Mantle viscosity controls a variety of geodynamic processes such as glacial isostatic adjustment (GIA), but it is poorly constrained because it cannot be measured directly from geophysical measurements. Here we develop a method that calculates viscosity using empirical viscosity flow laws coupled with mantle parameters (temperature and water content) inferred from seismic and magnetotelluric (MT) observations. We find that combining geophysical constraints allows us to place significantly tighter bounds on viscosity estimates compared to using seismic or MT observations alone. In particular, electrical conductivity inferred from MT data can determine whether upper mantle minerals are hydrated, which is important for viscosity reduction. Additionally, we show that rock composition should be considered when estimating viscosity from geophysical data because composition directly affects seismic velocity and electrical conductivity. Therefore, unknown composition increases uncertainty in temperature and water content, and makes viscosity more uncertain. Furthermore, calculations that assume pure thermal control of seismic velocity may misinterpret compositional variations as temperature, producing erroneous interpretations of mantle temperature and viscosity. Stress and grain size also affect the viscosity and its associated uncertainty, particularly via their controls on deformation regime. Dislocation creep is associated with larger viscosity uncertainties than diffusion creep. Overall, mantle viscosity can be estimated best when both seismic and MT data are available and the mantle composition, grain size and stress can be estimated. Collecting additional MT data probably offers the greatest opportunity to improve geodynamic or GIA models that rely on viscosity estimates.

The prominent seismic low-velocity zone (LVZ) in the oceanic low-viscosity asthenosphere is approximately coincident with a zone of high seismic attenuation (or low seismic Q). Small grain sizes in the asthenosphere could link these seismic and rheological properties as small grain sizes reduce viscosity and also lower seismic velocity and seismic Q. Because grain-size is reduced by rock deformation, the asthenosphere’s seismic properties can place constraints on asthenospheric deformation or flow. To determine dominant flow patterns, we develop a selfconsistent analytical 1-D channel flow model that accounts for upper mantle rheology and its dependence on flow-modified grain-sizes, water content and melt fraction, both for flow driven by surface plate motions (Couette flow) and/or by horizontal pressure gradients (Poiseuille flow). From our flow models, Couette flow dominates if the upper mantle is dry, and plug flow (a Poiseuille flow for power law rheology) if it is wet. A plug flow configuration spanning the upper 670 km of the mantle best explains the low seismic Q zone in the asthenosphere, which can be attributed to significant grain-size reduction due to extensive shearing across the asthenosphere. Below the asthenosphere, high water content and minimal shear deformation promote large grain sizes and high seismic Q. We suggest that asthenospheric low-Q and LVZ can be largely explained by grain-size variations associated with plug flow in the wet upper mantle.

Mantle viscosity controls a variety of geodynamic processes, e.g. Glacial Isostatic Adjustment (GIA). Constraining GIA using better viscosity estimates would improve our estimates of recent ice mass loss from the Greenland and Antarctic ice sheets and the associated sea level rise. However, mantle viscosity is poorly constrained as it can rarely be measured directly, making geophysical observations that could place constraints on viscosity more essential. Empirically, viscosity is mainly controlled by temperature, water content of nominally anhydrous minerals, partial melt, grain size and stress. Of these, temperature, water content, and the presence of partial melt can be inferred from seismic and magnetotelluric (MT) measurements, which are important tools in imaging the subsurface of the Earth. In this study, we develop a method to estimate mantle viscosity in which we: (1) constrain temperature from MT, seismic, and surface heat flow observations; (2) constrain compositional structure (i.e., water content and partial melt) from MT and seismic data coupled with experimental mineral physics data; and finally, (3) convert the calculated thermal and compositional structures into a viscosity structure. In each step, we assess and quantify the involved uncertainties. In addition, we introduce a useful parameter – the viscosity ratio (a ratio between viscosities of a target region and a nearby reference region at the same stress and grain size), and quantify its amplitude and uncertainty for a range of temperatures and water contents. We find that the uncertainty in this ratio is relatively small when computed from both seismic and MT observations, compared to either constraint applied alone. We also explore how viscosity ratio uncertainties vary with grain size and stress. Information about grain size can potentially be obtained from seismic attenuation or tectonic history. Overall, we find that both seismic and MT observations can considerably improve estimates of mantle viscosity, and place useful constraints on its lateral variations in the upper mantle. Geophysically-derived mantle viscosity models can be calibrated in areas like Scandinavia, which has well-constrained GIA models, and applied to polar regions where the GIA response is poorly known.