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Theses

Time-Domain Full Waveform Inversion using advanced Discontinuous Galerkin method

Abstract : In this project, we developed tools for the reconstruction of subsurface media for seismic imaging and reservoir characterization in an industrial context. For that purpose, we used the Full Waveform Inversion (FWI) method. It is a reconstruction technique using data taken from seismic disturbances and whose behavior reflects the properties of the environment in which they propagate. In the framework of this thesis, we consider acoustic waves which are simulated thanks to Discontinuous Galerkin methods. These methods offer a very flexible discretization in space allowing to approach complex models and geometries. Discontinuous Galerkin methods are characterized by the use of fluxes in between each cell. Those fluxes contribute to have low communication costs which are highly recommended for High Performance Computing. Here, the wave equation is solved in time domain to overcome the memory limitations encountered in frequency domain for the reconstruction of large-scale 3D industrial media.To reconstruct quantitatively the physical model under study, we wrote the inverse problem as a minimization problem solved by adjoint state method. This method makes it possible to obtain the gradient of the cost function with respect to the physical parameters for the cost of two simulations; the direct problem and the backward problem also called adjoint problem.The adjoint state will be the solution of the discretized continuous adjoint problem ("Optimize Then Discretize"). This choice is justified by a 1D comparison with the strategy which consists in "Discretize then Optimize" completed by an algebraic study in superior dimension. The gradient thus calculated, is a key in the optimization procedure developed and integrated in the industrial environment provided by the industrial partner, Total.The propagator is a keystone in solving the inverse problem. Indeed, it is repeated successively and represents the majority of the computation time of the optimization process. It is therefore important to control the discretization by the Discontinuous Galerkin method as well as possible. In particular, in this thesis, we have considered the idea of using different polynomial bases of approximation (Legendre or Bernstein-Bézier) as well as the choice of the parameterization, which can either be constant per element or variable thanks to the use of the Weight Adjusted Discontinuous Galerkin (WADG) method. This last strategy offers the opportunity to enlarge the mesh cells without losing information on the model and thus allows a more advanced use of the hp-adaptivity that we propose to fully exploit thanks to an adaptive mesh that is adjusted to the model meant to evolve with the iterations of the inverse problem.
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Submitted on : Thursday, July 22, 2021 - 1:23:11 PM
Last modification on : Monday, September 20, 2021 - 4:58:41 PM

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Pierre Jacquet. Time-Domain Full Waveform Inversion using advanced Discontinuous Galerkin method. Analysis of PDEs [math.AP]. Université de Pau et des Pays de l'Adour, 2021. English. ⟨NNT : 2021PAUU3010⟩. ⟨tel-03295876⟩

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