the north american late wisconsin ice sheet and mantle viscosity from glacial rebound analyses abstract observations of sea level and crustal response to glacial loading cycles provide constraints on the mantle rheology function e and as well as on the ice load i with the latter being largely free from a priori glaciological or climate assumptions and appropriate therefore for testing any such hypotheses this paper presents new results for both continental mantle e and i for the late wisconsin ice sheet using geological evidence for relative sea level change rsl and tilting of palaeo lake shorelines complemented with loose constraints from observations of present day radial crustal displacement across north america the focus is on evidence from near or within the former maximum ice margins and the resulting earth response is representative of sub continental mantle conditions the inversion of the sea level information has limited resolution for earth rheology and simple three layer models characterized by depth averaged effective lithospheric thickness h and upper and lower mantle viscosities um and um respectively adequately describe the response function yielding parameters earth model e 6 of h 102 85 120 km um 5 1 1020 3 5 7 5 x1020 lm 1 3 1022 0 8 2 8 x1022 where the numbers in parenthesis are 95 confidence limits the details of the ice sheet with one exception are not strongly dependent on the rheological assumptions within this range the exception is the lower mantle viscosity that remains correlated with the magnitude scaling of the ice sheet a link that is largely broken by introducing constraints from glacial loading effects on the earth s rotation and dynamic flattening the difference between the continental um and the comparable estimate of 1 2 5 x1020 for ocean mantle is statistically significant shoreline gradient information from glacial lakes mcconnell agassiz algonquin and ojibway provide strong constraints on the response within the interior of the ice sheet and the resulting ice sheet model lw 6 is characterized by multiple ice domes from at least 17 18 ka onwards the resolution for earlier periods is largely constrained by global ice volume considerations the two principal domes are over southern nunavut the keewatin dome and over quebec labrador both of 3500 m thickness separated by an ice ridge some 1500 m lower than the domes the latter a requirement imposed by the gradient information over western canada ice thickness gradients east of the cordilleras are partly constrained by the shoreline data for former lake mcconnell as is the lateglacial ice thickness of the keewatin dome and indicate that any ice free corridor between the laurentian and cordilleran components is unlikely to have existed before 13ka reconstructions of the glacial lakes are consistent with the locations and timing of the observational evidence for the four major lake systems with the likely drainage routes identified the evolution of the lw 6 ice volume function expressed as equivalent sea level is characterized by a rapid decrease in ice volume from 15 to 14 5 ka corresponding to the bolling allerod period in the main from rapid ice retreat along the southern margin with further contributions from drainage through the st lawrence river valley and from ice retreat from the major northern straits and gulfs but not hudson strait where the rsl data point to late removal of ice after 10 ka the contribution of the drainage of the lakes to global sea level rise is small

itrf2000 a new release of the international terrestrial reference frame for earth science applications 1 for the first time in the history of the international terrestrial reference frame the itrf2000 combines unconstrained space geodesy solutions that are free from any tectonic plate motion model minimum constraints are applied to these solutions solely in order to define the underlying terrestrial reference frame trf the itrf2000 origin is defined by the earth center of mass sensed by satellite laser ranging slr and its scale by slr and very long baseline interferometry its orientation is aligned to the itrf97 at epoch 1997 0 and its orientation time evolution follows conventionally that of the no net rotation nnr nuvel 1a model the itrf2000 orientation and its rate are implemented using a consistent geodetic method anchored over a selection of itrf sites of high geodetic quality ensuring a datum definition at the 1 mm level this new frame is the most extensive and accurate one ever developed containing about 800 stations located at about 500 sites with better distribution over the globe compared to past itrf versions but still with more site concentration in western europe and north america about 50 of station positions are determined to better than 1 cm and about 100 sites have their velocity estimated to at or better than 1 mm yr level the itrf2000 velocity field was used to estimate relative rotation poles for six major tectonic plates that are independent of the trf orientation rate a comparison to relative rotation poles of the nuvel 1a plate motion model shows vector differences ranging between 0 03 and 0 08 m y equivalent to approximately 1 7 mm yr over the earth s surface itrf2000 angular velocities for four plates relative to the pacific plate appear to be faster than those predicted by the nuvel 1a model the two most populated plates in terms of space geodetic sites north america and eurasia exhibit a relative euler rotation pole of about 0 056 0 005 m y faster than the pole predicted by nuvel 1a and located about 10 n 7 e more to the northwest compared to that model

global glacial isostatic adjustment palaeogeodetic and space geodetic tests of the ice 4g vm2 model analyses of the global process of glacial isostatic adjustment and post glacial relative sea level change continue to deliver important insights into earth system form and process one successful model of the related phenomenology is based upon a spherically symmetric internal viscoelastic structure for the solid earth which has been denoted vm2 and a model of the most recent deglaciation event of the current ice age denoted ice 4g the primary purpose of this paper is to describe several new a posteriori tests that have recently been performed to further investigate the quality of this global solution to the inverse problem for both mantle viscosity and deglaciation history that is posed by the observables associated with this large scale geodynamic phenomenon i focus especially upon the misfits of observations to the theoretical predictions of this model which i am currently using to further refine its properties and upon predictions made using it of geophysical signals that should soon become visible in the context of the gravity recovery and climate experiment grace satellite mission among the required refinements to ice 4g one that is necessary to eliminate a recently revealed misfit to space geodetic constraints on the present day rate of radial motion at the yellowknife location well to the west of hudson bay and a similar misfit to absolute gravity measurements to the southwest of the bay is the insertion of a keewatin dome of thick ice centred over yellowknife with a ridge of ice extending to the south east in the geomorphological literature the existence of such a keewatin dome previously has been hypothesised but chronological control was lacking on the surface features that suggested its former existence an important additional constraint that requires the late glacial existence of this important feature consists of new inferences of the last glacial maximum lowstand of the sea from sites in the far field of the main concentrations of land ice copyright 2002 john wiley sons ltd

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

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 gal 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

glacial isostatic adjustment i the forward problem summary the isostatic adjustment of a radially stratified visco elastic spheroid is treated using space time green functions for the associated surface mass load boundary value problem these impulse response functions are convolved with a heaviside function to give the time dependent deformation of the planet which would be produced by a unit point mass brought up from infinity at t 0 and allowed to remain on the surface the resulting heaviside green functions can be employed to simulate all of the important signatures of glacial isostatic adjustment given a space time dependent surface mass load consisting of ice sheet ablation histories and a model of the simultaneous filling of the ocean basins these source terms are simply convolved with the heaviside green function appropriate to a specific response signature a realistic model of the spatial distribution of the main late pleistocene ice loads and of their temporal disintegration is constructed the response of two visco elastic earth models is computed and compared to a global set of relaxation data relative sea level curves on the basis of this initial comparison of theory and observation the possibility that the lower mantle has a viscosity which is significantly in excess of the viscosity of the upper mantle is excluded in addition clear evidence of the presence of the lithosphere has been found in relaxation data from sites which were near the edge of the laurentide ice sheet such data should therefore prove useful as a basis for analysis of lateral variations in lithosphere thickness further extensions of the calculation are suggested

subglacial hydrology in north western germany during the last glaciation groundwater flow tunnel valleys and hydrological cycles abstract numerical modelling of groundwater dynamics in an overpressured system of subglacial aquifers and aquitards under the marginal portion of the scandinavian ice sheet in northwestern germany has been coupled with calculations of basal meltwater production rates and with field evidence of meltwater erosional features largely fine grained subglacial sediments with relatively low hydraulic conductivities had a capacity to drain only about 25 of all basal meltwater produced in the relevant subglacial catchment area the rest of the meltwater was evacuated through tunnel valleys in spontaneous outburst events subglacial drainage cycles are proposed in which each cycle begins with meltwater drainage through the substratum groundwater flow followed by water ponding at the ice bed interface and ends in catastrophic meltwater releases through tunnel valleys

glaciation induced perturbations in the earth s rotation a new appraisal we revisit the theory and predictions of glaciation induced perturbations in both the rotation rate of the earth or j 2 and the wander of the rotation pole with respect to the surface geography the two most common theoretical formulations associated with polar wander driven by the surface loading of a viscoelastic earth e g sabadini et al 1982 wu and peltier 1984 appear to disagree by one on the number of rotational normal modes associated with a surface gravitational response having n normal modes we show using a generalized theory that the two formalisms yield essentially equivalent predictions we next consider a benchmark comparison of recent predictions of present day polar wander speed due to glacial isostatic adjustment henceforth gia these comparisons confirm the validity of certain previous analyses e g spada et al 1992a they also reveal that predictions of polar wander speed can be sensitive to an assumption of incompressibility previous studies have noted that predictions of j 2 rotation rate as a function of lower mantle viscosity differ significantly in form from analogous predictions of polar wander speed we investigate these differences by considering the contribution to the predicted anomalies from the individual normal modes of relaxation we find that the normal mode structure of the j 2 rotation rate predictions is fundamentally different from that which characterizes the polar wander response and this difference reflects the distinct physical mechanisms which govern these anomalies finally using a large suite of forward computations as well as the calculation of a set of frechet kernels we investigate the sensitivity of our predictions to variations in the viscoelastic earth model we find for example that a previously noted sensitivity of polar wander speed predictions to variations in lithospheric thickness is only valid for earth models with relatively weak lower mantle viscosities 5 x 10 21 pa s

a gps velocity field for fennoscandia and a consistent comparison to glacial isostatic adjustment models in fennoscandia the process of glacial isostatic adjustment gia drives ongoing crustal deformation crustal velocities from gps observations have proved to be a useful tool in constraining gia models however reference frame uncertainties plate tectonics intraplate deformations as well as other geophysical processes contaminate the results former studies have shown that different international terrestrial reference frames have large discrepancies especially in the vertical component which hamper geophysical interpretation we present new velocity estimates for the fennoscandian and north european gps network our gps velocity field is directly realized in a gia reference frame using this method named the gia frame approach we are able to constrain gia models with minimal influence of errors in the reference frame or biasing signals from plate tectonics the drawbacks are more degrees of freedom that might mask real but unmodeled signals monte carlo tests suggest that our approach is robust at the 97 level in terms of correctly separating different models of ice history but depending on deformation patterns the identified earth model may be slightly biased in up to 39 of cases we compare our results to different one and three dimensional gia models employing different global ice load histories the gia models generally provide good fit to the data but there are still significant discrepancies in some areas we suggest that these differences are mainly related to inaccuracies in the ice models and or lateral inhomogeneities in the earth structure under fennoscandia thus gia models still need to be improved but the gia frame approach provides a base for further improvements

sea level change glacial rebound and mantle viscosity fornorthern europe northwestern europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the last glacial maximum models for this rebound and associated sea level change require a detailed knowledge of the ice sheet geometry including the ice thickness through time existing ice sheet reconstructions are strongly model dependent and inversions of sea level data for the mantle response may be a function of the model assumptions thus inverse solutions for the sea level data are sought that include both ice and earth model parameters as unknowns sea level data from fennoscandia the north sea the british isles and the atlantic and english channel coasts have been evaluated and incorporated into the solutions the starting ice sheet for fennoscandia is based on a reconstruction of a model by denton hughes 1981 that is characterized by quasi parabolic cross sections and symmetry about the load centre both global northwestern europe as a whole and regional subsets of the data solutions have been made for earth model parameters and ice height scaling parameters the key results are as follows 1 the response of the upper mantle to the changing ice and water loads is spatially relatively homogenous across scandinavia the north sea and the british isles 2 this response can be adequately modelled by an effective elastic lithosphere of thickness 65 85 km and by an effective upper mantle viscosity from the base of the lithosphere to the 670 km depth seismic discontinuity of about 3 4 1020 pa s the effective lower mantle viscosity is at least an order of magnitude greater 3 the ice thickness over scandinavia at the time of maximum glaciation was only about 2000 m much less than the 3400 m assumed in the denton hughes model 4 the ice profiles are asymmetric about the centre of the ice sheet with those over the western part being consistent with quasi parabolic functions whereas the ice heights over the eastern and southern regions increase much more slowly with distance inwards from the ice margin

water load definition in the glacio hydro isostatic sea level equation abstract models of glacio hydro isostatic rebound and the concomitant sea level change have been progressively improved over the past three decades recently the procedures used by the group at the australian national university anu for the hydro isostatic component of the theory have been questioned quat sci rev 21 2002 409 although the details of the anu group s procedures have not been published because they are mainly computational in nature rather than representing significant conceptual advances because of this criticism we set out here in detail the procedures that have been used for the treatment of the migration of shorelines as sea levels rise and fall the effect of retreat and advancing grounded ice on shelves and shallow seas and the transitions from grounded to floating ice and vice versa we conclude that there is no basis for the criticism that these formulations and their implementation provide a high resolution and complete description of both sea level change and of the estimates of volumes of ice exchanged with the oceans the results from this formulation are confirmed by the entirely independent analyses of milne et al quat sci rev 21 2002 361 and mitrovica and milne geophys j int 2002 submitted for publication who conclude that our formulation is significantly more accurate than the procedure advocated by peltier science 265 1994 195 rev geophys 36 1998a 603 geophys res lett 25 1998b 3955

constraints on the greenland ice sheet since the last glacial maximum from sea level observations and glacial rebound models abstract geomorphological descriptions of changes in the extent of the greenland ice sheet gis have been combined with glacial isostatic adjustment models to reproduce the sea level history of greenland since the last glacial maximum lgm the contribution to past sea level change around greenland due to ice load changes outside of that region has been considerable 10 s of meters while still contributing a rise of several mm yr 1 today the isostatic contribution to relative sea level around greenland from changes in the gis is found by iteratively perturbing preliminary ice models with different lgm extents and deglaciation starting times the resulting first order model that provides the best agreement between observed and predicted sea level contributes 3 1 and 1 9 m water equivalent of additional ice relative to present day ice volumes at the lgm and younger dryas respectively the gis in most areas does not appear to have extended far onto the continental shelf the exceptions being southern most southwest greenland and northern east greenland as well as at the coalescence of the northwest greenland and innuitian ice sheets changes in ice thickness since the lgm were 500 m along the present day outer coast and 1500 m along some parts of the present day ice margin the observed mid to late holocene fall in sea level to below the present day level and the subsequent transgression seen in some areas implies that the gis retreated behind the present day margin by distances of the order of 40 km before readvancing

continuous gps measurements of postglacial adjustment in fennoscandia 1 geodetic results 1 data collected under the auspices of the bifrost gps project yield a geographically dense suite of estimates of present day three dimensional 3 d crustal deformation rates in fennoscandia johansson et al 2002 a preliminary forward analysis of these estimates milne et al 2001 has indicated that models of ongoing glacial isostatic adjustment gia in response to the final deglaciation event of the current ice age are able to provide an excellent fit to the observed 3 d velocity field in this study we revisit our previous gia analysis by considering a more extensive suite of forward calculations and by performing the first formal joint inversion of the bifrost rate estimates to establish insight into the physics of the gia response in the region we begin by decomposing a forward prediction into the three contributions associated with the ice ocean and rotational forcings from this analysis we demonstrate that recent advances in postglacial sea level theory in particular the inclusion of rotational effects and improvements in the treatment of the ocean load in the vicinity of an evolving continental margin involve peak signals that are larger than the observational uncertainties in the bifrost network the forward analysis is completed by presenting predictions for a pair of fennoscandian ice histories and an extensive suite of viscoelastic earth models the former indicates that the bifrost data set provides a powerful discriminant of such histories the latter yields bounds on the assumed constant upper and lower mantle viscosity nu um nu lm specifically we derive a 95 confidence interval of 5 x 10 20 less than or equal to nu um less than or equal to 10 21 pa s and 5 x 10 21 less than or equal to nu lm less than or equal to 5 x 10 22 pa s with some preference for elastic lithospheric thickness in excess of 100 km the main goal of the bayesian inverse analysis is to estimate the radial resolving power of the bifrost gps data as a function of depth in the mantle assuming a reasonably accurate ice history we demonstrate that this resolving power varies from similar to 200 km near the base of the upper mantle to similar to 700 km in the top portion of the lower mantle we conclude that the bifrost data are able to resolve structure on radial length scale significantly smaller than a single upper mantle layer however these data provide little constraint on viscosity in the bottom half of the mantle finally elements of both the forward and inverse analyses indicate that radial and horizontal velocity estimates provide distinct constraints on mantle viscosity

the lageos constraint on deep mantle viscosity results from a new normal mode method for the inversion of viscoelastic relaxation spectra the recently observed acceleration in the node of the orbit of the lageos satellite has previously been shown to provide a good constraint on the viscosity of the earth s mantle beneath the 670 km seismic discontinuity this paper explores the extent to which the previously inferred lower mantle viscosity may be traded off against variations of other properties of the radial viscoelastic structure we show explicitly that the nontidal acceleration of rotation inferred from the lageos data and predicted as a consequence of the earth s response to the last deglaciation event of the current ice age is relatively insensitive both to variations of lithospheric thickness and to the presence or absence of plausible chemical heterogeneity across the 670 km interface it therefore provides a high quality constraint on the viscosity of the deep mantle with the upper mantle viscosity fixed at the nominal value of 1021 pa s the bounds on lower mantle viscosity lm are such that 2 1021 pa s lm 6 1021 pa s even when allowance is made for the presence of a viscous boundary layer at the base of the upper mantle such as would exist if the mantle convective circulation were layered

glacial rebound and relative sea level variations a new appraisal summary late pleistocene and holocene changes in sea level at technically stable shorelines contain information on the melting history of the ice sheets and on the response of the earth to changes in surface loads on time scales of 104yr some separation of parameters defining the ice loads and the earth s response can be achieved by examining sea level change at different sites around the world and at different epochs this paper examines the mathematical requirements for obtaining satisfactory solutions for the sea level equation rather than emphasizing results for the earth s response to the surface loads an examination of the equation expressing the sea level variation on a viscoelastic earth indicates that careful consideration needs to be given to both the definition of the ice load and the geometry of the redistributed water load if geophysically significant earth response parameters are to be deduced from observations of relative sea level the spectrum of the 5 x 5 area mean description of the ice load widely used in glacial rebound studies contains significant power at high degrees n 30 and can result in substantial spatial variations in sea level unless a thick lithosphere is introduced in the earth s response function a smoothed 1 1 description of the ice model avoids these high degree oscillations in relative sea level and produces satisfactory sea level results without requiring a thick lithosphere at far field sites the holocene sea levels are sensitive to the earth s response to the meltwater loading in the vicinity of the site and a high degree spatial resolution of coastline geometry is required to model the mantle flow driven by the differential loading about the site at some sites convergence of the solution to the sea level equation is not obtained even when the solution is expanded to degree 180 convergent solutions at lower degrees can be achieved by introducing earth models with a moderately thick lithosphere if high resolution ice and meltwater load models are not used then the tendency will be to overestimate the effective elastic thickness of the lithosphere estimates of mantle viscosity are also of questionable value if these high resolution models are not used a preliminary examination of sea levels at sites in both the near and far field places an upper limit of about 50 80 km on the effective lithospheric thickness these sea level observations are also consistent with an upper mantle viscosity of about 1021 pas with a lower mantle viscosity in the range of 1021 1023pa s

constraining models of postglacial rebound using space geodesy a detailed assessment of model ice 5g vm2 and its relatives summary using global positioning system very long baseline interferometry satellite laser ranging and doppler orbitography and radiopositioning integrated by satellite observations including the canadian base network and fennoscandian bifrost array we constrain in models of postglacial rebound the thickness of the ice sheets as a function of position and time and the viscosity of the mantle as a function of depth we test model ice 5g vm2 t90 rot which well fits many hundred holocene relative sea level histories in north america europe and worldwide ice 5g is the deglaciation history having more ice in western canada than ice 4g vm2 is the mantle viscosity profile having a mean upper mantle viscosity of 0 5 1021 pa s and a mean uppermost lower mantle viscosity of 1 6 1021 pa s t90 is an elastic lithosphere thickness of 90 km and rot designates that the model includes rotational feedback earth s response to the wander of the north pole of earth s spin axis towards canada at a speed of 1 myr 1 the vertical observations in north america show that relative to ice 5g the laurentide ice sheet at last glacial maximum lgm at 26 ka was 1 much thinner in southern manitoba 2 thinner near yellowknife northwest territories 3 thicker in eastern and southern quebec and 4 thicker along the northern british columbia alberta border or that ice was unloaded from these areas later thicker or earlier thinner than in ice 5g the data indicate that the western laurentide ice sheet was intermediate in mass between ice 5g and ice 4g the vertical observations and grace gravity data together suggest that the western laurentide ice sheet was nearly as massive as that in ice 5g but distributed more broadly across northwestern canada vm2 poorly fits the horizontal observations in north america predicting places along the margins of the laurentide ice sheet to be moving laterally away from the ice centre at 2 mm yr 1 in ice 4g and 3 mm yr 1 in ice 5g in disagreement with the observation that the interior of the north american plate is deforming more slowly than 1 mm yr 1 substituting vm5a t60 for vm2 t90 that is introducing into the lithosphere at its base a layer with a high viscosity of 10 1021 pa s greatly improves the fit of the horizontal observations in north america ice 4g vm5a t60 rot predicts most of the north american plate to be moving horizontally more slowly than 1 mm yr 1 in agreement with the data ice 5g vm5a t60 rot well fits both the vertical and horizontal observations in europe the space geodetic data cannot distinguish between models with and without rotational feedback in the vertical because the velocity of earth centre is uncertain and in the horizontal because the areas of the plate interiors having geodetic sites is not large enough to detect the small differences in the predictions of rotational feedback going across the plate interiors

carnallite mineralization in the nonmarine qaidam basin china evidence for the early diagenetic origin of potash evaporites modern potash evaporites carnallite mgkcl 3 6h 2 o occur at the qarhan salt plain qaidam basin china field and petrographic evidence shows that carnallite formed at the surface on the margins of dabusun lake is an extensively modified ephemeral deposit carnallite preserved at depth 0 13 m consists of coarse crystals formed as cement in primary halite layers and as displacive crystals in muds carnallite from the subsurface of qarhan salt plain displays textures identical to ancient potash evaporites from the permian salado formation new mexico and the devonian prairie formation saskatchewan canada the early diagenetic formation of carnallite on the northern shoreline of dabusun lake is probably a modern phenomenon because 1 groundwater brines at or above carnallite saturation occur to depths of up to 17 m and 2 brines trapped in fluid inclusions in primary halites from 0 to 45 m depth are well below carnallite saturation but become progressively more concentrated toward the modern surface fluid inclusion brines in the youngest halites less than 1 m depth reflecting modern surface brines are the most concentrated lake waters observed sinking and cooling of these surface brines to temperatures consistent with measured temperature profiles produces carnallite supersaturated conditions because of the strong temperature control on carnallite solubility

defining the translational velocity of the reference frame of earth summary earth s centre is fundamental to geodesy and geoscience because motions of sites on the surface are estimated relative to it international terrestrial reference frames itrf2000 and itrf2005 are defined by the centre of mass of earth s system cm consisting of solid earth the ice sheets the oceans and the atmosphere satellite lageos rotates about cm satellite laser ranging slr is used to estimate the velocity of cm relative to sites on the surface however itrf2000 and itrf2005 differ by 1 8 mm yr 1 suggesting that the velocity of cm is constrained poorly by slr in this study we define earth s reference frame with the centre of mass of solid earth ce site velocities estimated using slr vlbi gps and doris are corrected for a postglacial rebound model and inverted for the rotational velocities of the plates and the rotational and translational velocities of the four space techniques because the postglacial rebound predictions are relative to ce the velocity of ce relative to sites on the surface is estimated because the input slr site velocities are relative to cm the output slr translational velocity is the velocity of cm relative to ce the estimated velocity of ce does not depend strongly on the postglacial rebound model corrected for equal within uncertainties and having a root mean square of 0 5 mm yr 1 are estimates of the velocity of ce determined assuming that plate interiors are deforming radially as predicted by three postglacial rebound models and an estimate of the velocity of ce determined assuming that parts of plate interiors neither beneath nor along the margins of the late pleistocene ice sheets are not deforming laterally the velocity of ce equals within uncertainties probability greater than 5 per cent the velocity of cm in itrf2000 the velocity of ce differs significantly 0 05 per cent probability from the velocity of cm in itrf2005 earth s reference frame and we believe itrf s should be defined with the tightly constrained velocity of ce not with the poorly constrained velocity of cm because ce is believed to be moving relative to cm no faster than 0 5 mm yr 1 the velocity of ce estimated in this study is likely to be nearer the true velocity of cm than is the velocity of cm estimated using slr

itrf2005 a new release of the international terrestrial reference frame based on time series of station positions and earth orientation parameters 1 unlike the past international terrestrial reference frame itrf versions where global long term solutions were combined the itrf2005 uses as input data time series weekly from satellite techniques and 24 h session wise from very long baseline interferometry of station positions and daily earth orientation parameters eops the advantage of using time series of station positions is that it allows to monitor station non linear motion and discontinuities and to examine the temporal behavior of the frame physical parameters namely the origin and the scale the itrf2005 origin is defined in such a way that it has zero translations and translation rates with respect to the earth center of mass averaged by the satellite laser ranging slr time series spanning 13 years of observations its scale is defined by nullifying the scale and its rate with respect to the very long baseline interferometry vlbi time series spanning 26 years of observations the itrf2005 orientation at epoch 2000 0 and its rate are aligned to the itrf2000 using 70 stations of high geodetic quality the estimated level of consistency of the itrf2005 origin at epoch 2000 0 and its rate with respect to the itrf2000 is respectively 0 1 0 8 5 8 mm and 0 2 0 1 1 8 mm yr along the x yand z axis we estimate the formal errors on these components to be 0 3 mm and 0 3 mm yr we believe that this low level of agreement between the two frame origins is most probably due to the poor slr network geometry and its degradation over time the itrf2005 combination involving 84 co location sites revealed a scale inconsistency of 1 ppb 6 3 mm at the equator at epoch 2000 0 and 0 08 ppb yr between the slr and vlbi long term solutions as obtained by the stacking of their respective time series possible causes of this inconsistency may include the poor slr and vlbi networks and their co locations local tie uncertainties systematic effects and possible inconsistent model corrections used in the data analysis of both techniques for the first time of the itrf history the itrf2005 rigorous combination provides self consistent series of eops including polar motion from vlbi and satellite techniques and universal time and length of day from vlbi only a velocity field of 152 sites with an error less than 1 5 mm yr is used to estimate absolute rotation poles of 15 tectonic plates that are consistent with the itrf2005 frame this new absolute plate motion model supersedes and significantly improves that of the itrf2000 which involved six major tectonic plates citation altamimi z x collilieux j legrand b garayt and c boucher 2007 itrf2005 a new release of the international terrestrial reference frame based on time series of station positions and earth orientation parameters j geophys res 112 b09401

evidence for postglacial signatures in gravity gradients a clue in lower mantle viscosity abstract the earth s surface was depressed under the weight of ice during the last glaciations glacial isostatic adjustment gia induces the slow recession of the trough that is left after deglaciation and is responsible for a contemporary uplift rate of more than 1 cm yr around hudson bay the present day residual depression an indicator of still ongoing gia is difficult to identify in the observed topography which is predominantly sensitive to crustal heterogeneities according to the most widespread gia models which feature a viscosity of 2 3 10 21 pa s on top of the lower mantle the trough is approximately 100 m deep and cannot explain the observed gravity anomalies across north america these large anomalies are therefore usually attributed to subcontinental density heterogeneities in the tectosphere or to slab downwelling in the deep mantle here we use observed gravity gradients gg to show that the uncompensated gia trough is four times larger than expected and that it is the main source of the north american static gravity signal we search for the contribution to these ggs from mantle mass anomalies which are deduced from seismic tomography and are mechanically coupled to the global mantle flow this contribution is found to be small over laurentia and at least 82 of the ggs are caused by gia such a contribution from gia in these gg observations implies a viscosity that is greater than 10 22 pa s in the lower mantle our conclusions are a plea for gia models with a highly viscous lower mantle which confirm inferences from mantle dynamic models any change in gia modelling has important paleoclimatological and environmental implications encouraging scientists to re evaluate the past ice history at a global scale these implications in turn affect the contribution of bedrock uplift to the contemporaneous mass balance over antarctica and greenland and thus the present day ice melting rate as deduced from the grace space mission additionally studies of the thermo chemical structure of the lithosphere crust under north america that exploit gravity or geodetic data should be corrected for a gia model which is not the case today

ice age cycles earth s rotation instabilities and sea level changes a new class of multilayered viscoelastic earth models based on prem is applied to the modeling of earth s rotation instabilities and associated sea level changes induced by the occurrence of pleistocene ice age cycles that match the oxygen isotope records over the last 0 8 myr the novelty of our approach stands on the usage for the first time in post glacial rebound induced sea level studies of a fully analytical scheme based on normal mode theory that allows to deal with complexities of the real earth such as lithospheric and mantle layering sphericity and self gravitation the ice models are based on ice 3g our results show that differences in true polar wander tpw and tpw induced sea level changes between earth models with a few layers and models having enough layers so that saturated continuum limits are reached can amount factors 2 to 3 this may change conclusions derived from some earlier studies on polar wander induced changes in climate that were based on earth models with a limited amount of layers the results indicate that models containing about 15 layers with a stratified lower mantle and transition zone have reached saturated continuum responses for both tpw and tpw induced sea level changes stratification of the lithosphere is not important this is in contrast with the sensitivity of post seismic deformation models this difference in sensitivity on the radial profile of the earth model can be explained with simple arguments on the dependence on zonal degree

ice 3g a new global model of late pleistocene deglaciation based upon geophysical predictions of post glacial relative sea level change a new high resolution global model of late pleistocene deglaciation is inferred on the basis of geophysical predictions of postglacial relative sea level variations in which the ice ocean solid earth interaction is treated in a gravitationally self consistent fashion for the purpose of these analyses the radial viscoelastic structure of the planet is assumed known on the basis of previously published sensitivity tests on solutions of the forward problem only radiocarbon controlled relative sea level histories from sites that were actually ice covered with one or two additions are employed to constrain the model leaving relative sea level rsl data from sites that were not ice covered to be employed to confirm its consistency results for these confirmatory analyses are reported elsewhere here the new deglaciation model referred to as ice 3g is compared to previous models derived by several independent means and tested against a number of additional observations other than sea level histories including geologically controlled retreat isochrones oxygen isotope data from deep sea sedimentary cores and coral terrace elevations the latter two observations strongly constrain the net sea level rise that has occurred since the onset of deglaciation and therefore the mass of ice that melted during the last glacial interglacial transition

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 abstract 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 5 m relative to belgium since 8 cal ka bp 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

omori like decay of postseismic velocities following continental earthquakes various mechanisms have been proposed to explain the transient enhanced surface deformation rates following earthquakes unfortunately these different mechanisms can produce very similar surface deformation patterns leading to difficulty in distinguishing between them here we return to the observations themselves and compile near field postseismic velocity measurements following moderate to large continental earthquakes we find that these velocities have a remarkably consistent pattern with velocity inversely proportional to time since the earthquake this suggests that postseismic velocities show an omori like decay and that postseismic displacements increase logarithmically over time these observations are inconsistent with simple linear maxwell or burgers body viscoelastic relaxation mechanisms but are consistent with rate and state frictional afterslip models and power law shear zone models the results imply that near field postseismic surface deformation measurements are primarily the result of fault zone processes and therefore that the inference of lower crustal viscosities from near field postseismic deformation requires care

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

lithosphere thickness and mantle viscosity inverted from gps derived deformation rates in fennoscandia summary crustal deformation in fennoscandia is associated with the glacial isostatic adjustment gia process that is caused by ongoing stress release of the mantle after removal of the late pleistocene ice sheet by 10 cal ka bp with an earth model of defined structure and rheology and an ice sheet model of known melting history the gia process can be simulated by geophysical models and the surface deformation rates can be calculated and used to compare with global positioning system gps observations therefore the crustal deformation rates observed by gps in fennoscandia provide constraints on the geophysical models on the basis of two ice sheet models anu ice and ice 5g reconstructed independently by the australian national university anu and university of toronto we use the gps derived deformation rates to invert for lithosphere thickness and mantle viscosity in fennoscandia the results show that only a three layer earth model can be resolved from current gps data providing robust estimates of effective lithosphere thickness upper and lower mantle viscosity the earth models estimated from inversion of gps data with two different ice sheet models define a narrow range of parameter space the lithosphere thickness between 93 and 110 km upper mantle viscosity between 3 4 and 5 0 1020 pa s and lower mantle viscosity between 7 1021 and 13 1021 pa s the estimates are consistent with those inverted from relative sea level indicators

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

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

effects of partial melting on seismic velocity and attenuation a new insight from experiments the effects of partial melting on seismic velocity and attenuation have long been studied by focusing on the direct effects of melt such as the poroelastic effect the direct effects are generally very small for a very small melt fraction because geochemical studies have shown that the melt fraction during partial melting is very small 0 1 it is difficult to explain upper mantle low velocity regions by the direct effects of melt recent experimental studies by using a rock analog have captured a significant enhancement of polycrystal anelasticity just before partial melting in the absence of melt this newly recognized effect enables us to interpret seismological and geochemical observations consistently the new anelasticity model significantly changes the interpretation of upper mantle seismic structures this review summarizes the recent progress in the understanding of polycrystal anelasticity starting from a basic knowledge of linear anelasticity

simultaneous estimation of global present day water transport and glacial isostatic adjustment global water transport between oceans and continents during the transition from glacial to interglacial times has been enormous the viscoelastic solid earth has been responding to this unloading of large ice masses with a rise of the land masses in a process termed glacial isostatic adjustment in addition significant changes in the land ocean water distribution occur at present as both present day changes in the ice water thickness and glacial isostatic adjustment affect space geodetic measurements it is difficult to untangle the relative contributions of these two processes here we combine gravity measurements and geodetic data of surface movement with a data assimilating model of ocean bottom pressure to simultaneously estimate present day water transport and glacial isostatic adjustment we determine their separate contributions to movements in the geocentre which occur in response to changes in the earth s mass distribution with uncertainties below 0 1 mm yr 1 according to our estimates mass losses between 2002 and 2008 in greenland alaska yukon and west antarctica are 104 23 101 23 and 64 32 gt yr 1 respectively our estimates of glacial isostatic adjustment indicate a large geocentre velocity of 0 72 0 06 mm yr 1 in the polar direction we conclude that a significant revision of the present estimates of glacial isostatic adjustments and land ocean water exchange is required present day changes in the thickness of ice sheets and glacial isostatic adjustment both affect space geodetic measurements a combination of gravity measurements and geodetic data of surface movement with a data assimilating model of ocean bottom pressure allows the simultaneous estimation of present day water transport and glacial isostatic adjustment

the impact of lateral variations in lithospheric thickness on glacial isostatic adjustment in west antarctica differences in predictions of glacial isostatic adjustment gia for antarctica persist due to uncertainties in deglacial history and earth rheology the earth models adopted in many gia studies are defined by parameters that vary in the radial direction only and represent a global average earth structure referred to as 1 d earth models oversimplifying the actual earth structure leads to bias in model predictions in regions where earth parameters differ significantly from the global average such as west antarctica we investigate the impact of lateral variations in lithospheric thickness on gia in antarctica by carrying out two experiments that use different rheological approaches to define 3 d earth models that include spatial variations in lithospheric thickness the first experiment defines an elastic lithosphere with spatial variations in thickness inferred from seismic studies we compare the results from this 3 d model with results derived from a 1 d earth model that has a uniform lithospheric thickness defined as the average of the 3 d lithospheric thickness irrespective of the deglacial history and sublithospheric mantle viscosity we find higher gradients of present day uplift rates i e higher amplitude and shorter wavelength in west antarctica when using the 3 d models due to the thinner than 1 d average lithosphere prevalent in this region the second experiment uses seismically inferred temperature as an input to a power law rheology thereby allowing the lithosphere to have a viscosity structure modelling the lithosphere with a powerlaw rheology results in a behaviour that is equivalent to a thinner lithospheremodel and it leads to higher amplitude and shorter wavelength deformation compared with the first experiment we conclude that neglecting spatial variations in lithospheric thickness in gia models will result in predictions of peak uplift and subsidence that are biased low in west antarctica this has important implications for ice sheet modelling studies as the steeper gradients of uplift predicted from the more realistic 3 d model may promote stability in marine grounded regions of west antarctica including lateral variations in lithospheric thickness at least to the level of considering west and east antarctica separately is important for capturing shortwavelength deformation and it has the potential to provide a better fit to global positioning system observations as well as an improved gia correction for the gravity recovery and climate experiment data