The geoid constraint in global geodynamics: viscosity structure, mantle heterogeneity models and boundary conditions

Abstract

S U M M A R YThe Earth's non-hydrostatic gravity field, or geoid, provides a first-order constraint on mantle density structure and dynamics. Geodynamic models for the geoid have proliferated since the advent of seismic mapping of mantle heterogeneity structure (tomography) because the geoid offers perhaps the best-measured independent constraint on mantle density heterogeneity. However, dynamic geoid models involve a number of questionable physical assumptions and uncertainties whose effects need to be evaluated before geodynamic inferences based upon the geoid can be considered sound. Troubling issues include the appropriate surface boundary conditions (free-slip, no-slip, plates?) and parametrization of radial viscosity variations (how many layers can be resolved?), in addition to lateral viscosity variations, possible chemical layering of the mantle, phase transitions, etc. There are also uncertainties in the density heterogeneity models used as 'input' to dynamic geoid models, most of which are derived from seismic tomography and require weakly constrained, empirical conversion factors to go from seismic velocity variations to density variations. Here we address several of the most straightforward problems inherent in geoid modelling, namely the issues of viscosity structure resolution, uncertainties in appropriate boundary conditions, and differences among mantle heterogeneity models. A robust feature of all models is a lower-mantle viscosity at least a factor of 30 greater than that of the upper mantle, but there is little resolution with regard to finer details such as lithospheric or uppermost mantle ('low-viscosity zone') viscosity. Ironically, free-slip boundary conditions result in the best fits to the geoid in all cases, but all boundary conditions exhibit predictable trade-offs with the uppermostmantle viscosity. Models with a single viscosity layer representing the lower mantle yield similar dynamic topography estimates of the order of 700-1000 m in amplitude, regardless of the finer details of upper-mantle viscosity structure, boundary conditions or input heterogeneity models. Comparing mantle heterogeneity models based on two independent seismological determinations (Harvard and Berkeley models) and on the history of subduction, we find that these models are virtually indistinguishable regarding inferences of mantle viscosity structure and amplitude of dynamic topography, and in terms of the effects of different boundary conditions. Uncertainties concerning which type of boundary condition is appropriate are much more important than which mantle heterogeneity model is chosen. Given other uncertainties in modelling the geoid, particularly the strong effects due to lateral viscosity variations for intermediate (< 10 000 km) wavelengths, we conclude that the class of dynamic geoid models explored so far cannot reliably elucidate the details of upper-mantle viscosity structure.

Dynamic topography, gravity and the role of lateral viscosity variations from inversion of global mantle flow

“…7b). The viscosity pre-factors for the lithosphere and upper mantle strongly trade off with each other, noted earlier for radial dependent viscosity inversions (Thoraval and Richards, 1997) (Fig. 7).…”

“…5a), the best-fitting cost function is not significantly reduced. This suggests that the surface observations invoked here are not sensitive to the asthenosphere viscosity or that the asthenosphere viscosity trades off with the lithosphere and upper mantle viscosities (Thoraval and Richards, 1997). Other observations, e.g.…”

A global geoid model with imposed plate velocities and partial layering

“…As has been shown in several previous studies [King, 1995;Thoraval and Richards, 1997;Pari and Peltier, 1998], the robustness of models inferred from the geoid strongly decreases with the number of free parameters. Our six model parameters, discussed in section 3.1, obviously compose a minimum set necessary to characterize the physical system under consideration.…”

Influence of variable uncertainties in seismic tomography models on constraining mantle viscosity from geoid observations

“…The uncertainty in radial mantle viscosity inferred from the geoid observations stems from a difficulty in modeling appropriate surface boundary conditions [Thoraval and Richards, 1997], compressibility of the mantle [Forte and Peltier, 1991;Panasyuk et al, 1996], possible chemical layering and phase transitions [Wen and Anderson, 1997;Čadek et al, 1998], lateral 4 viscosity variations (LVV), etc. Furthermore, the uncertainty associated with the a priori assumption of the Earth's density structure, which is derived mostly from seismic (velocity) tomography models and a velocity-to-density conversion factor, is critical, because the Earth's density anomalies are used typically as "model constants" in geoid computation.…”