Full-waveform inversion using level set and cut elements for sharp-interface problems

Hélio Emmendoerfer

doi:10.1016/j.jcp.2023.112561

Full-waveform inversion using level set and cut elements for sharp-interface problems

2023-12-01

1

PRE

AI

H

Hélio Emmendoerfer *

P

Paulo Bastos de Castro

B

Bruno Carmo

E

Emílio Carlos Nelli Silva

E

Eduardo Alberto Fancello

DOI：10.1016/j.jcp.2023.112561

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Abstract

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This paper proposes a topology optimization procedure to reconstruct sharp interfaces of salt bodies in a background medium with known properties. The reconstruction technique uses the time-domain acoustic wave equation that provides the pressure field to minimize a data misfit objective function. The salt-background distinction is described by the level set-cut element approach proposed by Andreasen et al. (2020) [1]. This approach preserves the abrupt transition of properties across interfaces and provides accurate solutions to the problem. The nodal values of the level set function are parameterized as an explicit function of the design variables, and a discretize (space)-then-deriveapproach is implemented consistently with the discretized optimization problem. This setting allows for solving the minimization problem with mathematical programming methods; we use the conjugate gradient to update the level set shapebased reconstruction. A set of numerical examples demonstrate that the optimization algorithm is quite robust and is able to identify complex geometries of salt bodies.

Keywords:

Inverse problems

Topology optimization

Level set methods

Cut elements

Full-waveform inversion using level set and cut elements for sharp-interface problems

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