Section: Research Program

Introduction

Probing the invisible is a quest that is shared by a wide variety of scientists such as archaeologists, geologists, astrophysicists, physicists, etc... Magique-3D is mainly involved in Geophysical imaging which aims at understanding the internal structure of the Earth from the propagation of waves. Both qualitative and quantitative information are required and two geophysical techniques can be used: seismic reflection and seismic inversion. Seismic reflection provides a qualitative description of the subsurface from reflected seismic waves by indicating the position of the reflectors while seismic inversion transforms seismic reflection data into a quantitative description of the subsurface. Both techniques are inverse problems based upon the numerical solution of wave equations. Oil and Gas explorations have been pioneering application domains for seismic reflection and inversion and even if numerical seismic imaging is computationally intensive, oil companies clearly promote the use of numerical simulations to provide synthetic maps of the subsurface. This is due to the tremendous progresses of scientific computing which have pushed the limits of existing numerical methods and it is now conceivable to tackle realistic 3D problems. However, mathematical wave modeling has to be well-adapted to the region of interest and the numerical schemes which are employed to solve wave equations have to be both accurate and scalable enough to take full advantage of parallel computing. Today, geophysical imaging tackles more and more realistic problems and we contribute to this task by improving the modeling and by deriving advanced numerical methods for solving wave problems.

MAGIQUE-3D research program is divided into four axes that are: (1) Imaging the Earth; (2) Exploring the Sun; (3) Detecting defaults in complex media; (4) Designing objects with a variety of shapes. Those applications stand out from the collaborations that we have established with interested end-user groups. It is worth noting that they share basic common methodologies which imparts consistency to our program despite they may appear quite distant. MAGIQUE-3D keep modeling and simulating geophysical phenomena for understanding the Earth interior and developing its resources sustainably, and our xperience with numerical geophysics may help us to address other challenging applications. We mainly used DG finite elements and spectral elements and both have demonstrated very good performance. However, in particular for reducing the computational costs and/or for better capturing the propagation characteristics, we are working on the development of hybrid solvers based on the coupling of different finite element methods. Other open questions deserve attention like the problem of numerical pollution or the poor scalability of decomposition domain techniques which are both significantly hampering computations in very large domains. For those purposes, we focus ourselves on the development of Trefftz-like approximations that are based on a particular computation of the fluxes by making a judicious use of an auxiliary numerical method (e.g. boundary integral equations, spectral elements, etc...). Those problems cannot be ignored and can be found in all of our research axes. In addressing those issues, we participate in the construction of new numerical schemes and for that purpose, we continuously need to improve our understanding of the underlying physics. By this way, we make our mathematical models evolve to more realistic representations of the wave propagation phenomenon. This motivated us to introduce experimental studies in our activities and to collaborate with geophysicists of the UPPA who own experimental devices adapted to our concerns. Moreover, we have hired recently Yder Masson who is an experienced researcher developing modeling and imaging methods to investigate the Earth’s internal structure. This creates all the conditions for improving our mathematical representation of waves in complex media. It is worth noting that modeling is a concern for both geophysicists and mathematicians. Indeed, the Physics must be reproduced accurately and the underlying mathematical properties should be clarified. By this way, we can develop a numerical scheme respecting the main properties of the continuous problem of interest (energy conservation or attenuation, stability, well-posedness, etc...). Magique-3D proposes to define its research program from in-house accurate solution methodologies for simulating wave propagation in realistic scenarios to various applications involving trans-disciplinary efforts. The development of high-order numerical methods for wave simulations is serving as a basis for our contributions regarding applications. In particular, we pursue and strengthen our collaboration with HPC teams, in order to improve the scalability of our codes and to run them on very large heterogeneous architectures (using task based programming libraries as StarPU developed by Inria project-team Storm, improving the I/O by collaborating with UFRGS at Porto Alegre, using the metaprogramming framework Boast developed by Inria project-team Corse to produce portable and efficient computing kernels). We are also continuing our collaboration with Inria project team Hiepacs on the use of hybrid linear solvers, by considering the multiple Right-Hand Sides feature and by integrating appropriate transmission conditions between the various domains. During 2019, we have worked a lot on: (a) High-order numerical methods for modeling wave propagation in porous media: development and implementation; (b) Understanding the interior of the Earth and the Sun by solving inverse problems; (c) Full waveform inversion for the optimal design of wind musical instruments.