Stable reconstruction of simple Riemannian manifolds from unknown interior sources
de Hoop, M. V., Ilmavirta, J., Lassas, M., & Saksala, T. (2023). Stable reconstruction of simple Riemannian manifolds from unknown interior sources. Inverse Problems, 39(9), Article 095002. https://doi.org/10.1088/1361-6420/ace6c9
Julkaistu sarjassa
Inverse ProblemsPäivämäärä
2023Oppiaine
MatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse ProblemsTekijänoikeudet
© 2023 The Author(s). Published by IOP Publishing Ltd Printed in the UK
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
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IOP PublishingISSN Hae Julkaisufoorumista
0266-5611Asiasanat
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https://converis.jyu.fi/converis/portal/detail/Publication/184473625
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M V d H was supported by the Simons Foundation under the MATH + X program, the National Science Foundation under Grant DMS-1815143, and the corporate members of the Geo-Mathematical Imaging Group at Rice University. J I was supported by the Academy of Finland (Projects 332890 and 336254). M L was supported by Academy of Finland (Projects 284715 and 303754). T S was supported by the Simons Foundation under the MATH + X program and the corporate members of the Geo-Mathematical Imaging Group at Rice University. ...Lisenssi
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