Subducted slabs and the geoid: 1. Numerical experiments with temperature‐dependent viscosity

Abstract

One of the most powerful constraints on mantle viscosity comes from the correlation of the long‐wavelength (degree 4–9) geoid with that predicted by a density model for subducted slabs. The effect of lateral variations of viscosity should be most pronounced at subduction zones, due to the strong effect of temperature on viscosity. An idealized slab model with temperature‐dependent viscosity is considered, with various lateral and vertical viscosity structures, using a two‐dimensional finite element formulation. The viscosity parameterization affects the amplitude of the long‐wavelength geoid anomaly but not the sign of the correlation between the geoid and density anomalies. Depth‐dependent viscosity models with a high‐viscosity lithospheric layer do not completely match the temperature‐dependent (laterally varying) results, suggesting that the rheology of the slab does have an effect on the long‐wavelength surface topography and geoid; however, this affect is minor, suggesting that the radial models of mantle viscosity inferred from surface observables are correct to first order. In contrast, the short‐wavelength features are dramatically affected by the rheology of the region surrounding the downwelling. Further study of the shorter‐wavelength geoid over subduction zones may provide better insight into subduction zone processes.

A community benchmark for subduction zone modeling

“…While fully dynamic models are needed to develop an understanding of the dynamics of subduction zones and the selfconsistent generation of plate tectonics in mantle convection (Gurnis and Hager, 1988;King and Hager, 1994;King and Ita, 1995;Kincaid and Sacks, 1997;Chen and King, 1998;Zhong et al, 1998;Van Hunen et al, 2002;Billen and Hirth, 2007), models that prescribe the kinematics of the slab are simpler and better suited in some cases. Such models are particularly appropriate for the study of the Earth's subduction zones where the slab geometry is well described by Benioff zone seismicity and local seismic studies and those where the relative plate motion can be extracted from global tectonic models (e.g.…”

Geoid and topography over subduction zones: The effect of phase transformations

“…Subsequent work has demonstrated that the long-wavelength geoid associated with subduction zones requires that subducting slabs encounter a resistance to flow, modeled as an increase in effective viscosity by a factor of 30 or more, between the asthenosphere and lower mantle [Hager, 1984;Richards and Hager, 1989;Hager and Clayton, 1989;Zhong and Gurnis, 1992;King and Hager, 1994]. The argument can be summarized as follows: convection in the Earth deforms the surface, coremantle boundary, and any internal chemical discontinuities that may exist within the Earth.…”

“…The first of these assumptions, the importance (or lack of importance) of lateral variations in mantle viscosity on surface deformation, has been examined by several investigators Ritzert and Jacoby, 1992;Zhang and Christensen, 1993;King and Hager, 1994;Chen and King, 1998]. When the viscosity of the fluid is assumed to be uniform or only depth varying, then it is possible to decouple the problem and solve each mode independently [e.g., Hager and Clayton, 1989].…”

“…The longest wavelength geoid anomalies appear to be the result of broad, long-wavelength thermal anomalies in the lower mantle and are not significantly contaminated by mode coupling if the lower mantle structure is dominated by long-wavelength thermal anomalies . There are much stronger effects on short wavelength modes [e.g., Ritzert and Jacoby, 1992]; however, the consensus is that temperature-dependent viscosity affects the amplitude of the geoid anomaly by $10 -20% but is not sufficient to change the sign of geoid anomalies over downwelling features [e.g., King and Hager, 1994;Chen and King, 1998]. In addition to the twodimensional (2-D) geometries discussed above, a similar conclusion has been reached in 3-D spherical convection models [Zhang and Christensen, 1993].…”

“…[5] Using an imposed plate and slab thermal structure with a temperature-dependent viscosity, King and Hager [1994] found that lateral variations in viscosity up to a factor of 1000 reduce the amplitude of the geoid anomaly over a thermal downwelling (slab); however, this form of viscosity variation was not sufficient to change the sign of the geoid anomaly. In fact, with a temperaturedependent viscosity, the short-wavelength component of the geoid became even more negative.…”