Abstract
In this paper we show that in anisotropic elasticity, in the particular case of transversely isotropic media, under appropriate convexity conditions, knowledge of the qSH wave travel times determines the tilt of the axis of isotropy as well as some of the elastic material parameters, and the knowledge of qP and qSV travel times conditionally determines a subset of the remaining parameters, in the sense that if some of the remaining parameters are known, the rest are determined, or if the remaining parameters satisfy a suitable relation, they are all determined, under certain non-degeneracy conditions. Furthermore, we give a precise description of the additional issues, which are a subject of ongoing work, that need to be resolved for a full treatment.
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Acknowledgements
The authors thank Joey Zou for pointing out an incorrect statement in Lemma 3.2 in an earlier version of the paper. The authors are very grateful to the Hong Kong University of Science and Technology (HKUST) and the University of Jyväskylä for their hospitality during stays which led to this work. The authors also gratefully acknowledge partial support from the National Science Foundation, and G.U. is grateful for partial support from a Si Yuan professorship from the Institute for Advanced Study of HKUST, while M.V.d.H. and A.V. thank the Simons Foundation for partial support.
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de Hoop, M.V., Uhlmann, G. & Vasy, A. Recovery of Material Parameters in Transversely Isotropic Media. Arch Rational Mech Anal 235, 141–165 (2020). https://doi.org/10.1007/s00205-019-01421-5
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DOI: https://doi.org/10.1007/s00205-019-01421-5