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Abstract Constraining the long-term evolution of geoid anomalies is essential for unraveling Earth's internal dynamics. While most studies focus on present-day geoid snapshots, we reconstruct the time-dependent evolution of Earth’s strongest geoid depression, the Antarctic Geoid Low (AGL), over the Cenozoic. Unlike geodetic reference frames that place the deepest geoid low in the Indian Ocean, a geodynamic perspective (relative to a hydrostatic ellipsoid) reveals the strongest nonhydrostatic geoid depression actually resides over Antarctica. Using a back-and-forth nudging technique for time-reversed mantle convection modeling, we leverage 3-D mantle density structures derived from seismic tomography and geodynamic constraints. Our results show that the AGL has persisted for at least ~70 Myr, undergoing a major transition in amplitude and position between 50 and 30 Ma. This coincides with abrupt lateral shifts in Earth’s rotation axis at ~50 Ma, validated through paleomagnetic constraints on True Polar Wander. Initially, stable lower mantle contributions dominated the AGL, but over the past ~40 Myr, increasing upper-mantle buoyancy, particularly above ~1300 km depth, amplified the AGL magnitude. This shift stems from the interplay between long-term deep subduction beneath the Antarctic Peninsula and a buoyant, thermally driven upwelling of hot, low-density material from the lowermost mantle. These new results contrast with earlier interpretations, clarifying the crucial role of evolving mantle buoyancy in shaping global geoid anomalies. By incorporating seismic, geodynamic, and mineral-physics data, our reconstructions provide a more comprehensive understanding of mantle flow beneath Antarctica and offer new insights into the dynamic coupling between lower and upper mantle processes that govern Earth’s long-wavelength geoid evolution. 

Abstract Mantle convection drives changes in Earth's ellipsoidal figure and corresponding moment of inertia, causing shifts in the planet's rotation axis known as true polar wander (TPW). Using seismic tomography and the Back-and-Forth Nudging (BFN) method, we developed a time-dependent convection model that reconstructs the evolution of mantle density distribution and Earth’s moment of inertia over the past 70 million years. This modelling approach provides a close match with independent paleomagnetic constraints on the Cenozoic shifts of Earth’s rotation pole, specifically resolving the previously unexplained U-turn in TPW trajectory at approximately 50 million years ago. Our findings reveal TPW shifts exceeding 5 degrees, despite the temporal stability imposed by high lower-mantle viscosity and the stabilizing effect of Earth's remnant rotational bulge. Verification of our predicted changes in Earth’s ellipsoidal figure through independent paleomagnetic data provides a robust calibration for new predictions of convection-induced dynamic flattening variations. Over the past 70 million years, we find convection-induced changes of flattening that shift from -0.2% to +0.1 % during the Paleogene. Our predictions of Earth's axial precession frequency in the Paleogene align with recent independent cyclostratigraphic studies, thus validating our model's accuracy and supporting the hypothesis of reduced luni-solar tidal dissipation during this period. 

Despite progress in tomographic imaging of Earth’s interior, a number of critical questions regarding the large-scale structure and dynamics of the mantle remain outstanding. One of those questions is the impact of phase-boundary undulations on global imaging of mantle heterogeneity and on geodynamic (i.e. convection-related) observables. To address this issue, we developed a joint seismic-geodynamic-mineral physical tomographic inversion procedure that incorporates lateral variations in the depths of the 410- and 660-km discontinuities. This inversion includes S-wave traveltimes, SS precursors that are sensitive to transition-zone topography, geodynamic observables/data (free-air gravity, dynamic surface topography, horizontal divergence of tectonic plates and excess core-mantle boundary ellipticity) and mineral physical constraints on thermal heterogeneity. Compared to joint tomography models that do not include data sensitivity to phase-boundary undulations in the transition zone, the inclusion of 410- and 660-km topography strongly influences the inference of volumetric anomalies in a depth interval that encompasses the transition zone and mid-mantle. It is notable that joint tomography inversions, which include constraints on transition-zone discontinuity topography by seismic and geodynamic data, yield more pronounced density anomalies associated with subduction zones and hotspots. We also find that the inclusion of 410- and 660-km topography may improve the fit to the geodynamic observables, depending on the weights applied to seismic and geodynamic data in the inversions. As a consequence, we find that the amplitude of non-thermal density anomalies required to explain the geodynamic data decreases in most of the mantle. These findings underline the sensitivity of the joint inversions to the inclusion of transition-zone complexity (e.g. phase-boundary topography) and the implications for the inferred non-thermal density anomalies in these depth regions. Finally, we underline that our inferences of 410- and 660-km topography avoid a commonly employed approximation that represents the contribution of volumetric heterogeneity to SS-wave precursor data. Our results suggest that this previously employed correction, based on a priori estimates of uppermantle heterogeneity, might be a significant source of error in estimating the 410- and 660-km topography. 

Abstract Earth's topography arises from the linear superposition of isostatic and dynamic contributions. The isostatic contribution reflects the distribution of thickness and density of the crust overlying a static, non‐convecting mantle. We argue that isostatic topography should be limited to the crust, thereby delimiting all sources for dynamic topography below the Moho. Dynamic topography is the component of the topography produced by normal stresses acting on the Moho that deflect the isostatic topography away from crustal isostatic equilibrium largely as a consequence of mantle flow dynamics. These normal stresses arise from pressure variations and vertical gradients of the radial flow in the convecting mantle. The best estimate of dynamic topography is from the residual topography, which is the difference between observed topography and crustal isostatic topography. Dynamic and residual topography are the same. It is clear that thermal anomalies horizontally advected by plate motions would not exist if the mantle were not convecting, therefore their contribution to topography is inherently dynamic in origin. The global integral of dynamic topography that encompasses all non‐crustal buoyancy sources is demonstrated to be equal to zero. It follows that mantle convection cannot change the mean radius or mean elevation of the Earth. Since changes in ocean basin volume driven by changes in mean depth of the oceans are inherently part of dynamic topography, thereby requiring that continental elevations must also change, such that the global integral of these perturbations must also be equal to zero. This constraint has important implications for global long‐term sea level and the stratigraphic record, among other features of the Earth system impacted by changes in Earth's dynamic topography.