contribution of small glaciers to global sea level observed long term changes in glacier volume and hydrometeorological mass balance models yield data on the transfer of water from glaciers excluding those in greenland and antarctica to the oceans the average observed volume change for the period 1900 to 1961 is scaled to a global average by use of the seasonal amplitude of the mass balance these data are used to calibrate the models to estimate the changing contribution of glaciers to sea level for the period 1884 to 1975 although the error band is large these glaciers appear to account for a third to half of observed rise in sea level approximately that fraction not explained by thermal expansion of the ocean

mountain building and earth rotation summary whereas the present day true polar wander and the secular non tidal acceleration of the earth have usually been attributed to postglacial rebound it has recently been suggested that non glacially induced vertical tectonic movements taking place under non isostatic conditions can also be effective in changing the earth s rotation we present a case study in which we analyse the effects of some simple uplift histories of the himalayas and the tibetan plateau on the rotational axis and on the second degree zonal harmonic of the geoid for time scales of up to a few million years we first assume a permanent amount of overcompensation which is consistent with observed geoid anomalies over the himalayas and then we model by means of the normal mode techniques the viscous relaxation in the mantle with the elastic lithosphere supporting elastically 2 per cent of isostatic disequilibrium in our normal mode analysis the earth is divided into five layers an effectively elastic lithosphere a viscoelastic shallow upper mantle transition zone and lower mantle characterized by the maxwell rheology and an inviscid core the readjustment of the equatorial bulge due to viscous flow in the mantle is taken into account in our studies by solving the linearized liouville equations for the conservation of angular momentum via the love numbers formalism polar wander is sensitive to the rate of relaxation of the modes m1 and m2 due to the discontinuities between the three mantle layers positioned at 420 and 670 kilometres depth the rate of readjustment is sensitive to the viscosity of the transition zone whenever the lower mantle shallow upper mantle viscosity ratio is small the highest present day velocity of polar wander due to himalayan and tibetan plateau uplift is estimated to be 1 myr 1 for an isoviscous mantle that has the same magnitude of the observed value reduced to 0 1 myr 1 for a factor 50 viscosity increase in the lower mantle these numbers are about the same as those found from postglacial rebound that occurs on the short time scale of a thousand years instead of the million years of our analysis but represent upper bounds for mountain building obtained only in the case in which a permanent deviation from isostasy of at least 2 per cent is assumed in general the proposed mechanism is less efficient in driving long term rotation instabilities than deep seated processes characterized by the same time scale of a million years such as subduction polar wander velocity is extremely sensitive to the depth of the uncompensated anomalous root of the topography for the models in which full mantle relaxation is allowed

postglacial rebound observed by lageos and the effective viscosity of the lower mantle sixty four observations of the orbital node made by the lageos satellite over a five year time interval reveal an acceleration of 8 1 or 1 8 x 10 to the 8 power arcseconds day 2 due to a source which is not presently modeled in the geodyn orbit determination computer program this acceleration cannot be explained by the ocean tide with 18 6 year period assuming it to be an equilibrium tide instead it seems to be due to postglacial rebound which changes the j 2 coefficient in the spherical harmonic expansion of the earth s gravitational field at the rate of 8 2 or 18 x 10 to the 19th power s this in turn accelerates the node this rate does not agree with the 32 x 10 to the 19th power s predicted by wu and peltier s 1982 l2 model which has upper and lower mantle effective viscosities of 10 to the 21st and 22nd powers pa s respectively it does agree well with their l1 model which gives about 10 x 10 to the 19th power s since the effective viscosity is 10 to the 21st power pa s throughout the entire mantle in the l1 model the results support the contentions that the efective viscosity is near 10 to the 21st power pa s everyhere in the mantle and this relatively low value for the effective viscosity may have permitted several degrees of polar wander due to glaciation during the quaternary ice age previously announced in star as n84 13705

the melting history of the late pleistocene antarctic ice sheet spatial and temporal variations in the sea levels of the past 20 000 years around the globe place constraints on the melting history of the major late pleistocene ice sheets 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 9 000 6 000 years ago when it may have lagged behind minor melting of the antarctic ice sheet continued throughout the holocene

global geodetic signatures of the antarctic ice sheet four scenarios of present day antarctic ice sheet mass change are developed from comprehensive reviews of the available glaciological and oceanographic evidence the gridded scenarios predict widely varying contributions to secular sea level change ranging from 1 1 to 0 45 mm yr and predict polar motion and time varying low degree gravitational coefficients that differ significantly from earlier estimates a reasonably linear relationship between the rate of sea level change from antarctica a and the predicted antarctic is found for the four scenarios this linearity permits a series of forward models to be constructed that incorporate the effects of ice mass changes in antarctica greenland and distributed smaller glaciers as well as postglacial rebound assuming the ice 3g deglaciation history with the goal of obtaining optimum reconciliation between observed constraints on and sea level rise numerous viable combinations of lower mantle viscosity and hydrologie sources are found that satisfy observed in the range of 1 to 2 2 5 mm yr and observed for degrees 2 3 and 4 in contrast rates of global sea level rise above 2 5 mm yr are inconsistent with available observations the successful composite models feature a pair of lower mantle viscosity solutions arising from the sensitivity of to glacial rebound the paired values are well separated at mm yr but move closer together as is increased and in fact merge around 2 2 5 mm yr revealing an intimate relation between and preferred lower mantle viscosity this general pattern is quite robust and persists for different solutions for variations in source assumptions and for different styles of lower mantle viscosity stratification tighter constraints for l 2 may allow some viscosity stratification schemes and source assumptions to be excluded in the future for a given total observed the sea level rise from antarctica a is tightly constrained and ranges from 0 to 1 mm yr corresponding to an ablating ice sheet as estimates of are raised from 1 to 2 5 mm yr however when the degree 3 zonal harmonic constraint is removed the solutions show little sensitivity to antarctic mass balance emphasizing the need for a well determined odd degree secular zonal harmonic for determining polar ice mass balance

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

new constraints on antarctic plate motion and deformation from gps data four years 1995 1998 of continuous global positioning system gps data recorded by 11 permanent international gps service igs stations in antarctica and surrounding regions have been processed using an optimized method for regional geodetic networks the 4 year time series has allowed us to extract nonlinear variations and constant horizontal velocities for all the stations in december 1997 we have set up a permanent gps station at dumont d urville in terre adelie the resulting data along with those of the scientific committee on antarctic research scar campaigns 1995 and 1996 are included in our processing a coseismic displacement 1 to 2 cm is detected in the horizontal components of this station we relate this to the march 25 1998 mw 8 1 balleny islands earthquake for which a dislocation model yields prediction in the right direction for the six antarctic stations the horizontal rates are very consistent with the rigid plate rotation all the residual velocities are negligible less than 2 mm yr except at o higgins in the head of the peninsula 7 mm yr toward the continent the position of the rotation pole 62 0 n 146 7 w and its rate 0 264 ma are significantly different from the nnr nuvel la predictions for the antarctic tectonic plate but are consistent with the australian relative motion the high horizontal residual in the peninsula area where iceberg calving rates and ice shelf disintegration have recently increased can be interpreted as the horizontal component of the elastic crustal response to the load variations

melting of ice shelves and the mass balance of antarctica we calculate the present ice budget for antarctica from measurements of accumulation minus iceberg calving run off and in situ melting beneath the floating ice shelves the resulting negative mass balance of 469 gt year 1 differs substantially from other recent estimates but some components are subject to high temporal variability and budget uncertainties of 20 50 annual accumulation from an earlier review is adjusted to include the antarctic peninsula for a total of 2144 gt year 1 an iceberg production rate of 2016 gt year 1 is obtained from the volume of large icebergs calculated from satellite images since 1978 and from the results of an international iceberg census project ice shelf melting of 544 gt year 1 is derived from physical and geochemical observations of meltwater outflow glaciological field studies and modeling of the sub ice ocean circulation the highest melt rates occur near ice fronts and deep within sub ice cavities run off from the ice sheet surface and from beneath the grounded ice is taken to be 53 gt year 1 less than half of the negative mass balance need come from the grounded ice to account for the unattributed 0 45 mm year 1 in the ipcc best estimate of the recent global sea level rise

predictions of antarctic crustal motions driven by present day ice sheet evolution and by isostatic memory of the last glacial maximum detectable crustal motion and secular rate of change of solid surface gravity may be produced by the earth s response to present day and past ice mass changes in antarctica scenarios of present day ice mass balance previously utilized to explore the global geodetic signatures of the antarctic ice sheet produce elastic crustal responses that are typically bounded by uplift rates 5 mm yr horizontal motion 1 mm yr and solid surface gravity change rates 1 gal yr in a restricted locality one scenario produces uplift rates slightly in excess of 10 mm yr and correspondingly enhanced horizontal and gravity rates in contrast the viscoelastic response to ice mass changes occurring since last glacial maximum lgm exceeds 5 mm yr uplift over substantial portions of west antarctica for a wide range of plausible choices of timing and magnitude of deglaciation and mantle viscosity similarly viscoelastic gravity rate predictions exceed 1 gal yr decrease over large regions confirming suggestions that a global positioning system gps and absolute gravity based program of crustal monitoring in antarctica could potentially detect postglacial rebound a published revision to the climap model of the antarctic ice sheet at lgm herein called the d91 model features a substantially altered west antarctic ice sheet reconstruction this revision predicts a spatial pattern of present day crustal motion and surface gravity change that diverges strikingly from climap based models peak d91 crustal rates assuming deglaciation begins at 12 kyr and ends at 5 kyr are around 16 mm yr uplift 2 mm yr horizontal and 2 5 gal yr gravity tabulated crustal response predictions for selected antarctic bedrock sites indicate critical localities in the interior of west antarctica where expected responses are large and d91 predictions differ from climap based models by a factor of 2 or more observations of the postglacial rebound signal in antarctica might help constrain antarctic mass balance and contribution to sea level rise over the past 20 000 years

boreholes in mississippian spiriferide brachiopods and their implications for paleozoic gastropod drilling abstract bored specimens of the spiriferide brachiopod genera brachythyris and spirifer from several localities of the mississippian fort payne formation kentucky usa represent 7 0 of the total sampled population the boreholes are typically single complete circular in plan view and with their long axes perpendicular to the valve these traits and stereotypy with respect to the pedicle valve and the fold and sulcus are consistent with a predatory parasitic origin of the holes the presence of platyceratid gastropods in the fort payne localities with bored brachiopods the previously documented drilling abilities of these gastropods and the occurrence of a platyceratid snail attached to specimen of a bored devonian brachiopod atrypa argue for platyceratids as the most probable culprits

constraints on the age and duration of the last interglacial period and on sea level variations the relation between height and age of shorelines formed during the last interglacial period as revealed by coral reefs cannot be related directly to changes in ocean volume because of the effect of isostatic uplift in response to changes in ice sheet loading sea level changes at sites near the melting ice sheet such as bermuda and the caribbean islands differ from those along the australian margin modelling of these differences constrains the times of onset and termination of the last interglacial which are at variance with those deduced from oxygen isotope studies of deep sea cores

late pleistocene and holocene melting history of the antarctic ice sheet derived from sea level variations abstract spatial and temporal variations of the late pleistocene and holocene sea levels provide important constraints on the melting history of the major ice sheets in this study we have examined the sea level variations at eight sites along the coast of antarctica to investigate the melting history of antarctic ice sheet complexes comparisons of sea level variations between observations and predictions due to glacio hydro isostatic adjustment suggest that the ice thicknesses removed from the last glacial maximum lgm around the weddell sea are significantly thicker than those around the ross embayment sea level observations also indicate that climap derived models predict too much relative sea level change and that consequently ice mass change along the coast has to be scaled down improvement of the late pleistocene antarctic ice model is required to evaluate more accurate predictions of present day geophysical observables associated with this history thus these more accurate predictions can then be subtracted from observables and the residual field can be analyzed to constrain ongoing mass changes from the ice sheet we therefore predicted present day geophysical observables such as the rate of change of solid surface gravity and crustal movement these geophysical observables based on the ice models constructed from observed sea level variations are significantly different from those based on previous models on the other hand detailed sea level observations around syowa indicate the existence of a sea level highstand of about 10 m around 40 kyr bp to investigate these sea level observations we have performed preliminary numerical calculations comparisons between these observations and predictions indicate the synchronous melting of the northern and southern ice sheets suggesting a strong link between the melting histories of both polar ice sheets

present day antarctic ice mass changes and crustal motion the peak vertical velocities predicted by three realistic but contrasting present day scenarios of antarctic ice sheet mass balance are found to be of the order of several mm a one scenario predicts local uplift rates in excess of 5 mm a these rates are small compared to the peak antarctic vertical velocities of the ice 3g glacial rebound model which are in excess of 20 mm a if the holocene antarctic deglaciation history portrayed in ice 3g is realistic and if regional upper mantle viscosity is not an order of magnitude below 10 exp 21 pa s then a vast geographical region in west antarctica is uplifting at a rate that could be detected by a future global positioning system gps campaign while present day scenarios predict small vertical crustal velocities their overall continent ocean mass exchange is large enough to account for a substantial portion of the observed secular polar motion omega m bar and time varying zonal gravity field j sub 1

changes in greenland ice sheet elevation attributed primarily to snow accumulation variability the response of grounded ice sheets to a changing climate critically influences possible future changes in sea level recent satellite surveys over southern greenland show little overall elevation change at higher elevations but large spatial variability using satellite studies alone it is not possible to determine the geophysical processes responsible for the observed elevation changes and to decide if recent rates of change exceed the natural variability here we derive changes in ice sheet elevation in southern greenland for the years 1978 88 using a physically based model of firn densification and records of annual snow accumulation reconstructed from 12 ice cores at high elevation our patterns of accumulation driven elevation change agree closely with contemporaneous satellite measurements of ice sheet elevation change and we therefore attribute the changes observed in 1978 88 to variability in snow accumulation similar analyses of longer ice core records show that in this decade the greenland ice sheet exhibited typical variability at high elevations well within the long term natural variability our results indicate that a better understanding of ice sheet mass changes will require long term measurements of both surface elevation and snow accumulation

excitation of true polar wander by subduction true polar wander the global motion of the mantle relative to the earth s rotation axis is known from the analysis of palaeomagnetic data hotspot tracks and plate motions to have occurred at velocities of up to 0 5 myr 1 since the late cretaceous period1 4 we address here the longstanding question of how fast episodes of true polar wander tpw can be excited5 by analysing the impact of the distribution and activity of subduction zones on polar motion using nonlinear liouville equations which allow us to treat large excursions of the polar axis we show that unrealistically fast tpw is excited by subduction episodes unless the lower mantle has a viscosity at least 10 times that of the upper mantle this need for a viscosity increase with depth in the mantle reinforces the conclusions of previous studies on post glacial rebound and geoid anomalies theoretical creep laws and some preliminary results on tpw induced by density anomalies embedded in the mantle6 10 the lower viscosity in the upper mantle means that upper mantle density anomalies are most effective in exciting tpw changes in the pattern of subduction through time may be responsible for both episodes of fast tpw and times of quiescence in polar motion

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

total volume and temporal variation of meltwater from last glacial maximum inferred from sea level observations at barbados and tahiti abstract it is very important to determine the temporal variation of meltwater volume from the last glacial maximum lgm for studying climate changes and for constraining mantle rheology sea level observations have been obtained at barbados at the lgm and in late glacial phase and tahiti in late glacial phase and suggest that two events of rapid sea level rise existed at about 14 000 and 11 000 calendar years before present we examine the total meltwater volume and temporal variation of meltwater volume by comparing sea level observations and predictions at barbados and tahiti comparison between observations and predictions for barbados indicates that the total meltwater volume from the lgm is 103 117 m for eustatic sea level rise the predicted sea level variations at tahiti based on the ice model satisfying observations for barbados are however inconsistent with late glacial sea level observations at tahiti thus two events of rapid sea level rise are not supported from the comparison between observations and predictions at tahiti more in situ observational data are required for the period from the lgm to late glacial phase in order to study the relationship between rapid sea level rise and climate change

three dimensional geometrical ray theory and modelling of transmitted seismic energy of data from the nevada test site this paper presents a geometrically based algorithm for computing synthetic seismograms for energy transmitted through a 3 d velocity distribution 3 d ray tracing is performed to compute the traveltimes and geometrical spreading amplitude the formulations of both kinematic and dynamic ray tracing systems are presented the two point ray tracing problem is solved by systematically updating the initial conditions and adjusting the ray direction until the ray intersects the specified endpoint the amount of adjustment required depends on the derivatives of the position with respect to the given starting angles between consecutive rays the algorithm uses derivatives to define the steepest descent direction and to update the initial directions the convergence rate depends on the complexity of the model test seismograms compare favourably with those from a 2 d asymptotic ray theory algorithm and a 3 d gaussian beam algorithm the algorithm is flexible in modelling arbitrary source and recorder geometries for various smoothly varying 3 d velocity distributions the algorithm is further tested by simulating surface to tunnel vibroseis field data shear waves as well as compressional waves may be approximately included application of the algorithm to a data set from the rainier mesa of the nevada test site produced a good fit to the transmitted first arrival traveltimes and amplitudes with approximately 15 per cent variation in the local 3 d velocity

changes of the earth s rotation axis owing to advection of mantle density heterogeneities polar wander the secular motion of the earth s rotation axis relative to its surface has been studied for many years dynamical arguments1 3 show that polar wander can arise from the redistribution of mass in a plastic deformable earth the rate depending on both the rate of mass redistribution and the rate at which the earth s rotational bulge can readjust to the changing rotation axis here we use a viscosity structure obtained through geoid modelling4 a mantle flow field consistent with tomographic anomalies5 and time dependent lithospheric plate motions6 to calculate the advection of mantle density heterogeneities and corresponding changes in the degree two geoid during the cenozoic era we show that the rotation axis will follow closely any imposed changes of the axis of maximum non hydrostatic moment of inertia the resulting path of the rotation axis agrees well with palaeomagnetic results7 with the model predicting a current rate of polar motion that explains 40 of that observed geodetically8

perturbations of the earth s rotation and their implications for the present day mass balance of both polar ice caps summary the present day perturbations of the earth s rotation are sensitive to the glacial isostatic adjustment gia arising from the late pleistocene glacial cycles and also to the recent mass balance of polar ice caps in this study we evaluate the polar wander and the change of degreetwo harmonic of the earth s geopotential j 2 proportional to the rotation rate for four late pleistocene ice models we examine these perturbations as a function of lower and uppermantle viscosities and lithospheric thickness and rheology elastic or viscoelastic in which a compressible earth model with elasticity and density given by the seismological model prem is used by considering the observations and predictions including the gia process arising from the late pleistocene ice and recent mass balance of polar ice caps we discuss the recent mass balance of the antarctic and greenland ice sheets we also examine the effects of internal processes and the melting of mountain glaciers although this work is only preliminary the results shown below seem to be supported even if these effects are included two solutions are obtained for source areas of the recent antarctic melting we denote an equivalent sea level esl rise mm yr 1 from the greenland and antarctic ice sheets as gl and