English

Recovery of material parameters in transversely isotropic media

Analysis of PDEs 2019-09-04 v2 Differential Geometry

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 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.

Keywords

Cite

@article{arxiv.1902.09394,
  title  = {Recovery of material parameters in transversely isotropic media},
  author = {Maarten V. de Hoop and Gunther Uhlmann and Andras Vasy},
  journal= {arXiv preprint arXiv:1902.09394},
  year   = {2019}
}

Comments

22 pages; minor changes: some signs in Lemma 3.2 fixed