Digital Twins of Earth's Mantle: Adjoint Inverse Approaches for Reconstructing Mantle Dynamics

Earth's mantle drives fundamental processes that shape our planet and directly impact us. Convective flow induces both lateral and vertical motion of the surface, with consequences across timescales. Over geological time, dynamic topography modulates continental flooding, sedimentary basin development, and global sea level. On shorter timescales, glacial isostatic adjustment governs the ongoing response to ice sheet fluctuations, reshaping coastlines and redistributing ocean mass. These vertical motions, coupled with lateral plate displacements, also control the burial and exhumation of rocks, processes central to the genesis of mineral and critical resource deposits. Quantitative models of mantle dynamics are therefore essential not only for understanding Earth's past but for anticipating its future trajectory.

Traditional forward modelling approaches, while physically rigorous, fail to fully exploit the wealth of observational constraints now available, including seismic tomography, geodetic measurements, tectonic reconstructions, and geological indicators of past topography. These data encode invaluable information about mantle structure and rheology that forward models cannot systematically assimilate.

Here I present a framework for constructing Digital Twins of Earth's Mantle, physics-based models systematically optimised against observations using formal inverse methods. Central to this approach is the adjoint method, which enables efficient computation of gradients through complex time-dependent simulations, making large-scale inversions tractable.

I demonstrate this framework across three complementary problems spanning temporal scales. For long-term mantle evolution, I show how seismic tomography and plate reconstructions can be inverted to recover Earth's mantle history in the Cenozoic. Turning to the present day, I illustrate how observations of dynamic topography constrain three-dimensional variations in mantle rheology. Finally, addressing shorter timescales, I consider glacial isostatic adjustment, where the joint reconstruction of ice loading history and mantle viscosity structure emerges from geodetic and geological sea-level data.

Together, these applications establish adjoint-based Digital Twins as powerful tools for synthesis across Earth science disciplines, enabling both retrodiction of past states and predictions that inform sea level projections, coastal vulnerability assessment, and mineral exploration.