In the course of the past decade, full-waveform inversion has matured from a largely idealistic dream into a commonly applied method to image the internal structure of inaccessible bodies. Despite undeniable success, a major problem remains: The quantification of uncertainties in this often strongly nonlinear inverse problem.
In this lecture, I will present a series of computational approaches that brings probabilistic full-waveform inversion with complete uncertainty quantification within reach:
1) Hamiltonian Monte Carlo sampling of the posterior probability density treats model parameters as particles that orbit through model space, obeying Hamilton’s equations from classical mechanics. The scaling properties of Hamiltonian Monte Carlo allow us to consider high-dimensional model spaces that often cannot be considered with more traditional, derivative-free sampling methods.
2) Autotuning based on limited-memory quasi-Newton methods provides nearly optimal mass matrices for Hamiltonian Monte Carlo, thereby largely removing laborious manual tuning. A factorised version of the L-BFGS algorithm, in particular, can increase the effective sample size by more than an order of magnitude.
3) Wavefield-adapted spectral-element meshes exploit prior knowledge on the geometry of wavefields. Such prior knowledge is frequently available for media that are smooth relative to the minimum wavelength. Wavefield-adapted meshes have the potential to drastically reduce the number of elements, leading to a computational forward modelling cost that makes Monte Carlo sampling possible.
Joint work with Lars Gebraad & Christian Boehm.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
Practical details: the seminar will be held online using Microsoft Teams.
If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).
You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.