Non-linear optimization plays a big role in many tasks in geophysics, such as full waveform inversion (FWI). Visualization of the objective function is useful for the analysis and development of algorithms and formulations. However, in high-dimensional problems, we do not have the capabilities to perform such visualization. Instead, one often works with one or two predefined directions in which to slice the objective.In this work we present an approach to visualizing the misfit landscape together with the optimization trajectories based on principal component analysis. Here, the directions along which to slice the objective are chosen in accordance with the optimization trajectory. We demonstrate the approach through a numerical example using the Marmousi model.
SEG Annual Meeting

Izzatullah, M, van Leeuwen, T, & Peter, D. (2019). Visualizing the misfit landscape for full waveform inversion. In SEG Technical Program Expanded Abstracts 2019 (pp. 1460–1464). doi:10.1190/segam2019-3216070.1