Full waveform inversion (FWI) is a recent technique in seismic tomography to reconstruct physical parameters sampled by seismic waves. Compared with other methods relying only on partial waveform information such as travel times or phase velocities, FWI exploits the entire waveform content and iteratively minimizes the nonlinear misfit between synthetic and observed seismic data. Therefore, facilitated by recent advances in computer performance, FWI is particularly suitable for high-resolution imaging in geological and industrial applications.

Our research project focuses on the numerical analysis for acoustic FWI on the basis of hyperbolic PDE-constrained optimization. Theoretical investigations include the first- and second-order analysis of the corresponding least squares minimization problem. They are fundamental for the numerical analysis of Newton-type methods such as SQP methods.

This project is supported by the DFG research grants YO159/5-1.

Luis Ammann and Irwin Yousept: Acoustic Full Waveform Inversion via Optimal Control: First- and Second-Order Analysis [PDF] SIAM Journal on Control and Optimization, 61:4, 2468-2496, 2023.

Yuri Flores Albuquerque, Antoine Laurain, Irwin Yousept: Level set-based shape optimization approach for sharp-interface reconstructions in time-domain full waveform inversion [PDF] SIAM Journal on Applied Mathematics, 81:3, 939-964, 2021.