Local uniqueness of the density from partial boundary data for isotropic elastodynamics. (28th September 2018)

• Record Type: Journal Article
• Authors: Bhattacharyya, Sombuddha
• Is Part Of: Inverse problems. Volume 34:Number 12(2018:Dec.)
• Publication Date: 2018-09-28
• Subjects: inverse problems -- elastodynamics -- partial differential equation -- geophysical inverse problems; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aade76
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider an inverse problem in elastodynamics arising in seismic imaging. We prove locally uniqueness of the density of a non-homogeneous, isotropic elastic body from measurements taken on a part of the boundary. We measure the Dirichlet to Neumann map, only on a part of the boundary, corresponding to the isotropic elasticity equation of a 3D object. In earlier works it has been shown that one can determine the sheer and compressional speeds on a neighborhood of the part of the boundary (accessible part) where the measurements have been taken. In this article we show that one can determine the density of the medium as well, on a neighborhood of the accessible part of the boundary.