or shear waves) as measurements. The results are\ngiven for both the impenetrable obstacles, with traction boundary conditions,\nand the penetrable obstacles. In the analysis, we require the surfaces of the\nobstacles to be Lipschitz regular and, for the penetrable obstacles, the Lam 'e\ncoefficients to be measurable and bounded with the usual jump conditions across\nthe interface.\n