How Well Is the Mantle Sampled? A Global Voxel-Based Analysis of Residence Time and Flux from Forward- and Reverse-Time Mantle Convection

How well mixed is Earth's mantle? Are there primordial reservoirs? What fraction of the mantle feeds surface volcanism? We attempt to address these questions using large-scale Lagrangian particle tracking in time-reversed and forward convection models. We track particles backward in time using a Back-and-Forth Nudging (BFN) method applied to time-reversed thermal convection, initialized with a present-day seismic–geodynamic–mineral physics model (Glisovic & Forte, 2016, 2025). We likewise carried out long-term (multi-hundred-million-year) forward-in-time mantle convection simulations initialized with present-day mantle structure inferred from tomography. In all cases, we employ mantle viscosity structure that has been independently constrained and verified against a wide suite of present-day geodynamic observables that include free-air gravity anomalies, dynamic surface topography, horizontal divergence of plate velocities, excess core-mantle boundary ellipticity, and glacial isostatic adjustment data. A voxel-based analysis quantifies sampling density, residence time, and flux throughout the mantle.

We use different particle starting conditions, each designed to address a specific aspect of mantle mixing. To identify long-lived isolated regions, we track uniformly distributed particles both forward and backward in time, calculating residence times to locate candidate reservoirs. To estimate the sampling of lower mantle material in the upper mantle, we initialize particles in the D" layer and track them forward to determine what fraction reaches the upper mantle. To address plume dynamics and sampling, we place cylindrical arrays of particles beneath present-day hotspots and track them backward, using the statistical evolution of their standard deviation to quantify mixing along transport pathways, with transit time, and voxel analysis. To measure upper-to-lower mantle exchange, we initialize particles uniformly in the upper mantle. By combining these approaches, we systematically identify regions of low flux and high residence time, candidates for reservoirs. We further take a statistical approach based on voxel density sampling to quantify mixing across the volume of the mantle.