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.     

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.     

Glacial isostatic adjustment in 3-D earth models: Implications for the analysis of tide gauge records along the U.S. east coast

Tide gauge records of recent sea-level change along the U.S. east coast have received significant attention within the literature of glacial isostatic adjustment (GIA). Geographic trends in these tide gauge rates are not reduced by a GIA correction based on a commonly adopted radial viscosity profile (characterized, in particular, by a lower mantle viscosity 1−2×10²¹ Pa s), and this has led to speculation that the residual trends reflect contributions from neotectonics or oceanographic processes. While the trends can be significantly reduced by adopting an Earth model with a stiffer lower mantle, such a model appears to be incompatible with independent constraints from post-glacial decay times in Hudson Bay. We use a finite-element model of the GIA process to investigate whether 3-D viscosity variations superimposed onto the “common” radial viscosity profile may provide a route to reconciling the east coast sea-level trends. We find that the specific 3-D structure we impose has little impact on the geographic trends in the GIA-corrected rates. However, we do find that the imposed lateral variations in lower mantle viscosity introduce a nearly uniform upward shift of 0.5 mm/yr in GIA-induced sea-level rates along the U.S. east coast. Thus, inferences of regional (U.S. east coast) sea-level rise due to modern melting of ice reservoirs, based on tide gauge rates corrected using 1-D GIA models, may be significantly biased by this simplifying assumption.     

大地测量观测和相对海平面联合约束的冰川均衡调整模型

利用大地测量和历史相对海平面变化数据,结合地震剪切波层析模型,联合确定了新的末次冰期冰川均衡调整（GIA）模型,其中地幔黏滞度不仅沿径向而且沿横向变化.研究思路是,先尝试性地选择比例系数β,利用与地震剪切波速异常的线性关系,计算地幔黏滞度横向扰动,并与横向均匀的黏滞度参考模型叠加给出3D地幔黏滞度模型;再利用耦合拉普拉斯方程的有限元法算法进行GIA预测;然后,重复该过程,直到预测与观测之间的吻合满意为止.主要结论有：（1）给出了横向非均匀的地幔黏滞度模型（RF3L20(β=0.4)）,发现了黏滞度显著的横向非均匀性和其对GIA预测的显著影响,指出横向非均匀不完全是由热效应引起的,可能还与化学组分等其他因素有关,该模型可用于地幔动力学研究.（2）给出了全球现今多种GIA预测速率,可为板块运动、陆地水储量、海水质量变化和冰川冰雪质量非平衡监测提供重要的改正.     

Short scale heterogeneity in the lowermost mantle: insights from PcP-P and ScS-S data

We compare lateral variations at the base of the mantle as inferred from a global dataset of PcP-P travel time residuals, measured on broadband records, and existing P and S tomographic velocity models, as well as ScS-S travel time data in some selected regions. In many regions, the PcP-P dataset implies short scale lateral variations that are not resolved by global tomographic models, except under eastern Eurasia, where data and models describe a broad region of fast velocity anomalies across which variations appear to be of thermal origin. In other regions, such as central America and southeastern Africa, correlated short scale lateral variations (several hundred kilometers) are observed in PcP and ScS, implying large but not excessive values for the ratio R=∂ ln V_s/∂ ln V_p (∼2.5). On the other hand, in at least two instances, in the heart of the African Plume and on the edge of the Pacific Plume, variations in P and S velocities appear to be incompatible, implying strong lateral gradients across compositionally different domains, possibly also involving topography on the core-mantle boundary. One should be cautious in estimating R at the base of the mantle from global datasets, as different smoothing and sampling of P and S datasets may result in strong biases and meaningless results.     

Glacial isostatic adjustment at the Laurentide ice sheet margin: Models and observations in the Great Lakes region

Glacial Isostatic Adjustment (GIA) modelling in North America relies on relative sea level information which is primarily obtained from areas far away from the uplift region. The lack of accurate geodetic observations in the Great Lakes region, which is located in the transition zone between uplift and subsidence due to the deglaciation of the Laurentide ice sheet, has prevented more detailed studies of this former margin of the ice sheet. Recently, observations of vertical crustal motion from improved GPS network solutions and combined tide gauge and satellite altimetry solutions have become available. This study compares these vertical motion observations with predictions obtained from 70 different GIA models. The ice sheet margin is distinct from the centre and far field of the uplift because the sensitivity of the GIA process towards Earth parameters such as mantle viscosity is very different. Specifically, the margin area is most sensitive to the uppermost mantle viscosity and allows for better constraints of this parameter. The 70 GIA models compared herein have different ice loading histories (ICE-3/4/5G) and Earth parameters including lateral heterogeneities. The root-mean-square differences between the 6 best models and the two sets of observations (tide gauge/altimetry and GPS) are 0.66 and 1.57 mm/yr, respectively. Both sets of independent observations are highly correlated and show a very similar fit to the models, which indicates their consistent quality. Therefore, both data sets can be considered as a means for constraining and assessing the quality of GIA models in the Great Lakes region and the former margin of the Laurentide ice sheet.     

Glacial isostatic adjustment at the Laurentide ice sheet margin: Models and observations in the Great Lakes region

Glacial Isostatic Adjustment (GIA) modelling in North America relies on relative sea level information which is primarily obtained from areas far away from the uplift region. The lack of accurate geodetic observations in the Great Lakes region, which is located in the transition zone between uplift and subsidence due to the deglaciation of the Laurentide ice sheet, has prevented more detailed studies of this former margin of the ice sheet. Recently, observations of vertical crustal motion from improved GPS network solutions and combined tide gauge and satellite altimetry solutions have become available. This study compares these vertical motion observations with predictions obtained from 70 different GIA models. The ice sheet margin is distinct from the centre and far field of the uplift because the sensitivity of the GIA process towards Earth parameters such as mantle viscosity is very different. Specifically, the margin area is most sensitive to the uppermost mantle viscosity and allows for better constraints of this parameter. The 70 GIA models compared herein have different ice loading histories (ICE-3/4/5G) and Earth parameters including lateral heterogeneities. The root-mean-square differences between the 6 best models and the two sets of observations (tide gauge/altimetry and GPS) are 0.66 and 1.57 mm/yr, respectively. Both sets of independent observations are highly correlated and show a very similar fit to the models, which indicates their consistent quality. Therefore, both data sets can be considered as a means for constraining and assessing the quality of GIA models in the Great Lakes region and the former margin of the Laurentide ice sheet.     

Axial and equatorial rotations of the Earth's cores associated with the Quaternary ice age

The differential axial and equatorial rotations of both cores associated with the Quaternary glacial cycles were evaluated based on a realistic earth model in density and elastic structures. The rheological model is composed of compressible Maxwell viscoelastic mantle, inviscid outer core and incompressible Maxwell viscoelastic inner core. The present study is, however, preliminary because I assume a rigid rotation for the fluid outer core. In models with no frictional torques at the boundaries of the outer core, the maximum magnitude of the predicted axial rotations of the outer and inner cores amounts to ∼2° year⁻¹ and ∼1° year⁻¹, respectively, but that for the secular equatorial rotations of both cores is ∼0.0001° at most. However, oscillating parts with a period of ∼225 years are predicted in the equatorial rotations for both cores. Then, I evaluated the differential rotations by adopting a time-dependent electromagnetic (EM) torque as a possible coupling mechanism at the core-mantle boundary (CMB) and inner core boundary (ICB). In a realistic radial magnetic field at the CMB estimated from surface magnetic field, the axial and equatorial rotations couple through frictional torques at the CMB, although these rotations decouple for dipole magnetic field model. The differential rotations were evaluated for conductivity models with a conductance of 10⁸ S of the lowermost mantle inferred from studies of nutation and precession of the Earth and decadal variations of length of day (LOD). The secular parts of equatorial rotations are less sensitive to these parameters, but the magnitude for the axial rotations is much smaller than for frictionless model. These models, however, produce oscillating parts in the equatorial rotations of both cores and also in the axial rotations of the whole Earth and outer and inner cores. These oscillations are sensitive to both the magnitude of radial magnetic field at the CMB and the conductivity structure. No sharp isolated spectral peaks are predicted for models with a thin conductive layer (∼200 m) at the bottom of the mantle. In models with a conductive layer of ∼100 km thickness, however, sharp spectral peaks are predicted at periods of ∼225 and ∼25 years for equatorial and axial rotations, respectively, although these depend on the strength of radial magnetic field at the CMB. While the present study is preliminary in modelling the fluid outer core and coupling mechanism at the CMB, the predicted axial rotations of the whole Earth may be important in explaining the observed LOD through interaction between the equatorial and axial rotations.     

冰川均衡调整对东亚重力和海平面变化的影响

新的全球冰川均衡调整(GIA)模型RF3L20(β=0.4)+ICE-4G考虑了地幔黏滞度沿横向的变化,其黏滞度参数得到大地测量、历史相对海平面变化观测和地震剪切波层析模型的较好约束.本文利用该模型预测了东亚现今重力变化和海平面变化,根据当前末次冰川时空变化和黏滞度参考模型中下地幔下部黏滞度认识的差异,评估了预测的不确定性.结果表明,GIA对东亚地区重力场和海平面长期变化有显著的影响:例如,在哈尔滨、长春、泰安、蓟县、郑州、武汉等测站,GIA重力影响达几十纳伽,可用超导重力仪和未来原子重力仪观测出来;在东亚大陆GIA对GRACE监测的等效水柱长期变化的影响为3%~10%,其中青藏高原西部、华北和三峡地区的影响较大.在东海-太平洋区,GIA的相对影响高达20%~40%;GIA使东亚海域绝对海平面以0.27~0.37 mm/a的速率在长期下降,在黄海、东海卫星测高监测的绝对海平面长期变化中,GIA的相对影响分别达6.9%和7.5%;在58个验潮站,平均相对海平面长期上升速率为2.22 mm/a,GIA影响为-0.17 mm/a,其中14个测站GIA的影响达-0.3~-0.4 mm/a.本文GIA预测的结果,对在东亚地区发现弱的地球动力学过程信号、监测水质量长期变化、监测海平面长期变化和分析其机制,提供精密的改正模型.     

Possible effects of lateral viscosity variations induced by plate-tectonic mechanism on geoid inferred from numerical models of mantle convection

In a traditional analytical method, the convective features of Earth’s mantle have been inferred from surface signatures obtained by the geodynamic model only with depth-dependent viscosity structure. The moving and subducting plates, however, bring lateral viscosity variations in the mantle. To clarify the effects of lateral viscosity variations caused by the plate-tectonic mechanism, I have first studied systematically instantaneous dynamic flow calculations using new density-viscosity models only with vertical viscosity variations in a three-dimensional spherical shell. I find that the geoid high arises over subduction zones only when the vertical viscosity contrast between the upper mantle and the lower mantle is O(10³) to O(10⁴), which seems to be much larger than the viscosity contrast suggested by other studies. I next show that this discrepancy may be removed when I consider the lateral viscosity variation caused by the plate-tectonic mechanism using two-dimensional numerical models of mantle convection with self-consistently moving and subducting plates, and suggest that the observed geoid anomaly on the Earth’s surface is significantly affected by plate-tectonic mechanism as a first-order effect.     

A stability analysis of a conduit flow model for lava dome eruptions

Periodic variations in magma discharge rate and ground deformation have been commonly observed during lava dome eruptions. We performed a stability analysis of a conduit flow model by Barmin et al. [Barmin, A., Melnik, O., Sparks, R.S.J., 2002. Periodic behavior in lava dome eruptions. Earth and Planetary Science Letters 199 (1-2), 173–184], in which the periodic variations in magma flow rate and chamber pressure are reproduced as a result of the temporal and spatial changes of the magma viscosity controlled by the kinetics of crystallization. The model is reduced to a dynamical system where the time derivatives of the magma flow rate (dQ/dt) and the chamber pressure (dP/dt) are functions of Q and P evaluated at a shifted time t − t_?. Here, the time delay t_? represents the time for the viscosity of fluid particle to increase in a conduit. The dynamical system with time delay is approximated by a simple two-dimensional dynamical system of Q and P where t_? is given as a parameter. The results of our linear stability analyses for these dynamical systems indicate that the transition from steady to periodic flow depends on nonlinearities in the steady state relation between Q and P. The steady state relation shows a sigmoidal curve in Q − P phase plane; its slope has negative values at intermediate flow rates. The steady state solutions become unstable, and hence P and Q oscillate periodically, when the negative slope of the steady state relation ([dP/dQ]_S) exceeds a critical value; that is [dP/dQ]_S < − t_?γ/(2V_ch), where V_ch is the chamber volume and γ is an elastic constant which is related to the rigidity of chamber wall. We also found that the period and the pattern of oscillation of the conduit flow primarily depend on a quantity defined by LV_ch/r⁴, where L is the conduit length and r is the conduit radius.     

Glacial isostatic adjustment: New developments from advanced observing systems and modeling

The measurement of glacial isostatic adjustment (GIA) is one of the key ways in which geophysicists probe the long-term mantle rheology and Pleistocene ice history. GIA models are also tied to global and regional relative sea-level (RSL) histories, to 20th century tide-gauge (TG) data and to space and terrestrial geodetic measurements. Two new types of observation are related to the high-resolution space–gravity data recovered from the Gravity and Climate Experiment (GRACE) satellite pair and the soon-to-be launched Gravity and Ocean Circulation Experiment (GOCE) with on-board three-component gradiometer. Gravity mapping has the unique capability of isolating those regions that lack isostatic equilibrium. When coupled with other space and terrestrial geodetic measurements, such as those of the Global Positioning System (GPS) networks and with multi-decade terrestrial gravity data, new constraints on GIA are in the offing and should soon illuminate new interpretations of ice-sheet history and mantle response. GIA studies also incorporate space-based altimetry data, which now provide multi-decadal coverage over continents, oceans and lakes. As we are approaching 72 monthly solutions of GRACE gravity coefficients for determining the Earth's secular component of gravity change over the continents, a new issue has surfaced: the problem of relying on interannual hydrological modeling to determine the hydrological contribution to the linear trend in the gravity field. Correctly extracting this contribution is germane to using the GIA-driven component for modeling solid-Earth and paleo-climatic parameters.Seismic and heat-flux-based models of the Earth's interior are emerging with ever higher levels of sophistication regarding material strength (or viscosity). A basic question raised is: how good are traditional Newtonian and non-Newtonian viscosity models that only allow radial variations of Earth parameters? In other words: under what circumstances must this assumption be abandoned for joint interpretations of new and traditional data sets. In this short review we summarize the issues raised in the papers forming this special issue (SI) dedicated to GIA.     

Metamorphic effect on zircon Lu-Hf and U-Pb isotope systems in ultrahigh-pressure eclogite-facies metagranite and metabasite

The Hf isotope composition of original igneous or detrital zircons in high-grade metamorphic rocks can be used to trace protolith origin, but metamorphic effect on the Hf isotope composition of newly grown domains remains to evaluate. We report a detailed in situ combined study of intragrain U-Pb and Lu-Hf isotopes in zircons from granitic gneiss and eclogite in the Dabie orogen of China that experienced ultrahigh-pressure eclogite-facies metamorphism. The results show correlations in ²⁰⁶Pb / ²³⁸U age, initial Hf isotope composition, and Th / U and Lu / Hf ratios between the domains of different origins. The metamorphic domains are characterized by low Th / U and Lu / Hf ratios but high ?_Hf(t) values relative to the igneous core and mantle of pre-metamorphic ages. Positive correlations are observed between Th / U and Lu / Hf ratios, pointing to the similar effect of metamorphism on both U-Th-Pb and Lu-Hf isotope systems. Thus the metamorphic domains are distinguished from the igneous core and mantle by their low Lu / Hf ratios that are less than 0.001 for the granitic gneiss and less than 0.0001 for the eclogite. Despite differences in both protolith age and geochemical source between granitic gneiss and eclogite, rim ?_Hf(t) values are variably 3.1 to 13.5 greater than core ?_Hf(t) values when calculated at timing of protolith formation. This indicates that the zircon overgrowth was associated with a metamorphic medium that has high ¹⁷⁶Hf / ¹⁷⁷Hf but low ¹⁷⁶Lu / ¹⁷⁷Hf ratios. While the metamorphic domains contain more radiogenic Hf isotopes than the original igneous core and mantle, their Lu / Hf ratios are significantly lower than those of core and mantle. Therefore, the metamorphic zircons acquired their initial Hf isotope ratios from metamorphic fluids that have high ¹⁷⁶Hf / ¹⁷⁷Hf ratios but low Lu / Hf ratios with sound variability depending on the Lu-Hf isotope compositions of pre-existing and co-precipitating phases.     

Glacial isostatic adjustment in Fennoscandia from GRACE data and comparison with geodynamical models

The Earth’s gravity field observed by the Gravity Recovery and Climate Experiment (GRACE) satellite mission shows variations due to the integral effect of mass variations in the atmosphere, hydrosphere and geosphere. Several institutions, such as the GeoForschungsZentrum (GFZ) Potsdam, the University of Texas at Austin, Center for Space Research (CSR) and the Jet Propulsion Laboratory (JPL), Pasadena, provide GRACE monthly solutions, which differ slightly due to the application of different reduction models and centre-specific processing schemes. The GRACE data are used to investigate the mass variations in Fennoscandia, an area which is strongly influenced by glacial isostatic adjustment (GIA). Hence the focus is set on the computation of secular trends. Different filters (e.g. isotropic and non-isotropic filters) are discussed for the removal of high frequency noise to permit the extraction of the GIA signal. The resulting GRACE based mass variations are compared to global hydrology models (WGHM, LaDWorld) in order to (a) separate possible hydrological signals and (b) validate the hydrology models with regard to long period and secular components. In addition, a pattern matching algorithm is applied to localise the uplift centre, and finally the GRACE signal is compared with the results from a geodynamical modelling. The GRACE data clearly show temporal gravity variations in Fennoscandia. The secular variations are in good agreement with former studies and other independent data. The uplift centre is located over the Bothnian Bay, and the whole uplift area comprises the Scandinavian Peninsula and Finland. The secular variations derived from the GFZ, CSR and JPL monthly solutions differ up to 20%, which is not statistically significant, and the largest signal of about 1.2 Gal/year is obtained from the GFZ solution. Besides the GIA signal, two peaks with positive trend values of about 0.8 Gal/year exist in central eastern Europe, which are not GIA-induced, and also not explainable by the hydrology models. This may indicate that the recent global hydrology models have to be revised with respect to long period and secular components. Finally, the GRACE uplift signal is also in quite good agreement with the results from a simple geodynamical modelling.     

Body tides on a 3-D elastic earth: Toward a tidal tomography

The deformational and gravitational response of the Earth to the tide generating potential has generally involved 1-D (i.e., depth varying) Earth models. Progressive improvement in observational constraints on body tides, generated from both ground and space-based surveys, suggests that an examination of the potential impact of lateral variations in Earth structure is warranted. We present a suite of predictions of the body tide response within the semi-diurnal, diurnal and long-period tidal bands computed using a finite-volume numerical code. The calculations adopt 3-D density and elastic structure taken from seismic inferences and, in a subset of the calculations, dynamic topography on the surface and internal interfaces. We find that perturbations in the radial displacement and surface gravity within the semi-diurnal band reach ~ 1 mm and 0.15 µgal, respectively. The perturbations in the diurnal band are comparable to these values, and within the long-period band they are a factor of 3–5 smaller. We also demonstrate that lateral variations in the elastic moduli, which have been ignored in recent work, contribute greater than 50% of the total perturbation. The level of perturbation associated with 3-D structure exceeds the current observational uncertainty obtainable using space-geodetic methods, and this suggests the possibility of performing tidal tomographic inversions of such data.     

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.     

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.     

Iron isotope fractionation during planetary differentiation

The Fe isotope composition of samples from the Moon, Mars (SNC meteorites), HED parent body (eucrites), pallasites (metal and silicate) and the Earth's mantle were measured using high mass resolution MC-ICP-MS. These high precision measurements (δ⁵⁶Fe ≈ ± 0.04‰, 2 S.D.) place tight constraints on Fe isotope fractionation during planetary differentiation.Fractionation during planetary core formation is confined to < 0.1‰ for δ⁵⁶Fe by the indistinguishable Fe isotope composition of pallasite bulk metal (including sulfides and phosphides) and olivine separates. However, large isotopic variations (≈ 0.5‰) were observed among pallasite metal separates, varying systematically with the amounts of troilite, schreibersite, kamacite and taenite. Troilite generally has the lightest (δ⁵⁶Fe ≈ − 0.25‰) and schreibersite the heaviest (δ⁵⁶Fe ≈ + 0.2‰) Fe isotope composition. Taenite is heavier then kamacite. Therefore, these variations probably reflect Fe isotope fractionation during the late stage evolution and differentiation of the S- and P-rich metal melts, and during low-temperature kamacite exsolution, rather than fractionation during silicate-metal separation.Differentiation of the silicate portion of planets also seems to fractionate Fe isotopes. Notably, magmatic rocks (partial melts) are systematically isotopically heavier than their mantle protoliths. This is indicated by the mean of 11 terrestrial peridotite samples from different tectonic settings (δ⁵⁶Fe = + 0.015 ± 0.018‰), which is significantly lighter than the mean of terrestrial basalts (δ⁵⁶Fe = + 0.076 ± 0.029‰). We consider the peridotite mean to be the best estimate for the Fe isotope composition of the bulk silicate Earth, and probably also of bulk Earth. The terrestrial basaltic mean is in good agreement with the mean of the lunar samples (δ⁵⁶Fe = + 0.073 ± 0.019‰), excluding the high-Ti basalts. The high-Ti basalts display the heaviest Fe isotope composition of all rocks measured here (δ⁵⁶Fe ≈ + 0.2‰). This is interpreted as a fingerprint of the lunar magma ocean, which produced a very heterogeneous mantle, including the ilmenite-rich source regions of these basalts.Within uncertainties, samples from Mars (SNC meteorites), HED (eucrites) and the pallasites (average olivine + metal) have the same Fe isotope compositions as the Earth's mantle. This indicates that the solar system is very homogeneous in Fe isotopes. Its average δ⁵⁶Fe is very close to that of the IRMM-014 standard.     

Effect of lateral viscosity variations in the core-mantle boundary region on predictions of the long-wavelength geoid

Seismic studies of the lowermost mantle suggest that the core-mantle boundary (CMB) region is strongly laterally heterogeneous over both local and global scales. These heterogeneities are likely to be associated with significant lateral viscosity variations that may influence the shape of the long-wavelength non-hydrostatic geoid. In the present paper we investigate the effect of these lateral viscosity variations on the solution of the inverse problem known as the inferences of viscosity from the geoid. We find that the presence of lateral viscosity variations in the CMB region can significantly improve the percentage fit of the predicted data with observations (from 42 to 70% in case of free-air gravity) while the basic characterisics of the mantle viscosity model, namely the viscosity increase with depth and the rate of layering, remain more or less the same as in the case of the best-fitting radially symmetric viscosity models. Assuming that viscosity is laterally dependent in the CMB region, and radially dependent elsewhere, we determine the largescale features of the viscosity structure in the lowermost mantle. The viscosity pattern found for the CMB region shows a high density of hotspots above the regions of higher-than-average viscosity. This result suggests an important role for petrological heterogeneities in the lowermost mantle, potentially associated with a post-perovskite phase transition. Another potential interpretation is that the lateral viscosity variations derived for the CMB region correspond in reality to lateral variations in the mechanical conditions at the CMB boundary or to large-scale undulations of a chemically distinct layer at the lowermost mantle.