2015/05/26 by Maarten V. de Hoop, Gen Nakamura, de Hoop, Maarten V. +3
Engineering · Environmental Science · Mathematics · #Analysis of PDEs (math.AP) #Electrical and Bioimpedance Tomography #FOS: Mathematics #Numerical methods in inverse problems #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.1505.06960
openalex publication_date 2015/05/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in ℝ3 via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann map. More precisely, using the full symbol of the transformed Dirichlet-to-Neumann map viewed as a semiclassical pseudodifferential operator, we give an explicit reconstruction of both Lamé parameters and the density, as well as their derivatives, at the boundary. We also show how this boundary reconstruction leads to a decomposition of incoming and outgoing waves.