The Geoid-Topography Paradox in Multiscale Dynamic Models of Subduction Zones

Regional 3-D dynamic models of the Tonga-Kermadec and Aleutian subduction zones are used to constrain lateral variations in viscosity in the upper mantle. The overriding plate of the Tonga-Kermadec subduction zone is characterized by active island-arc volcanism and back-arc spreading, shallow bathymetry, and large positive geoid anomalies (Δ N) on length-scales of 100--2000 km (regional variations of Δ N=10--50 m). The overriding plate of the central portion (170--200^o longitude) of the Aleutians has an active island-arc system but no back-arc spreading, deep bathymetry and only moderate geoid anomalies (regional variations of Δ N=10--25 m). Dynamic models include age variations of the lithosphere, crustal thickness variations associated with active and remnant arcs and slab density due to thermal anomalies based on a kinematic model of subduction. Modeling the dynamic topography of the overriding plate for the Tonga-Kermadec subduction zone requires a low viscosity wedge above the slab to decouple the flow of the slab from the surface and a region of low density material (δ ρ =20~kg/m³) coincident with the low viscosity region. While these efforts lead to a good fit of the observed bathymetry for a slab with a density anomaly of ~0.08~g/cm³, consistent with the density anomaly for old lithosphere due to temperature, the geoid above the subduction zone is too large by 20--40 m at lengthscales of 100--1000 km. A reduction of the slab density by a factor of 2 is needed to match both the geoid and topography, suggesting the density anomaly of the slab due to temperature is compensated within the upper mantle ( ~100--300 km). Similar modeling for the Aleutians, including a low viscosity wedge but no low density region in the wedge, is able to fit the geoid and topography without reducing the slab density. The differing results for these two regions may reflect differences in the history of subduction including subduction rates, age of the lithosphere, influences of back-arc spreading, dewatering of the slab and melting in the wedge.