Sesión Análisis Numérico y OptimizaciónCombining Reduced Order Modelling with Bayesian schemes to drastically accelerate stochastic inversions
Sergio Zlotnik
Universidad Politécnica de Cataluña, España - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
We propose a combination of well stablished methodologies for the solution of large scale inversion problems in geophysics. In one hand we use a Markov chain Monte Carlo (MCMC) approach, based on the Metropolis Hastings algorithm to solve the inverse problem. Within, we use a reduced order (RO) approach to accelerate each one of the forward problems that are tested by MCMC. The dimensionality of the parametric space does not allow to sample it completely, so the reduced basis is enriched during the inversion and guided by the MCMC scheme. Our application is based in one of the main challenges in modern geophysics: the understanding and characterizing the present-day physical state of the thermal and compositional structure of the Earth. In doing so, high resolution inverse problems need to be solved (with thousands of parameters to determine). One of the most abundant and better constrained data used for the inversion is the Earth’s topography. Despite its quality, the topography models included in inversion schemes are usually very simplistic, based on density contrasts and neglecting dynamic components. The reason for this is simply computational efficiency; 3D dynamical models require the solution of a Stokes problem and are too expensive to be embedded within inversion schemes. We tested the proposed approach in a synthetic experiment aiming to recover the base of the African plate. It is well-agreed within the geophysical community that the dynamic component in the region is of first order importance. Our scheme is able to successfully recover the expected shape of the plate while reducing the computational time to less than 1% when compared to a full Finite Element approach.
Trabajo en conjunto con: Olga Ortega Gelabert (Geo3Bcn, CSIC, Spain), Constanza Manassero (University of Tasmania, Australia), Pedro Díez (UPC, Spain), Juan Carlos Afonso (University of Twente, The Netherlands), Shahzaib Mir (UPC, Spain) y Luis Tao (UPC, Spain).
Referencias
[1] “Fast Stokes flow simulations for geophysical-geodynamic inverse problems and sensitivity analyses based on reduced order modeling”, Ortega O., S. Zlotnik, J.C. Afonso and P. Díez, Journal of Geophysical Research: Solid Earth, Vol. 125, 1–25, doi:10.1029/2019JB018314, 2020.
[2] “A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation”, Manassero M.C., J.C. Afonso, F. Zyserman and S. Zlotnik, Geophysical Journal International, Vol. 223, Issue 3, pags. 1837–1863, doi:10.1093/gji/ggaa415, 2020.
[3] “A Reduced Order Approach for Probabilistic Inversions of 3D Magnetotelluric Data II: Joint inversion of MT and Surface-WaveData”, Manassero M., J.C. Afonso, F. Zyserman, A. Jones, S. Zlotnik and I. Fomin, Journal of Geophysical Research - Solid Earth, doi:10.1029/2021JB021962, 2021.