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Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
Trong D. Dang, Chanh V. Le, Khoa D. Luu, Loc H Nguyen
https://arxiv.org/abs/2506.13000

Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave propagation. The key idea is to employ a novel spectral representation in time, using an orthonormal basis composed of Legendre polynomials weighted by exponential functions. This Legendre polynomial-exponential basis enables a stable and accurate decomposition in the…