Gravity, Topography, and Melt Generation Rates From Simple 3‐D Models of Mantle Convection

Abstract

Convection in fluid layers at high Rayleigh number (Ra ∼ 10 6 ) have a spoke pattern planform. Instabilities in the bottom thermal boundary layer develop into hot rising sheets of fluid, with a component of radial flow toward a central upwelling plume. The sheets form the "spokes" of the pattern, and the plumes the "hubs." Such a pattern of flow is expected to occur beneath plate interiors on Earth, but it remains a challenge to use observations to place constraints on the convective planform of the mantle.Here we present predictions of key surface observables (gravity, topography, and rates of melt generation) from simple 3-D numerical models of convection in a fluid layer. These models demonstrate that gravity and topography have only limited sensitivity to the spokes and mostly reflect the hubs (the rising and sinking plumes). By contrast, patterns of melt generation are more sensitive to short-wavelength features in the flow. There is the potential to have melt generation along the spokes but at a rate which is relatively small compared with that at the hubs. Such melting of spokes can only occur when the lithosphere is sufficiently thin (≲ 80 km) and mantle water contents are sufficiently high (≳ 100 ppm). The distribution of volcanism across the Middle East, Arabia, and Africa north of the equator suggests that it results from such spoke pattern convection.

The Influence of the North Anatolian Fault and a Fragmenting Slab Architecture on Upper Mantle Seismic Anisotropy in the Eastern Mediterranean

“…In fact, the areas of greatest recent uplift and volcanism in Anatolia are those where we infer an introduction of subslab material into the Anatolian asthenosphere, either vertically through the Cyprus slab tear or laterally through the slab gap (Figure 10, Section 5.4). This suggests that any hot material being introduced originates below the African slabs, perhaps part of a regional North African/Mediterranean upwelling (Nikogosian et al., 2018) or simply a background ‘spoke‐pattern’ mantle convection pattern that has been suggested to occur in the region (Lees et al., 2020; McKenzie, 2020).…”

Blue Marble, Stagnant Lid: Could Dynamic Topography Avert a Waterworld?

“…Low viscosities imply higher temperatures and low convective stresses. For the isoviscous case, the association of low viscosity with low topography can be seen clearly in Table 2 of Lees et al (2020), from which we get a numerical scaling of h ¢ µh rms 0.6 , with interior temperature and lithospheric thickness fixed. If we have two isoviscous layers with a stiffer top layer (i.e., approximating a cool viscous lithosphere), then there is an analytical solution for the surface normal stress induced by a spherical density anomaly at some depth (Equation (34) in Morgan 1965).…”

“…This choice is based on the reasoning that the rms value may be less sensitive to the model geometry-crucial for inferring 3D behavior from 2D models, as we will be doing. As such, we ran preliminary isoviscous convection simulations to confirm that neither Cartesian nor cylindrical 2D geometries show the same peak topographies as the equivalent 3D spherical experiments from Lees et al (2020), whereas, for all three setups, the rms topographies align well. That the same result holds for non-isoviscous simulations is an outstanding caveat of this study.…”

“…Purely dynamic topography, meanwhile, both originates from and is supported by the sole process of thermal convection. It is directly obtained from any numerical convection model (e.g., McKenzie 1977;Kiefer & Hager 1992;Kiefer & Kellogg 1998;Huang et al 2013;Arnould et al 2018;Lees et al 2020); its prediction requires less prior knowledge.…”

The structure of the lithosphere and upper mantle beneath the Eastern Mediterranean and Middle East

“…It is the presence of hubs that led to Wilson and Morgan's proposals. Recent numerical experiments by Lees et al (2020) in large aspect ratio boxes show that the spokes, as well as the hubs, can deform the surface, generate gravity anomalies and magma, provided the overlying lithosphere is sufficiently thin.…”