Sparse Linear Algebra and Geophysical Migration

The pre-stack depth migration of reflection seismic data can be expressed, with the framework of waveform inversion, as a linear least squares problem. While defining this operator precisely, additional main characteristics of the forward model, like its huge size, its sparsity and the composition with convolution are detailed. It ends up with a so-called discrete ill-posed problem, whose acceptable solutions have to undergo a regularization procedure. Direct and iterative methods have been implemented with specific attention to the convolution, and then applied on the same data set: a synthetic bidimensional profile of sensible dimensions with some added noise. The efficiency with regard to computational effort, storage requirements and regularizing effect is assessed. From the standpoint of the global inverse problem, the extra feature of providing a solution that can be differentiated with respect to a parameter such as background velocity is also discussed

Domain decomposition methods for large linearly elliptic three dimensional problems

Projet MENUSINThe idea of solving large problems using domain decomposition techniques appears particularly attractive on present day large scale parallel computers. But the performance of such techniques used on a parallel computer depends on both the numerical efficiency of the proposed algorithm and the efficiency of its parallel implementation. The approach proposed herein splits the computational domain in unstructured subdomains of arbitrary shape, and solves for unknowns on the interface using the associated trace operator (the Steklov Poincare operator on the continuous level or the Schur complement matrix after a finite element discretization) and a preconditioned conjugate gradient method. This algorithm involves the solution of Dirichlet and of Neumann problems, defined on each subdomain and which can be solved in parallel. This method has been implemented on a CRAY 2 computer using multitasking and on an INTEL hypercube. It was tested on a large scale, industrial, ill-conditioned, three dimensional linear elasticity problem, which gives a fair indication of its performance in a real life environment. In such situations, the proposed method appears operational and competitive on both machines : compared to standard techniques, it yields faster results with far less memory requirements

Table ronde : Mer et littoral, quelles filières professionnelles d\u27avenir ?

Il est question ici de la première table ronde de la deuxième journée du forum "Bodlanmè". Il s\u27agira entre autre, de : - découvrir quelques uns des projets encadrés par OSEO. - prendre connaissance de quelques recherches menées à l\u27IRD, étant appelées à être valorisée dans le milieu de la mer et du littoral. - tabler sur la relocalisation du secteur industriel en Martinique

Sparse Linear Algebra and Geophysical Migration

The pre-stack depth migration of reflection seismic data can be expressed, with the framework of waveform inversion, as a linear least squares problem. While defining this operator precisely, additional main characteristics of the forward model, like its huge size, its sparsity and the composition with convolution are detailed. It ends up with a so-called discrete ill-posed problem, whose acceptable solutions have to undergo a regularization procedure. Direct and iterative methods have been implemented with specific attention to the convolution, and then applied on the same data set: a synthetic bidimensional profile of sensible dimensions with some added noise. The efficiency with regard to computational effort, storage requirements and regularizing effect is assessed. From the standpoint of the global inverse problem, the extra feature of providing a solution that can be differentiated with respect to a parameter such as background velocity is also discussed