Browsing by Author "Lassas, Matti"

Now showing 1 - 3 of 3
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    Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem
    (Taylor & Francis, 2023) de Hoop, Maarten V.; Lassas, Matti; Lu, Jinpeng; Oksanen, Lauri
    We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular, our result applies to the elasticity system and also the Maxwell system. As an application, we study the kinematic inverse rupture problem of determining the jump in displacement and the friction force at the rupture surface, and we obtain new features on the stable unique continuation up to the rupture surface.
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    Stable reconstruction of simple Riemannian manifolds from unknown interior sources
    (IOP Publishing Ltd, 2023) Hoop, Maarten V. de; Ilmavirta, Joonas; Lassas, Matti; Saksala, Teemu
    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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    Stable Recovery of Coefficients in an Inverse Fault Friction Problem
    (Springer Nature, 2024) de Hoop, Maarten V.; Lassas, Matti; Lu, Jinpeng; Oksanen, Lauri
    We consider the inverse fault friction problem of determining the friction coefficient in the Tresca friction model, which can be formulated as an inverse problem for differential inequalities. We show that the measurements of elastic waves during a rupture uniquely determine the friction coefficient at the rupture surface with explicit stability estimates.