A comprehensive review of strategies to mitigate non-convexity in full waveform inversion

Sumamry The introduction of full waveform inversion has been the starting point of four decades of investigation in seismic imaging, which aim to reduce the ill-posedness of this nonlinear and quantitative imaging method. In this review, we propose a comprehensive overview of these investigations. Beyond simply cataloging proposed approaches, this work aims to classify them, identify similarities and differences between methods, establish connections with common concepts and practices in full waveform inversion, and emphasize the few core ideas underlying this long-term research effort. We introduce a general mathematical framework that encompasses all proposed methods, which we use throughout this study to support their presentation, analysis, and comparison. The concluding discussion should promote a better understanding of the current state of research on this topic. In particular, we examine which methods have been applied to field data and which have not, highlighting the main difficulties and the requirements such techniques must fulfill to transition to such applications.