An illustrated guide to: Parsimonious multi-scale full-waveform inversion

Having been a seemingly unreachable ideal for decades, 3-D full-waveform inversion applied to massive seismic datasets has become reality in recent years. Often achieving unprecedented resolution, it has provided new insight into the structure of the Earth, from the upper few metres of soil to the entire globe. Motivated by these successes, the technology is now being translated to medical ultrasound and non-destructive testing. Despite remarkable progress, the computational cost of full-waveform inversion continues to be a major concern. It limits the amount of data that can be exploited, and it largely inhibits quantitative and comprehensive uncertainty analyses. These notes complement a presentation on recent developments in full-waveform inversion that are intended to reduce computational cost and assimilate more data, thereby improving tomographic resolution. The suite of strategies includes flexible and user-friendly spectral-element simulations, the design of wavefield-adapted meshes that harness prior information on wavefield geometry, dynamic mini-batch optimisation that naturally takes advantage of data redundancies, and collaborative multi-scale updating to jointly constrain crustal and mantle structure.