Discontinuous Galerkin Method, from seismic modelling to full waveform inversion...

Seismic modelling can be performed with a wide range of numerical methods. Ideally, we seek for a method allowing an optimal discretisation based on the medium properties. From this point of view, finite-element methods (FEM) are appealing. Recently, two classes of FEM have gained a lot of interests in the seismological community, namely the spectral element method (SEM) and the discontinuous Galerkin finite-element method (DG-FEM). My talk focuses on DG-FEM. I will first depict the imaging context in which we intend to apply such method. Then, I will introduce the mathematical concepts we adopted to solve the first order elastodynamic system in 3D with tetrahedral mesh. Computing aspects and absorbing conditions will also be discussed while I will emphasize the benefits of hp-adaptivity when dealing with complex media. Finally, I will present 2 applications of seismic modelling with DG-FEM. The first one with a reference model used in the oil industry and the second with a challenging seismological model where the computation of surface waves is critical for the prediction of site effects. The results will be compared with solutions computed with SEM.