Browsing by Author "Oksanen, Lauri"

Now showing 1 - 3 of 3
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    An exact redatuming procedure for the inverse boundary value problem for the wave equation
    (Society for Industrial and Applied Mathematics, 2018) de Hoop, Maarten V.; Kepley, Paul; Oksanen, Lauri
    Redatuming is a data processing technique to transform measurements recorded in one acquisition geometry to an analogous data set corresponding to another acquisition geometry, for which there are no recorded measurements. We consider a redatuming problem for a wave equation on a bounded domain, or on a manifold with boundary, and model data acquisition by a restriction of the associated Neumann-to-Dirichlet map. This map models measurements with sources and receivers on an open subset $\Gamma$ contained in the boundary of the manifold. We model the wavespeed by a Riemannian metric and suppose that the metric is known in some coordinates in a neighborhood of $\Gamma$. Our goal is to move sources and receivers into this known near boundary region. We formulate redatuming as a collection of unique continuation problems and provide a two-step procedure to solve the redatuming problem. We investigate the stability of the first step in this procedure, showing that it enjoys conditional Hölder stability under suitable geometric hypotheses. In addition, we provide computational experiments that demonstrate our redatuming procedure.
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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 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.