PhD opportunities

Parsimonious models for uncertainty in seismic tomography

Thesis proposal

Area of expertiseGeoscience and Geoengineering
Doctoral SchoolGRNE - Gosciences, Ressources Naturelles et Environnement
SupervisorMme Alexandrine GESRET
Research unitGeosciences
ContactGESRET Alexandrine
Starting dateOctober 1st 2020
Keywordsinverse problems, seismic tomography, surrogate models, Markov chains, uncertainties
AbstractSeismic tomography is commonly used to image the subsurface from observed traveltimes recorded at a set of seismometers. The obtained seismic wave propagation velocity model is required for subsequent analyses, it is thus of primary importance to estimate accurate velocity models with associated uncertainties in order to lead reliable interpretations. Markov Chain Monte Carlo algorithms which sample the model parameter space are generally appreciated to tackle this issue [1]. However the computation time is high due to the large number of required evaluations of the forward problem to calculate the traveltimes even if the solver is very efficient [2]. Recent works [3] have illustrated the interest of using surrogate models to replace the forward model and thus drastically accelerate the inverse problem resolution. Even with surrogate models, probabilistic seismic tomography approaches can only be applied with a restricted number of parameters of the velocity model. In order to address this problem, we propose to test two approaches to build efficient relations between velocity model and traveltimes. In the first approach, we propose to seek a sparse representation of the arrival times given a high dimensional velocity model. In particular, we plan to exploit the fact that the travel times depend only on the characteristic of the field along the wave-paths. Therefore, the representation and computational effort should focus on areas that can be inferred. In the second approach, the representation of the velocity model should be parsimonious and minimize the dimensionality of the parameter space. We will rely on modal decomposition (Karhunen-Loeve) weighted by the local density of the wave-paths. We shall start with smooth fields before going on with more complex situations involving heterogeneities.

Seismic tomography allows to estimate seismic wave propagation velocities from observed traveltimes. Recent results demonstrated that surrogates allow to represent accurately these traveltimes [3]. It should be interesting to introduce other observations than traveltimes in the probabilistic seismic tomography. Indeed the simulation of the wave polarization or of its amplitude require a computation time that prevents integration of these attributes in the tomography. The use of surrogate models could allow to introduce these observations and thus reduce the uncertainties on the velocity model.
ProfileStrong background in applied mathematics and/or physics with an interest in geophysical applications. Knowledge in probability/statistics. An experience in scientific programming is required.
FundingAutre type de financement