A Legendre polynomial-exponential basis reduces the inverse elastic wave initial-data problem to elliptic systems solved by quasi-reversibility, with a convergence theorem and 2D reconstructions for isotropic, inhomogeneous, and anisotropic media.
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Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
A Legendre polynomial-exponential basis reduces the inverse elastic wave initial-data problem to elliptic systems solved by quasi-reversibility, with a convergence theorem and 2D reconstructions for isotropic, inhomogeneous, and anisotropic media.