New Scaling between Plume Buoyancy Fluxes and Dynamic Topography from Numerical Modelling

Mantle plumes are hot upwellings that transport heat from the core to the base of the lithosphere, and sample lowermost-mantle chemical structure. Plume buoyancy flux Q_B measures the vigor of upwellings, which relates to the mass and heat fluxes that mantle plumes convey to sub-lithospheric depths. Hotspot swells are broad regions of anomalous topography generated by the interaction between mantle plumes and the overlying lithosphere, yet the links between plume properties and swell morphology remain poorly understood.

Traditional approaches to measure Q_B are based on two assumptions: (1) the asthenosphere moves at the same speed as the overriding plate; (2) hotspot swells are fully isostatically compensated, in other words, the seafloor is uplifted due to the isostatic effect of replacing ”normal” asthenosphere with hot plume material. However, at least some plumes (e.g., Iceland) can spread laterally faster at the base of the lithosphere than the corresponding plate motion. Also, hotspot swells are partly dynamically compensated. With increasingly accurate observational constraints on dynamic seafloor topography, it is the time to update plume buoyancy fluxes globally and build a scaling law between the surface dynamic topography and plume buoyancy flux.

Here, we conduct thermomechanical models to study plume-lithosphere interaction and hotspot swell support. We use the finite-element code ASPECT in a high-resolution, regional, 3D Cartesian framework. We consider composite diffusion-dislocation creep rheology, and a free-surface boundary at the top. We systematically investigate the effects of plume excess temperature (∆T), plume radius (r_p), plate velocity (v_p), plate age, and mantle rheological parameters. From these results, we develop a scaling law that relates swell geometry to plume parameters. We find that swell height and cross-sectional area (A_swell) have a robust power-law relationship with Q_B. A_swell shows an almost linear dependence and provides the most reliable geometric indicator of Q_B. Empirical fitting further reveals that r_p has a dominantly positive correlation with swell height, width, and A_swell, while ∆T contributes secondarily. On the contrary, v_p has a relatively small (and mostly negative) effect on swell parameters. Higher viscosities in the asthenosphere lead to wider swells, higher A_swell andQ_swell. Applying these empirical fits to Hawaii indicates a minimum Q_B of ~3,860 kg/s.

Figure 1. Results of example cases at 300 Myr. Each row represents the cases A2, A7, and C7. The left column displays the potential temperature isosurface (contours at 1500K and 1700K), while the right column presents the dynamic topography.

We demonstrate that previous swell-geometry-based estimates underestimate the true buoyancy fluxes of the underlying upwelling, partly because plumes spread faster than plate motion for high Q_B and low v_p. The empirical fits developed here highlight the need for future models to incorporate melting, compositional effects, and variable lithospheric structure.

As a final step, we invert these predictive fittings and apply them to intraplate hotspot swells in all ocean basins to quantify the heat and material fluxes carried by plumes on Earth. This effort will help to inform the Core-Mantle Boundary heat flux.