Postglacial Rebound Studies Research Articles

Convection of a fluid with strongly temperature and pressure dependent viscosity

Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection.

Viscosity undulations in the lower mantle: The dynamical role of iron spin transition

A proper determination of the lower-mantle viscosity profile is fundamental to understanding Earth geodynamics. Based on results coming from different sources, several models have been proposed to constrain the variations of viscosity as a function of pressure, stress and temperature. While some models have proposed a relatively modest viscosity variation across the lower mantle, others have proposed variations of several orders of magnitude. Here, we have determined the viscosity of ferropericlase, a major mantle mineral, and explored the role of the iron high-to-low spin transition. Viscosity was described within the elastic strain energy model, in which the activation parameters are obtained from the bulk and shear wave velocities. Those velocities were computed combining first principles total energy calculations and the quasi-harmonic approximation. As a result of a strong elasticity softening across the spin transition, there is a large reduction in the activation free energies of the materials creep properties, leading to viscosity undulations. These results suggest that the variations of the viscosity across the lower mantle, resulting from geoid inversion and postglacial rebound studies, may be caused by the iron spin transition in mantle minerals. Implications of the undulated lower mantle viscosity profile exist for both, down- and up-wellings in the mantle. We find that a viscosity profile characterized by an activation free energy of G⁎(z0)∼300–400 kJ/mol based on diffusion creep and dilation factor δ=0.5 better fits the observed high velocity layer at mid mantle depths, which can be explained by the stagnation and mixing of mantle material. Our model also accounts for the growth of mantle plume heads up to the size necessary to explain the Large Igneous Provinces that characterize the start of most plume tracks.

Using the Nordic Geodetic Observing System for land uplift studies

Abstract. Geodetic observing systems have been planned and developed during the last decade. An ideal observing system consists of a network of geodetic observing stations with several techniques at the same site, publicly accessible databases, and as a product delivers data time series, combination of techniques or some other results obtained from the data sets. Globally, there is the International Association of Geodesy (IAG) Global Geodetic Observing System (GGOS), and there are ongoing attempts to create also regional observing systems. In this paper we introduce one regional system, the Nordic Geodetic Observing System (NGOS) hosted by the Nordic Geodetic Commission (NKG). Data availability and accessibility are one of the major issues today. We discuss in general data-related topics, and introduce a pilot database project of NGOS. As a demonstration of the use of such a database, we apply it for postglacial rebound studies in the Fennoscandian area. We compare land uplift values from three techniques, GNSS, tide gauges and absolute gravity, with the Nordic Geodetic Commission NKG2005LU land uplift model for Fennoscandia. The purpose is to evaluate the data obtained from different techniques and different sources and get the most reliable values for the uplift using publicly available data. The primary aim of observing systems will be to produce data and other products needed by multidisciplinary projects, such as Upper Mantle Dynamics and Quaternary Climate in Cratonic Areas (DynaQlim) or the European Plate Observing System (EPOS), but their needs may currently exceed the scope of an existing observing system. We discuss what requirements the projects pose to observing systems and their development. To make comparisons between different studies possible and reliable, the researcher should document what they have in detail, either in appendixes, supplementary material or some other available format.

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.

Ice-ocean mass balance during the Late Pleistocene glacial cycles in view of CHAMP and GRACE satellite missions

During the last glacial cycles, global sea level dropped several times by about 120 m and large ice sheets covered North America, northern Europe and Antarctica during the glacial stages. The changes in the ice–ocean mass balance have displaced mantle material mainly via viscous flow, and the perturbation of the equilibrium figure of the Earth by glacial isostatic adjustment is still observable today in time-dependent changes of gravitational and rotational observations. Contemporary ice–ocean mass balance from volume changes of polar ice caps also contributes to secular variations of the Earth’s gravitational field. In the near future, several satellite gravity missions will significantly improve the accuracy of the observed time-dependent gravitational field. In view of the expected improvements in the observations, we predict glacially induced perturbations of the gravitational field, induced by Late Pleistocene and contemporary ice volume changes, for a variety of radial mantle viscosity profiles. We assess the degree of uncertainty for the glacially induced contributions to gravitational and rotational parameters, both in the spectral and the spatial domain. Predictions of power spectra for the glacially induced free-air gravity and geoid anomalies are about one order of magnitude lower than the observed values, and uncertainties arising from different plausible viscosity profiles are around 0.15–0.4 mGal and 0.2–1.5 m, respectively. Uncertainties from different ice models are of secondary importance for the predicted power spectra. Predicted secular changes in geoid anomalies in formerly glaciated areas are mainly controlled by the viscosity profile and contemporary ice volume changes. We also show that the simple three-layer viscosity profiles currently employed for the majority of postglacial rebound studies represent a limited subset for model predictions of the time-dependent gravitational field.

Postglacial rebound at the northern Cascadia subduction zone

Postglacial rebound is the response of the Earth to the decay of ice-sheets. A postglacial rebound model explains crustal tilting and rapid uplift at the northern Cascadia subduction zone that occurred during retreat of the Cordilleran ice-sheet. Observations explained by the model include the shoreline tilts of two proglacial lakes that formed at 13.5–14 ka ( 14 C yr ago) and rapid sea level fall (land uplift) at 12–12.5 ka. Modelled mantle viscosity values range from 5×10 18 to 5×10 19 Pa s, and are consistent with previous viscosity inferences from observations of crustal deformation following subduction zone earthquakes (10 18–10 19 Pa s). No lower limit to subduction zone mantle viscosity is apparent from our model, but viscosity values equal to or larger than 10 20 Pa s are definitely ruled out. Our modelled subduction zone viscosity values are smaller than most upper-mantle viscosity estimates derived from postglacial rebound studies of tectonically less-active regions (10 20–10 21 Pa s). The rapid observed uplift at 12 ka requires, in addition to a low mantle viscosity, rapid unloading from a sudden collapse of remaining coastal portions of the southern Cordilleran ice-sheet. The sudden collapse provides 0.18 m of global eustatic sea level rise, approximately 0.7% of the sea level rise associated with melt-water pulse IA. Predictions of a global postglacial rebound model (ICE-3G) with a 10 21 Pa s upper-mantle viscosity were previously applied to geodetic data from this region to isolate signals associated with the earthquake cycle. Owing to the low-viscosity values, and resulting rapid recovery of glacial deformation, our model predicts present-day postglacial rebound uplift rates at least 10 times smaller than ICE-3G (less than about 0.1 mm/yr). As the ICE-3G adjustments were substantial, this indicates the need for re-evaluation of the geodetic data.

Global surface heat flux anomalies from seismic tomography‐based models of mantle flow: Implications for mantle convection

We investigate the very long‐wavelength, global pattern of surface heat flux anomalies within the context of whole‐mantle and layered‐mantle anelastically compressible internal loading theories. Since the internal loading framework does not yield a direct estimate of the geotherm, we argue that accurate predictions for the surface heat flux may nevertheless be obtained by assuming that it is linearly related to the radial component of flow velocity at shallow depth in the mantle. The mantle convective circulation is assumed to be driven by density heterogeneity inferred from global seismic tomography models. Best results for the pattern of surface heat flux anomalies are obtained for models that significantly impede the circulation at a depth of 670 km. Total variance reductions of 60–65% (degree 1–5) are obtained when the viscosity profile includes a low‐viscosity asthenosphere. Within the context of our modeling assumptions, however, whole‐mantle circulation models provide best descriptions of the long‐wavelength nonhydrostatic gravity data. In order to resolve the gravity‐heat flux impasse that is revealed herein, we consider the possibility of modifying the a priori global seismic models employed in the calculations. We show that the rigidly layered‐mantle internal loading theory is equivalent to a theory in which no explicit flow‐blocking boundary condition is imposed at 670 km but in which the buoyancy field inferred from the a priori tomographic model is supplemented by flow‐blocking heterogeneity in the form of an appropriately constrained sheet mass load. We develop a general mathematical formalism describing how the introduction of appropriately constrained sheet mass loads allows the exact reconciliation of a number of a priori constraints or hypotheses concerning the structure of the circulation. Using this formalism, we explore the extreme nonuniqueness that not only characterizes internal loading theory inferences of the depth profile of mantle viscosity but also inferences of the radial style of the circulation. On this basis, we suggest that great caution is warranted with respect to tomography‐based inferences of mantle properties. Based on a viscosity profile whose depth dependence is close to that independently inferred within the context of postglacial rebound studies, we present plausible resolutions of the gravity‐heat flux impasse effected either within the framework of whole‐mantle or layered‐mantle circulation models.

Post-glacial rebound and present-day three-dimensional deformations

The WEGENER † † Working group of European Geo-scientists for the Establishment of Networks for Earth Research. activities related to the study of post-glacial rebound are presented together with a review of the present state-of-the-art in this study field. Post-glacial rebound research is an unique tool for studying the viscoelastic behaviour of the Earth's mantle on time scales of thousands of years. The viscosity structure of the Earth's mantle determined from an inversion of observations of glacially induced deformations is a basic requirement for modelling long-term phenomena such as the convection in the Earth's mantle, and for better understanding unsolved questions such as the nature of the mantle discontinuities or the vertical scale of convection. First, an introduction to the scientific background is given, and the three principal ingredients for post-glacial rebound studies, namely the ice model, the Earth model, and the observations are briefly considered. For the ice model, the uncertainties due to a trade-off between ice model and Earth rheology are outlined. The different approaches used to model the Earth and its deformations in post-glacial rebound studies are discussed emphasising the preliminary nature of the derived rheologies and depth dependencies. The observations, in particular the relative sea-level changes and three-dimensional surface deformations, are described with special emphasis on observational gaps. Based on the discussion of the ingredients, an outline of the future developments in post-glacial rebound research is attempted with particular emphasis on the Earth model and the theory of deformations. For several decades extreme efforts have been made to precisely monitor the land uplift in Scandinavia. However, for the height component the existing data still are associated with large uncertainties while reliable data on the horizontal component are practically nil. The ongoing long-term (longer than ten years) spacegeodetic measurements are likely to provide the three-dimensional deformations with the spatial resolution and accuracy required in order to substantially contribute to post-glacial rebound studies. Thus, present-day three-dimensional deformations of the Earth's surface beneath and around the former ice sheets as a constraint for the mantle rheology and viscosity structure will increasingly become important as they become known from space-geodetic measurements with high spatial resolution and an accuracy approaching the mm/a-level.

Combining geomorphological and geodetic data to determine postglacial tilting in Manitoba

Estimates of postglacial rebound in central North America from Laurentide deglaciation to the present time are uncertain as a result of lack of data from the continental interior. A more precise knowledge of postglacial tilt history will assist studies of the evolution of the major lakes in Manitoba and will facilitate the engineering and environmental management of the present-day hydrological system. This paper explores the benefits of combining geomorphological data with high-precision, real-time geodetic data (GPS positioning and absolute gravity) and lake-gauge tilt data now being collected for postglacial rebound studies in Manitoba and adjacent regions in the US. Presently-available data sets representing these data types are (1) tilting of the 9.5 kyr B.P. Campbell strand line south and west of Lake Winnipeg, (2) the rate of decrease in absolute gravity values measured from 1987 to 1995 at Churchill, Manitoba, and (3) the present-day regional tilt rate derived from water-level gauges in southern Manitoba lakes. These data are compared to theoretical predictions based on the published ICE-3G loading history and on a model of Earth rheology characterized by a 1066B density and elastic structure, an upper-mantle viscosity of 10 21Pa s, a lower-mantle viscosity of 2 × 10 21Pa s, and a lithosphere thickness of 120 km (Tushingham & Peltier, 1991). All three data types show disagreement in Manitoba with ICE-3G and the ‘standard’ Earth model. ICE-4G does better but could not be investigated in any detail. The constraints on model parameters provided by the different data types were investigated by varying, one at a time, three key parameters, (1) the thickness of the lithosphere in excess of 120 km, (2) the lower mantle viscosity, and (3) the thickness of Laurentide ice over the Prairies, to obtain better fits to the data. The present data do not appear to constrain lithosphere thickness in excess of 120 km very well. While both the Campbell strand line data and the Churchill absolute gravity data are consistent with an increase in lower-mantle viscosity, the present-day, lake-gauge data are not. All three data types are consistent with a thinning of the Laurentide ice-sheet over the Prairies relative to the ICE-3G model. Simultaneous adjustment of model parameters with the advantage of anticipated new data in Manitoba and adjacent regions in the US will lead to better understanding of the trade-offs between Earth rheology and ice sheet history and hence to an improved Laurentide postglacial rebound model.

An analysis of anisotropic mantle viscosity, and its possible effects on post-glacial rebound

This paper presents a preliminary analysis of the possibility of using post-glacial rebound observations to place constraints on the anisotropy of upper-mantle viscosity. We extend existing analyses by considering a visco-elastic, spherical, self-gravitating Earth. We show that three independent viscosity parameters are required to describe a Maxwell solid with transversely isotropic viscosity and isotropic elasticity. We develop a theoretical formalism for including the effects of transversely isotropic visco-elasticity in post-glacial rebound models. Using this formalism to describe anisotropy in the upper mantle, we model the free air gravity anomaly, relative sea-level changes, and present-day horizontal motion caused by the rebound, to assess their dependence on the upper-mantle viscosity parameters. We find that as long as those parameters are no larger than the lower-mantle (isotropic) viscosity, the results for the gravity and sea-level changes are notably sensitive to only one of the three viscosity parameters. This suggests, at least for the case where the lower-mantle viscosity is significantly larger than the upper-mantle viscosity, that post-glacial rebound studies of gravity and sea-level will be hard pressed to usefully constrain viscous anisotropy. We do find that the horizontal motion is relatively sensitive to transverse isotropy and so might be used, in principle, to constrain the anisotropy. In practice, though, it is likely that the strong dependence of horizontal motion on details of the ice model, coupled with the uncertainties in existing ice models, would make such attempts impractical.

Rayleigh-Taylor instabilities of a self-gravitating Earth

In the upper mantle and crust, common Earth models derived from seismic observations have density gradients greater than the adiabatic one, and the Brunt-Väisälä frequency indicates the gravitational instability of these layers. Here we use the linear viscoelastic theory of a self-gravitating compressible planet to determine the characteristic times and excitation amplitudes of the Rayleigh-Taylor (RT) instabilities of the preliminary reference earth model (PREM) augmented by reasonable viscosity-depth profiles. Four different viscosity profiles are considered, with one of them varying continuously with depth. The RT modes are determined for spherical harmonic degrees up to 100. For each spherical degree, a discrete spectrum of modes is found, with the distribution of the characteristic times strongly depending on the viscosity profile, while the amplitudes are less dependent on the viscosity. The excitation amplitudes of the modes are of the same order of magnitude as those for stable eigenmodes taken into account in the modelling of post-glacial rebound. For typical viscosity profiles derived from post-glacial rebound studies, the characteristic times are of the order of 10 7 to 10 8y, while for a profile with a very low viscosity in the asthenosphere the characteristic times found here are as low as 6 × 10 3y. Owing to the limitations of the linear viscoelastic theory, which is valid for small deformations only and neglects all dynamic thermal effects, we can only describe the existence of these modes but not their relative importance compared to thermal instabilities. Nevertheless, the characteristic times determined with this theory are descriptive of the time scales required for a gravitational overturning to result in significant deformations after being excited by surface mass loads. If excited, the RT modes introduce a non-linear element into the interaction between surface loads and internal planetary dynamics. In regions of low asthenospheric viscosity, RT instabilities may significantly change the crustal response to glacial loading and deloading and even introduce a feedback between loading and crustal response. In fact, depending on the planetary repertoire of surface mass transport processes, these modes could effect the evolution of a planet.

Evidence for small‐scale mantle convection from Seasat altimeter data

Evidence for the early development of convective instability in the thermal boundary layer associated with cooling plates has been found from gravity anomalies and residual sea surface heights derived from Seasat altimeter data. Subtle lineated patterns trending in the direction of plate motion in the hot spot reference frame are observed over the younger portions of the fast‐moving Pacific and Indo‐Australian plates. In particular, for the east central Pacific Ocean, the Seasat‐derived data sets reveal lineations with (1) wavelengths in the range 150–500 km (perhaps increasing with plate age), and (2) peak‐to‐trough amplitudes of 5–20 mGal for gravity anomalies. The lineated pattern over the Pacific plate, which first becomes discernable over seafloor 5‐ to 10‐m.y.‐old west of the East Pacific Rise, is clearly oblique to the trends of the prominent Pacific‐Farallon fracture zones. Onset of convective instability at such early ages can be understood if young oceanic lithosphere is underlain by a layer having a viscosity of about 1018 Pa s (1019 P), which is about 3 orders of magnitude less than mantle viscosity inferred from postglacial rebound studies. Recent numerical studies of convection in fluids with a temperature‐ and pressuredependent viscosity support an early onset time for convective instability and low‐viscosity zones in the upper mantle beneath young lithosphere. Such low‐viscosity zones may correspond to similarly located regions of low shear wave velocities resolved through studies of surface waves.