A Bayesian level set method for identifying subsurface geometries and rheological properties in Stokes flow

We aim to simultaneously infer the shape of subsurface structures and material properties such as density or viscosity from surface observations. Modelling mantle flow using incompressible instantaneous Stokes equations, the problem is formulated as an infinite-dimensional Bayesian inverse problem. Subsurface structures are described as level sets of a smooth auxiliary function, allowing for geometric flexibility. As inverting for subsurface structures from surface observations is inherently challenging, knowledge of plate geometries from seismic images is incorporated into the prior probability distributions. The posterior distribution is approximated using a dimension-robust Markov-chain Monte Carlo sampling method, allowing quantification of uncertainties in inferred parameters and shapes. The effectiveness of the method is demonstrated in two numerical examples with synthetic data. In a model with two higher-density sinkers, their shape and location are inferred with moderate uncertainty, but a trade-off between sinker size and density is found. The uncertainty in the inferred is significantly reduced by combining horizontal surface velocities and normal traction data. For a more realistic subduction problem, we construct tailored level-set priors, representing "seismic" knowledge and infer subducting plate geometry with their uncertainty. A trade-off between thickness and viscosity of the plate in the hinge zone is found, consistent with earlier work.