- Mathematical modeling of wave propagation and of the underlying physical phenomena
The development of migration software with preserved amplitudes is of great interest for imaging geological structures based on the propagation of seismic waves. Most of the geophysicists use the Kirchhoff formalism with a posteriori corrections of the amplitude. Magique-3D proposes instead to evaluate the exact amplitude directly by developing more complete modeling techniques. This implies the construction of new models and the analysis of their qualitative properties and their numerical i. New models must incorporate absorbing conditions in order to be able to compute the solution in bounded domains. The construction of such conditions is optimized in order to improve the accuracy of the numerical solution and/or reduce the computational cost.
- Numerical simulation, parallel computing, GRID computing
The spectral element method (SEM) has recently shown its efficiency for the computation of synthetic seismograms compared to more classical approaches such as finite difference schemes. Magique-3D uses the SEM to quantify the effects of both topography and variations of geological structures on the propagation of seismic waves. Magique-3D also considers simplified inverse problems for 3D structures, which makes it possible for instance to analyze the propagation of surface waves in weathered zones in the context of active seismic experiments performed by the petroleum industry. Magique-3D also intends to develop a finite element method optimized to run on a parallel computer for the study of geomorphology. This project could in part be done jointly with Scalapplix. Magique-3D also intends to study the propagation of elastic waves in fractured media by coupling quasi-analytic methods near the fractures with a finite element method in the surrounding medium. The numerical methods involved in this work all result in a high computational cost, and we therefore want to benefit from recent technological advances by developing algorithms that can not only run on very large parallel computers but also on so-called “grids” of computers (“GRID computing”).