Variations In Mantle Viscosity Research Articles

Ice age effects on the satellite-derived [formula omitted] datum: Mapping the sensitivity to 3D variations in mantle viscosity

Studies of glacial isostatic adjustment (GIA) based on spherically symmetric viscoelastic Earth models have argued that the rate of change of the degree 2 zonal harmonic of the Earth's geopotential, or J˙2, provides an important constraint on mean viscosity in the deep mantle (Mitrovica and Peltier, 1993; Nakada et al., 2015; Lau et al., 2016). To refine this constraint, we compute Fréchet kernels using an adjoint methodology that reveal the sensitivity of the datum to 3D variations in mantle viscosity. We demonstrate that the mantle sensitivity of the datum is largely limited to the region below the ancient Laurentide ice sheet that covered Canada and significant portions of the northeastern United States at Last Glacial Maximum (LGM). In the bottom half of the lower mantle, this region of maximum sensitivity lies outside the location of Large Low Shear Velocity Provinces (LLSVPs) imaged from seismic tomographic studies. Thus, if the low shear velocity of these provinces originates from thermal effects, previous inferences of viscosity based upon the J˙2 datum are likely higher than the actual mean viscosity of the lower mantle.

Comparing Glacial‐Geological Evidence and Model Simulations of Ice Sheet Change since the Last Glacial Period in the Amundsen Sea Sector of Antarctica

AbstractSince the Last Glacial Maximum ∼20,000 years ago, the Antarctic Ice Sheet has undergone extensive changes, resulting in a much smaller present‐day configuration. Improving our understanding of basic physical processes that played important roles during that retreat is critical to providing more robust model projections of future retreat and sea‐level rise. Here, a limited‐area nested ice sheet model was applied to the last deglacial retreat of the West Antarctic Ice Sheet in the Amundsen Sea Embayment (ASE), at 5 km resolution. The ice sheet response to climate and sea‐level forcing was examined at two sites along the flowlines of Pine Island Glacier and Pope Glacier, close to the Hudson Mountains and Mount Murphy respectively, and the simulated responses compared with ice sheet thinning histories derived from glacial‐geological data. The sensitivity of results to selected model parameters was also assessed. The model simulations predict a broadly similar response to ocean forcing in both the central and eastern ASE, with an initial rapid phase of thinning followed by a slower phase to the modern configuration. Although there is a mismatch of up to 5,000 years between the timing of simulated and observed thinning, the modeling suggests that the upstream geological records of ice surface elevation change reflect a response to retreat near the grounding line. The model‐data mismatch could potentially be improved by accounting for regional variations in mantle viscosity, sea‐surface heights and basal sliding properties across the continental shelf.

Bayesian Inference of Mantle Viscosity From Whole‐Mantle Density Models

AbstractThe long‐wavelength geoid is sensitive to Earth's mantle density structure as well as radial variations in mantle viscosity. We present a suite of inversions for the radial viscosity profile using whole‐mantle models that jointly constrain the variations in density, shear‐ and compressional‐wavespeeds using full‐spectrum tomography. We use a Bayesian approach to identify a collection of viscosity profiles compatible with the geoid, while enabling uncertainties to be quantified. Depending on tomographic model parameterization and data weighting, it is possible to obtain models with either positive‐ or negative‐buoyancy in the large low shear velocity provinces. We demonstrate that whole‐mantle density models in which density and VS variations are correlated imply an increase in viscosity below the transition zone, often near 1,000 km. Many solutions also contain a low‐viscosity channel below 650 km. Alternatively, models in which density is less‐correlated with VS—which better fit normal mode data—require a reduced viscosity region in the lower mantle. This feature appears in solutions because it reduces the sensitivity of the geoid to buoyancy variations in the lowermost mantle. The variability among the viscosity profiles obtained using different density models is indicative of the strong nonlinearities in modeling the geoid and the limited resolving power of the geoid kernels. We demonstrate that linearized analyses of model resolution do not adequately capture the posterior uncertainty on viscosity. Joint and iterative inversions of viscosity, wavespeeds, and density using seismic and geodynamic observations are required to reduce bias from prior assumptions on viscosity variation and scalings between material properties.

A baseline Antarctic GIA correction for space gravimetry

Within the past decade, newly collected GPS data and geochronological constraints have resulted in refinement of glacial isostatic adjustment (GIA) models for Antarctica. These are critical to estimating and understanding ice mass changes at present-day. A correction needs to be made when using space gravity for ice mass balance assessments due to the fact that any vertical movements of the solid Earth masquerade as changes in ice mass, and these must be carefully removed. The main upshot of the new Antarctic GIA models is a downward revision of negative ice mass trends deduced from the Gravity Recovery and Climate Experiment (GRACE), resulting from a reduced GIA correction. This revision places GRACE inferred trend in mass balance within the one sigma uncertainty of mass balance deduced by altimetry. Because uncertainties in Holocene ice history and the low viscosity rheology beneath the West Antarctic Ice Sheet (WAIS) continue to vex further improvement in predictions of present-day GIA gravity rate, more emphasis has been given to regional-scale GIA models. Here we use a Bayesian method to explore the gravimetric GIA trend over Antarctica, both with and without the impact of a late Pleistocene Antarctic ice loads, along with the contribution of oceanic loads. We call this model without loads associated with Antarctica a baseline for regional GIA models to build upon. We consider variations of the radial mantle viscosity profile and the volume of continental-scale ice sheets during the last glacial cycle. The modeled baseline GIA is mainly controlled by the lower mantle viscosity and continental levering caused by ocean loading. We find that the predicted baseline GIA correction weakly depends on the ice history. This correction averages to +28.4 [16.5–41.9, 95% confidence] Gt/yr, of which +23.6±5.3 are contributed by East Antarctica. In contrast, with late-Pleistocene Antarctic-proximal ice included, the total modeled mass trend due to GIA is +73.7 [30.1–114.7] Gt/yr. A baseline GIA correction of 28.4 Gt/yr is of order 50% of the mean net mass trend measured during the period 1992-2017. The statistical analysis provides tools for properly synthesizing any regional Antarctic GIA model with a self-consistent far-field component. This may prove important for accounting for both global and regional 3-D variations in mantle viscosity.

Inferences of Mantle Viscosity Based on Ice Age Data Sets: The Bias in Radial Viscosity Profiles Due to the Neglect of Laterally Heterogeneous Viscosity Structure

AbstractInferences of mantle viscosity using glacial isostatic adjustment (GIA) data are hampered by data sensitivity to the space‐time geometry of ice cover. A subset of GIA data is relatively insensitive to this ice history: the Fennoscandian relaxation spectrum (FRS), postglacial decay times in Canada and Scandinavia, and the rate of change of the degree‐2 zonal harmonic of the geopotential ( ). These geographically limited data have been inverted to constrain the radial (one‐dimensional [1D]) mantle viscosity profile. We explore potential biases in these 1D inversions introduced by neglecting a three‐dimensional (3D) viscosity structure. We perform 1D Bayesian inversions of synthetic GIA data generated from Earth models with realistic 3D variations in mantle viscosity and lithospheric thickness and compare results to the 1D viscosity profile associated with the 3D model used to generate the synthetics. Differences between these two 1D profiles reflect GIA data resolution and biasing introduced by neglecting, in the inversions, a 3D viscosity structure. We focus on the second issue, demonstrating that the largest bias occurs within the upper mantle (in particular, the transition zone). This remains consistent when varying inversion parameters (e.g., prior/starting models) and the 1D/3D viscosity fields adopted in generating the synthetics. Inversions of individual data sets show 3D biasing increases for data exhibiting shallower (thus more localized) sensitivity to viscosity. Of the data considered herein, inversions of the FRS are subject to the largest bias followed by decay time data. The bias is minimal for , as its deeper sensitivity is accompanied by broader averaging of structure in radial and lateral directions.

The timing of the Black Sea flood event: Insights from modeling of glacial isostatic adjustment

We present a suite of gravitationally self-consistent predictions of sea-level change since Last Glacial Maximum (LGM) in the vicinity of the Bosphorus and Dardanelles straits that combine signals associated with glacial isostatic adjustment (GIA) and the flooding of the Black Sea. Our predictions are tuned to fit a relative sea level (RSL) record at the island of Samothrace in the north Aegean Sea and they include realistic 3-D variations in viscoelastic structure, including lateral variations in mantle viscosity and the elastic thickness of the lithosphere, as well as weak plate boundary zones. We demonstrate that 3-D Earth structure and the magnitude of the flood event (which depends on the pre-flood level of the lake) both have significant impact on the predicted RSL change at the location of the Bosphorus sill, and therefore on the inferred timing of the marine incursion. We summarize our results in a plot showing the predicted RSL change at the Bosphorus sill as a function of the timing of the flood event for different flood magnitudes up to 100 m. These results suggest, for example, that a flood event at 9 ka implies that the elevation of the sill was lowered through erosion by ∼14–21 m during, and after, the flood. In contrast, a flood event at 7 ka suggests erosion of ∼24–31 m at the sill since the flood. More generally, our results will be useful for future research aimed at constraining the details of this controversial, and widely debated geological event.

The role of glacial isostatic adjustment in the present-day crustal motion and sea levels of East Asia

The aim of this paper is to model and remove the contribution of glacial isostatic adjustment (GIA) from the observed crustal velocities and sea-level rates in East Asia, so that the signal from other geological processes such as tectonic uplift or global change can be better revealed. State-of-the-art GIA models that include 3D variations in mantle viscosity and lithospheric thickness are employed in this study. Uncertainties of the GIA response are estimated from different ice history and background viscosity models. It is demonstrated that the uncertainties in the GIA response in East Asia are generally small compared with the response itself. For example, the land uplift rate near the east coast of China due to GIA has magnitudes of about 0.1 mm/yr while the uncertainties are generally less than 0.04 mm/yr. These are small compared with the observed magnitude of uplift rate (∼1.0 mm/yr) and the measurement uncertainties of GPS. For the height rates in leveling observation, relative sea-level rates in tide gauge data, absolute seal-level rates from satellite altimetry and tangential velocities from GPS data, the GIA effects are also shown to be generally small compared with observed data. This technique of “cleaning” geodetic data will become more useful in the future when the uncertainties of geodetic measurements can be reduced to less than 0.1 mm/yr.

The rotational stability of a triaxial ice‐age Earth

Mitrovica et al. (2005), following calculations by Nakada (2002), demonstrated that the traditional approach for computing rotation perturbations driven by glacial isostatic adjustment significantly overestimates present‐day true polar wander (TPW) speeds by underestimating the background oblateness on which the ice‐age loading is superimposed. The underestimation has two contributions: the first originates from the treatment of the hydrostatic form and the second from the neglect of the Earth's excess ellipticity supported by mantle convection. In Mitrovica et al. (2005), the second of these two contributions was computed assuming a biaxial nonhydrostatic form (i.e., the principal equatorial moments of inertia were assumed to be equal to their mean value). In this article we outline an extended approach that accounts for a triaxial planetary form. We show that differences in the TPW speed predicted using the Mitrovica et al. (2005) approach and our triaxial theory are relatively minor (∼0.1°/Myr) and are limited to Earth models with lower mantle viscosity less than ∼5 × 1021 Pa s. However, for this same class of Earth models, the angle of TPW predicted for a triaxial Earth is rotated westward (toward the axis of maximum equatorial inertia) by as much as ∼20° relative to the biaxial case. We demonstrate that these effects are a consequence of the geometry of the ice‐age forcing, which has a dominant equatorial direction that is intermediate to the axes defining the principal equatorial moments of inertia of the planet. We complete the study by computing updated Frechet kernels for the TPW speed datum, which provide a measure of the detailed depth‐dependent sensitivity of the predictions to variations in mantle viscosity. We show, in contrast to earlier efforts to explore this sensitivity based on the traditional rotation theory, that the datum does not generally have a sensitivity to viscosity that peaks near the base of the mantle.

Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model. Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.

Decontaminating tide gauge records for the influence of glacial isostatic adjustment: The potential impact of 3-D Earth structure

We investigate the potential impact of lateral variations in mantle viscosity and lithospheric thickness on predictions of present‐day relative sea‐level change due to glacial isostatic adjustment (GIA). We consider three viscoelastic Earth models. The first is a 1‐D model with a lithospheric thickness of 120 km and upper and lower mantle viscosities of 5 × 1020 Pa s and 5 × 1021 Pa s, respectively. The second model includes global lithospheric thickness variations and lateral heterogeneities in upper mantle viscosity ranging over three orders of magnitude, while the third model includes lateral variations in lower mantle viscosity alone. We find that the impact of 3‐D structure is significant. Indeed, the difference between the 3‐D and 1‐D model predictions at ∼300 sites with tide gauge records longer than 40 years duration is greater than 0.2 mm/yr and 0.5 mm/yr for 50% and 25% of the sites, respectively. The maximum difference exceeds several mm/yr. We conclude that efforts to decontaminate tide gauge records for ongoing GIA, to determine the rate and origin of global sea‐level rise, should incorporate 3‐D mantle structure into the GIA modelling.

Tectonic velocities, dynamic topography, and relative sea level

A simple dynamic model based on boundary layer theory shows that dynamic topography is unlikely to vary significantly in response to short term (≤20 Myr) variations in the mean tectonic velocity. Tectonic velocities essentially mirror variations in mantle viscosity, but are not indicative of substantial modification of dynamic topography, which primarily reflects mass anomalies in the mantle. This implies that relative sea level is unlikely to be affected by “tectonic pulses” and also that observed tilting of cratonic margins cannot result from a pulse of increased tectonic velocities. Thus, relative sea level is primarily controlled by the seafloor age distribution, although long term (≥100 Myrs) changes in tectonic velocity will produce dynamic topography that reinforces sea level changes associated with changing ridge volume.

Effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced relative sea levels and long wavelength gravity field in a spherical, self-gravitating Maxwell Earth

The effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced relative sea level (RSL) changes and the secular rate of change of the Earth's long wavelength gravity field in a spherical, self-gravitating, incompressible visco-elastic earth are investigated using the Coupled-Laplace-Finite-Element method. The ICE-4G deglaciation model is used with gravitationally self-consistent sea levels in realistic oceans to describe the load. Lateral variations in mantle viscosity and lithospheric thickness are inferred from seismic tomography model S20A. The full 3-D earth model, which includes all the lateral heterogeneities in the lithosphere and mantle, gives a better fit to the global RSL data than the related laterally homogeneous model. However, the situation is less clear for the observed secular drift of the low degree geopotential coefficients J˙ l because of the uncertain contribution of recent melting. But, the full 3-D model can fit the J˙ 2 observation if recent melting contributes about 1.0 mm/a of equivalent sea level rise. It predicts that the GIA induced secular gravity rate of change to be detected by the GRACE mission in the southern part of Hudson Bay is about 1.2 to 1.6 μgal/a. Moreover, the contributions of lateral heterogeneities from individual layers in the mantle or in the lithosphere are studied. The contribution from the transition zone (420–670 km) is generally opposite to that from its neighboring layers and thus can mask their effects. As a consequence, the effects from the deep lower mantle become dominant for RSL and secular rate of change of gravity over Laurentide. For the secular rates of change for degrees 2–4 geopotential coefficients, the contribution is mostly from lateral heterogeneities in the deeper mantle. The effects of background viscosity profiles are also investigated and are found to be significant for all these observables.

Effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced surface motion on a spherical, self-gravitating Maxwell Earth

The effects of lateral variations in lithospheric thickness and mantle viscosity on surface motions on a spherical, self-gravitating, incompressible viscoelastic earth are investigated using the Coupled Laplace–Finite Element Method. The ICE-4G deglaciation model is used together with gravitationally self-consistent sea levels in realistic oceans to describe the load. Lateral variations in mantle viscosities and lithospheric thickness are inferred from seismic tomography model S20A using well known scaling relationships. The laterally homogeneous background viscosity has viscosity increases across 670 km and 1330 km depths and is a simplification of Peltier's VM2 model. The effect of interaction between ice complexes in North America, Greenland, Eurasia and Antarctica are investigated and found to be significant for tangential motion. The predicted motion in Laurentide and Antarctica are also compared with results obtained with flat-earth models and found that there is general agreement between the two types of modeling although spherical earth models are more realistic because they take into account the interaction between ice complexes and there is no problem with edge effects. The effects of lateral heterogeneity on uplift rate are found to be large enough to be resolved by current GPS technology. It confirms that the effect of the reverse viscosity contrast in the transition zone under the Laurentian and Fennoscandian craton may mask the effect of lateral heterogeneity in the neighboring layers on uplift rate. For tangential motion, lateral heterogeneity is found to be able to overprint the divergent motion from the centers of rebound predicted in laterally homogeneous models. This finding is new for Laurentide and is due to the contribution from the deep part of the lower mantle – although the contribution from the upper mantle is also important on tangential motion, its effects are compromised by the effects from the other layers.

GIA-induced secular variations in the Earth's long wavelength gravity field: Influence of 3-D viscosity variations

Abstract Predictions of present day secular variations in the Earth's long wavelength geopotential driven by glacial isostatic adjustment (GIA) have previously been analyzed to infer the radial profile of mantle viscosity and to constrain ongoing cryospheric mass balance. These predictions have been based on spherically symmetric Earth models. We explore the impact of lateral variations in mantle viscosity using a new finite-volume formulation for computing the response of 3-D Maxwell viscoelastic Earth models. The geometry of the viscosity field is constrained from seismic-to-mographic images of mantle structure, while the amplitude of the lateral viscosity variations is tuned by a free parameter in the modeling. We focus on the zonal J˙ l harmonics for degrees l = 2,…,8 and demonstrate that large-scale lateral viscosity variations of two to three orders of magnitude have a modest, 5–10%, impact on predictions of J˙ 2 . In contrast, predictions of higher degree harmonics show a much greater sensitivity to lateral variation in viscosity structure. We conclude that future analyses of secular trends (for degree l > 2) estimated from ongoing (GRACE, CHAMP) satellite missions must incorporate GIA predictions based on 3-D viscoelastic Earth models.

Nonlinear free thermal convection in a spherical shell: A variable viscosity model

In mantle convection models, the mantle viscosity is generally assumed constant or dependent on depth. In this paper, a laterally variable viscosity is introduced into mantle convection model in which the mantle viscosity consists of a constant background and latitude-dependent viscosity with small fluctuations. The features of toroidal field dependent on depth and Rayleigh number are discussed under two boundary conditions, i.e., the top rigid and bottom stress-free boundaries (R-F boundary for short) and both rigid ones (R-R boundary for short), respectively. The results show that the energy of toroidal field mainly concentrates in the middle and upper parts of a spherical shell, and the ratio of toroidal to total velocities amounts to only a few percents and hardly depends on Rayleigh number, while the convection patterns of toroidal field have been strongly affected by Rayleigh number. It is found that the convection patterns and velocities of toroidal field have obvious differences in latitudinal direction, which clearly reflects the effects of lateral mantle viscosity variations on the convection patterns. These preliminary results give us a possible hint to study some global tectonic phenomena, e.g. the asymmetry of the southern and northern hemispheres and the Earth’s differential rotation.

Glacial isostatic adjustment in Fennoscandia with a three-dimensional viscosity structure as an inverse problem

Glacial isostatic adjustment data are commonly used to invert for the radial viscosity structure of the mantle. However, the effects of lateral variations in mantle viscosity in such inversions are not yet accounted for. Here we analysed synthetic sea-level data for the Fennoscandian region, which are derived from a three-dimensional (3D) earth model with realistic lateral and vertical viscosity variations deduced from seismological and geological information. The inversion of the 3D synthetic data for a best-fitting 1D viscosity profile reveals that (i) lateral lithospheric thickness variations can be detected with 1D model predictions, if the data are grouped into regional subsets, (ii) combined lateral variations in lithospheric thickness and asthenospheric viscosity are not properly resolved with 1D model predictions, and (iii) the spatial and temporal distribution of observational data strongly affects the resulting 1D viscosity profile.

Surface loading of a viscoelastic planet--III. Aspherical models

Summary In Paper I of this series we developed a generalized normal-mode formalism for computing the response of an aspherical, self-gravitating, linear viscoelastic earth model to a surface load. In the present article we introduce an expansion for the normal modes of an aspherical earth model, using as basis functions the normal modes of a spherically symmetric reference model. This expansion leads to a non-linear eigenvalue problem for the expansion coefficients and decay rates. We develop a linearization of this problem using perturbation theory, which incorporates arbitrary levels of coupling between normal-mode multiplets. As an illustration, we consider the special case of radial perturbations to a spherically symmetric model, and compare predictions based upon perturbation theory with those based upon the usual non-perturbative forward theory. We demonstrate that including overtone coupling is necessary for the accurate prediction of perturbations to the normal-mode decay times and eigenfunctions. These calculations suggest that our theory can accurately accommodate order of magnitude lateral variations in mantle viscosity and significant changes in lithospheric thickness.

Radial models of mantle viscosity: results from a genetic algorithm

SUMMARY The long-wavelength component of the geoid has been used to constrain radial variations in mantle viscosity using 3-D velocity anomaly models determined from seismic tomography as the buoyancy forces driving viscous flow. Using a Genetic Algorithm (GA), the robustness of mantle viscosity models obtained by calculusbased optimization methods is investigated. GAS are a relatively new class of optimization techniques, which are generating a growing interest in the geophysics community. These methods can be particularly useful for solving highly non-linear optimization problems. Unlike traditional techniques, GAS do not require derivative information to form a Jacobian matrix or sensitivity kernels. Models are constructed from pieces of successful models following a simple set of rules. These simple rules are driven by stochastic, rather than deterministic, means. Because of the efficiency of the GA for the mantle viscosity problem, it is possible to explore a greater range of potential solutions than with a traditional optimization method. It is found that, while both calculus-based and GA optimization methods find viscosity models with a low-viscosity transition zone, the GA finds another class of models, with a high viscosity in the transition zone, that also satisfies the geoid data. The geoid alone is unable to resolve low-viscosity transition-zone models from high-viscosity transitionzone models. The effect of the scaling between seismic velocity and density on the preferred viscosity model is also explored. While a velocity-to-density scaling with a pronounced increase in the transition zone provides the best fit to the geoid, the preferred vertical viscosity profile is insensitive to the velocity-to-density scaling.

A dynamic model of Venus's gravity field

Unlike on Earth, long‐wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near‐surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by neglect of lateral variations in mantle viscosity. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth.