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This study investigates reduced-order modeling (ROM) techniques for solving inverse problems in layered media, specifically recovering impedance profiles from time-domain electromagnetic measurements. The researchers use the Goupillaud structure to model wave propagation as a discrete dynamical system and define a ROM-based objective function at the level of reduced operators. Testing on a 5-layer medium with various perturbations shows that ROM-based inversion achieves better reconstruction than classical data misfit methods in clean settings and certain structured perturbation scenarios, while performing competitively across all test cases.
Why it matters
This work could improve techniques for subsurface imaging and material characterization in applications like geophysical exploration, non-destructive testing, and medical imaging. The ROM approach may enable more efficient and accurate inverse problem solutions when dealing with layered structures, potentially reducing computational costs while maintaining or improving reconstruction quality.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: We study reduced-order modeling for inverse problems in layered media, focusing on the recovery of impedance profiles from time-domain measurements. Using the Goupillaud structure, we formulate the forward problem as a discrete dynamical system and introduce a ROM-based objective defined at the level of reduced operators. Through numerical experiments on a 5-layer medium under various structured perturbations, we compare the ROM-based objective with a classical data misfit. The results show that the ROM-based inversion provides a more favorable reconstruction in the clean setting and in certain structured perturbation regimes, while remaining consistently competitive with the classical approach across all cases considered.
Source: Reduced-order modeling for electromagnetic inverse problems: a layered medium benchmark