A Biased Tour of Geophysical Inversion

The modern field of geophysical inversion has its origins more than 50 years ago, with seminal contributions by George Backus and Freeman Gilbert on the theory of linear problems. Since then we have seen major advances in the development and application of methods for statistical inference, parameter estimation, optimization, and probabilistic sampling as well as simulation of physical and chemical systems. These have underpinned our ability to learn about the Earth, and indeed other planets. Over recent decades there has also been generational change in the character, volume, and reliability of Earth Science data sets as well as a comparable acceleration of computational power, data transmission and storage capabilities. Seismologists have often been in the vanguard of these changes, finding new ways to record and exploit the seismic wave train with ever increasing ingenuity. This data explosion has been mirrored across all the physical, life and social sciences, giving rise to the (somewhat ill-defined) field of Machine Learning. The role of `Data Scientist' has been described as the `Sexiest job of the 21^st century'. Perhaps geophysicists can claim this accolade too, as coaxing signal from data lies at the core of what we do.

This presentation will chart a small fraction of this half-century story of how we have developed and applied new tools to see the unseen within the planet, and to shine a light onto Earth's 4.5 billion year history. While pausing briefly on the present we will focus on the future and speculate about what the next decade will bring for this field. The story to be presented will be selective - and therefore biased - but with a focus on novel ideas and possibilities. Some areas of particular attention will be Trans-dimensional inference, Machine Learning and Optimal Transport: all concepts that seismologists have borrowed from other fields, in keeping with long standing tradition.