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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This research work was performed under supervision of Tristan van Leeuwen during the first author's research visit to Mathematical Institute of Utrecht University, Netherlands from 20th January to 5th February 2019. The first author would like to thank Tristan van Leeuwen for his guidance throughout the visit. The research visit and the work reported here was supported by funding from King Abdullah University of Science and Technology (KAUST). We would like to thank Nick Luiken, Ajinkya Kadu, and Sarah Gaaf from Mathematical Institute of Utrecht University, Netherlands and the members of the Seismic Modeling and Inversion (SMI) group at KAUST for constructive discussions.