by Maarten V. de Hoop, Joonas Ilmavirta and Matti Lassas
Abstract:
Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a Finsler manifold from certain sphere data in a given open subset of the manifold. We solve this problem locally along any geodesic through the measurement set.
Reference:
Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity (Maarten V. de Hoop, Joonas Ilmavirta and Matti Lassas), Journal de Mathématiques Pures et Appliquées, volume 196, pp. 103688, 2025.
[show abstract]
[hide abstract]
Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a Finsler manifold from certain sphere data in a given open subset of the manifold. We solve this problem locally along any geodesic through the measurement set.
[arXiv]
Bibtex Entry:
@article{finsler-dix,
author = {Maarten V. de Hoop and Joonas Ilmavirta and Matti Lassas},
title = {{Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity}},
journal = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es},
volume = {196},
pages = {103688},
month = apr,
year = {2025},
abstract = {Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a Finsler manifold from certain sphere data in a given open subset of the manifold. We solve this problem locally along any geodesic through the measurement set.},
url={http://users.jyu.fi/~jojapeil/pub/finsler-dix.pdf},
arxiv = {2102.10383},
gsid = {17153062567477078198},
doi = {10.1016/j.matpur.2025.103688}
}