Stable reconstruction of simple Riemannian manifolds from unknown interior sources

Abstract

Consider the geometric inverse problem: there is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to get an approximate reconstruction, and we indeed provide a discrete metric approximation to the manifold with explicit data-driven error bounds when the manifold is simple. This is the geometrization of a seismological inverse problem where we measure the arrival times on the surface of waves from an unknown number of unknown interior microseismic events at unknown times. The closeness of two metric spaces with a marked boundary is measured by a labeled Gromov–Hausdorff distance. If measurements are done for infinite time and spatially dense sources, our construction produces the true Riemannian manifold and the finite-time approximations converge to it in the metric sense

Description
Advisor
Degree
Type
Journal article
Keywords
Citation

Hoop, M. V. de, Ilmavirta, J., Lassas, M., & Saksala, T. (2023). Stable reconstruction of simple Riemannian manifolds from unknown interior sources. Inverse Problems, 39, 095002. https://doi.org/10.1088/1361-6420/ace6c9

Has part(s)
Forms part of
Rights
Except where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license. Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
Citable link to this page