prediction of decadal slope changes in canada by glacial isostatic adjustment modellingthis article is one of a series of papers published in this special issue on the theme geodesy in canada glacial isostatic adjustment gia is the dominant process to cause vertical motion of the land surface a gia model is presented herein that can be used to predict slope changes at given locations in north america where gia is the primary cause for vertical motion uncertainty in pleistocene ice cover and viscosity in the earth s mantle prevent one from picking a single gia model from the literature to predict uplift rates in the region therefore in this study a range of mantle viscosity values as well as two different ice loading histories are used in a forward model of the gia process the combination of viscosities and ice model that gives the best fit to recently available continuous and episodic gps observations is assumed to provide the best prediction of slope changes in north america this model can be used to quantify gia induced vertical deformation in local geomorphologic studies we show that the predicted differential uplift rate in the nelson river with respect to lake winnipe

validation of the ice 3g model of wurm wisconsin deglaciation using a global data base of relative sea level histories a global data base consisting of radiocarbon controlled relative sea level rsl histories from 392 different geographic locations has been compiled for use in analyses of the glacial isostatic adjustment process these data may be employed to constrain both the spatiotemporal characteristics of the last deglaciation event of the current ice age and the rheological structure of the planetary interior in a previous paper in this series tushingham and peltier 1991 we employed the rsl data in this set from sites that were once ice covered to refine the apriori model of deglaciation that had been delivered by past research in the area of pleistocene geomorphology peltier and andrews 1976 wu and peltier 1983 to produce a new global model of this event that we have called ice 3g in the present paper following a description of the full data base and of the methods used to compile it we employ data from the sites that were not ice covered 200 time series to verify the plausibility of this refined model of deglaciation and to test the extent to which the totality of the observations constrain the radial viscoelastic structure of the planet the analysis of solutions to the forward problem presented here reinforce previous inferences of a preference for a thick lithosphere by rsl data from sites along the u s east coast and a preference by data from most near field sites for an increase in viscosity across the 670 km discontinuity in the mantle by a factor of approximately 2 when the viscosity of the upper mantle is fixed to the value of 1021 pa s originally deduced by haskel 1935 on the basis of his analysis of the data from fennoscandia

haskell 1935 revisited the haskell 1935 value of 1021 pa s for mantle viscosity is a classic and enduring constraint on the rheology of the earth s interior we revisit this inference using spherically symmetric self gravitating maxwell viscoelastic earth models our inference is based on both forward and inverse analyses of decay times associated with uplift at two sites considered by haskell angerman river sweden and oslo norway rather than the raw relative sea level rsl data at these sites we demonstrate that predictions of the decay time associated with the angerman river data are insensitive to variations in both the late pleistocene ice load history and the lithospheric thickness of the earth model the predictions at oslo are sensitive to both these inputs and hence decay times at this site provide a remarkably robust constraint on mantle viscosity we derive a constraint on the average viscosity of the mantle of 0 65 1 10 1021 pa s where the average resolved by the data encompasses a region which extends from the base of the lithosphere to a depth of near 1400 km this indicates that many previous analyses which have invoked the haskell value of 1021 pa s as a constraint on the average upper mantle i e above 670 km depth viscosity alone have misinterpreted the resolving power of the inference furthermore our analysis indicates that a number of apparently contradictory inferences of viscosity based on fennoscandian data satisfy the new rigorous interpretation of the haskell constraint finally we demonstrate how the ambiguity in the upper mantle lower mantle viscosity contrast associated with the haskell average may be reduced by invoking decay time constraints estimated from rsl curves in hudson bay a preliminary inversion of decay times at angerman river and richmond gulf in hudson bay suggests a contrast of approximately an order of magnitude between the average viscosities of the upper mantle and the top 1000 km of the lower mantle however a conclusive analysis in this regard must await the determination of consistent decay time estimates for the hudson bay region

impact of air sea coupling on the madden julian oscillation in a general circulation model abstract the impact of air sea coupling on the dynamics of the tropical madden julian oscillation mjo is investigated with an atmospheric general circulation model gcm coupled to an ocean mixed layer model in the uncoupled gcm where climatological sea surface temperature sst is specified realistic space time spectra of near equatorial zonal wind and precipitation are produced with power concentrated at eastward wavenumbers 1 3 with periods of 35 90 days however the simulated mjo is roughly 50 stronger than observed largely resulting from enormous activity during northern summer furthermore during southern summer when the observed mjo is most dominant across the indian and western pacific oceans intraseasonal variance in the uncoupled model is overly concentrated to the north and east of australia with little activity extending into the equatorial indian ocean contrary to other recent modeling studies coupling did not alleviate either of these problems nor did it have any other apprecia

investigations of fennoscandian glacial isostatic adjustment using modern sea level records we present a new method for determining the rates from a network of regional tide gauge data the method involves using a model for the sea level observations annual averages of relative sea level that explicitly includes a term for the interannual sealevel variations which are assumed to be constant for all sites in the network the resulting simultaneous analysis of all the sea level observations yields sea level rates which are biased by the unknown temporal slope of the interannual variations by differencing sea level rate estimates with respect to one site site referenced sea level rates are calculated which are free from this bias the differencing procedure also removes any signal due to a common sea level rate such as might be associated with eustatic sea level rise the resulting site referenced sea level rates therefore in principle reflect only the relative vertical crustal motions of the tide gauge sites with respect to the geoid these site referenced sea level rates represent a potentially more accurate data set than have previously been used for sea level studies we have used these rates to investigate glacial isostatic adjustment gia in fennoscandia specifically we have used the site referenced sea level rates within the baltic sea to estimate adjustments to the ice history and earth model which are used to calculate vertical rates of adjustment due to gia a method never before used for fennoscandia the parameters selected were lithospheric thickness the viscosities of assumed isoviscous upper and lower mantles and a fennoscandian ice thickness scaling parameter we present the results of this estimation procedure for a specific test ice model we also find evidence that the sea level record for the site nearest the center of uplift furuogrund may be contaminated by systematic errors of unknown origin data from this site have previously been used to determine a rate for the maximum uplift that we find is perhaps 1 mm yr 1 or 10 too large

mantle phase transitions and the free air gravity anomalies over fennoscandia and laurentia the interpretation of free air gravity anomalies over present day centers of postglacial rebound has always been controversial we show that the observed gravity anomalies over both fennoscandia and laurentia and the associated relative sea level variations since deglaciation are explicable with a simple newtonian viscoelastic model of the earth if the earth model includes the density jumps in the mantle associated with the phase transitions at 420 and 670 km depth the result has important implications for mantle convection since the observed free air anomalies are very sensitive to the viscosity of the mantle beneath the deepest phase transition

the influence of dynamically supported topography on estimates of te abstract the effective elastic thickness t e of continental lithosphere can be estimated from the relationship between gravity and topography in the spectral domain two methods have been used one of which depends on the coherence between bouguer gravity anomalies and topography whereas the other uses the transfer function commonly known as the admittance between the free air gravity and topography the two methods give estimates of t e which differ by as much as an order of magnitude in those continental regions where variations in elevation are small this problem has led to much controversy an important concern is the extent to which estimates of t e are affected by dynamically maintained gravity and topography arising from mantle convection and postglacial recovery unlike elastically supported anomalies these processes can generate gravity and topographic long wavelength 500 km anomalies if such anomalies are modelled as being supported by elastic forces the resulting values of t e are overestimated often by a large amount

glacial isostatic adjustment in fennoscandia with a three dimensional viscosity structure as an inverse problem abstract glacial isostatic adjustment data are commonly used to invert for the radial viscosity structure of the mantle however the effects of lateral variations in mantle viscosity in such inversions are not yet accounted for here we analysed synthetic sea level data for the fennoscandian region which are derived from a three dimensional 3d earth model with realistic lateral and vertical viscosity variations deduced from seismological and geological information the inversion of the 3d synthetic data for a best fitting 1d viscosity profile reveals that i lateral lithospheric thickness variations can be detected with 1d model predictions if the data are grouped into regional subsets ii combined lateral variations in lithospheric thickness and asthenospheric viscosity are not properly resolved with 1d model predictions and iii the spatial and temporal distribution of observational data strongly affects the resulting 1d viscosity profile

space geodetic constraints on glacial isostatic adjustment in fennoscandia analysis of global positioning system gps data demonstrates that ongoing three dimensional crustal deformation in fennoscandia is dominated by glacial isostatic adjustment our comparison of these gps observations with numerical predictions yields an earth model that satis es independent geologic constraints and bounds both the average viscosity in the upper mantle 5 x 10 20 to 1 x 10 21 pascal seconds and the elastic thickness of the lithosphere 90 to 170 kilometers we combined gps derived radial motions with fennoscandian tide gauge records to estimate a regional sea surface rise of 2 1 0 3 mm year furthermore ongoing horizontal tectonic motions greater than 1 mm year are ruled out on the basis of the gps derived three dimensional crustal velocity field

time variable gravity from grace first results eleven monthly grace gravity field solutions are now available for analyses we show those fields can be used to recover monthly changes in water storage both on land and in the ocean to accuracies of 1 5 cm of water thickness when smoothed over 1000 km the amplitude of the annually varying signal can be determined to 1 0 cm results are 30 better for a 1500 km smoothing radius and 40 worse for a 750 km radius we estimate the annually varying component of water storage for three large drainage basins the mississippi the amazon and a region draining into the bay of bengal to accuracies of 1 0 1 5 cm

late quaternary ice sheet history of northern eurasia the maximum limits of the eurasian ice sheets during four glaciations have been reconstructed 1 the late saalian 140 ka 2 the early weichselian 100 80 ka 3 the middle weichselian 60 50 ka and 4 the late weichselian 25 15 ka the reconstructed ice limits are based on satellite data and aerial photographs combined with geological field investigations in russia and siberia and with marine seismic and sediment core data the barents kara ice sheet got progressively smaller during each glaciation whereas the dimensions of the scandinavian ice sheet increased during the last ice age the barents kara ice sheet attained its maximum size as early as 90 80 000 years ago when the ice front reached far onto the continent a regrowth of the ice sheets occurred during the early middle weichselian culminating about 60 50 000 years ago during the late weichselian the barents kara ice sheet did not reach the mainland east of the kanin peninsula with the exception of the nw fringe of taimyr a numerical ice sheet model forced by global sea level and solar changes was run through the full weichselian glacial cycle the modeling results are roughly compatible with the geological record of ice growth but the model underpredicts the glaciations in the eurasian arctic during the early and middle weichselian one reason for this is that the climate in the eurasian arctic was not as dry then as during the late weichselian glacial maximum

glacial isostatic adjustment in fennoscandia for a laterally heterogeneous earth glaciation and deglaciation in fennoscandia during the last glacial cycles has significantly perturbed the earth s equilibrium figure changes in the earth s solid and geoidal surfaces due to external and internal mass redistributions are recorded in sequences of ancient coastlines now either submerged or uplifted and are still visible in observations of present day motions of the surface and glacially induced anomalies in the earth s gravitational field these observations become increasingly sophisticated with the availability of gps measurements and new satellite gravity missions observational evidence of the mass changes is widely used to constrain the radial viscosity structure of the earth s mantle however lateral changes in earth model properties are usually not taken into account as most global models of glacial isostatic adjustment assume radial symmetry for the earth model this simplifying assumption contrasts with seismological evidence of significant lateral variations in the earth s crust and upper mantle throughout the fennoscandian region we compare predictions of glacial isostatic adjustment based on an ice model over the fennoscandian region for the last glacial cycle for both radially symmetric and fully 3 d earth models our results clearly reveal the importance of lateral variations in lithospheric thickness and asthenospheric viscosity for glacially induced model predictions relative sea level predictions can differ by up to 10 20 m uplift rate predictions by 1 3 mm yr 1 and free air gravity anomaly predictions by 2 4 mgal when a realistic 3 d earth structure as proposed by seismic modelling is taken into account

on postglacial geoid subsidence over the equatorial oceans we develop two new spectral formalisms for the gravitationally self consistent solution of the sea level equation which governs the redistribution of glacial meltwater on a visco elastic earth the first is a purely spectral technique based on an extension of theory outlined by dahlen 1976 for determining the equilibrium oceanic tide on an elastic planet using this technique with a feasible spherical harmonic truncation level l 30 we can obtain convergence in the computed sea level variations within the degree range l 10 we also develop a second pseudospectral technique however which permits the construction of gravitationally self consistent solutions to much higher degree and order l 100 the pseudospectral formalism is employed here to develop a comprehensive physical explanation for the global pattern of present day sea level variations due to ongoing glacial isostatic adjustment in particular we focus upon a mechanism which we term equatorial ocean syphoning that acts to draw water toward the oceanic portion of the collapsing peripheral bulge that encircles previously glaciated regions the collapse of the forebulge induces a flow of water which is required to maintain hydrostatic equilibrium the syphoning mechanism dominates the relative sea level rsl variation in oceans in the far field of the ice sheets that is beyond the peripheral bulge during periods such as the interglacial of the past 4000 years during which the volume of the ice sheets has not apparently changed appreciably while at the same time isostatic adjustment persists the rsl change in the near field is in contrast dominated by the local vertical displacement of the solid surface finally comparison of gravitationally self consistent predictions of rsl change in the far field with the observational data at small pacific island sites has provided an upper bound of 1 to 2 m for the eustatic sea level rise produced by any recent last 3000 years melting of the antarctic ice sheet

limitations on the inversion for mantle viscosity from postglacial rebound summary observations of postglacial rebound pgr can provide important constraints on mantle viscosity structure in this study we investigate how well pgr observations are able to constrain the spherically symmetric 1 d viscosity structure of the earth we generate synthetic pgr data by calculating the response of an earth model with realistic 3 d viscosity the viscosity model is constructed starting from seismic tomography models we generate synthetic pgr data from this model including relative sea levels exponential relaxation times j2 polar wander and grace time variable gravity measurements where most of the data is concentrated in the laurentide region we then attempt an inversion for a 1 d spherically symmetric viscosity structure based on minimizing the misfit to these pgr data using a monte carlo algorithm to invert for two layers of viscosity upper and lower mantle um and lm we obtain well constrained values which correspond to the two layer average of the logarithm of the 3 d viscosity structure in the vicinity of laurentia we then attempt to invert for four layers of viscosity in this case we find a trade off effect in which neighbouring layers may have highly variable viscosities while maintaining a constant average between them since the pgr data are insensitive to this trade off in neighbouring layers the viscosity of any one of the four layers cannot be well constrained by repeating the inversion with synthetic data derived from an earth model which itself is 1 d with four viscosity layers we demonstrate that it is the insensitivity of the pgr data not complications due to 3 d structure that allow the trade off effect and the resulting failure of the inversion we also perform a resolution test to study the extent of the insensitivity of pgr to these viscosity trade offs finding that the limit of resolution in the um is about the size of the entire um and similarly for the lm this reinforces our findings that only two layers are obtainable in an inversion for viscosity from pgr

isostatic topography and crustal depth corrections for the fennoscandian geoid abstract the medium wavelength geoid wavelengths the result of this study demonstrate that crustal thickness variations are important for the interpretation of the fennoscandian geoid or gravity however submoho deviatoric stresses might become very high about 200 mpa if the entire anomaly is assumed to be supported by lateral density variations at less than 80 km depth this implies that the pronounced negative anomaly is additionally maintained by dynamical flow inside the mantle

glacial isostatic adjustment and the free air gravity anomaly as a constraint on deep mantle viscosity summary a gravitationally self consistent theory for relative sea level variations forced by pleistocene deglaciation events is employed to explore the extent to which rsl and free air gravity observations together constrain the viscosity of the mantle beneath the seismic discontinuity at 670 km depth a trade off is revealed between errors in the assumed deglaciation history and errors in the inferred value of the viscosity of the lower mantle taking full account of such uncertainty plausible values of the viscosity beneath the transition region are bounded above by 1023 poise cgs units the preferred value is at least a factor of 2 lower than this and is strongly constrained by the observed free air gravity anomaly over hudson bay the calculations described in detail here show for the first time that the relatively large gravity anomalies observed over sites of wurm wisconsin deglaciation do not require any pronounced increase of mantle viscosity with depth in order to explain them

epcrust a reference crustal model for the european plate summary we present a new crustal model for the european plate derived from collection and critical integration of information selected from the literature the model covers the whole european plate from north africa to the north pole 20 n 90 n and from the mid atlantic ridge to the urals 40 w 70 e the chosen parametrization represents the crust in three layers sediments upper crust and lower crust and describes the 3 d geometry of the interfaces and seismologically relevant parameters isotropic p and s wave velocity plus density with a resolution of 0 5 0 5 on a geographical latitude longitude grid we selected global and local models derived from geological assumptions active seismic experiments surface wave studies noise correlation receiver functions model epcrust presents significant advantages with respect to previous models it covers the whole european plate it is a complete and internally consistent model with all the parameters provided also for the sedimentary layer it is reproducible it is easy to update in the future by adding new contributions and it is available in a convenient digital format epcrust could be used to account for crustal structure in seismic wave propagation modelling at continental scale or to compute linearized crustal corrections in continental scale seismic tomography gravity studies dynamic topography and other applications that require a reliable crustal structure because of its resolution our model is not suited for local scale studies such as the computation of earthquake scenarios where more detailed knowledge of the structure is required we plan to update the model as new data will become available and possibly improve its resolution for selected areas in the future

mantle viscosity and ice age ice sheet topography ice age paleotopography and mantle viscosity can both be inferred from observations of earth s response to the most recent deglaciation event of the current ice age this procedure requires iterative application of a theoretical model of the global process of glacial isostatic adjustment results demonstrate that the iterative inversion procedure converges to a paleotopography that is extremely close to that from the ice 4g model the accompanying mantle viscosity profile is furthermore shown to reconcile the requirements of aspherical geoid anomalies related to the mantle convection process thus resolving a fundamental issue concerning mantle rheology the combined model also explains postglacial sea level histories for the east coast of the united states

the moho depth map of the european plate summary the european plate has a 4 5 gy long and complex tectonic history this is reflected in the present day large scale crustal structures a new digital moho depth map is compiled from more than 250 data sets of individual seismic profiles 3 d models obtained by body and surface waves receiver function results and maps of seismic and or gravity data compilations we have compiled the first digital high resolution map of the moho depth for the whole european plate extending from the mid atlantic ridge in the west to the ural mountains in the east and from the mediterranean sea in the south to the barents sea and spitsbergen in the arctic in the north in general three large domains within the european plate crust are visible the oldest archean and proterozoic crust has a thickness of 40 60 km the continental variscan and alpine crust has a thickness of 20 40 km and the youngest oceanic atlantic crust has a thickness of 10 20 km

long wavelength gravity field constraint on the lower mantle viscosity in north america the long wavelength negative gravity anomaly over hudson bay coincides with the area depressed by the laurentide ice sheet during the last glacial maximum suggesting that it is at least partly caused by glacial isostatic adjustment gia additional contributions to the static gravity field stem from surface dynamic topography core mantle boundary cmb topography and density anomalies in the subsurface previous estimates of the contribution of gia to the gravity anomaly range from 25 to more than 80 however these estimates did not include uncertainties in all components that contribute to the gravity field in this study we develop a forward model for the gravity anomaly based on density models and dynamic models investigating uncertainty in all components we derive lithospheric densities from equilibrium constraints but extend the concept of lithospheric isostasy to a force balance that includes the dynamic models the largest uncertainty in the predicted gravity anomaly is due to the lower mantle viscosity uncertainties in the ice history the crustal model the lithosphere asthenosphere boundary and the conversion from seismic velocities to density have a smaller effect a preference for lower mantle viscosities 1022 pa s is found in which case at least 60 of the observed long wavelength gravity anomaly can be attributed to gia this lower bound on the lower mantle viscosity has implications for inferences based on models for mantle convection and gia

determination of the earth s structure in fennoscandia from grace and implications for the optimal post processing of grace data summary analysis of data from the gravity recovery and climate experiment grace satellite mission allows us to identify regions of long term mass changes such as the areas of glacial isostatic adjustment gia in north america and fennoscandia as there are now more than 7 yr of data available the determined trends are robust enough for the inference of viscosity structure of the earth s mantle in this study we focus on the fennoscandian rebound area as there are abundant high quality terrestrial data to use as ground truth in the first step grace data are taken to fix the optimal radial 1 d viscosity profile and the lithospheric thickness combination which are needed as background parameters in 3 d earth modelling the results are in basic agreement with results based upon relative sea level and gps data showing a lithospheric thickness in fennoscandia between 90 and 160 km and an upper mantle viscosity of about 2 4 10 20 pa s the lower mantle viscosity is poorly resolved however in the second step grace data are used to constrain the 3 d viscosity using spherical finite element modelling in this case the results also agree with past investigations but grace data alone cannot discriminate between lateral heterogeneities in the mantle that are thermal in origin from those due to changes in chemical composition more notably we treat in detail grace related questions such as implementation of an adequate level 2 filter technique and identification of the best reduction method for hydrological mass change signals it turns out that the gaussian filter technique is the best for this type of investigation even the best global hydrology models used in grace investigations still fail to improve the mismatches thus one should be careful not to blindly use them for improving gia models in north america or other centres of rebound in conclusion our study clearly shows that grace data greatly complement the study of gia as there are new grace releases in progress and also in light of a new generation of ice history models grace is likely to sharpen our insights concerning earth structure and rheology within the next few years

structural effects of the crust on the geoid modelled using deep seismic sounding interpretations summary according to the theory of isostasy the earth has a tendency to deform its surface in order to reach an equilibrium state the land uplift phenomenon in the area of the fennoscandian shield is thought to be a process of this kind the geoid as an equipotential surface of the earth s gravity field contains information on how much the earth s surface departs from the equilibrium state in order to study the isostatic process through geoidal undulations the structural evects of the crust on the geoid have to be investigated the structure of the crust of the fennoscandian shield has been extensively explored by means of deep seismic sounding dss the data obtained from dss are used to construct a 3 d seismic velocity structure model of the area s crust the velocity model is converted to a 3 d density model using the empirical relationship that holds between seismic velocities and crustal mass densities structural evects are then estimated from the 3 d density model the structural evects computed from the crustal model show that the mass deficiency of the crust in fennoscandia has caused a geoidal depression twice as deep as that observed from the gravimetric geoid it proves again that the crust has been isostatically compensated by the upper mantle in other words an anomalously high density upper mantle must exist beneath fennoscandia

interglacial variability mis 5 and mis 7 and dinoflagellate cyst assemblages in the bay of biscay north atlantic the interglacial periods of the late quaternary are frequently investigated as they constitute potential analogues for our modem climate and may shed light on the key questions of natural climate variability and future developments the aim of this work is to reconstruct the paleoenvironmental history of marine isotope stages mis 5 and 7 in deep sea sediments of the northern bay of biscay north east atlantic ocean on the basis of a multiproxy compilation including analysis of dinoflagellate cyst assemblages we discuss the nature of the paleoenvironmental and paleoclimate changes that took place in this region recurrent successions of species marking the beginning and the termination of the interglacial complexes mis 5 and mis 7 revealed a coherent scheme of water mass migration during these key transitional periods moreover our data extend knowledge about the ecology of several dinoflagellate taxa in particular we discuss the ecology of spiniferites septentrionalis and note that this species can be used as a biostratigraphical tracer in north atlantic quaternary sediments until a major event of iceberg calving occurred during mis 6 dated to around 150 ka bp the dinocyst spinferites mirabilis appears to be an important proxy for recognizing warm intervals within interglacial complexes during mis 5e the last interglacial this species is represented by the highest percentages ever recorded in sediments from the north atlantic region peak occurrence of this species during mis 7 indicates that substage mis 7c the second warm interval of the penultimate interglacial represents the climatic optimum during the mis 7 interglacial complex

viscous gravitational relaxation summary this paper is concerned with a detailed examination of the response of maxwell models of the planet to surface mass loads particular attention is devoted to an examination of the factors which determine the isostatic response since the understanding of this response is crucial in a number of different geodynamic problems one particular example which we discuss in detail is concerned with the prediction of free air gravity anomalies produced by large scale deglaciation events using the methods developed here we are able to provide the first direct assessment of the importance of initial isostatic disequilibrium on the observed relative sea level variations and free air gravity anomalies forced by the melting of the laurentide ice sheet we are therefore able to estimate the extent to which such initial disequilibrium might influence the inference of mantle viscosity from isostatic adjustment data our calculations establish that free air gravity data although they are sensitive to the degree of initial disequilibrium provide an extremely high quality constraint upon the viscosity of the lower mantle

pleistocene deglaciation and the global gravity field the present day global geoid and free air gravity anomaly signals induced by pleistocene deglaciation have been computed along with their secular variations a revised green function has been derived for the free air gravity anomaly and we find that an earth model with a lower mantle viscosity moderately larger than the upper mantle value satisfies observations of the anomaly over both hudson s bay and fennoscandia using this preferred earth model the predicted global geoid anomaly map is characterized by peak negative values of 36 7 9 4 and 21 9 m over hudson s bay northern europe and antarctica respectively and by a smooth small amplitude 2 5 m upwarping over the major ocean basins although the field has an order of magnitude less power than the observed there is a significant spatial correlation between the two inferences of mantle viscosity based upon comparisons between the observed geoid and the computed deglaciation induced anomaly are hampered by the large contribution from the convective circulation in the earth s mantle we have subtracted a predicted convection signal based on seismic tomography from the observed field however the residual geoid thus obtained is still too inaccurate to allow a useful comparison in contrast a filtered version of the observed geoid over canada which retains harmonic coefficients in the degree range 10 22 provides a relatively uncontaminated by convection datum that is indeed satisfied by the preferred earth model secular variations in the earth s gravitational field are naturally dominated by the signal from pleistocene deglaciation in this respect we compute zonal harmonics in the expansion of the present day rate of change of the geopotential and in particular we predict amplitudes comparable to that for the previously analysed j2 for j4 j5 j7 and j9 all of which reflect in large part the response due to the melting of the massive laurentide ice sheet this analysis suggests that measurement of these higher order secular variations of the zonal harmonics based upon analysis of long time series of lageos ranging data could provide very useful additional constraints on the radial variation of mantle viscosity these constraints along with all others described in this paper are shown to be relatively insensitive to assumptions concerning the deflection during the glacial isostatic adjustment process of the 400 and 670 km density discontinuities within the mantle

glacial isostatic adjustment in the static gravity field of fennoscandia in the central part of fennoscandia the crust is currently rising because of the delayed response of the viscous mantle to melting of the late pleistocene ice sheet this process called glacial isostatic adjustment gia causes a negative anomaly in the present day static gravity field as isostatic equilibrium has not been reached yet several studies have tried to use this anomaly as a constraint on models of gia but the uncertainty in crustal and upper mantle structures has not been fully taken into account therefore our aim is to revisit this using improved crustal models and compensation techniques we find that in contrast with other studies the effect of crustal anomalies on the gravity field cannot be effectively removed because of uncertainties in the crustal and upper mantle density models our second aim is to estimate the effects on geophysical models which assume isostatic equilibrium after correcting the observed gravity field with numerical models for gia we show that correcting for gia in geophysical modelling can give changes of several kilometer in the thickness of structural layers of modeled lithosphere which is a small but significant correction correcting the gravity field for gia prior to assuming isostatic equilibrium and inferring density anomalies might be relevant in other areas with ongoing postglacial rebound such as north america and the polar regions

radial and tangential gravity rates from grace in areas of glacial isostatic adjustment summary in areas dominated by glacial isostatic adjustment gia the free air gravity anomaly rate can be converted to uplift rate to good approximation by using a simple spectral relation we provide quantitative comparisons between gravity rates derived from monthly gravity field solutions gfz potsdam csr texas igg bonn from the gravity recovery and climate experiment grace satellite mission with uplift rates measured by gps in these areas the band limited gravity data from the grace satellite mission can be brought to very good agreement with the point data from gps by using scaling factors derived from a gia model the root mean square of differences is 0 55 mm yr 1 for a maximum uplift rate signal of 10 mm yr 1 the root mean square of the differences between grace derived uplift rates and gps derived uplift rates decreases with increasing grace time period to a level below the uncertainty that is expected from grace observations gps measurements and the conversion from gravity rate to uplift rate with the current length of time series more than 8 yr applying filters and a hydrology correction to the grace data does not reduce the root mean square of differences significantly the smallest root mean square was obtained with the gfz solution in fennoscandia and with the csr solution in north america with radial gravity rates in excellent agreement with gps uplift rates more information on the gia process can be extracted from grace gravity field solutions in the form of tangential gravity rates which are equivalent to a rate of change in the deflection of the vertical scaled by the magnitude of gravity rate vector tangential gravity rates derived from grace point towards the centre of the previously glaciated area and are largest in a location close to the centre of the former ice sheet forward modelling showed that present day tangential gravity rates have maximum sensitivity between the centre and edge of the former ice sheet while radial gravity rates are most sensitive in the centre of the former ice sheet as a result tangential gravity rates offer constraints on a two layer mantle viscosity profile that are different from radial gravity rates which can be exploited in future gia studies

rheological stratification of the lithosphere a direct inference based upon the geodetically observed pattern of the glacial isostatic adjustment of the north american continent 1 a sequence of new analyses of the process of glacial isostatic adjustment gia is described the focus is upon the resolution of a recognized flaw in the currently prevalent model of this process that denoted ice 5g vm2 the flaw concerns a previously noted inability of the model to simultaneously reconcile the vlbi and gps measured rates of vertical and horizontal motion in the region of the north american continent that lay outboard and to the south of the laurentide ice sheet lis at last glacial maximum this characteristic misfit of the model to the data has been suggested to be reconcilable only by recourse to models that explicitly incorporate the influence of lateral viscosity heterogeneity it is demonstrated herein that on the contrary this flaw is entirely and unambiguously attributable to the rheological stratification of the lithosphere an influence not previously accounted for in global models of the gia process but which must exist on a priori grounds

structure of the scandes lithosphere from surface to depth abstract in this review we give an overview of geophysical data and models available for the scandinavian mountains and adjacent areas as they are of relevance to the debate about the existence and cause of neogene uplift emphasis is given to potential field and petrophysical data of which the earth science communities of norway and sweden have a long tradition of acquisition and interpretation this is reflected in the wealth and dense coverage of data available the topography of the scandes mountain chain correlates to a large degree with a bouguer gravity low which suggests isostatic compensation but comparison with magnetic and petrophysical data shows that the gravity low is partly influenced by the trans scandinavian igneous belt signals due to the effects of surface geology can be further eliminated by considering the near surface density distribution as provided by petrophysical sampling to illuminate the entire lithospheric structure active and passive seismic and magnetotelluric data can be used recent and ongoing experiments are aimed at improving the existing models of the lithosphere integration of these different geophysical data sets allows the structure of the lithosphere of the scandes and its surroundings to be addressed seismic models show no pronounced crustal root below the scandes which could provide isostatic compensation but instead an increase of crustal thickness towards the central fennoscandian shield from the integrated model isostatic compensation is inferred to be largely controlled by the density distribution of the crust and that a high density lower crust to the east of the scandes is necessary to achieve isostatic equilibrium on a regional scale we demonstrate the typical crustal structure with profiles crossing from the scandes into the shield and a combined onshore offshore basement map

global glacial isostasy and the surface of the ice age earth the ice 5g vm2 model and grace abstract the 100 kyr quasiperiodic variation of continental ice cover which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of earth history has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n body effects in the solar system on the geometry of earth s orbit around the sun the impacts of the changing surface ice load upon both earth s shape and gravitational field as well as upon sea level history have come to be measurable using a variety of geological and geophysical techniques these observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid earth and on the detailed spatiotemporal characteristics of glaciation history this review focuses upon the most recent advances that have been achieved in each of these areas advances that have proven to be central to the construction of the refined model of the global process of glacial isos

postglacial rebound and sea level contributions to changes in the geoid and the earth s rotation axis summary the rate of change of the spherical harmonic degree 2 component of the earth s gravitational potential coa 20 and polar wander velocity are two signals which are sensitive to late pleistocene deglaciation current changes in sea level and deep mantle viscosity diierent load and earth models have been used in earlier papers to predict the component of these geophysical signals caused by the collapse of the last great ice sheets and recent melting of polar ice caps in this paper we present a systematic analysis of the dependence of the predictions on parameters of the ice and earth model we show that the key parameters of the ice model which govern the predictions are the mass the location of the centre of mass and the midpoint of the deglaciation phase of secondary importance is the length of the deglaciation phase and the mean ice load prior to the last glacial maximum these conclusions enable us to make a more robust inference of mantle viscosity than has been made before allowing for the uncertainties in the model of late pleistocene and present deglaciation as previous authors have shown the lower mantle viscosity is the most important rheological parameter and therefore thecoa 20 observation complements sea level observations which are primarily sensitive to lithospheric thickness and the viscosity of the upper part of the mantle using realistic constraints on the sizes locations and timing of deglaciation of the late pleistocene ice sheets and current changes in polar ice caps the observation of coa 20 is used to infer lower mantle viscosity as a function of the present rate of sea level change if the present rate of non steric sea level change is 1 mm yr 1 and that change has been occurring for less than 1000 years then the lower mantle viscosity satis es log10 glm 21 82 0 15 which is consistent with inferences drawn from recent sea level analyses and con rms other analyses of thecoa 20 observation if the polar wander signal is produced entirely by postglacial rebound and current sea level change no more than 20 per cent of the present contribution to global sea level change comes from greenland the above conclusions also hold if the density discontinuities at 420 and 670 km are modelled as phase boundaries rather than material chemical boundaries

an integrated gravity model for europe s crust and upper mantle we present an integrated gravity model of the european lithosphere based on an analysis of a number of new data sets leading to a much higher resolution than provided by previous models first of all a recent crustal model eucrust 07 is used to quantify the crustal contribution to the observed gravity field and to identify the effect of mantle heterogeneity the new gravity field model is based on a combination of satellite champ and grace and terrestrial data we also use these data sets to estimate residual mantle gravity anomalies and residual topography reflecting the effect of mantle density variations induced by temperature and compositional heterogeneity the separation of these effects is vital for a proper assessment of mantle structure and evolution in addition we utilize a new tomographic model for p and s velocity anomalies beneath europe which is a priori corrected for crustal structure using eucrust 07 the seismic velocity anomalies were subsequently converted into temperature anomalies using a mineral physics approach we estimate the effect of temperature variations on the gravity field and subtract it from the total mantle field the residual fields point to an important role of compositional density anomalies in the upper mantle a number of key features of the compositional density distribution so far invisible in seismic tomography data are detected for the first time