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Reconstruction of generic anisotropic stiffness tensors from partial data around one polarization

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RNTW01 - Rich and Nonlinear Tomography (RNT) in Radar, Astronomy and Geophysics

We combine techniques from algebraic geometry and microlocal analysis to study geometric inverse problems associated with wave propagation in anisotropic elastic media using a single, namely qP, polarization. The Christoffel matrix determined by the stiffness tensor appearing in the analysis of propagation of singularities of elastic waves generates a slowness polynomial. Generic anisotropy ensures a certain “algebraic coupling” between the branches of the slowness surface determined by this polynomial, on which our approach relies. The qP branch of the slowness surface determines a metric in Finsler geometry. The recovery of the stiffness tensor from the slowness surface uses Gröbner bases.   Joint research with J. Ilmavirta, M. Lassas and A. Várilly-Alvarado.

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