Stable reconstruction of simple Riemannian manifolds from unknown interior sources
Stable reconstruction of simple Riemannian manifolds from unknown interior sources
复制标题
从未知内部源稳定重建简单黎曼流形
作者：
Maarten V. de Hoop;Joonas Ilmavirta;M. Lassas;Teemu Saksala
考虑几何逆问题：时空中有一组δ源，它们发射出以单位速度传播的波。如果我们知道所有到达时空边界圆柱的时间，我们能重建空间，一个有边界的黎曼流形吗？对于一组有限的源，我们只能希望得到一个近似的重建，当流形是简单的时，我们确实提供了一个离散的度量逼近流形，并具有显式的数据驱动误差界。这是一个地震学逆问题的几何化，在这个逆问题中，我们测量来自未知数量的未知内部微震事件在未知时间的波在表面上的到达时间。两个具有标记边界的度量空间的接近性由标记Gromov-Hausdorff距离度量。如果对无限时间和空间密集源进行测量，我们的构造产生真正的黎曼流形，并且有限时间近似在度量意义上收敛到它
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
拉普拉斯连接的反演问题
DOI：
10.48550/arxiv.1509.02645
发表时间：
2015
期刊：
arXiv e-prints
影响因子：
--
作者：
Kurylev Yaroslav
通讯作者：
Kurylev Yaroslav
有边界紧黎曼流形上的走时差函数反问题
DOI：
10.1007/s12220-018-00111-0
发表时间：
2019
期刊：
The Journal of Geometric Analysis
影响因子：
--
作者：
de Hoop, Maarten V.;Saksala, Teemu
通讯作者：
Saksala, Teemu