Deep mantle viscous structure with prior estimate and satellite constraint

Abstract

Radial viscosity profiles are constructed for the mantle using plausible temperature profiles and high‐temperature creep models in olivine. While it is possible to specifically design mantle thermal profiles that produce relatively constant viscosity, temperatures deduced from parametric and/or full numerical simulation of convection predict steep increases of viscosity with depth. The most ubiquitous trend is an increase in viscosity from about 800 to 900 km depth to the top of the D″ layer. Predicted increase of viscosity in this portion of the lower mantle ranges from a factor of 102 to 104. Precise estimates are impossible due uncertainty in determining activation volume V* and activation energy E*. Zeroth‐order extrapolation of a creep law to lower mantle conditions requires the assumption that diffusion of a single ionic species controls dislocation mobility. The extrapolation is useful in spite of its great uncertainty. Our rationale consists of two essential elements: (1) Creep laws with depth‐dependent prefactor A(r) and depth‐dependent activation volume V*(r), energy E*(r), and enthalpy S*(r) can be parameterized using estimates of diffusion constants based on elasticity. (2) Secular changes in Earth's gravity field, particularly the zonal coefficients Jl are now detected in the orbits of artificial satellites such as LAGEOS and Starlette. These secular changes are believed to be dominated by postglacial rebound, although there is some contribution from present‐day glacial melting. These gravity field measurements, when combined with constraints on glacial melting, provide a sensitive set of constraints on lower mantle viscous response to the Last glacial epoch and, hence, provide a test of a priori estimates. A radially stratified and incompressible Earth model is used to test sensitivity of data to viscosity increases with depth and convective boundary layer structure. Prior estimates and observed nontidal J2(−C20) are consistent with a layered lower mantle viscosity. Details of this layering are examined by comparing predicted and observed J3, J4. Speculation that a high‐viscosity layer exists above D″ is considered. With a 650‐km‐thick deep high‐viscosity layer (η ≈ 6.0 × 1023 Pa s) the remaining lower mantle is in one of two ranges: 1.5 to 3.5 × 1020 or 3.5 to about 10. × 1022 Pa s. Observational bounds on secular gravity coefficients C30, C40, C50, and C70 using LAGEOS, Starlette, or Etalon satellite data could eliminate the ambiguity between these two viscosity ranges.