Recovery of discontinuous Lam 'e parameters from local dynamic boundary\n data

2019/03/13 by Peter Caday, Caday, Peter, Maarten V. de Hoop +5
Mathematics · Earth and Planetary Sciences · Computer Science · #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1903.05553

Abstract

Consider an isotropic elastic medium \Ω \⊂ \ℝ³ whose\nLam 'e parameters are piecewise smooth. In the elastic wave initial value\ninverse problem, we are given the solution operator for the elastic wave\nequation, but only outside \Ω and only for initial data supported outside\n\Ω. Using the recently introduced scattering control series in the\nacoustic case, we prove that piecewise smooth Lam 'e parameters are uniquely\ndetermined by this map under certain geometric conditions. We also show the\nextent that multiple scattering in the interior may be suppressed and\neliminated with access to only this partial solution map, which is akin to the\ndynamic Dirichlet-to-Neumann map.\n

Citations

• Reflection of singularities of solutions to systems of differential equations

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