Viscosity Structure Research Articles

Instantaneous dynamics of the cratonic Congo basin

Understanding the formation mechanisms of cratonic basins provides an examination of the rheological, compositional and thermal properties of continental cratons. However, these mechanisms are poorly understood because there are few currently active cratonic basins. One cratonic basin thought to be active is the Congo basin located in equatorial Africa. The Congo basin is coincident with a large negative free‐air gravity anomaly, an anomalous topographic depression, and a large positive upper mantle shear wave velocity anomaly. Localized admittance models show that the gravity anomaly cannot be explained by a flexural support of the topographic depression at the Congo. We analyze these data and show that they can be explained by the depression of the Congo basin by the action of a downward dynamic force on the lithosphere resulting from a high‐density object within the lithosphere. We formulate instantaneous dynamic models describing the action of this force on the lithosphere. These models show that the gravity and topography of the Congo basin are explained by viscous support of an anomalously dense region located at 100 km depth within the lithosphere. The density anomaly has a magnitude within the range of 27–60 kg m−3 and is most likely compositional in origin. Our models do not provide a constraint on the lithospheric viscosity of the Congo craton because the shallow location of the anomaly ensures strong coupling of the anomaly to the surface regardless of viscosity structure.

Adjoint models of mantle convection with seismic, plate motion, and stratigraphic constraints: North America since the Late Cretaceous

We apply adjoint models of mantle convection to North America since the Late Cretaceous. The present‐day mantle structure is constrained by seismic tomography and the time‐dependent evolution by plate motions and stratigraphic data (paleoshorelines, borehole tectonic subsidence, and sediment isopachs). We infer values of average upper and lower mantle viscosities, provide a synthesis of North American vertical motions (relative sea level) from the Late Cretaceous to the present, and reconstruct the geometry of the Farallon slab back to the Late Cretaceous. In order to fit Late Cretaceous marine inundation and borehole subsidence, the adjoint model requires a viscosity ratio across 660 km discontinuity of 15:1 (reference viscosity of 1021 Pa s), which is consistent with values previously inferred by postglacial rebound studies. The dynamic topography associated with subduction of the Farallon slab is localized in western North America over Late Cretaceous, representing the primary factor controlling the widespread flooding. The east coast of the United States is not stable; rather, it has been experiencing continuous dynamic subsidence over the Cenozoic, coincident with an overall eustatic fall, explaining a discrepancy between sea level derived from the New Jersey coastal plain and global curves. The east coast subsidence further constrains the mantle viscosity structure and requires an uppermost mantle viscosity of 1020 Pa s. Imposed constraints require that the Farallon slab was flat lying during Late Cretaceous, with an extensive zone of shallow dipping Farallon subduction extending beyond the flat‐lying slab farther east and north by up to 1000 km than previously suggested.

Modeling petrological geodynamics in the Earth's mantle

We have developed an approach that combines principles of fluid dynamics and chemical thermodynamics into a fully coupled scheme to model geodynamic and petrological evolution of the Earth's mantle. Transport equations involving pressure, temperature, velocities, and bulk chemical composition are solved for one or more dynamic phases and interfaced with the thermodynamic solutions for equilibrium mineralogical assemblages and compositions. The mineralogical assemblage and composition are computed on a space‐time grid, assuming that local thermodynamic equilibrium is effectively achieved. This approach allows us to simultaneously compute geophysical, geochemical, and petrological properties that can be compared with a large mass of observational data to gain insights into a variety of solid Earth problems and melting phenomena. We describe the salient features of our numerical scheme and the underlying mathematical principles and discuss a few selected applications to petrological and geophysical problems. First, it is shown that during the initial stage of passive spreading of plates, the composition of the melt near Earth's surface is in reasonable agreement with the average major element composition of worldwide flood basalts. Only the silica content from our model is slightly higher that in observational data. The amount of melt produced is somewhat lower than the estimated volumes for extrusive and upper crustal intrusive igneous rocks from large igneous provinces suggesting that an active upwelling of a larger mantle region should be considered in the process. Second, we have modeled a plume upwelling under a moving plate incorporating the effects of mineralogy on the density structure and viscous dissipation on the heat transport equation. The results show how these effects promote mantle instability at the base of the lithosphere. Third, we have considered a mantle convection model with viscosity and density directly related to the local equilibrium mineralogical assemblage. Interesting lateral variations and significant differences in the viscosity structure of the upper and lower mantle are revealed from our model results. The averaged viscosity variations with depth retrieved from our numerical simulations seem to reproduce the main features of the mantle viscosity structure under the Pacific ocean obtained from recent studies based on inversion of seismic data.

Does the mantle control the maximum thickness of cratons?

Geochemical observations suggest that cratonic xenoliths originate from depths no greater than 250 km, which implies a maximum craton thickness. What determines this thickness? In general, the stability and longevity of cratons depend on their ability to resist deforming forces exerted from below by the flowing, evolving mantle. We employ an analytical approach to relate the lithospheric viscosity structure of a craton to shear tractions exerted by asthenospheric shear flow. As the net thickness of the chemical and thermal components of a craton increases, these tractions increase dramatically for non-Newtonian rheology and begin to deform the cratonic base. Thus, overly thick lithosphere is subjected to large basal stresses that weaken the thermal boundary layer and diminish its ability to buffer the craton from destructive mantle flow. This feedback prevents cratonic lithosphere from growing thicker than a maximum value. However, we show that this maximum thickness increases slightly with increasing vigor of mantle convection but decreases rapidly as convective vigor decreases. Thus, we predict relative stability of cratonic thickness during most of Earth's history but instability in the future.

Subduction adjacent to deep continental roots: Enhanced negative pressure in the mantle wedge, mountain building and continental motion

Subduction near to a deep continental root is modeled with finite elements. The root restricts asthenospheric corner flow, which increases mantle-wedge suction. The suction pulls the continental root toward the subduction zone, simultaneously promoting trenchward continental motion and compressive tectonics in the lithosphere between the root and the subduction zone. In a 2-D model with a root that extends to 250 km depth and lies 300 km from the mantle-wedge corner, we find two-fold increase in mantle-wedge suction and nearly a four-fold increase in continental compression (to 5 × 10 12 N/m) compared to a rootless reference model. In 3-D modeling, we find that distance to the subduction zone is more important than root width (in subduction strike direction) or reasonable variations in sub-lithospheric viscosity structure, with the root-enhanced suction effects diminishing rapidly as the wedge corner-root distance increases beyond 400 km. When finite-width roots are wider than the distance to the mantle-wedge corner and closer than 400 km, compression of the continent between the root and the subduction zone is > 50% that found in the infinite-width root.

Southern San Andreas‐San Jacinto fault system slip rates estimated from earthquake cycle models constrained by GPS and interferometric synthetic aperture radar observations

We use ground geodetic and interferometric synthetic aperture radar satellite observations across the southern San Andreas (SAF)‐San Jacinto (SJF) fault systems to constrain their slip rates and the viscosity structure of the lower crust and upper mantle on the basis of periodic earthquake cycle, Maxwell viscoelastic, finite element models. Key questions for this system are the SAF and SJF slip rates, the slip partitioning between the two main branches of the SJF, and the dip of the SAF. The best‐fitting models generally have a high‐viscosity lower crust (η = 1021 Pa s) overlying a lower‐viscosity upper mantle (η = 1019 Pa s). We find considerable trade‐offs between the relative time into the current earthquake cycle of the San Jacinto fault and the upper mantle viscosity. With reasonable assumptions for the relative time in the earthquake cycle, the partition of slip is fairly robust at around 24–26 mm/a for the San Jacinto fault system and 16–18 mm/a for the San Andreas fault. Models for two subprofiles across the SAF‐SJF systems suggest that slip may transfer from the western (Coyote Creek) branch to the eastern (Clark‐Superstition hills) branch of the SJF from NW to SE. Across the entire system our best‐fitting model gives slip rates of 2 ± 3, 12 ± 9, 12 ± 9, and 17 ± 3 mm/a for the Elsinore, Coyote Creek, Clark, and San Andreas faults, respectively, where the large uncertainties in the slip rates for the SJF branches reflect the large uncertainty in the slip rate partitioning within the SJF system.

Relating viscosities from postseismic relaxation to a realistic viscosity structure for the lithosphere

SUMMARY Models of geodetic observations of postseismic relaxation most often represent the lithosphere with only a few layers with constant viscosity. This is surpr ising, because rock mechanical experiments consistently demonstrate that we should expect a profound vertical gradient in lithospheric viscosities, due to the geothermal gradient i n this thermal boundary layer. We isolate the effect of lower crustal flow, where the effect of visc osity gradients has the largest impact on surface deformation. We therefore explore postseismic deformation in models with realistic vertical viscosity gradients, and seek to illustrate th e differences between these models and those with idealized uniform viscosity layers. By means of synthetic experiments with a semianalytical viscoelastic relaxation model, we show how, for a given earthquake, the averaged viscosity value obtained for a thick viscoelastic layer is d ependent on both the layout of the geodetic network and on the observation time window.

Long-term true polar wander of the Earth including the effects of convective processes in the mantle and continental drift

SUMMARY Long-term true polar wander (TPW) of the Earth was examined by taking into account the effects of simplified convective processes in the Earth’s mantle and continental drift. The TPW, for a given viscoelastic earth model, is wholly determined by both the magnitude of non-forcing elements of moment of inertia (I 11, I 22 and I 33) and I 12 element of product of inertia, and the rates for forcing elements, dI 13/dt and dI 23/dt. The forcing rates are largely related to time-dependent convective processes in the mantle and also continental drift. In this study, I examined the TPW on a convecting mantle with oscillating moments of inertia, inferred from a convective process of alternating degree-one and degree-two structure changes of mantle convection by Zhongetal. (2007). In the phase for a relatively hydrostatic Earth, corresponding to largely degree-one planform, the predicted TPW is sensitive to the viscosity structure of the mantle, particularly to the lithospheric viscosity structure, and its magnitude may be larger than ∼30 ◦ even for the forcing rates with ∼10 30 kg m 2 Myr −1 related to continental drift (Dickman 1979). In the phase for a non-hydrostatic Earth characterized by largely degree-two planform such as for the present-day, however, the TPW is less sensitive to the viscosity structure, and its magnitude may be ∼10 ◦ at most. These results may provide quantitative constraints on examining relationship between rheological structure and convective processes in the mantle, continental drift and TPW.

The Effect of Weight Fraction of H-PDMS on the Latex Membrane and the Stability of Composite Emulsion of H-PDMS/Acrylate

High hydrogen-containing polymethylsiloxane(H-PDMS)/polyacrylate composite emulsion was synthesized by a drop-adding method for monomer emulsion. The effects of weight fraction of H-PDMS on the stability of composite emulsion, water resistance and heat-aging resistance of the latex membrane have been investigated. The TEM demonstrated that latex particles are a core-shell structure. By analyzing the spectrums of FTIR and 1H-NMR, it can be indicated that H-PDMS had reacted with acrylate monomer resulting chemical bond formation. The core-shell structure and chemical bond play an important role to restrain phase separation of composite emulsion and enhance the stability of the emulsion. By analyzing the surface tension, apparent viscosity and morphological structure, the results showed that the stable composite emulsion system can be obtained in which the average latex particle size was smaller than 90 nm when weight fraction of H-PDMS is below 16% (based on the weight of acrylate monomer), the stable emulsion system can be obtained in which the average latex particle size becomes larger than 90 nm when the weight fraction of H-PDMS is above 20% of the acrylate monomer. The DSC demonstrated that the Tg of pure polyacrylate is 49°C, and there is only one Tg (35°C) when the weight fraction of H-PDMS is 13%, but there are two Tg (15°C and 25°C) when the weight fraction of H-PDMS is 16%. In addition, the water resistance and heat-aging resistance of composite latex membrane enhanced gradually with the increase of amount of H-PDMS.

Water in minerals of the continental lithospheric mantle and overlying lower crust: A comparative study of peridotite and granulite xenoliths from the North China Craton

Water contents of clinopyroxene, orthopyroxene and olivine in mantle peridotite xenoliths from the Hannuoba and Nushan basaltic volcanoes (North China Craton) were determined by Fourier transform infrared spectroscopy (FTIR). Results show that contents vary from 50 to 155 ppm (H 2O wt.) for clinopyroxene and from 20 to 55 ppm for orthopyroxene in Hannuoba peridotites, and from 5 to 355 ppm for clinopyroxene and from 5 to 140 ppm for orthopyroxene in Nushan peridotites. Water contents in clinopyroxene and orthopyroxene define a good positive correlation with a ratio of ~ 2.1. This, together with the roughly homogeneous distribution of hydrogen from core to rim region in pyroxene grains, suggests that they have preserved the initial water content of the mantle source. By contrast, olivine in these peridotites contain very little, if any, water, which were probably caused by significant loss of H during their ascent due to the faster H diffusion in olivine relative to pyroxenes and by the relatively lower water content in the mantle source of Hannuoba and Nushan. Previous studies [Xia, Q.K., Yang, X.Z., Deloule, E., Sheng, Y.M., Hao, Y.T., 2006. Water in the lower crustal granulite xenoliths from Nushan, eastern China. Journal of Geophysical Research, 111(B11202) doi:10.1029/2006JB004296; Yang, X.Z., Deloule, E., Xia, Q.K., Fan, Q.C., Feng, M., in press. Water contrast between Precambrian and Phanerozoic continental lower crust of eastern China. Journal of Geophysical Research doi:10.1029/2007JB005541] have shown that the water content ranges from 275 to 720 ppm for clinopyroxene, from 60 to 185 ppm for orthopyroxene and from 65 to 205 ppm for plagioclase in Hannuoba mafic granulite xenoliths, and from 200 to 2330 ppm for clinopyroxene, from 140 to 1270 ppm for orthopyroxene and from 145 to 900 ppm in plagioclase in Nushan mafic granulite xenoliths. The significant difference between the water content of peridotite and that of coexisting mafic granulite xenoliths, e.g. 0–100 ppm (mostly < 50 ppm) vs. 100–1000 ppm (mostly > 200 ppm) for the estimated bulk concentration, demonstrates that the distribution of water in the deep continental lithosphere is vertically heterogeneous. This may be due to the different genesis of peridotites and granulites (the residue of partial melting vs. the product of melt crystallization). Based on these water data, we define the rheological structure of the lowermost crust and uppermost mantle below the Hannuoba and Nushan regions. The viscosity (strength) of the underlying shallow mantle is similar, whereas the deep crust is relatively stronger at Hannuoba and weaker at Nushan. Difference in the viscosity structure may further influence the dynamical processes between different zones in this craton.

Relation of Viscosity and Inner Structure of Suspension under Magnetic Field

When an external magnetic field was applied on the suspension composed of ferromagnetic Ni and nonmagnetic ZrO_2 particles,the viscosity of the suspension increased drastically.The relation of viscosity and inner structure of suspension was investigated by using magnetic coils,rotational vis- cometer and optical microscope.The results show that the viscosity increases with the magnetic field strength and Ni content increasing because of the formation of chain-like clusters in the suspension. As the magnetic field increases,Ni clusters become larger,which hinders the free move of particles,so the viscosity increases.Similarly,Ni clusters in the suspension increase with Ni content increasing,and hence the viscosity increases.

Viscous Relaxation and Early Planetary Evolution

Through observation and modeling, a great deal has been learned about the viscosity structure of the Earth and its influence on such processes as plate tectonics, mantle convection, postglacial rebound, and continental uplift. In particular, it has been shown that where the crust is unusually thick and/or warm, the lower crust is able to flow to relax stresses produced by crustal thickness variations and crustal extension or shortening [e.g., McKenzie et al., 2000]. Viscous relaxation models have been applied to other planets since the 1960s, and the results show that some large impact basins may have formed in the presence of a warm, ductile lower crust [e.g., Solomon et al., 1982].

Plate motions and the viscosity structure of the mantle — Insights from numerical modelling

The viscosity structure of the Earth's mantle is likely to play an important role with respect to the motion of the lithospheric plates. A zone of low viscosity in the upper mantle, as postulated by seismological studies and also by investigations of postglacial uplift, has been proposed to facilitate plate motion. Another inferred feature of the viscosity profile in the mantle is a significant increase at greater depth. We have employed a three-dimensional mantle convection model to explore the relation between the appearance of plate motion and the viscosity structure of the mantle beneath. The model allows for a complex fluid rheology (strong temperature, pressure and stress dependence of the viscosity) and can so account for the self-consistent formation of plates at the surface of the convecting mantle. Plate-like motion appears only in a limited parameter range, and we demonstrate that this appearance is closely linked to a specific viscosity structure. The viscosity is characterized by a local minimum at shallow depth (low viscosity zone) and by a local maximum at greater depth. Self-consistent plate motion is only observed if such a viscosity structure exists. In order to determine the functional relationship between the viscosity structure and plate motion, we also employ an approach, in which a certain viscosity profile is prescribed. These studies again reveal the importance of the local extrema in the viscosity profile. Taking into account an increased interior viscosity (also obtained by the pressure dependence), we find stable plate motion. As a general result we observe that the balance of the temperature and stress dependence of the viscosity is necessary to obtain plate motion. At the same time we find a viscosity profile showing a minimum at shallow depth and a maximum at greater depth.

Influence of temperature- and depth-dependent viscosity structures on postseismic deformation predictions for the large 1946 Nankai subduction zone earthquake

To investigate the influence of spatial change of viscosity on postseismic deformation associated with the interplate 1946 Nankai earthquake (M 8.0) at the Nankai Trough, southwest Japan, we newly constructed a realistic viscoelastic structure model, taking into account temperature- and depth-dependent viscosity of materials. For this purpose, we first compiled leveling and triangulation data during postseismic periods and clarified characteristics of the amount and spatial patterns of postseismic vertical displacement and principal strain fields. Then, we calculated the spatial distributions of viscosity from temperature and flow fields, which were obtained from 2D subduction models. By incorporating the obtained viscosity structure into 3D viscoelastic finite element models, we constructed a temperature- and depth-dependent viscosity structure model (MODEL P2). Based on MODEL P2, we constructed a viscoelastic structure model, taking into account Poisson's ratio for the oceanic plate and low-velocity regions and the existence of low-viscosity materials beneath the Shikoku and Chugoku districts (MODEL P3), which were revealed from seismic tomography. We also constructed a conventional layered viscoelastic structure model (MODEL L1) and plate subduction model (MODEL P1) with constant viscosity for each region and evaluated the effects of different viscoelastic structures on postseismic surface deformations, using the coseismic slip distribution obtained by inversion analyses of geodetic data. We also compared the calculated surface deformations with the observed postseismic crustal deformations in and around Shikoku. The results show that postseismic surface deformation fields for the newly constructed MODEL P2 are rather different from those for MODELs L1 and P1. Landward horizontal displacements for MODEL P2 are smaller than those for MODELs L1 and P1, seaward horizontal displacements are negligible, and vertical displacement is characterized by small subsidence over Shikoku. The postseismic horizontal principal strain field for MODEL P2 is characterized by contractions in the N–S to NW–SE directions at amounts smaller than those for MODELs L1 and P1. Postseismic surface deformations for MODEL P3 are almost the same as those for MODEL P2. The observed postseismic vertical displacement and horizontal principal strain fields could not be explained by the viscoelastic response for the realistic viscoelastic structure models P2 and P3. This indicates that the effects of elastic and viscoelastic responses due to interplate coupling on the plate interface, after-slip at the extension of the coseismic slipped region, and poroelasticity should be taken into account to precisely estimate postseismic surface deformation. This also suggests that, in order to evaluate postseismic crustal deformations derived from a large interplate subduction zone earthquake, it is essential to use realistic temperature- and depth-dependent viscoelastic structure models.

Three-dimensional mechanical modeling of large-scale crustal deformation in China constrained by the GPS velocity field

We present a quantitative model for the crustal movement in China with respect to the Eurasia plate by using the three-dimensional finite element code ADELI. The model consists of an elastoplastic upper lithosphere and a viscoelastic lower lithosphere. The lithosphere is supported by the hydrostatic pressure at its base. The India–Eurasia collision is modeled as a velocity boundary condition. Ten large-scale faults are introduced as Coulomb-type frictional zones in the modeling. The values for the root mean square (RMS) of the east and north velocity components differences (RMS(Ue) and RMS(Un)), which are between the observation and the prediction, are regarded as the measurements to evaluate our simulations. We model the long-term crustal deformation in China by adjusting the faults frictions ranged from 0.01 to 0.5 and considering the effects resulted from lithospheric viscosity variation and topographic loading. Our results suggest most of the large-scale faults frictions are not larger than 0.1, which is consistent with other large-scale faults such as the North Anatolian fault (Provost, A.S., Chery, J., Hassani, R., 2003. Three-dimensional mechanical modeling of the GPS velocity field along the North Anatolian fault. Earth Planet. Sci. Lett. 209, 361–377) and the San Andreas fault (Mount, V.S., Suppe, J., 1987. State of stress near the San Andreas fault: implications for wrench tectonics. Geology, 15, 1143–1146). Further, we examine the effects on the long-term crustal deformation in China of three causes: the large-scale faults, lithospheric viscosity structure and topographic loading. Results indicate that the lithospheric viscosity structure and the topographic loading have important influences on the crustal deformation in China, while the influences caused by the large-scale faults are small. Although our simulations satisfactorily reproduce the general picture of crustal movement in China, there is a poor agreement between the model and the observed GPS velocity field in Sichuan–Yunnan area. It may result from our simple models such as that the faults are all vertical from model surface to bottom and that the effects caused by the subduction of Burma slab are neglected.

Holocene relative sea-level change, isostatic subsidence and the radial viscosity structure of the mantle of northwest Europe (Belgium, the Netherlands, Germany, southern North Sea)

A comprehensive observational database of Holocene relative sea-level (RSL) index points from northwest Europe (Belgium, the Netherlands, northwest Germany, southern North Sea) has been compiled in order to compare and reassess the data collected from the different countries/regions and by different workers on a common time–depth scale. RSL rise varies in magnitude and form between these regions, revealing a complex pattern of differential crustal movement which cannot be solely attributed to tectonic activity. It clearly contains a non-linear, glacio- and/or hydro-isostatic subsidence component, which is only small on the Belgian coastal plain but increases significantly to a value of ca 7.5m relative to Belgium since 8cal.kaBP along the northwest German coast. The subsidence is at least in part related to the Post-Glacial collapse of the so-called peripheral forebulge which developed around the Fennoscandian centre of ice loading during the Last Glacial Maximum. The RSL data have been compared to geodynamic Earth models in order to infer the radial viscosity structure of the Earth's mantle underneath NW Europe (lithosphere thickness, upper- and lower-mantle viscosity), and conversely to predict RSL in regions where we have only few observational data (e.g. in the southern North Sea). A very broad range of Earth parameters fit the Belgian RSL data, suggesting that glacial isostatic adjustment (GIA) only had a minor effect on Belgian crustal dynamics during and after the Last Ice Age. In contrast, a narrow range of Earth parameters define the southern North Sea region, reflecting the greater influence of GIA on these deeper/older samples. Modelled RSL data suggest that the zone of maximum forebulge subsidence runs in a relatively narrow, WNW–ESE trending band connecting the German federal state of Lower Saxony with the Dogger Bank area in the southern North Sea. Identification of the effects of local-scale factors such as past changes in tidal range or tectonic activity on the spatial and temporal variations of sea-level index points based on model-data comparisons is possible but is still complicated by the relatively large range of Earth model parameters fitting each RSL curve, emphasising the need for more high-quality observational data.

Postglacial relative sea‐level observations from Ireland and their role in glacial rebound modelling

AbstractThe British Isles have been the focus of a number of recent modelling studies owing to the existence of a high‐quality sea‐level dataset for this region and the suitability of these data for constraining shallow earth viscosity structure, local to regional ice sheet histories and the magnitude/timing of global meltwater signals. Until recently, the paucity of both glaciological and relative sea‐level (RSL) data from Ireland has meant that the majority of these glacial isostatic adjustment (GIA) modelling studies of the British Isles region have tended to concentrate on reconstructing ice cover over Britain. However, the recent development of a sea‐level database for Ireland along with emergence of new glaciological data on the spatial extent, thickness and deglacial chronology of the Irish Ice Sheet means it is now possible to revisit this region of the British Isles. Here, we employ these new data to constrain the evolution of the Irish Ice Sheet. We find that in order to reconcile differences between model predictions and RSL evidence, a thick, spatially extensive ice sheet of ∼600–700 m over much of north and central Ireland is required at the LGM with very rapid deglaciation after 21 k cal. yr BP. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Inference of mantle viscosity from GRACE and relative sea level data

SUMMARY Gravity Recovery And Climate Experiment (GRACE) satellite observations of secular changes in gravity near Hudson Bay, and geological measurements of relative sea level (RSL) changes over the last 10 000 yr in the same region, are used in a Monte Carlo inversion to infer-mantle viscosity structure. The GRACE secular change in gravity shows a significant positive anomaly over a broad region (>3000 km) near Hudson Bay with a maximum of ∼2.5 μGal yr−1 slightly west of Hudson Bay. The pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ICE-5G deglaciation history, strongly suggesting a postglacial rebound origin for the gravity change. We find that the GRACE and RSL data are insensitive to mantle viscosity below 1800 km depth, a conclusion similar to that from previous studies that used only RSL data. For a mantle with homogeneous viscosity, the GRACE and RSL data require a viscosity between 1.4 × 1021 and 2.3 × 1021 Pa s. An inversion for two mantle viscosity layers separated at a depth of 670 km, shows an ensemble of viscosity structures compatible with the data. While the lowest misfit occurs for upper- and lower-mantle viscosities of 5.3 × 1020 and 2.3 × 1021 Pa s, respectively, a weaker upper mantle may be compensated by a stronger lower mantle, such that there exist other models that also provide a reasonable fit to the data. We find that the GRACE and RSL data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle.

Supercontinent cycles, true polar wander, and very long-wavelength mantle convection

We show in this paper that mobile-lid mantle convection in a three-dimensional spherical shell with observationally constrained mantle viscosity structure, and realistic convective vigor and internal heating rate is characterized by either a spherical harmonic degree-1 planform with a major upwelling in one hemisphere and a major downwelling in the other hemisphere when continents are absent, or a degree-2 planform with two antipodal major upwellings when a supercontinent is present. We propose that due to modulation of continents, these two modes of mantle convection alternate within the Earth's mantle, causing the cyclic processes of assembly and breakup of supercontinents including Rodinia and Pangea in the last 1 Ga. Our model suggests that the largely degree-2 structure for the present-day mantle with the Africa and Pacific antipodal superplumes, is a natural consequence of this dynamic process of very long-wavelength mantle convection interacting with supercontinent Pangea. Our model explains the basic features of true polar wander (TPW) events for Rodinia and Pangea including their equatorial locations and large variability of TPW inferred from paleomagnetic studies. Our model also suggests that TPW is expected to be more variable and large during supercontinent assembly, but small after a supercontinent acquires its equatorial location and during its subsequent dispersal.

Glacio‐isostatic deformation around the Vatnajökull ice cap, Iceland, induced by recent climate warming: GPS observations and finite element modeling

Glaciers in Iceland began retreating around 1890, and since then the Vatnajökull ice cap has lost over 400 km3 of ice. The associated unloading of the crust induces a glacio‐isostatic response. From 1996 to 2004 a GPS network was measured around the southern edge of Vatnajökull. These measurements, together with more extended time series at several other GPS sites, indicate vertical velocities around the ice cap ranging from 9 to 25 mm/yr, and horizontal velocities in the range 3 to 4 mm/yr. The vertical velocities have been modeled using the finite element method (FEM) in order to constrain the viscosity structure beneath Vatnajökull. We use an axisymmetric Earth model with an elastic plate over a uniform viscoelastic half‐space. The observations are consistent with predictions based on an Earth model made up of an elastic plate with a thickness of 10–20 km and an underlying viscosity in the range 4–10 × 1018 Pa s. Knowledge of the Earth structure allows us to predict uplift around Vatnajökull in the next decades. According to our estimates of the rheological parameters, and assuming that ice thinning will continue at a similar rate during this century (about 4 km3/year), a minimum uplift of 2.5 meters between 2000 to 2100 is expected near the current ice cap edge. If the thinning rates were to double in response to global warming (about 8 km3/year), then the minimum uplift between 2000 to 2100 near the current ice cap edge is expected to be 3.7 meters.