# Recovery of material parameters in transversely isotropic media

## TL;DR

This paper demonstrates that in transversely isotropic media, wave travel times can determine key material parameters and the axis tilt, under certain conditions, advancing the understanding of parameter recovery in anisotropic elasticity.

## Contribution

It provides conditions under which wave travel times uniquely determine the elastic parameters and axis orientation in transversely isotropic media, with a detailed analysis of the inverse problem.

## Key findings

- Travel times determine the tilt of the axis of isotropy.
- Travel times determine some elastic parameters.
- Additional issues for full parameter recovery are identified.

## 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.