Section: Overall Objectives

General setting

Magique-3D  is a joint project-team between Inria and the Department of Applied Mathematics (LMA) of the University of Pau, which is associated with CNRS. Gathering several researchers of different backgrounds in mathematics and scientific computing, MAGIQUE-3D team aims at developing sophisticated modeling tools, validating them in a rigorous way and applying them to real cases of geophysical interest. This project is intrinsically multi-disciplinary and is strongly related to the regional and national industrial environment. In particular, we develop strong collaborations with TOTAL but the topics studied can lead to applications other than petroleum engineering. Since it has been created, MAGIQUE-3D works `Depth Imaging': this topic is related to modeling of seismic wave propagation in complex geological structures, taking into account underlying physical phenomena. It has been defined jointly by working groups composed of members of MAGIQUE-3D and of its main industrial partner TOTAL in order to make sure that actual results of interest in the context of the oil industry could be reached. One usually tackles such problems by adopting two different approaches. The first one consists in defining approximate models that lead to less expensive numerical methods (for example by decreasing the number of unknowns by means of an approximation of the original equations). The second approach is based on high-performance numerical methods applied to the full system, which lead to an accurate solution but implies a high computation cost. Both of these approaches are considered in the project.

Reagrding `Advanced modeling in wave propagation', the team is involved in realistic numerical simulation of complex three-dimensional geophysical phenomena and its comparison with real data recorded in the field. One of the main issues is the choice of the numerical method, which implicitly defines the subset of configurations that can be studied. Comparisons with recorded seismic data for real geological cases have been carried out and then, numerical algorithms have been optimized and implemented on parallel computers with a large number of processors and a large memory size, within the framework of message-passing programming. We have reached a maximum resolution in terms of the seismic frequencies that can be accurately simulated on currently available supercomputers.

MAGIQUE-3D works on the development of optimized software for the simulation of 3D phenomena in geophysics. The team tackled this question addressing different and complementary issues such as the development of new discretization schemes, the construction of new boundary conditions used to reduce the size of the computational domain, the porting of our software on GPU to speed up their performances. All the algorithms we have proposed are compatible with high resolution techniques. More recently, we have begun to apply our knowledge on the direct problem to the solution of inverse problems. It is now a natural goal for the team since we develop a significant research program with Total, in particular in the context of the research program DIP (Depth Imaging Partnership), where the solution of inverse problems has become a big challenge for oil industry.