Post-Doctoral Research Visit F/M Inverse problem in elasticity with wave separation

We propose a two-years postdoc opportunity in computational inverse problems in the context of the ERC-StG European project Incorwave which aims to develop advanced numerical and mathematical strategies for passive imaging. This postdoctoral position focuses on developing new inversion techniques for elastic media, where body waves play a critical role, and can be decomposed into Primary (P) waves (compressional) and Secondary (S) waves (shear). Traditional inversion methods treat these waves as coupled (working with the full displacement), but separating them offers significant potential to improve the accuracy of the inversion. The successful candidate will spearhead the development of cutting-edge methods and sophisticated software tools designed to efficiently compute P- and S- wave components. To achieve this, we will rely on Discontinuous Galerkin methods which are capable of handling complex discontinuities in the solutions, ensuring high-fidelity wave separation.  Once the waves are decomposed, the successful candidate will lead the inversion process for the separated P- and S-wave components, and develop the appropriate strategy for optimal reconstructions. This will directly contribute to the project's overarching goal of improving passive seismic imaging. The research aims to provide more detailed and accurate subsurface characterizations, which are crucial for a wide range of applications, from geophysical exploration to monitoring subsurface processes.

The program will be divided into two main phases which corresponds to the modeling of the decoupled elastic waves, and the quantitative inversion. All software development and numerical implementation will be performed in the open-source code Hawen (https://ffaucher.gitlab.io/hawen-website/) developed in the team Makutu, with help from from the developer's team.

Phase 1: modeling
The first phase of the project focuses on the efficient numerical solution of the decoupled P- and S-wave systems, which form the foundation for subsequent inversion tasks. The successful candidate will begin by deriving the corresponding pseudo-differential equations that govern the propagation of these separated waves. Special attention will be given to the mathematical structure of the decoupled systems to ensure physical consistency and numerical stability. To solve these equations, the candidate will investigate Discontinuous Galerkin (DG) discretization techniques, which are well-suited for handling the discontinuities of the separated body waves.

Phase 2: inversion
In Phase 2, the nonlinear inverse problem will be addressed. The first step involves deriving the adjoint-state formulation corresponding to the governing equations obtained in the previous phase. This derivation is essential for computing the gradient of the misfit functional efficiently, enabling large-scale optimization. Following this, the candidate will explore computational strategies to improve the performance and stability of the inversion process. A key aspect of this investigation will focus on the optimal selection and use of data (whether P-wave, S-wave, or combined datasets) in relation to the physical parameters being reconstructed (e.g., Lamé parameters, density, anisotropic properties). The goal is to design an inversion framework that maximizes sensitivity to the targeted model parameters. In addition, one could also study the separation of partial data, for instance using learning techniques.

The applicant will review the bibliography and develop an appropriate framework for elastic wave separation and hierarchical inversion. They will be responsible for the computational implementation and testing. The role also involves writing reports or scientific papers and presenting results at international conferences. As a member of the Inria Makutu team, the applicant will collaborate with the group to support and enhance its activities.

• Subsidized meals
• Partial reimbursement of public transport costs
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

2788€ / month before taxs