Full-Wavefield Inversion: An Extreme-Scale PDE-Constrained Optimization Problem

Full-wavefield inversion is a geophysical method aimed at estimating the mechanical properties of the earth subsurface. This parameter estimation problem is solved iteratively using optimization techniques aimed at minimizing some measure of misfit between computer-simulated data and real data measured in a seismic survey. This PDE-constrained optimization problem poses many challenges due to the extreme size of the surveys considered. Practical issues related to the physical fidelity and numerical accuracy of the forward problem are presented. Also, issues related to the inverse problem such as the limitations of the optimization methods employed, and the many heuristic strategies used to obtain a solution are discussed. The goal of this paper is to demonstrate some of the progress achieved over the last decades while highlighting the many areas where further investigation could bring this method to full technical maturity. It is our hope that this paper, together with other contributions in this book, will motivate a new generation of researchers to contribute to this broad and challenging research area.