| Autor: |
ELLER, MATTHIAS, GRIESMAIER, ROLAND, RIEDER, ANDREAS |
| Předmět: |
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| Zdroj: |
SIAM Journal on Applied Mathematics; 2024, Vol. 84 Issue 2, p412-432, 21p |
| Abstrakt: |
We discuss mapping properties of the parameter-to-state map of full waveform inversion and generalize the results of [M. Eller and A. Rieder, Inverse Problems, 37 (2021), 085011] from the acoustic to the viscoelastic wave equation. In particular, we establish injectivity of the Fréchet derivative of the parameter-to-state map for a semidiscrete seismic inverse problem in the viscoelastic regime. Here the finite-dimensional parameter space is restricted to functions having global support in the propagation medium (the nonlocal case) and that are locally linearly independent. As a consequence, we deduce local conditional well-posedness of this nonlinear inverse problem. Furthermore, we show that the tangential cone condition holds, which is an essential prerequisite in the convergence analysis of a variety of inversion algorithms for nonlinear ill-posed problems. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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