Full waveform inversion has evolved into a processing commodity with a firm foothold in the exploration workflow. However FWI still faces several major challenges. One of these is the occasional stagnation of inversion algorithms where no local model perturbation improves data fit. This "cycle-skip" phenomenon can hide kinematic information inherent in the data that would permit large updates in wave velocity fields. One approach to alleviating cycle-skip, extended inversion, transfers the data kinematics to the an extended model with more degrees of freedom than physical models. Variants fall into two categories, according to whether extra degrees of freedom are added to subsurface parameter fields or to source representations. A common theme is that the model should be so extended that the data can be fit throughout the inversion process, thus rendering cycle-skipping impossible. Model updates reduce a penalty that measures distance from the extended model to the original, physical model subspace. Some penalties are mathematically equivalent to a traveltime tomography objective. I will give a rough taxonomy of extended waveform inversion, with several examples, and describe some of the successes achieved and challenges facing this class of methods.


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