Section: Research Program

Understanding the interior of the Earth and the Sun by solving inverse problems

Even if the Earth and the Sun are actually very different media, their imaging is based on the same solution methodology  [64]. However, our knowledge on Earth inversion is far more developed than for the Sun. Earth inversion is in the continuation of previous MAGIQUE-3D achievements while Sun inversion requires developing new technologies based on modeling, numerical analysis and implementation of a piece of software which is able to ask for new developments. For instance, we would like to develop a HDG software package for solving Galbrun and Linearized Euler equations. To the best of our knowledge, this has never be done and would be a major milestone for tackling vectorial equations. Regarding the modeling, we are pursuing our collaboration with the Max Planck Institute for Solar System Research (Göttingen, Germany) in the framework of the associate team ANTS. This partnership is essential to us for understanding a complex (and new to us) physics including gravity waves that we have never considered in the past. Even if we dispose of advanced solvers dealing with elasticity, the development of fast and accurate solvers for reproducing waves travelling in large 3D domains is still one of the positive developments towards realistic simulations. In particular, the techniques for the forward discretization and linear system solver must evolve accordingly to resolve large scale time-harmonic problems. For instance, we have elaborated a space-time Trefftz-DG formulation of the elasto-acoustic problem  [58], which performs very well regarding the number of dofs and the order of convergence. We have also coupled spectral and DG elements to take advantage of both methods and we have performed some simulations which are very promising  [57]. The formulation of FWI is in progress in the framework of Pierre Jacquet thesis launched in November 2017. Finally, we have also initiated research on seismology at the planetary scale, with the arrival of Yder Masson on the subject and new collaborators (such as Berkeley lab). This will further help widen our expertise on inverse wave problems and will feed all the four research axes of the future team-project. Regarding industrial partnerships, we have collaboration with Total and the SME RealtimeSeismic (Pau, France). We also continue to work with the UPV, the BCAM and the BSC, namely in the framework of Mathrocks project.