new inferences of mantle viscosity from joint inversion of long wavelength mantle convection and post glacial rebound data we perform joint inversions for mantle viscosity of geophysical observables associated with both mantle convection and glacial isostatic adjustment gia our data include coefficients of the non hydrostatic geoid up to degree 8 and decay times associated with post glacial relative sea level rsl variations in hudson bay and fennoscandia we find that both data sets may be reconciled using a single profile of mantle viscosity which is characterized by a significant increase with depth across this region this result weakens previous arguments that the mantle rheology has significant transient effects the viscosity profiles we obtain are found to reconcile the observed free air gravity anomaly over hudson bay

on secular geocenter motion the impact of climate changes abstract we investigate the impact of recent climate changes on the long term displacement of the center of figure cf of the earth also defined as the geocenter in our convention with respect to the center of mass of the whole earth cm the two realizations of the international terrestrial reference system itrs entitled itrf2000 and itrf2005 present a difference of 1 8 mm yr between the velocities of their respective frame origins suggesting an acceleration of the geocenter towards the north pole we investigate if such a displacement could be explained by geophysical phenomena such as the present ice melting and the sea level rise using published observations on ice caps and glaciers we calculated the range of geocenter motion that may occur today we found that the global ice melting induces long term displacements of the geocenter mainly along the z axis toward the north pole the geocenter velocity is today between 0 3 and 0 7 0 8 mm yr and has doubled during last decade with the recent acceleration of ice melting combining with greff lefftz 2000 results on post glacial rebound we conclude that a present secular geocenter velocity of 1 mm yr is possible however the recent increase of the geocenter velocity cannot explain the difference observed between the two last realizations of the itrs our results comfort the previous conclusions about itrf2000 and itrf2005 and the pre analysis of itrf2008 data suggesting that the large z translation rate between the itrs realizations is probably due to an imprecise itrf2000 origin finally we show that determining precisely the geocenter velocity would give a new type of information that may be useful to more precisely constrain mass exchanges associated with climate changes

itrf2008 contribution to glacial isostatic adjustment and recent ice melting assessment 1 we investigate what information station vertical velocities of the itrf2008 provide on global geodetic parameters and by extension on glacial isostatic adjustment gia and recent ice melting rim processes we infer degree 2 spherical harmonic coefficients shc of the earth figure change and thej2 gravity rate j 2 which we compare with five gia models we find j 2 to be 0 0 2 4 10 11 yr 1 which is consistent with recent studies that propose a j 2 change in the 1990s due to rim whose contribution to the j 2 would be today around 3 5 4 0 2 4 10 11 yr 1 such results favor peltier 2004 vm2 or paulson et al 2007 gia models the itrf2008 shc that are directly impacted by the gia rotational feedback confirm with a good precision recent results from grace mission that initiated a debate on gia rotational feedback and about peltier gia model quality we find a coefficient consistent with paulson s and other model and more than 7 times smaller than coefficients in peltier s models two explanations are possible 1 if the model of peltier 2004 vm2 were to be correct then the strong rotational feedback in the model must be counteracted by a strong rotational feedback in the opposite direction generated by current ice loss 2 if the model of paulson et al 2007 were to be correct therefore gia and rim separately induce negligible rotational feedbacks both answers are quite extreme and call for more investigation on gia modeling and rotational feedback

post glacial rebound and transient lower mantle rheology summary although post glacial rebound data have been conventionally interpreted as being governed by the steady state component of the mantle viscosity spectrum the radial profile of this parameter which is then inferred by fitting a model to observations is characterized by the fact that it exhibits rather slight variation with depth this disagrees with expectations based upon microphysical models of the solid state creep process it also disagrees with very recent inferences of the viscosity stratification based on isostatic geoid anomalies expected on the basis of the internal lateral heterogeneity of mantle density obtained from seismic tomographic analyses the new calculations of the signatures of post glacial rebound reported here show that these two types of information are easily reconciled if the previously inferred value of the lower mantle viscosity is interpreted as a transient value as originally suggested by weertman on the basis of qualitative considerations in these new models considered here the steady state creep resistance of the lower mantle is not constrained at all by post glacial rebound observations it can be futed only by an appeal to other geophysical data whether such models are actually required by the data should become clear in the very near future

a complete formalism for the inversion of post glacial rebound data resolving power analysis summary a formal inverse theory for mantle viscosity based upon the data of glacial isostatic adjustment is here formulated and applied to synthetic data in this theory full account has been taken of the normal mode nature of the forward problem for realistic viscoelastic maxwell models of the planet since it is impossible to accurately infer the excitation and decay constants of the individual normal modes from the observations the formalism is cast in terms of the observed gross earth data in the time domain in this analysis expressions are required for the first order perturbations in both the modal amplitudes and relaxation times that are induced by an arbitrary radial perturbation to the starting viscosity profile a numerical technique is developed which enables us to accurately determine differential kernels for the modal amplitudes the analogous kernels for the modal decay times are derived analytically peltier 1976 and the complete set of kernels is shown to satisfy the physical constraint imposed by the uniqueness of the state of isostatic equilibrium for the viscously incompressible maxwell models that we employ when the problem is parametrized in terms of the logarithm of viscosity the kernels are capable of accurately predicting shifts in the normal mode characteristics for at least an order of magnitude variation in mantle viscosity using bayesian statistics a formal inversion is applied to a set of synthetically generated data these data chosen to reproduce the space time coverage of the actual observables include a subset related to the global gravity field and a large sequence of idealized relative sea level rsl curves it is found that even very weak a priori constraints can provide a stable and accurate inversion a resolving power analysis indicates a spatial resolution of approximately 1200km near the core mantle boundary cmb with a gradual improvement to better than 350km in the middle of the upper mantle subsets of the synthetic data are inverted in order to examine conditions on stability and accuracy and to determine their relative contributions to the spatial resolution data from progressively older beaches are shown to contribute most to the spatial resolution at all depths though the improvement in lower mantle resolution converges for data obtained from beaches formed within the last 5000 yr furthermore the rsl curves in the vicinity of the peripheral bulge of the ancient laurentide ice sheet are significant contributors to lower mantle resolution as demonstrated in previous analyses of the forward problem the inversion of this subset of the data also appears to be encouragingly stable

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

dynamic mantle density heterogeneities and global geodetic observables summary we investigate the influence of mantle dynamics on low degree deformations of the earth at geological timescale we first compute surface deformations and discuss the analytical form of the tangential surface displacement induced by internal loads in a reference frame related to the centre of mass of the planet we use the theoretical love numbers formalism since the earth has a viscoelastic behaviour at geological timescale then we quantify degree one and degree two deformations induced by upwelling domes and subducted plates sinking into the mantle we use a simple model in which the slabs are modelled as blobs diving vertically through the mantle and in which the domes are assumed to be stable over the last 120 ma their location is modelled from seismic tomography within the lower mantle the temporal evolutions of the j2 gravitational potential coefficient and of the geocentre motion are plotted since 120 ma we find that 1 the mantle density heterogeneities within the mantle can explain the present day non hydrostatic flattening of the earth however they vary at a too slow timescale to significantly perturb the coefficient 2 although there is a significant discrepancy of about a few hundred metres between the centre of figure and the centre of mass of the earth the secular variation of the geocentre motion is one order of magnitude smaller than the one induced by surface loads

effects on post glacial rebound from the hard rheology in the transition zone summary we analyse the influences of a viscosity increase in the transition zone between 420 and 670 km on the geophysical signatures induced by post glacial rebound ranging from the perturbations in the earth s rotation to the short wavelength features associated with the migration of the peripheral bulge a self gravitating model is adopted consisting of an elastic lithosphere a three layer viscoelastic mantle and an inviscid core the horizontal displacements and velocities and the stress pattern are extremely sensitive to the viscosity increase and to the chemical stratification of the transition zone the hardening of the upper and the chemical density jumps in mantle below the 420 discontinuity induces a channel effect which contaminates the horizontal deformation both in the near field and in the far field from the ice sheets these findings indicate that intraplate geodetic data can be used to put bounds on the viscosity increase in the transition zone and on the amount of chemical stratification in the mantle the stress field induced in the lithosphere by the pleistocenic ice sheet disintegration is a very sensitive function of mantle viscosity stratification the existence of seismic activity along passive continental margins of previously glaciated areas requires a substantial viscosity increase in the mantle with the viscosity of the transition zone acting as a controlling parameter a viscously stratified mantle is responsible for a delayed upward migration of stress in the lithosphere which can account for the seismicity today

radial profile of mantle viscosity results from the joint inversion of convection and postglacial rebound observables we present new inferences of the radial profile of mantle viscosity that simultaneously fit long wavelength free air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions hudson bay arctic canada and fennoscandia the relative sea level variation at these latter sites is constrained by age height pairs obtained by geological survey rather than the subjective trends which are commonly used in glacial isostatic adjustment gia studies our viscosity inferences are generated using two approaches first we adopt a relative viscosity profile which is known to provide a good fit to the free air gravity harmonics and determine an absolute scaling which yields a best fit to the gia decay time constraints second we perform an iterative nonlinear joint inversion of the two data sets in both cases our inferred profiles are characterized by a significant increase of viscosity 2 orders of magnitude with depth to values of 1022 pa s in the bottom half of the lower mantle the new viscosity profiles are shown to satisfy constraints based on the postglacial uplift of both fennoscandia the classic haskell 1935 number and hudson bay which have commonly been invoked to argue for an isoviscous mantle furthermore the models are used to predict a set of long wavelength signatures of the gia process these include predictions of gia induced variations in 1 the length of day over the late holocene period 2 the earth s precession constant and obliquity over the last 2 6 myr and 3 the present day zonal harmonics of the geopotential jl l 7 the predictions 1 and 3 bound the late holocene and ongoing mass flux between the large polar ice sheets greenland and antarctic and the global oceans to small values 0 4 mm yr equivalent eustatic sea level rise

secular variation of the geocenter the degree 1 deformations of earth induced by a surface load are computed in a reference frame related to the center of mass of the planet using a theoretical approach love number formalism at secular timescale where earth has a viscoelastic behavior the temporal variation of the coordinates of the geocenter induced by the pleistocenic deglaciation is investigated for two loading histories three ice sheets with the same time dependence or ice 3g model testing different viscosity profiles within the mantle the present day secular variation of earth s geocenter induced by postglacial rebound is found to be from 0 2 up to 0 5 mm yr and consequently we suggest that observations from space geodesy of this rate could be used to constrain the viscosity contrast between upper and lower mantle

mantle viscosity inferences from joint inversions of pleistocene deglaciatio induced changes in geopotential with a new slr analysis and polar wander joint inversions of post glacial rebound induced secular changes in low degree harmonics of the geopotential and true polar wander tpw systematically indicate that the upper mantle viscosity has a value that is considerably smaller than 10 21 pas the lower mantle viscosity is about one order of magnitude larger than the upper mantle viscosity discrepancies in the viscosity profiles inferred from even and odd zonals are likely an indication of recent unmodeled glacial forcings and or insufficient precision in the evaluation of the mass loss from pleistocene ice sheets the influence of systematic errors in slr data reduction due to thermal drag on the lageos satellites for the uneven zonals of the geopotential is avoided by making use of the starlette and stella satellites to recover the uneven zonals and by considering lumped coefficients for these uneven terms

the inference of mantle viscosity from an inversion of the fennoscandian relaxation spectrum summary a formal inverse theory for mantle viscosity is here applied to a relaxation spectrum derived from the post glacial uplift of fennoscandia the spectrum represents the set of eigenfrequencies or inverse decay times for the fundamental mode of viscous gravitational relaxation between the spherical harmonic degrees 14 to 45 and 65 to 80 theoretical predictions of the eigenfrequencies are based upon the determination of the zeroes of the secular determinant function derived for a spherically symmetric self gravitating visco elastic planet differential kernels relating shifts in the eigenfrequencies to arbitrary perturbations in the radial viscosity profile i e frechet kernels are computed using the variational principle derived by peltier 1976 the inversions are performed within the framework of non linear bayesian inference and the problem has been parameterized in terms of the logarithm of viscosity the inversions have yielded a set of robust constraints which all models for the radial viscosity profile below fennoscandia must satisfy the a posteriori estimates and variance reduction are found to be insensitive to the a priori variance ascribed to the model layers the constraints have furthermore been summarized into a set of a posteriori estimates of the average model viscosity value in radial regions consistent with the resolving power of the data which decreases from a radial length scale of approximately 120km at the base of the lithosphere to 1200km at 1000km depth the data provide essentially no information regarding the mantle rheology below 1200km depth for example for earth models with a lithospheric thickness lt of 100 km the volumetric average logarithm of viscosity in regions in the depth ranges 1040 400 km 670 210 km and 235 100 km is constrained to be respectively 21 03 0 09 20 70 0 08 and 20 37 0 19 we have repeated the inversions for a number of assumed lithospheric thicknesses and have found that a relatively low viscosity layer in the sublithospheric region with respect to the underlying upper mantle is required for lt 120km in this respect we have quantified the previously described trade off between a decrease in the viscosity of this region and a decrease in lt cathles 1975 in forward analyses of the glacial isostatic adjustment data set it is common to use earth models with isoviscous upper and lower mantle regions to investigate this two layer case we have also performed inversions which assume perfect correlation amongst the model layers in the upper and separately the lower mantle under this strict model space limitation the inversions yield models with upper and lower mantle viscosities in the range 3 7 1020 4 5 1020 pa s and 2 2 1021 1 9 1021 pa s respectively the ranges are obtained from a suite of inversions using lithospheric thickness from 70 km to 145 km the a posteriori constraints generated from the bayesian inversions are used together with a statistic based on the computed misfit to the fennoscandian relaxation spectrum to rule out a number of previously published viscosity models

geophysical interpretation of observed geocenter variations geocenter variations are caused by mass redistribution within the earth system especially the atmosphere oceans and continental water using surface pressure fields and soil moisture and snow depth fields of the ncep ncar climate data assimilation system i cdas i 1 we estimate contributions from variations in atmospheric surface pressure and continental water storage to the earth s geocenter center of mass variation in addition sea surface anomalies determined by the topex poseidon altimeter are used to investigate geocenter variations resulting from ocean mass redistribution these sea surface height data were corrected using a simplified steric model a comparison with observed geocenter variations derived from lageos 1 and 2 satellite laser ranging data indicates that the atmosphere oceans and continental hydrological cycle all provide significant contributions at different frequencies geocenter variations estimated in this paper are in reasonably good agreement with results given by dong et al 1997 for atmospheric and ocean contributions but not for the estimates of continental hydrological contributions

slaking behavior of clay bearing rocks during a one year exposure to natural climatic conditions abstract slaking of clay bearing rocks upon exposure to natural climatic conditions is a common problem at many engineering projects depending upon the regional climate clay bearing rocks slake in response to heating and cooling wetting and drying and freezing and thawing cycles however laboratory methods used for assessing the slaking behavior of clay bearing rocks including the standardized methods by the american society for testing and materials astm and the international society for rock mechanics isrm involve only wetting and drying treatments in this study we investigated the slaking behavior of clay bearing rocks by exposing them to natural climatic conditions for a period of one year twenty clay bearing rocks consisting of 5 claystones 5 mudstones 5 siltstones and 5 shales were selected for the study twelve replicate samples of each rock type were prepared so that each sample consisted of 10 pieces each piece weighing 40 60 g with a total weight of 450 to 550 g the samples were placed in separate metallic pans and exposed to natural climatic conditions from september 2009 to september 2010 each month one replicate sample of each rock type was removed from natural exposure and its grain size distribution was determined disintegration ratio d r defined as the ratio of the area under the grain size distribution curve of the slaked material for a given sample to the total area encompassing all grain size distributions was used to evaluate the extent of disintegration upon slaking d r can range from 0 to 1 with 0 indicating 100 slaking and 1 indicating no slaking after 3 months of exposure to natural climatic conditions claystones mudstones siltstones and shales exhibited d r values of 0 223 0 302 0 698 and 0 494 respectively these results suggest that over a given period of time claystones slake the most and siltstones the least relating d r to clay content of the rocks studied reveals that rocks with higher clay contents slake more rapidly and extensively under natural climatic conditions than those with lower clay contents

constraints provided by ground gravity observations on geocentre motions the geocentre motion is the motion of the centre of mass of the entire earth considered an isolated system in a terrestrial system of reference we first derive a formula relating the harmonic degree 1 lagrangian variation of the gravity at a station to both the harmonic degree 1 vertical displacement of the station and the displacement of the whole earth s centre of mass the relationship is independent of the nature of the earth deformation and is valid for any source of deformation we impose no constraint on the system of reference except that its origin must initially coincide with the centre of mass of the spherically symmetric earthmodel next we consider the geocentre motion caused by surface loading in a system of reference whose origin is the centre of mass of the solid earth we obtain a specific relationship between the gravity variation at the surface the geocentre displacement and the load love number h 1 which demands the earth s structure and rheological behaviour be known for various networks of real or fictitious stations we invert synthetic signals of surface gravity variations caused by atmospheric loading to retrieve the degree 1 variation of gravity we then select six well distributed stations of the global geodynamics project which is a world network of superconducting gravimeters to invert actual gravity data for the degree 1 variations and determine the geocentre displacement between the end of 2004 and the beginning of 2012 assuming it to be due to surface loading we find annual and semi annual displacements with amplitude 0 5 2 3 mm

on the stability of a geodetic no net rotation frame and its implication for the international terrestrial reference frame 1 one of the important implications of a no net rotation nnr model of the earth s horizontal surface velocity is that it is used as a constraint in the definition of the international terrestrial reference frame itrf we present here our most recent estimates of an nnr model gsrm nnr 2 that uses over 5700 geodetic station velocities we test the sensitivity of our model by varying data input and model assumptions the difference between our various models is maximally 0 6 mm yr 1 but can be larger if we use only a geographically limited core velocity data set or if a significant bias in frame origin translation rate exists although plate boundary zones should not be considered as being part of rigid plates kreemer and holt 2001 the details of the velocity field within the plate boundaries have an insignificant effect on the nnr frame the difference between the various nnr models that we test is small compared to the difference between our nnr models and itrf2000 which can be up to 3 1 mm yr 1 we conclude that the itrf2000 does not satisfy the nnr condition when considering an nnr model that is based on the actual present day velocity of the entire earth s surface instead of nnr nuvel 1a

contribution of glacial isostatic adjustment to the geocenter motion abstract the geocenter motion describes the surface net displacement of the entire solid earth with respect to the center of mass of the entire earth including surface masses therefore it resembles an integrative quantity of surface displacement and mass redistribution inside the earth as well as at its surface seasonal variations of this quantity are understood to originate mainly from mass redistribution in the water cycle in contrast a secular trend of the geocenter motion is possible to result also from the dynamics of the earth s interior one mechanism inducing a secular geocenter motion is the glacial isostatic adjustment describing the deformation and mass redistribution in the earth s interior due to glaciations during the pleistocene focusing on this contribution we compute the geocenter motion from the displacement and gravity potential fields calculated for a spherical self gravitating incompressible and viscoelastic earth model loaded by the last pleistocene glacial cycle we discuss the fluid core approximation usually adopted and assess the influence of a list of modelling parameters which are the upper and lower mantle viscosity lithosphere thickness and glaciation history we find a rather robust geocenter motion with respect to parameter variations which is directed towards northeast canada and shows velocities that vary between 0 1 and 1 mm yr depending on the adopted earth model and glaciation history parameterizations

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

heat flow in the trans hudson orogen of the canadian shield implications for proterozoic continental growth fourteen new heat flow and radiogenic heat production measurements have been obtained in the paleo proterozoic trans hudson orogen of the canadian shield this orogen which consists of several distinctive belts corresponds to a pulse of crustal growth through island arc magmatism between 1 9 and 1 8 ga the data now available include 17 previously published measurements heat flow variations that are related to the history of magmatism and internal differentiation of the belts provide constraints on the crustal assemblages in the different belts of the orogen the average and standard deviation of heat flow values for the entire orogen 425 11 mw m 2 are identical to those of the older superior province and of the younger grenville province for the orogen as a whole heat flow is weakly correlated to the heat production of surface rocks high heat flow values are found in the thompson belt consisting of metasedimentary rocks deposited on the ancient continental margin of the superior craton there the accumulation of sediments derived from older and differentiated continental upper crust has resulted in significant concentrations of rdioelements in large volumes of rocks the heat flow is low in the belts that expose juvenile proterozoic crust consisting mostly of arc related volcanic rocks in the flin flon snow lake belt the average heat flow is the same as the average of the orogen the low heat production and the lack of correlation between heat flow and heat production suggest that the supracrustal volcanics exposed a t the surface are thin and rest on a basement richer in radioelements in the lynn lake belt the heat flow is significantly lower than the average for the orogen although the surface heat production is not low the heat flow data require a thin 10 kin surface layer overlying the mid and lower crust depleted in ra dioelements around the town of lynn lake heat flow is consistently low over a distance of m40 kin the coincidence between this cold spot and anomalously thick crust suggests that deep crustal roots may be preserved because of the stronger rheology implied by the low temperatures the evolution of the trans hudson orogen exemplifies the interplay between the processes generating rocks of evolved composition which require crustal thickening and those forming normal continental crust with average thickness which require crustal flow and soft crustal rheology

late pleistocene and holocene sea level change in the australian region and mantle rheology summary spatial and temporal variations in sea level are produced by the melting of the late pleistocene ice and by the earth s response to the redistribution in surface loads by examining different parts of the sea level curves of the past 20 000 yr from geographically widely distributed regions it becomes possible to constrain models of the melting history of the ice sheets and of the earth s rheology observations from sites away from the former arctic ice sheets such as the australian and south pacific region are particularly important for constraining the total meltwater volumes added into the oceans in the past 20 000 yr and the rates at which this occurred these observations indicate that the antarctic ice sheets provided a significant contribution to the sea level rise at a rate that was approximately synchronous with the melting of the laurentide ice sheet except for the interval 9000 6000 yr ago when it may have lagged behind minor melting of the antarctic ice sheet appears to have continued throughout the late holocene differential observations of the late holocene sea level change recorded at sites in the same region are particularly useful for estimating parameters describing the earth s non elastic response to surface loading the effective parameters used here are a lithospheric thickness an upper mantle viscosity and a lower mantle viscosity describing the response below 670 km depth with the observations used here it is not possible to separate the lithospheric thickness h from the upper mantle viscosity and the viscosity results are based on the assumption that 50 h 100 km neither do these observations provide a resolution of the depth dependence of viscosity in the upper mantle and the resulting estimates are effective parameters only differential sea levels along continental margins and along the shores of large gulfs and bays constrain the effective upper mantle viscosity to be about 1 2 1020 pa s 1 while differential values from islands of different sizes are suggestive of a somewhat lower value the lower mantle taken to be below 670 km depth viscosity is about two orders of magnitude greater than this the estimated ice and rheological models explain many of the holocene sea level observations throughout the australian and southern pacific region the tilting of continental margins as exemplified by observations of variable amplitudes of the holocene high stands and the variable times at which sea levels first reached their present level along the north queensland coast and great barrier reef is well represented by these models differential holocene sea levels observed along the narrow spencers gulf of south australia are also well explained by the models and in neither case is it necessary to invoke tectonic motions predicted late holocene sea levels at small to medium sized islands are characterized by small amplitude high stands that reached their maximum values about 4000 2000 yr ago consistent with observations from the society cook and tuamotu islands

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

present day secular variations in the zonal harmonics of earth s geopotential we develop a new formalism for the prediction of secular variations in the gravitational potential field of a spherically symmetric self gravitating maxwell viscoelastic planetary model subjected to an arbitrary surface load which may include a gravitationally self consistent ocean loading component the theory is applied to generate the most accurate predictions to date of the present day secular variations in the zonal harmonics of the geopotential the so called for degree arising as a consequence of the late pleistocene glacial cycles in this respect we use the very recent ice 3g reconstruction of the last late pleistocene deglaciation event tushingham and peltier 1991 a comparison of these predictions with those generated using simplified disk models of the ice sheets which have been used in all previous studies of the harmonics 2 indicates that the disk model approximation introduces unacceptably large errors at all spherical harmonic degrees except perhaps 2 predictions have also been made using a eustatic loading approximation also used in previous studies in place of a gravitationally self consistent ocean loading component and we have found that the resulting discrepancy is largest at degrees 2 8 and 10 in the case of the magnitude of the error incurred using the eustatic approximation can be as large as order 10 15 of the predicted value we have attributed this discrepancy to the present day net flux of water away from the equatorial regions arising from the remnant present day adjustment associated with the late pleistocene glacial cycles the effect represents a heretofore unrecognized contribution to the harmonics or alternatively the nontidal acceleration of earth s axial rate of rotation in terms of the latter the maximum anomaly in the length of day is approximately 1 7 s yr we also consider the sensitivity of the data to variations in the radial mantle viscosity profile by using a suite of forward calculations and an examination of frechet kernels the theory required for the computation of those kernels is described herein we find that the radial variation in sensitivity can be a strong function of the viscosity model used in the calculations for models with a uniform upper mantle viscosity um of 1021 pa s forward predictions of the harmonics exhibit a pronounced peak when a wide enough range of lower mantle viscosities lm are considered we denote the lm value at this peak as at the lowest degrees 4 frechet kernels computed for a series of increasing lm values 1021 pa s lm 1023 pa s indicate a migration of the dominant sensitivity of the data to variations in viscosity from regions below approximately 1200 km depth for to regions above this depth in the lower mantle for the sensitivity of the data to variations in the viscosity profile in the shallowest parts of the lower mantle for the case is also reflected in a set of forward calculations described herein as an example predictions made using earth models in which the viscosity above 1200 km depth is constrained to be 1021 pa s do not exhibit the multiple solutions characteristic of the um 1021 pa s calculations the same is true of earth models in which the upper mantle viscosity is weakened an order of magnitude to 1020 pa s the theory described herein is also applied to compute the signal 10 arising from the retreat of small ice sheets and glaciers described by meier 1984 and also from any potential variations in the mass of the antarctic and greenland ice sheets the present day signal due to the late pleistocene glacial cycles dominates the signal from meier s sources at all degrees except 3 in contrast the signal arising from mass variations in the antarctic and greenland ice sheets is potentially comparable to the former a comparison of observational constraints on the data with predictions of the postglacial rebound signal described in this paper in order to infer mantle rheology cannot proceed until constraints are placed on the present day mass flux of these large polar ice sheets we show that the constraints required are weakest at degrees 2 and 4 finally we outline a potentially important procedure for incorporating predictions of the signal due to the late pleistocene glacial cycles and meier s sources with an observational constraint on the datum to yield bounds on the present day net mass flux from the antarctic and greenland ice sheets a rigorous application of this procedure must wait until observational constraints on are reestablished in the literature

changes in rotation induced by pleistocene ice masses with stratified analytical earth models the rotational response of the earth to pleistocene deglaciation is studied by means of a multilayered viscoelastic earth model based on the preliminary reference earth model prem incompressible viscoelastic deformation is evaluated from a self compressed initial state the novelty of our approach stands on the application of a fully analytical normal mode theory to the response of the earth to surface loads and variations in the centrifugal potential for large numbers of viscoelastic layers as requested by prem assuming that both present day true polar wander tpw and changes in the second degree component of the geopotential are solely due to pleistocene postglacial rebound we obtain for a two layer viscosity model that the upper mantle viscosity must be lowered to about 1 5 1020 pa s with respect to the classical value of 1021 pa s this upper mantle viscosity is accompanied by an increase of the lower mantle viscosity by a factor of 25 in agreement with some recent relative sealevel rsl data analyses and convectively supported long wavelength geoid anomalies when the viscosity contrast is located at 1470 km depth tpw and require a viscosity of 1021 pa s in the upper part of the mantle above 1470 km depth with a moderate viscosity increase in the lowermost portion of the mantle this result indicates that a viscosity of 1021 pa s is appropriate for a wider portion of the mantle than the upper mantle in agreement with haskell s 1935 estimate that was not limited to the seismically inferred 670 km boundary

the angular velocities of the plates and the velocity of earth s centre from space geodesy summary using space geodetic observations from four techniques gps vlbi slr and doris we simultaneously estimate the angular velocities of 11 major plates and the velocity of earth s centre we call this set of relative plate angular velocities geodvel for geodesy velocity plate angular velocities depend on the estimate of the velocity of earth s centre and on the assignment of sites to plates most geodetic estimates of the angular velocities of the plates are determined assuming that earth s centre is fixed in an international terrestrial reference frame itrf and are therefore subject to errors in the estimate of the velocity of earth s centre in itrf2005 and itrf2000 earth s centre is the centre of mass of earth oceans and atmosphere cm the velocity of cm is estimated by slr observation of lageos s orbit herein we define earth s centre to be the centre of mass of solid earth ce we determine the velocity of ce by assuming that the portions of plate interiors not near the late pleistocene ice sheets move laterally as if they were part of a rigid spherical cap the geodvel estimate of the velocity of ce is likely nearer the true velocity of cm than are the itrf2005 and itrf2000 estimates because 1 no phenomena can sustain a significant velocity between cm and ce 2 the plates are indeed nearly rigid aside from vertical motion and 3 the velocity of cm differs between itrf2005 and itrf2000 by an unacceptably large speed of 1 8 mm yr 1 the velocity of earth s centre in geodvel lies between that of itrf2000 and that of itrf2005 with the distance from itrf2005 being about twice that from itrf2000 because the geodvel estimates of uncertainties in plate angular velocities account for uncertainty in the velocity of earth s centre they are more realistic than prior estimates of uncertainties geodvel differs significantly from all prior global sets of relative plate angular velocities determined from space geodesy for example the 95 per cent confidence limits for the angular velocities of geodvel exclude those of revel sella et al for 34 of the 36 plate pairs that can be formed between any two of the nine plates with the best constrained motion the median angular velocity vector difference between geodvel and revel is 0 028 myr 1 which is up to 3 1 mm yr 1 on earth s surface geodvel differs the least from the geodetic angular velocities that altamimi et al determine from itrf2005 geodvel s 95 per cent confidence limits exclude 11 of 36 angular velocities of altamimi et al and the median difference is 0 015 myr 1 geodvel differs significantly from nearly all relative plate angular velocities averaged over the past few million years including those of nuvel 1a the difference of geodvel from updated 3 2 myr angular velocities is statistically significant for all but two of 36 angular velocities with a median difference of 0 063 myr 1 across spreading centres eight have slowed down while only two have sped up we conclude that plate angular velocities over the past few decades differ significantly from the corresponding angular velocity averaged over the past 3 2 myr

polar motion of a viscoelastic earth due to glacial cycle mass loading the growth and decay of ice sheets can change the symmetry axis of the global mass distribution and thus excite motion of the rotation axis of the earth we develop a simple normal mode expansion of the operator which converts surface load histories into polar motion histories and use it to characterize the polar motion response to arbitrary surface loading excitation in terms of gain and phase for a wide range of earth models and excitation time scales uncertainties in loading history presently limit the utility of constraints on mantle rheology which can be obtained from matching the present direction and rate of motion of the pole because of its magnitude and distance from the pole the laurentide ice sheet alone can induce motion of the rotation pole by over 100 km this will influence the pattern of incident radiation on continents and oceans and may play a significant role in limiting ice sheet growth differential motion of the mantle and core on a glacial timescale may also influence the geomagnetic field

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

polar wandering and the forced responses of a rotating multilayered viscoelastic planet changes in the earth s rotation produced by the waxing and waning of large mobile ice sheets can be used to infer the viscosity of the mantle from a comparison with the recent secular polar drift as revealed in the international latitude service data and also in the estimates of the nontidal acceleration of the length of the day we have developed by using an analytical approach a physical model of a rotating earth consisting of an elastic lithosphere a viscoelastic mantle and an inviscid core forcings from the two major ice sheets laurentide and fennoscandia have been considered sensitivity analysis of the parameters governing the external forcings such as the length and the time of termination of the deglaciation phase show in general that there exist two families of mean mantle viscosities 0 1022 p and 0 1023 p which can match the data satisfactorily however we find it an improvement to incorporate some amount of shrinkage from the antarctic ice sheet obtaining simultaneously a better fit with the two rotational data sets to the lower viscosity solutions hence forcings from the southern hemisphere may be able to remove the ambiguity associated with the extraction of mantle viscosity from rotational data we have also solved the initial value problem of the components of instantaneous angular velocity by means of the laplace transform for applied loads characterizing the continental ice sheets which since the mid pliocene have periodically expanded and contracted over the northern hemisphere in consequence of this continual forcing polar wander of around 5 10 degrees can take place for a mean mantle viscosity 0 1022 p recent reanalysis of paleomagnetic data in conjunction with hot spot tracks have revealed that several degrees of true polar wander could have occurred in the last 5 m y these calculations thus provide a physical explanation for the observed movement of the rotation axis membrane stresses of 0 10 bars can develop from this secular polar motion

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