Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion
Abstract
Velocity models presenting sharp interfaces are highly relevant in seismic imaging, e.g., for imaging the subsurface of the Earth in the presence of salt bodies. In order to mitigate the oversmoothing of classical regularization strategies such as the Tikhonov regularization, we propose a shape optimization approach for the sharp-interface reconstruction in time-domain acoustic full waveform inversion. Our main result includes the shape differentiability of the cost functional measuring the misfit between observed and predicted data. In particular, it reveals the expression of the distributed shape derivative in tensor form, built on a Lagrangian-type approach and regularity results for the wave equation with discontinuous coefficients. Based on the achieved distributed shape derivative and the level set method, we propose a numerical approach and present several numerical tests supporting our approach.
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© 2021, Society for Industrial and Applied Mathematics.
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Submitted: 3 November 2020
Accepted: 21 January 2021
Published online: 20 May 2021
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Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : 159/2-2
Fundação de Amparo à Pesquisa do Estado de São Paulo https://doi.org/10.13039/501100001807 : 2014/50279-4
Conselho Nacional de Desenvolvimento Científico e Tecnológico https://doi.org/10.13039/501100003593 : 408175/2018-4, 304258/2018-0
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