a b s t r a c tThe results of mantle convection simulations are fully determined by the input parameters and boundary conditions used. These input parameters can be for initialisation, such as initial mantle temperature, or can be constant values, such as viscosity exponents. However, knowledge of Earth-like values for many input parameters are very poorly constrained, introducing large uncertainties into the simulation of mantle flow. Convection is highly non-linear, therefore linearised inversion methods cannot be used to recover past configurations over more than very short periods of time, which makes finding both initial and constant simulation input parameters very difficult. In this paper, we demonstrate a new method for making inferences about simulation input parameters from observations of the mantle temperature field after billions of years of convection. The method is fully probabilistic. We use prior sampling to construct probability density functions for convection simulation input parameters, which are represented using neural networks. Assuming smoothness, we need relatively few samples to make inferences, making this approach much more computationally tractable than other probabilistic inversion methods. As a proof of concept, we show that our method can invert the amplitude spectra of temperature fields from 2D convection simulations, to constrain yield stress, surface reference viscosity and the initial thickness of primordial material at the CMB, for our synthetic test cases. The best constrained parameter is yield stress. The reference viscosity and initial thickness of primordial material can also be inferred reasonably well after several billion years of convection.

The subduction of upper oceanic lithosphere acts as a primary driver of Earth's deep carbon and water cycles, providing a key transportation mechanism between surface systems and the deep Earth. Carbon and water are stored and transported in altered oceanic lithosphere. In this study, we present mass estimates of the subducted carbon and serpentinite flux from 320 to 0 Ma. Flux estimates are calculated using a fullplate tectonic reconstruction to build a descriptive model of oceanic lithosphere at points along mid-ocean ridges. These points then track the kinematic evolution of the lithosphere until subduction. To address uncertainties of modeled spreading rates in synthetic ocean basins, we consider the preserved recent (83-0 Ma) spreading history of the Pacific Ocean to be representative of the Panthalassa Ocean. This analysis suggests present-day subducting upper oceanic lithosphere contains 10-39 Mt/a of carbon and 900-3500 Mt/a of serpentinite (∼150-450 Mt/a of water). The highest rates of carbon delivery to trenches (20-100 Mt/a) occurred during the Early Cretaceous, as upper oceanic lithosphere subducted during this period formed in times of warm bottom water and the Cretaceous period experienced high seafloor production and consumption rates. Additionally, there are several episodes of high serpentinite delivery to trenches over the last 100 Ma, driven by extensive serpentinization of mantle peridotites exposed at slow spreading ridges. We propose variations in subduction regimes act as the principal control on the subduction of carbon stored in upper oceanic lithosphere, as since 320 Ma the volume of stored carbon across all ocean basins varies by less than an order of magnitude. For pre-Pangea times (<300 Ma), this suggests estimates of seafloor consumption represent a reasonable first-order approximation of carbon delivery. Serpentinite and associated water flux at subduction zones appear to be primarily controlled by the spreading regime at mid-ocean ridges. This is apparent during times of supercontinent breakup where slow spreading ridges produce highly serpentinized crust, and is observed in the present-day Atlantic, Arctic and Indian oceans, where our model suggests upper oceanic lithosphere is up to ∼100 times more enriched in serpentinite than the Panthalassa and Pacific oceans.

SUMMARY In the Earth’s upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present-day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modelling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter.