Section: Scientific Foundations
Wave propagation in porous media
The propagation of waves in porous media can be of interest in many applications. Magique-3D develops different axes of research on this subject. By using numerical methods like finite differences, finite elements or meshless techniques like the various boundary integral methods (Boundary Integral Method, Indirect Boundary Element Method, Meshless Galerkin Method...) we aim at solving the equations describing porous media. In a first attempt we will solve these equations by performing improvements of abosrbing boundary conditions by using different alternative formulations like the Perfect Matched Layer techniques and high-order paraxial methods. By using a Convolutional Perfectly Matched layer formulation similar to the one developed by Dimitri Komatitsch and Roland Martin (Geophysics 2006)to propagation of isotropic and anisotropic elastic case, we solve the PML absorbing boundary conditions with more than one auxiliary memory variable (instead of one in the isotropic and anisotropic cases and for each component of the velocity and stresses). The establishment of stability criteria for this specific PML procedure is currently under development with Abdelaâziz Ezziani, Roland Martin and Dimitri Komatitsch.
Abdelaâziz Ezziani did his PhD on numerical modeling of wave propagation in viscolastic and porous media based on a finite element method  . Dimitri Komatitsch is an expert on numerical modeling of elastic or viscoelastic seismic wave propagation, for instance using the three-dimensional spectral-element method, which is a finite-element method with an exactly diagonal mass matrix. In the context of a collaboration with Jeroen Tromp (Division of Geological and Planetary Sciences, California Institute of Technology (Caltech), USA), Dimitri Komatitsch and Abdelaâziz Ezziani have started to collaborate on writing a variational formulation of the poroelastic wave equation written in displacement that would remain explicit and therefore be suitable for the spectral-element method. In that context, in 2007 they will welcome Cristina Morency, who is a postdoctoral researcher at Caltech and who will spend several months in Pau to implement that variational formulation and fully test it.