MakutuThe Ph.D. thesis is defended on June 23rd, 2025.
A model order reduction strategy for parameterized PDEs: a new paradigm for efficient subsurface imaging.
Subsurface exploration plays a crucial role in many fields, ranging from energy production (oil, gas, geothermal) to civil engineering, including environmental issues such as CO2 storage. This thesis is part of the context of subsurface imaging, where the objective is to reconstruct the internal properties of the subsurface from recordings of artificially generated wavefields. This process, known as full waveform inversion (FWI), relies on the repeated resolution of wave equations, which entails a high computational cost, particularly in high-resolution and multi-parameter contexts. To address these challenges, this thesis explores model order reduction (MOR) approaches, which allow decreasing the dimension of the systems to be solved while preserving their essential dynamics. After presenting the foundations of FWI in the context of acoustic wave propagation, as well as the spectral element method used for discretization, the study focuses on the Proper Orthogonal Decomposition (POD) method and its application to the acoustic wave equation problem, then introduces a variant using a QR decomposition, aiming to mitigate the memory costs of the classic POD approach while maintaining an equivalent order of accuracy. One of the major difficulties of ROMs lies in their sensitivity to parameter variations. To remedy this, the thesis proposes a method based on the Fréchet derivatives of the problem considered, which makes it possible to build reduced bases that are more robust to parameter changes. This method is validated on 2D and 3D acoustic problems, then integrated into an FWI framework via the GEOS platform. In summary, this work brings an original contribution to the efficient resolution of inverse problems in geophysics, by combining advanced numerical methods and model reduction, paving the way for large-scale applications with reduced costs.