Development of numerical methods for seismic imaging using the full waveform

Mots clé :

• inverse problems
• seismic imaging
• numerical optimization
• optimal transport

My research activity mainly focuses on the development and the analysis of numerical methods for seismic imaging using the full waveform. This seismic imaging technique, despite its introduction in the early 80s and the increase of its use both in the industry and at the academy level, still faces methodological issues: accounting for more realistic wave propagation physics (elasticity, viscosity, anisotropy), extracting more information from the data, designing more robust workflow, less dependent on human expertise. These issues still prevent today the application of this strategy at more various scales (from laboratory experiments on rock samples to global seismology) with the objective of reaching unprecedented high resolution estimates of the mechanical properties of a material with noninvasive techniques.
Providing methods trying to overcome or mitigate these issues is the main motivation of my research activity. Full waveform inversion is an inverse problem, formulated as the minimization of the distance between simulated data and observed data. The contributions I have been able to bring so far are related both to the design of numerical strategies for the solution of the forward problem, i.e. the computation of the solution to the wave equation in complex media, and to the solution of the inverse problem itself.
In this presentation, I have chosen to focus on three of these contributions. The first is a strategy of absorbing layers which is stable when considering the solution of the elastodynamics equation in the presence of anisotropy, contrary to the state-of-the-art method for this category of computational problems (perfectly matched layers method). The second is the design and the analysis of a truncated Newton strategy adapted to the large-scale aspect of the problem. Using this method it is possible to better estimate the local curvature of the misfit function, which yields more stable reconstruction of the subsurface mechanical properties, in particular for multi-parameter problems. The third is related to the definition of the misfit function itself. In particular, I have been interested in the use of optimal transport distances to define the misfit between simulated and observed data. I have shown that the convexity of theses distances with respect to shifts between compared measures is a fundamental feature which might be a solution to a long standing problem in the seismic imaging community regarding the non-convexity of the conventional L2 misfit function, and the convergence towards spurious local minima. Avoiding these local minima requires a human expertise and a preprocessing of the data which is often cumbersome and difficult to set up, with no guarantee of success.

Président:

Mr Emmanuel Maitre (Professeur - Grenoble INP)

Raporteurs:

• Mr Yann Brenier (Directeur de recherche - CNRS, Centre de Mathématiques Laurent Schwartz, École Polytechnique, France )
• Mr René-Edouard Plessix (Chercheur expert - Shell Global Solution International, Pays-Bas )
• Mr William W. Symes (Professeur - Rice University, Houston, USA )

Examinateurs:

• Mr Jan Hesthaven (Professeur - École Polytechnique Fédérale de Lausanne, Suisse )
• Mr Jeannot Trampert (Professeur - Université d'Utrecht, Pays-Bas )
• Mr Michel Campillo (Professeur - Université Grenoble Alpes, France )