Numerical studies of non-Newtonian mantle convection

Numerical model computations have been carried out to determine how the stress-dependence of non-Newtonian viscosity affects the flow structure of thermal convection. The viscosity laws have been chosen in accordance with present knowledge of upper mantle rheology, based on the diffusion and dislocation creep laws of olivine. The results show that there are important differences between the structures of Newtonian and non-Newtonian convection. While the Newtonian models are insufficient in some respects, the non-Newtonian solutions can explain the characteristics of the real mantle flow. However, this may require a faster plastic deformation than power law dislocation creep, at least in the high-stress regions of the mantle, e.g. at the active plate margins.     

Rheology of the lower mantle

The rheology of the lower mantle of the Earth is examined from the viewpoint of solid state physics. Recent developments in high-pressure research suggest that the lower mantle contains a considerable amount of (Mg, Fe)O with Fe/Mg + Fe = 0.2–0.3. The pressure and temperature dependences of diffusion in (Mg, Fe)O are estimated by the theory of diffusion in ionic solids. Of the materials composing the lower mantle, (Mg, Fe)O may be the “softest”, and therefore the rheology of the lower mantle may be that of (Mg, Fe)O, unless the framework effect is important.Temperatures in the lower mantle are inferred from the depths of phase transitions and the melting temperatures of the core materials. A thermal boundary layer at the base of the mantle is suggested. The physical mechanisms of creep are examined based on a grain size-stress relation and non-Newtonian flow is shown to be the dominant flow mechanism in the Earth's mantle.The effective viscosity for the temperature models, with and without the thermal boundary layer, is calculated for constant stress and constant strain rate (with depth). For constant strain rate, which may be appropriate for discussing the mechanics of descending slabs, the increase in effective viscosity with depth is smaller than for the constant-stress case, which may be appropriate for discussing the flow induced by the surface motion of plates.The relatively small depth gradient of viscosity, for constant strain rate, suggests that the lower mantle could also participate in convection. The effective viscosity increases with depth, however, by at least 10² to 10³ from the top to the bottom of the lower mantle, for a reasonable range of activation volumes and temperatures. There will be a low-viscosity layer at the base of the mantle, in contrast to the high-viscosity layer at the top of the mantle (plates), if a thermal boundary layer is present. The constant Newtonian viscosity inferred from rebound data may be an apparent feature resulting from the difference in deformation mechanisms between isostatic rebound and large-scale flow.     

A fluid model for the shape of accretionary wedges

In this paper the accretionary wedges landward of most oceanic trenches are modelled assuming a Newtonian fluid rheology.It is shown that lubrication theory is applicable and that the addition of material to the wedges can be neglected in determining the shape of the wedges. The predicted shape of the wedges is in good agreement with bathymetric profiles across the Kurile, Ryukyu and Aleutian wedges. From the shape of the above wedges, it is deduced that accretionary sediments have viscosities between 10¹⁸ and 10¹⁹ poise.     

An examination of the rheology of flocculated clay suspensions

A dense cohesive sediment suspension, sometimes referred to as fluid mud, is a thixotropic fluid with a true yield stress. Current rheological formulations struggle to reconcile the structural dynamics of cohesive sediment suspensions with the equilibrium behaviour of these suspensions across the range of concentrations and shear. This paper is concerned with establishing a rheological framework for the range of sediment concentrations from the yield point to Newtonian flow. The shear stress equation is based on floc fractal theory, put forward by Mills and Snabre (1988). This results in a Casson-like rheology equation. Additional structural dynamics is then added, using a theory on the self-similarity of clay suspensions proposed by Coussot (1995), giving an equation which has the ability to match the equilibrium and time-dependent viscous rheology of a wide range of suspensions of different concentration and mineralogy.     

On the interaction between small- and large-scale convection and postglacial rebound flow in a power-law mantle

Some consequences arising from the superposition of flows of two different kinds or scales in a non-Newtonian mantle are discussed and applied to the cases mantle convection plus postglacial rebound flow as well as small- plus large-scale mantle convection. If the two flow types have similar magnitude, the apparent rheology of both flows becomes anisotropic and the apparent viscosity for one flow depends on the geometry of the other. If one flow has a magnitude significantly larger than the other, the apparent viscosity for the weak flow is linear but develops direction-dependent variations about a factorn (n being the power exponent of the rheology). For the rebound flow lateral variations of the apparent viscosity about at least 3 are predicted and changes in the flow geometry and relaxation time are possible. On the other hand, rebound flow may weaken the apparent viscosity for convection. Secondary convection under moving plates may be influenced by the apparent anisotropic rheology. Other mechanisms leading to viscous anisotropy during shearing may increase this effect. A linear stability analysis for the onset of convection with anisotropic linear rheology shows that the critical Rayleigh number decreases and the aspect ratio of the movement cells increases for decreasing horizontal shear viscosity (normal viscosity held constant). Applied to the mantle, this model weakens the preference of convection rolls along the direction of plate motion. Under slowly moving plates, rolls perpendicular to the plate motion seem to have a slight preference. These results could be useful for resolving the question of Newtonian versus non-Newtonian or isotropic versus anisotropic mantle rheology.     

Mantle rheology: radial and lateral viscosity variations inferred from microphysical creep laws

Inferences on the rheology of the mantle based on theoretical and experimental rate equations for steady state creep are discussed and compared with results from geophysical models. The radial increase of viscosity by one to three orders of magnitude across the mantle, required by inversion of postglacial rebound and geodynamic data, is confirmed by microphysical models based on the estimation of continuous and discontinuous changes of creep parameters with depth. The upper mantle (viscosity 10²⁰–10²¹ Pa s) is likely to show non-Newtonian rheology (power-law creep) for average grain sizes larger than 0.1 mm as an order of magnitude. Given the variability of both grain size and stress conditions, local regions of linear rheology can be present. The rheology of transition zone and lower mantle (viscosity 10²²–10²⁴ Pa s) cannot be definitely resolved at present. Estimation of creep parameters leads to possible nonlinear or mixed rheology, if grain sizes are not lower than 0.1 mm and flow conditions can be approximated by a constant strain rate of about 10⁻¹⁵ s⁻¹. This conclusion can be modified by different flow conditions (e.g. a decrease in strain rate or constant viscous dissipation). Furthermore, experiments on fine-grained garnetites and perovskite analogues have shown that diffusion creep is predominant at laboratory conditions. However, the pressure dependence of creep in these phases is unknown, and therefore direct extrapolation to lower mantle conditions is necessarily speculative. Lateral variations of viscosity, largest in the upper and lowermost mantle (up to 2–4 orders of magnitude) are predicted by models based on lateral temperature anomalies derived from seismic tomographic models.     

Theory of dispersion of solutes in non-Newtonian flows through a circular tube

Summary In the present paperTaylor's analysis of the dispersion of a soluble matter in Newtonian flow through a circular tube is extended in the case of non-Newtonian flows of Eyring and Reiner-Philippoff model fluids. It has been shown here that the results for the Newtonian fluid can be deduced from the corresponding results of both the two types non-Newtonian flows. Few specific cases of both the two types of fluids have been studied. Aris modification ofTaylor's analysis is also applicable to non-Newtonian flows discussed here. The results may be useful in connection with the study of the dispersion of soluble salts in blood vessels. It may also be useful to physicians who wish to study molecular diffusion coefficients.     

A numerical method for simulating non-Newtonian fluid flow and displacement in porous media

Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow.     

Non-Newtonian effects during injection in partially crystallised magmas

Injection of Newtonian crystal-free magmas into a partially crystallised host which may exhibit non-Newtonian properties produces magmatic structures such as pipes, syn-plutonic dikes or dendritic structures. Field relationships between the structure and the host rock commonly indicate what the rheological contrasts during the injection were. The manner in which a magma deforms in response to injection is mainly linked to crystal content and strain rate (i.e., injection rate). Three kinds of behaviour can be distinguished: (1) Newtonian at low crystal contents; (2) Non-Newtonian at intermediate (40–60%) crystal contents, or at high crystal contents if the strain rate is small; and (3) brittle failure at high crystal content or strain rates.Petrologic observations indicate that injection can take place when the host magma still behaves as a fluid. To investigate the physics of the injection process we review the results of injection experiments in non-Newtonian fluids. These experiments were performed to study viscous fingering in 2-D Hele Shaw cells. They provide the first step to establishing the main non-Newtonian effects during the formation of interfacial instabilities arising when a Newtonian fluid is injected into a more viscous fluid or paste. The qualitative comparison of the morphological features of the interfaces between the fluids in the experiments with those in nature suggests that, in magmas, irregularities of the interfaces (dikes and dendrites) result from non-Newtonian properties of the host. We conclude that fluid-like deformation, rather than brittle behaviour of the host, during injection is likely to produce the general features observed on the field. Cooling effects might be responsible for the widespread phenomenon of fragmentation. We emphasise that the main effect of non-Newtonian properties in partially crystallised magmas is to generate strongly heterogeneous media producing discontinuities which could explain the main morphological features of syn-plutonic injection structures.     

Upscaling of saturated conductivity for Hortonian runoff modelling

Stochastic and deterministic upscaling techniques are developed that upscale saturated conductivity at the support of 0.04 m² to representative actual infiltration (I_b) for support units (blocks) of 10¹–10⁴ m², as a function of steady state rainfall and runon to the block, under Hortonian runoff (infiltration excess overland flow). Parameters in the upscaling techniques represent the surface runoff flow pattern and the spatial probability distribution of saturated conductivity within the 10¹–10⁴ m² block. The stochastic upscaling technique represents the spatial process of infiltration and runoff using a simple process-imitating model, estimating I_b using Monte Carlo simulation. The deterministic upscaling technique aggregates these processes by a deterministic function relating rainfall and runon to I_b. The stochastic upscaling technique is shown to be capable to upscale saturated conductivity derived from ring infiltrometers to I_b values of plots (1 m²) corresponding to measured I_b values using rainfall simulators. It is shown that both upscaling techniques can be used to estimate I_b for each time step and each block in transient rainfall–runoff models, giving better estimates of cumulative runoff from a hillslope and a small catchment than model runs that do not use upscaling techniques.     

Shear viscosity of rhyolite-vapor emulsions at magmatic temperatures by concentric cylinder rheometry

The viscosity of natural rhyolitic melt from Lipari, Aeolian Islands and melt-bubble emulsions (30–50 vol% porosity) generated from Lipari rhyolite have been measured in a concentric cylinder rheometer at temperatures and shear rates in the range 925–1150°C and 10⁻³–10^−1.2 s⁻¹, respectively, in order to better understand the dependence of emulsion shear viscosity on temperature and shear rate in natural systems. Bubble-free melt exhibits Newtonian–Arrhenian behavior in the temperature range 950–1150°C with an activation energy of 395±30 kJ/mol; the shear viscosity is given by log η_m=−8.320+20624/T. Suspensions were prepared from natural rhyolite glass to which small amounts of Na₂SO₄ were added as a ‘foaming agent’. Reasonably homogeneous magmatic mixtures with an approximate log-normal distribution of bubbles were generated by this technique. Suspension viscosity varied from 10^6.1 to 10^8.37 Pa s and systematically correlates with temperature and porosity in the shear stress range (10^4.26–10^5.46 Pa) of the experiments. The viscosity of melt-bubble emulsions is described in terms of the relative viscosity, η_r=η_e/η_m where η_e is the emulsion viscosity and η_m is the viscosity of melt of the same composition and temperature. The dependence of relative viscosity on porosity for magmatic emulsions depends on the magnitude of the capillary number Ca≡G/(σr_b⁻¹η_m⁻¹), the ratio of viscous forces acting to deform bubbles to interfacial forces resisting bubble deformation. For inviscid bubbles in magmatic flows three regimes may be identified. For Ca<0.1, bubbles are nearly spherical and relative viscosity is an increasing function of porosity. For dilute systems, η_r=1+φ given by the classical result of Taylor [Proc. R. Soc. London A 138 (1932) 41–48]. For Ca in the range 0.1<Ca<10, emulsions behave as power law fluids and the relative viscosity depends on shear rate (or Ca) as well as porosity. At high Ca (Ca>10) an asymptotic regime is reached in which relative viscosity decreases with increasing porosity and is independent of Ca. Our experiments were carried out for 30<Ca<925 in order to quantify the maximal effect of bubbles in reducing the viscosity of magmatic emulsions relative to single-phase melt at identical conditions of shear rate and temperature. The viscosity of a 50 vol% emulsion is a factor of five smaller than that of melt alone. Rheometric measurements obtained in this study are useful in constraining models of magma transport and volcanic eruption mechanics relevant to transport of volatile-saturated magma in the crust and upper mantle.     

Thermal histories of the core and mantle

Recognition that the cooling of the core is accomplished by conduction of heat into a thermal boundary layer (D″) at the base of the mantle, partly decouples calculations of the thermal histories of the core and mantle. Both are controlled by the temperature-dependent rheology of the mantle, but in different ways. Thermal parameters of the Earth are more tightly constrained than hitherto by demanding that they satisfy both core and mantle histories. We require evolution from an early state, in which the temperatures of the top of the core and the base of the mantle were both very close to the mantle solidus, to the present state in which a temperature increment, estimated to be ～ 800 K, has developed across D″. The thermal history is not very dependent upon the assumption of Newtonian or non-Newtonian mantle rheology. The thermal boundary layer at the base of the mantle (i.e., D″) developed within the first few hundred million years and the temperature increment across it is still increasing slowly. In our preferred model the present temperature at the top of the core is 3800 K and the mantle temperature, extrapolated to the core boundary without the thermal boundary layer, is 3000 K. The mantle solidus is 3860 K. These temperatures could be varied within quite wide limits without seriously affecting our conclusions. Core gravitational energy release is found to have been remarkably constant at ～ 3 × 10¹¹ W. nearly 20% of the core heat flux, for the past 3 × 10⁹ y, although the total terrestrial heat flux has decreased by a factor of 2 or 3 in that time. This gravitational energy can power the “chemical” dynamo in spite of a core heat flux that is less than that required by conduction down an adiabatic gradient in the outer core; part of the gravitational energy is used to redistribute the excess heat back into the core, leaving 1.8 × 10¹¹ W to drive the dynamo. At no time was the dynamo thermally driven and the present radioactive heating in the core is negligibly small. The dynamo can persist indefinitely into the future; available power 10¹⁰ y from now is estimated to be 0.3 × 10¹¹ W if linear mantle rheology is assumed or more if mantle rheology is non-linear. The assumption that the gravitational constant decreases with time imposes an implausible rate of decrease in dynamo energy. With conventional thermodynamics it also requires radiogenic heating of the mantle considerably in excess of the likely content of radioactive elements.     

Estimates of effective permeability for non-Newtonian fluid flow in randomly heterogeneous porous media

An understanding of the interplay between non-Newtonian effects in porous media flow and field-scale domain heterogeneity is of great importance in several engineering and geological applications. Here we present a simplified approach to the derivation of an effective permeability for flow of a purely viscous power–law fluid with flow behavior index n in a randomly heterogeneous porous domain subject to a uniform pressure gradient. A standard form of the flow law generalizing the Darcy’s law to non-Newtonian fluids is adopted, with the permeability coefficient being the only source of randomness. The natural logarithm of the permeability is considered a spatially homogeneous and correlated Gaussian random field. Under the ergodic hypothesis, an effective permeability is first derived for two limit 1-D flow geometries: flow parallel to permeability variation (serial-type layers), and flow transverse to permeability variation (parallel-type layers). The effective permeability of a 2-D or 3-D isotropic domain is conjectured to be a power average of 1-D results, generalizing results valid for Newtonian fluids under the validity of Darcy’s law; the conjecture is validated comparing our results with previous literature findings. The conjecture is then extended, allowing the exponents of the power averaging to be functions of the flow behavior index. For Newtonian flow, novel expressions for the effective permeability reduce to those derived in the past. The effective permeability is shown to be a function of flow dimensionality, domain heterogeneity, and flow behavior index. The impact of heterogeneity is significant, especially for shear-thinning fluids with a low flow behavior index, which tend to exhibit channeling behavior.     

Properties of low‐frequency trapped mode in viscous‐fluid waveguides

We derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10^?3 Hz to 10³ Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity.     

Convection model of post-glacial uplift

A new approach to analytical and numerical study of the process of the post-glacial uplifting of the Earth’s surface was proposed within the framework of a viscous model. Displacement of the Earth’s surface is considered as the motion of the density boundary due to chemico-density convection. It is shown that the incorporation of the non-Newtonian rheology at observed velocities of post-glacial uplifts requires an obligatory presence of faults in the lithosphere and gives rise to quasi-uniform motion of the mantle material, whose viscosity under the lithosphere is, on the average, sufficiently small and amounts to ～10¹⁹ Pa. The study of the stability of the constructed model of the post-glacial uplift considered as the chemico-density convection relative to the thermal convection shows that the velocity of thermal convection developing in the presence of a quasiuniform mantle flow related to the post-glacial recovery is ～1 m/yr.     

Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σ 10³dyne/cm²), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σ = 10⁴ dyne/cm², if the flow rate is greater than 10⁵ g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.     

Analytical modelling of viscous diapirism through a strongly non-Newtonian overburden subject to horizontal forces

We study the early stages of diapirism and analyse the gravitational and buckling instabilities of a buoyant viscous layer overlain by a layer of strongly non-Newtonian power-law rheology (when a power-law exponent tends to infinity). This situation models rocksalt under a layer of a perfectly plastic overburden. The growth rate of small perturbations on the interface between the two layers and the wavelength of the most unstable perturbations are found and compared with those of structures consisting of two Newtonian or two strongly non-Newtonian viscous layers. Effects due to the effective viscosity and thickness ratios between the two layers are assessed. Considering the effective viscosity of the overburden to be much greater than the viscosity of the buoyant salt layer, we obtain the following results. In the case of simple gravitational instability and no-slip boundary conditions, the instability pattern is similar to that in a strongly non-Newtonian power-law material. An increase in the thickness of the overburden decreases the dominant wavelength of the most unstable mode, while the dominant wavelength is lengthened in the case of Newtonian viscous layers. When the system of layers is subjected to either horizontal extension or shortening, and the upper boundary of the system is stress-free, the buckling instability overwhelms the gravitational instability, and the dynamic growth rate of the instability depends linearly on the effective viscosity ratio. We conclude that the introduction of strongly non-Newtonian power-law rheology into diapir overburdens greatly affects instability parameters such as growth rate and dominant wavelength of perturbations and hence, alters interdiapir spacings.     

Plume capture by divergent plate motions: implications for the distribution of hotspots,geochemistry of mid-ocean ridge basalts,and estimates of the heat flux at the core–mantle boundary

The coexistence of stationary mantle plumes with plate-scale flow is problematic in geodynamics. We present results from laboratory experiments aimed at understanding the effects of an imposed large-scale circulation on thermal convection at high Rayleigh number (10⁶≤Ra≤10⁹) in a fluid with a temperature-dependent viscosity. In a large tank, a layer of corn syrup is heated from below while being stirred by large-scale flow due to the opposing motions of a pair of conveyor belts immersed in the syrup at the top of the tank. Three regimes are observed, depending on the ratio V of the imposed horizontal flow velocity to the rise velocity of plumes ascending from the hot boundary, and on the ratio λ of the viscosity of the interior fluid to the viscosity of the hottest fluid in contact with the bottom boundary. When V≪1 and λ≥1, large-scale circulation has a negligible effect on convection and the heat flux is due to the formation and rise of randomly spaced plumes. When V>10 and λ>100, plume formation is suppressed entirely, and the heat flux is carried by a sheet-like upwelling located in the center of the tank. At intermediate V, and depending on λ, established plume conduits are advected along the bottom boundary and ascending plumes are focused towards the central upwelling. Heat transfer across the layer occurs through a combination of ascending plumes and large-scale flow. Scaling analyses show that the bottom boundary layer thickness and, in turn, the basal heat flux q depend on the Peclet number, Pe, and λ. When λ>10, q∝Pe^1/2 and when λ→1, q∝(Peλ)^1/3, consistent with classical scalings. When applied to the Earth, our results suggest that plate-driven mantle flow focuses ascending plumes towards upwellings in the central Pacific and Africa as well as into mid-ocean ridges. Furthermore, plumes may be captured by strong upwelling flow beneath fast-spreading ridges. This behavior may explain why hotspots are more abundant near slow-spreading ridges than fast-spreading ridges and may also explain some observed variations of mid-ocean ridge basalt (MORB) geochemistry with spreading rate. Moreover, our results suggest that a potentially significant fraction of the core heat flux is due to plumes that are drawn into upwelling flows beneath ridges and not observed as hotspots.     

The simulation of sediment transport and erosion caused by free-surface flow based on two-phase SPH model with the improved Shields criterion

Ocean Dynamics - In this paper, a two-phase model based on the SPH method is established using the Newtonian fluid and non-Newtonian fluid to describe water and sediment respectively. In this...     

Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology

Since microphysics cannot say definitively whether the rheology of the mantle is linear or non-linear, the aim of this paper is to constrain mantle rheology from observations related to the glacial isostatic adjustment (GIA) process—namely relative sea-levels (RSLs), land uplift rate from GPS and gravity-rate-of-change from GRACE. We consider three earth model types that can have power-law rheology (n = 3 or 4) in the upper mantle, the lower mantle or throughout the mantle. For each model type, a range of A parameter in the creep law will be explored and the predicted GIA responses will be compared to the observations to see which value of A has the potential to explain all the data simultaneously. The coupled Laplace finite-element (CLFE) method is used to calculate the response of a 3D spherical self-gravitating viscoelastic Earth to forcing by the ICE-4G ice history model with ocean loads in self-gravitating oceans. Results show that ice thickness in Laurentide needs to increase significantly or delayed by 2 ka, otherwise the predicted uplift rate, gravity rate-of-change and the amplitude of the RSL for sites inside the ice margin of Laurentide are too low to be able to explain the observations. However, the ice thickness elsewhere outside Laurentide needs to be slightly modified in order to explain the global RSL data outside Laurentide. If the ice model is modified in this way, then the results of this paper indicate that models with power-law rheology in the lower mantle (with A ∼ 10⁻³⁵ Pa⁻³ s⁻¹ for n = 3) have the highest potential to simultaneously explain all the observed RSL, uplift rate and gravity rate-of-change data than the other model types.