Coupling Bayesian Inversion and Reduced-Order Modeling: Application to Lithosphere–Asthenosphere Boundary Estimation

Geophysical inverse problems are inherently ill-posed due to sparse, noisy, and indirect observations, making Uncertainty Quantification (UQ) a fundamental requirement for reliable subsurface characterization. Bayesian inversion provides a comprehensive probabilistic framework for inferring subsurface parameters by coherently combining prior knowledge with observational data through the likelihood function. However, the practical deployment of Bayesian methods in large-scale geophysical settings is often hampered by the prohibitive computational cost of repeated forward model evaluations. In this context, uncertainty is often not solely driven by observational noise; a substantial and sometimes dominant contribution arises from model error, resulting from simplified physical descriptions, numerical discretization, and uncertain boundary conditions. When these sources of uncertainty are neglected or inadequately represented, Bayesian inversions may yield biased posterior estimates and unrealistically narrow uncertainty bounds. These limitations are particularly acute in deep Earth applications, where complex rheologies, poorly constrained geometries, and computationally intensive forward models coexist.

A key challenge is the accurate delineation of the Lithosphere–Asthenosphere Boundary (LAB), which plays a central role in controlling mantle dynamics, lithospheric deformation, and deep geothermal processes. Despite the necessity of relying on Bayesian approaches to estimate the LAB and its associated uncertainties, the high computational cost of repeated evaluations of the forward solver makes this unfeasible within realistic time frames [1]. To address these limitations, this work investigates Reduced-Order Modeling (ROM) techniques to enable efficient Bayesian inversion of LAB geometry in geodynamical Stokes flow models. ROMs construct low-dimensional surrogates of high-fidelity solvers, allowing rapid forward simulations while preserving the dominant physical behavior of mantle flow. By integrating ROMs with Bayesian inference, the proposed framework enables effective and reliable UQ for LAB characterization.
Keywords: Geophysical inverse problems; Bayesian inversion; Uncertainty Quantification; Reduced-Order Modeling; Lithosphere–Asthenosphere Boundary

Acknowledgement This research was conducted within the EarthSafe Doctoral Network and has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101120556.

References [1] Olga Ortega-Gelabert, Sergio Zlotnik, Juan Carlos Afonso, and Pedro D´ıez. Fast stokes flow simulations for geophysical-geodynamic inverse problems and sensitivity analyses based on reduced order modeling. Journal of Geophysical Research: Solid Earth, 125(3):e2019JB018314, 2020.