From seismic images to plate dynamics: Towards the full inverse

Abstract:

Three-dimensional seismic images of slabs and other mantle structures provide a first order constraint on the forces driving plate motions. Previous attempts to invert for plate motions from seismic images have blurry slabs that do not act as stress guides. Using forward models, we describe characteristics needed to capture the coupling between mantle structures and plates. In forward models, we capitalized on advances in adaptive mesh refinement and scalable solvers to simulate global mantle flow and plate motions, with plate margins resolved down to 1 km. Cold thermal anomalies within the lower mantle are coupled into oceanic plates through narrow high-viscosity slabs, altering the velocity of oceanic plates. Back-arc extension and slab rollback are emergent consequences of slab descent in the upper mantle. The forward models require the solution of a highly ill-conditioned non-linear Stokes equation. Based on a realistic rheological model with yielding and strain rate weakening from dislocation creep, we formulate inverse problems casted as PDE-constrained optimization problems and derive adjoints of the nonlinear Stokes and incompressibility equations. An inexact-Gauss Newton method is used to infer the rheological parameters while quantifying the uncertainty using the Hessian at the maximum a posteriori (MAP) point. Through 2-D numerical experiments we demonstrate that when the temperature field is known from seismic images, we can recover all of these properties to varying levels of certainty: strength of plate boundaries, yield stress and strain rate exponent in the upper mantle. When the system becomes more unconstrained (when all three mechanical properties are unknown), there can be tradeoffs depending on how well the data approximates the realistic dynamics. As plate boundaries become weaker beyond a limiting value, the uncertainty of the inferred parameters increases due to insensitivity of plate motion to plate coupling. Using the inverse of the Hessian, we show approximations to tradeoffs between inferred quantities and compare them against tradeoffs exhibited by forward solves within a Markov Chain Monte Carlo (MCMC) approach. We find that posterior distribution using the Hessian at the MAP point is locally a good approximation to the posterior distribution found with MCMC.