Inverse problem of Travel time difference functions on compact Riemannian manifold with boundary
Differential Geometry
2018-07-10 v1
Abstract
We show that the travel time difference functions, measured on the boundary, determine a compact Riemannian manifold with smooth boundary up to Riemannian isometry, if boundary satisfies a certain visibility condition. This corresponds with the inverse microseismicity problem. The novelty of our paper is a new type of a proof and a weaker assumption for the boundary than it has been presented in the literature before. We also construct an explicit smooth atlas from the travel time difference functions.
Keywords
Cite
@article{arxiv.1807.02576,
title = {Inverse problem of Travel time difference functions on compact Riemannian manifold with boundary},
author = {Maarten V. de Hoop and Teemu Saksala},
journal= {arXiv preprint arXiv:1807.02576},
year = {2018}
}