Stable reconstruction of simple Riemannian manifolds from unknown interior sources

Simple item page
dc.citation.articleNumber095002
dc.citation.journalTitleInverse Problems
dc.citation.volumeNumber39
dc.contributor.authorHoop, Maarten V. de
dc.contributor.authorIlmavirta, Joonas
dc.contributor.authorLassas, Matti
dc.contributor.authorSaksala, Teemu
dc.date.accessioned2024-05-08T18:56:13Z
dc.date.available2024-05-08T18:56:13Z
dc.date.issued2023
dc.description.abstractConsider 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
dc.identifier.citationHoop, 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
dc.identifier.digitalde_Hoop_2023_Inverse_Problems_39_095002
dc.identifier.doihttps://doi.org/10.1088/1361-6420/ace6c9
dc.identifier.urihttps://hdl.handle.net/1911/115699
dc.language.isoeng
dc.publisherIOP Publishing Ltd
dc.rightsExcept 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.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleStable reconstruction of simple Riemannian manifolds from unknown interior sources
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
de_Hoop_2023_Inverse_Problems_39_095002.pdf
Size:
564.94 KB
Format:
Adobe Portable Document Format
Download
Collections
Faculty Publications
CAAM Publications