Romain Brossier: "Seismic imaging by full waveform inversion - toward uncertainty quantification using an ensemble method"
Characterization of the Earth subsurface properties at various scales relies on the inversion of seismic wave records, generally measured at the surface. Many different tomography methods have been derived for more than a century. Among them, the full waveform inversion aims at considering the whole seismic waveform as observation, through a large scale PDE-constrained inverse problem. As tomography results are used for geological interpretation or as input for further modeling or inversion processes, uncertainty quantification is a major issue for most geophysical tomography problems. Full waveform inversion involves generally hundreds of thousand to hundreds of million of parameters, and can therefore be tackled only with local-optimization methods. In such a frame, it is known that the inverse Hessian is associated to the posterior covariance matrix and can provides useful information on such uncertainties. However, computing and accessing such operator is out of reach for most large scale problems. In this presentation, the full waveform inversion concept will be first presented, showing promises and difficulties of such a method. Then, different methods proposed in the literature to probe the (inverse) Hessian will be presented, before introducing methods developed in the Data Assimilation community. Finally, a combination of Ensemble Kalman Filter and full waveform inversion will be presented, in order to access uncertainty information through the low-rank representation of the posterior covariance matrix provided by the ensemble.
Thomas Bodin: "Reconciling scales in global seismology"
For more than 30 years, seismologists have used seismic waves to produce 3D images of the structure of the Earth. Despite many successes, a number of key questions still remain, which are of the uttermost importance to understand plate tectonics. The problem is that different seismic observables sample the Earth at different scales; they have different sensitivity to structure, and are usually interpreted separately. Images obtained from short period converted and reflected body waves see sharp discontinuities, and are interpreted in terms of thermo-chemical stratification, whereas seismic models constructed from long period seismograms depict a smooth and anisotropic upper mantle, and are usually interpreted in terms of mantle flow.
In this presentation, we will first show that a non negligible part of the observed anisotropy in smooth tomographic models may be artificial and the result of unmapped fine layering in the mantle, i.e small-scale heterogeneities that cannot be resolved by long-period seismic waves. In this way, we will show that tomographic images do not represent the true Earth, but rather a smooth effective, apparent, or equivalent model that provides a similar long-wavelength data fit, and which cannot be interpret in terms of deformation. We will propose a fully probabilistic approach to explore the ensemble of small scale models equivalent to a given smooth tomographic profile. Finally, we will show how a joint interpretation of different frequency bands can allow to fully localizing the patterns of deformation in the mantle.