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

searching for eustasy in deglacial sea level histories abstract perturbations to the earth s gravity field and solid surface associated with glacial isostatic adjustment gia cause the total observable sea level change to depart from the eustatic curve which is defined as a spatially uniform height shift of the ocean surface to accommodate any mass gained lost from grounded ice in this study we apply a state of the art model of gia induced sea level change to quantify the magnitude and spatial form of this departure at the global scale for a range of model parameters with an aim to identify regions that are well suited to obtain accurate and precise estimates of eustatic sea level and therefore past grounded ice volume in general our results indicate that eustatic sea level is not a directly measurable quantity and so must be estimated by subtracting a model derived estimate of non eustatic contributions from observations in this regard we use our results to isolate regions where this procedure can be applied with optimal accuracy and precision that is where 1 the gia predictions are relatively insensitive to plausible ranges in input parameters and 2 where the non eustatic contribution is small i e the predicted sea level closely approximates the eustatic value we present maps that can be employed by the field community to identify areas where sea level reconstructions would be well suited to arrive at robust estimates of eustatic sea level note that sea level changes associated with tectonic motion and changes in ocean water temperature salinity which also lead to departures from eustasy are not considered in this analysis

the rotational stability of an ice age earth summary predictions of glaciation induced changes in the earth s rotation vector exhibit sensitivities to earth structure that are unique within the suite of long wavelength observables associated with glacial isostatic adjustment henceforth gia and despite nearly a quarter of a century of research these sensitivities remain enigmatic previous predictions of present day true polar wander tpw speed driven by gia have indicated for example a strong sensitivity to variations in the thickness of the elastic lithosphere and the treatment phase or chemical of the density discontinuity at 670 km depth nakada recently presented results that suggest that the predictions are also sensitive to the adopted rheology of the lithosphere however his results have introduced an intriguing paradox in particular predictions generated using a model with an extremely high viscosity lithospheric lid do not converge to results for a purely elastic lithosphere of the same thickness mitrovica as cited by nakada has suggested that the paradox originates from an inaccuracy in the traditional rotation theory e g wu peltier associated with the treatment of the background equilibrium rotating form upon which any load and rotation induced perturbations are superimposed we revisit these issues using a new treatment of the linearized euler equations governing load induced rotation perturbations on viscoelastic earth models we demonstrate that our revised theory in which the background form of the planet combines a hydrostatic component and an observationally inferred excess ellipticity resolves the apparent paradox calculations using the revised theory indicate that earlier predictions based on earth models with purely elastic lithospheric lids are subject to large errors indeed previously noted sensitivities of tpw speed predictions to the thickness and rheology elastic versus viscous of the lithosphere largely disappear in the application of the new theory significant errors are also incurred by neglecting the stabilizing influence of the earth s excess ellipticity finally we demonstrate that the contribution from rotational feedback on predictions of present day rates of change of the geoid sea surface and crustal velocities are overestimated by the traditional rotation theory and this has implications for analyses of ongoing satellite e g grace missions and geodetic gps surveys

holocene sea level changes in the indo pacific holocene sea level reconstructions exist from many locations in the indo pacific region despite being a large geographical region the nature of holocene sea level change is broadly similar in all locations differences do exist however in the timing and magnitude of the mid holocene high stand mhhs and the nature of late holocene sea level fall across the region when the indo pacific is subdivided into smaller regions these discrepancies do not disappear and in some cases the discrepancies are large within a single coastline it is clear from this analysis that the fundamental criteria to produce accurate local relative sea level curves are hardly ever met there are serious problems associated with the correct interpretation of sea level indicators and their relationship to mean sea level and with the quality of age determinations a consistent methodology throughout the indo pacific for the analysis of sea level data is lacking future sea level analysis from far field locations must involve the application of a consistent methodology in order to allow meaningful comparison between studies this should help to resolve the ongoing debate about the magnitude and timing of the mid holocene high stand and the nature of late holocene sea level fall across the region

recent controversies in predicting post glacial sea level change abstract we compare recent developments in the numerical prediction of post glacial sea level changes and comment on the controversies associated with these developments we conclude that 1 the broad shelf effect discussed by peltier and drummond 2002 in the context of water load modelling at migrating shorelines is incorporated into the sea level algorithms of johnston 1993 and milne et al 1999 and 2 the procedure used by yokoyama et al 2000 to infer an ice equivalent post lgm sea level rise of 130 135 m is technically sound

predicted bounds on peak global mean sea level during marine isotope stages 5a and 5c abstract estimates of marine isotope stage mis 5c and 5a global mean sea level gmsl based on marine terraces and coastal indicators range from 15 37 m and 9 30 m below present respectively tectonic displacement and glacial isostatic adjustment gia complicate efforts to refine this range we revisit this issue using numerical predictions of post glacial sea level change and updated estimates of site specific tectonic signals based upon these predictions laurentide and cordilleran peripheral bulge dynamics and variations in the gravitational effect of these ice masses dominate the gia signal along the east and west coasts of north america published compilations suggest that mis 5 sea level indicators extending from virginia to the caribbean lie on the outer flank of the peripheral bulge while those along a transect from oregon to baja california sit on the inner flank of the bulge our gia modeling reconciles these data by adopting a significantly weaker i e lower viscosity upper mantle in analyzing data on the pacific coast relative to the atlantic an inference supported by seismic tomography we present a sensitivity analysis that compares the observed elevation of globally distributed high stand markers to a suite of gia simulations that vary the earth model and gmsl from the last interglaciation mis 5e 130 115 ka to 70 ka we conclude that gmsl peaked at 8 5 4 6 m 1 during mis 5a and 9 4 5 3 m during mis 5c a more restrictive analysis yields slightly wider bounds corresponding to 10 5 5 5 m and 11 1 6 6 m respectively

non linear connections between dune activity and climate in the high plains kansas and oklahoma usa discrete dune fields are found throughout much of the great plains of north america and the timing of past dune activity is often used as a proxy for paleoclimate because of the intuitive link between dune activity and a more arid climate this research suggests that feedbacks in the soil geomorphic system create a relationship between dune activity and climate that varies both spatially and temporally older eolian landforms are more resistant to activation because of the long term accumulation of finer soil particles in a bt horizon which retain moisture and anchor the deposit even during more arid times conversely younger deposits lack these fines and are more easily reactivated this spatially variable relationship is supported by soil stratigraphy particle size analysis and optical age control additionally the water retention of the bt horizons is quantifiably greater than that of the soils found in the younger dunes of the area this complication in the relationship between eolian activity and climate is important because it suggests that caution is needed when using past dune activity as the lone proxy for paleoclimate

ice age paleotopography a gravitationally self consistent theory of postglacial relative sea level change is used to infer the variation of surface ice and water cover since the last glacial maximum lgm the results show that lgm ice volume was approximately 35 percent lower than suggested by the climap reconstruction and the maximum heights of the main laurentian and fennoscandian ice complexes are inferred to have been commensurately lower with respect to sea level use of these ice age boundary conditions in atmospheric general circulation models will yield climates that differ significantly from those previously inferred on the basis of the climap data set

glacial isostatic adjustment in response to changing late holocene behaviour of ice streams on the siple coast west antarctica the siple coast region of antarctica contains a number of fast flowing ice streams which control the dynamics and mass balance of the region these ice streams are known to undergo stagnation and reactivation cycles which lead to ice thickness changes that may be sufficient to excite a viscous solid earth response glacial isostatic adjustment gia this study aims to quantify siple coast ice thickness changes during the last 2000 yr in order to determine the degree to which they might contribute to gia and associated present day bedrock uplift rates this is important because accurate modelling of gia is necessary to determine the rate of present day ice mass change from satellite gravimetry recently published reconstructions of ice stream variability were used to create a suite of kinematic models for the stagnation related thickening of kamb ice stream since 1850 ad and a gia model was used to predict present day deformation rates in response to this thickening a number of longer term loading scenarios which include the stagnation and reactivation of ice streams across the siple coast over the past 2000 yr were also constructed and used to investigate the longer term gia signal in the region uplift rates for each of the ice loading histories based on a range of earth models were compared with regional gps observed uplift rates and an empirical gia estimate we estimate kamb ice stream to have thickened by 70 130 m since stagnation 165 years ago modelled present day vertical motion in response to this load increase peaks at 17 mm yr 1 i e 17 mm yr 1 subsidence for the weakest earth models tested here comparison of the solid earth response to ice load changes throughout the last glacial cycle including ice stream stagnation and reactivation across the siple coast during the last 2000 yr with an empirical gia estimate suggests that the upper mantle viscosity of the region is greater than 1 10 20 pa s when upper mantle viscosity values of 1 10 20 pa s or smaller are combined with our suite of ice load scenarios we predict uplift rates across siple coast that are at least 4 mm yr 1 smaller than those predicted by the empirical gia estimate gps data are unable to further constrain model parameters due to the distance of the gps sites from the study area our results demonstrate that late holocene ice load changes related to the stagnation and reactivation of ice streams on the siple coast may play a dominant role in defining the present day uplift signal however both the detailed earth structure and deglacial history of the region need to be better constrained in order to reduce uncertainties associated with the gia signal of this region

low post glacial rebound rates in the weddell sea due to late holocene ice sheet readvance many ice sheet reconstructions assume monotonic holocene retreat for the west antarctic ice sheet but an increasing number of glaciological observations infer that some portions of the ice sheet may be readvancing following retreat behind the present day margin a readvance in the weddell sea region can reconcile two outstanding problems i the present day widespread occurrence of seemingly stable ice streams grounded on beds that deepen inland and ii the inability of models of glacial isostatic adjustment to match present day uplift rates by combining a suite of ice loading histories that include a readvance with a model of glacial isostatic adjustment we report substantial improvements to predictions of present day uplift rates including reconciling one problematic observation of land sinking we suggest retreat behind present grounding lines occurred when the bed was lower and isostatic recovery has since led to shallowing ice sheet re grounding and readvance the paradoxical existence of grounding lines in apparently unstable configurations on reverse bed slopes may be resolved by invoking the process of unstable advance in accordance with our load modelling

vertical land motion from present day deglaciation in the wider arctic vertical land motion vlm from past and ongoing glacial changes can amplify or mitigate ongoing relative sea level change we present a high resolution vlm model for the wider arctic that include

interaction between climate volcanism and isostatic rebound in southeast alaska during the last deglaciation abstract observations of enhanced volcanic frequency during the last deglaciation have led to the hypothesis that ice unloading in glaciated volcanic terrains can promote volcanism through decompression melting in the shallow mantle or a reduction in crustal magma storage time however a direct link between regional climate change isostatic adjustment and the initiation of volcanism remains to be demonstrated due to the difficulty of obtaining high resolution well dated records that capture short term climate and volcanic variability traced to a particular source region here we present an exceptionally resolved record of 19 tephra layers paired with foraminiferal oxygen isotopes and alkenone paleotemperatures from marine sediment cores along the southeast alaska margin spanning the last deglacial transition major element compositions of the tephras indicate a predominant source from the nearby mt edgecumbe volcanic field mevf we constrain the timing of this regional eruptive sequence to 14 6 13 1 ka the sudden increase in volcanic activity from the mevf coincides with the onset of bolling allerod interstadial warmth the disappearance of ice rafted detritus and rapid vertical land motion associated with modeled regional isostatic rebound in response to glacier retreat these data support the hypothesis that regional deglaciation can rapidly trigger volcanic activity rapid sea surface temperature fluctuations and an increase in local salinity i e 18osw variability are associated with the interval of intense volcanic activity consistent with a two way interaction between climate and volcanism in which rapid volcanic response to ice unloading may in turn enhance short term melting of the glaciers plausibly via albedo effects on glacier ablation zones

glacial isostatic adjustment of the british isles new constraints from gps measurements of crustal motion summary we compared estimates of crustal velocities within great britain based on continuous global positioning system cgps measurements to predictions from a model of glacial isostatic adjustment gia the observed and predicted values for vertical motion are highly correlated indicating that gia is the dominant geodynamic process contributing to this field in contrast motion of the eurasian plate dominates the horizontal motion component a model of plate motion was adopted to remove this signal in order to estimate intraplate horizontal motion associated with gia however a coherent pattern of horizontal motion was not evident in the resulting velocity field we adopted a recently published model of the british irish ice sheet to predict vertical crustal motion for a large number of spherically symmetric earth viscosity models our results show that the adopted ice model is capable of producing a high quality fit to the observations the cgps derived estimates of vertical motion provide a useful constraint on the average value of viscosity within the upper mantle values of model lithospheric thickness and lower mantle viscosity are less well resolved however a suite of predictions based on an alternative ice model indicates that the vertical motion data are relatively insensitive to uncertainties in the ice loading history and so the constraints on upper mantle viscosity are robust

the influence of decadal to millennial scale ice mass changes on present day vertical land motion in greenland implications for the interpretation of gps observations 1 we show predictions of present day vertical land motion in greenland using a recently developed glacial isostatic adjustment gia model calibrated using both relative sea level rsl observations and geomorphological constraints on ice extent predictions from our gia model are in agreement with the relatively small number of gps measurements of absolute vertical motion from south and southwest greenland this suggests that our model of ice sheet evolution over the holocene period is reasonably accurate the uplift predictions are highly sensitive to variations of upper mantle viscosity thus depending on the earth model adopted different periods of ice loading change dominate the present day response in particular regions of greenland we also consider the possible influence of more recent changes in the ice sheet by applying a second ice model specifically a surface mass balance smb model which covers the period 1866 to 2005 predictions from this model suggest that decadal scale smb changes over the past 140 years play only a small role in determining the present day viscous response at the sub mm yr level in most locations for a range of earth model parameters high rates of peripheral thinning from 1995 to 2005 predicted using the smb model produce large elastic uplift rates 6 mm yr in west and southwest greenland this suggests that in some areas close to the ice margin modern surface mass balance changes have a dominant control on present day vertical land motion

driving mechanisms of holocene coastal evolution in the bonifacio strait western mediterranean abstract we produced a new suite of sea level data which allowed assessing the holocene evolution of the bonifacio strait a key coastal sector of the mediterranean sea which experienced significant morphological changes since the last glacial maximum squeezed between corsica and sardinia islands this strait connects the two major basins of the western mediterranean due to its peculiar geographic and morphological setting the bonifacio strait is affected by extreme meteomarine conditions characterized by severe winds waves and currents the millennial sea level changes were reconstructed through multiproxy investigations made of sediment coring and underwater beachrock sampling carried out on both sides of the strait these data provided fresh insights into the timing of the progressive opening of the bonifacio strait which followed the last glacial maximum when corsica and sardinia were connected forming the largest mediterranean island major palaeogeographic changes occurred before 7 ka bp since that period the significant decrease of the northern ice sheet melting triggered a significant sea level stabilization which induced only minor modifications in the palaeogeography of the strait in the late holocene the isostatic related subsidence became the dominant factor controlling the sea level changes which rose with rates 0 35 mm a 1 in the last four millennia our data have also an important archaeological implication because they indicate that the bonifacio strait has not represented a significant geographical barrier along the early neolithic migration path which connected mainland italy to northern corsica and finally to sardinia this further confirms the ability of early neolithic communities to navigate not also across large sea stretches but also maritime areas characterized by extremely complex meteomarine conditions

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

viscosity of the lower mantle as inferred from rotational data until recently most estimates of the deep mantle viscosity were based on analyses of postglacial uplifts and there were no serious estimates of the sensitivity of the derived viscosity solutions to variations of the input parameters such as those associated with the surface loading in this paper the viscosity of the lower mantle is arrived at by making comparisons of the observed secular motions of the earth s rotation axis with theoretical results from a layered viscoelastic rotating earth which has been subjected to glacial forcing our model consisting of an elastic lithosphere a two layer adiabatically stratified viscoelastic mantle and an inviscid core is essentially analytical and this makes it economically feasible to use as an aid in conducting an extensive sensitivity analysis of the lower mantle viscosity from changes in the parameters connected with the deglaciation phenomenon both sets of rotational data polar wander and nontidal deceleration of the length of the day have been employed to constrain the viscosity structure on the basis of this type of investigation the viscosity of the lower mantle is found invariably to be larger than that of the upper mantle and lies between 1 and 4 1022 p our results which just rely on the second degree harmonic of the strain field also lead to a determination of an upper bound to the thickness of the globally averaged lithosphere this value ranging between 130 and 190 km suggests that strong lateral heterogeneities between oceanic and continental plates may extend a few hundred kilometers into the upper mantle

a repeating secondary source of infrasound from the wells nevada earthquake sequence 1 the wells nevada earthquake of february 21 2008 generated a complex seismo acoustic wavefield epicentral infrasound was recorded at 5 seismo acoustic arrays in nevada utah and wyoming in addition to epicentral infrasound the earthquake triggered a secondary source of infrasound at the bgu array in utah which was also triggered by subsequent aftershocks by applying simple constraints on the propagation of seismic and infrasound waves we show that the secondary source is an isolated peak floating island that appears to efficiently generate infrasound through the interaction with seismic surface waves this hypothesized source location is broadly consistent with crosswind directions extracted from the ground to space g2s atmospheric model for the appropriate time and source receiver locations although modeling the propagation of infrasound predicts this source location to be within the so called zone of silence in contrast to epicentral infrasound secondary infrasound associated with the wells nevada earthquake sequence appears to be local to each array i e not observed at multiple arrays secondary infrasonic arrivals observed at bgu are much higher in amplitude than epicentral arrivals highlighting the importance of being able to clearly identify and separate epicentral and secondary arrivals for infrasonic event discrimination

late quaternary variations in relative sea level due to glacial cycle polar wander growth and decay of continental ice sheets can excite significant motion of the earth s rotation pole and cause a complex spatio temporal pattern of changes in relative sea level these two effects have generally been considered separately but may interact in important ways in particular a simple model of the melting of the laurentide ice sheet causes a uniform eustatic sea level rise of 55 m and also induces a motion of the rotation pole by 0 1 to 1 degree depending on viscosity structure in the mantle this motion produces a secular pole tide which is a spherical harmonic degree 2 order 1 component of the relative sea level pattern with peak to peak amplitude of 20 to 40 m the maximum effect is along the great circle passing through the path of the pole and at latitudes of 45 this secular pole tide has been ignored in most previous attempts to estimate ice sheet loading history and mantle viscosity from global patterns of relative sea level change it has a large influence along the east coast of north america and the west coast of south america and significantly contributes to present day rates of relative sea level change

ocean bottom deformation due to present day mass redistribution and its impact on sea level observations present day mass redistribution increases the total ocean mass and on average causes the ocean bottom to subside elastically therefore barystatic sea level rise is larger than the resulting global mean geocentric sea level rise observed by satellite altimetry and gps corrected tide gauges we use realistic estimates of mass redistribution from ice mass loss and land water storage to quantify the resulting ocean bottom deformation and its e ect on global and regional ocean volume change estimates over 1993 2014 the resulting globally averaged geocentric sea level change is 8 percent smaller than the barystatic contribution over the altimetry domain the di erence is about 5 percent and due to this e ect barystatic sea level rise will be underestimated by more than 0 1 mm y over 1993 2014 regional di erences are of ten larger up to 1 mm y over the arctic ocean and 0 4 mm y in the south paci c ocean bottom deformation should be considered when regional sea level changes are observed in a geocentric reference frame

deformation induced by polar motion variations in the geocentric position of the earth s rotation axis polar motion cause deformation within the earth we estimate the effects of this deformation on radial and horizontal positions of points on the earth s surface on baseline lengths between those points and on surface gravity the effects of the oceans and of the earth s anelasticity on this deformation are found to be negligible peak to peak variations in radial motion are typically 10 20 mm over a year horizontal displacements are less than 7 8 mm variations in baseline length can be as large as 30 40 mm variations of up to 13 gal in surface gravity are possible these numbers are all small enough that they can probably not be used to learn about the earth however they are large enough to affect noticeably present high quality geodetic observations

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

vertical tectonic crustal movements along the japanese coastlines inferred from late quaternary and recent relative sea level changes abstract observed relative sea level rsl changes during the past 130 kyr make it possible to evaluate the vertical crustal movement due to several tectonic processes such as the subduction of oceanic plates here we infer average rates of tectonic crustal movement along the japanese coastlines on three typical timescales of 50 yr 6 kyr and 125 kyr based on tide gauge and holocene rsl observations and the altitudes of marine terraces formed at the last interglacial lig phase at 125 ka the rates on a timescale of 50 yr are derived from tide gauge data thermosteric sea level changes due to thermal expansion of the oceans and predictions due to the glacio hydro isostatic adjustment gia for the last deglaciation and also recent melting of the mountain glaciers and greenland and antarctic ice sheets those for 6 kyr and 125 kyr are based on the rsl observations and the predictions by gia modelling considering uncertainties for temporal changes in eustatic sea level for the mid to late holocene and lig phase the inferred rates for 50 yr are significantly different from those for 125 kyr in most sites particularly for sites along the coastline from eastern hokkaido to northeastern japan shikoku and south kyushu facing the pacific ocean in these regions the rates for 125 kyr and 50 yr are positive uplift and negative subsidence respectively also the observed rsl changes at 6 ka are consistent with the inferred rsl changes using the rates for 125 kyr and gia predictions in many sites but inconsistent with those for 50 yr in most sites except for a few sites these results suggest that the rates on a timescale of 50 yr are not representative of the tectonic crustal movements for timescales longer than 6 kyr in most sites along the japanese coastlines however the inferred rates on these timescales may be useful in discussing the recurrence of megathrust earthquake with its interval of 1 kyr such as the 2011 earthquake off the pacific coast of tohoku

modelling sea level data from china and malay thailand to estimate holocene ice volume equivalent sea level change abstract this study presents a new model of holocene ice volume equivalent sea level esl extending a previously published global ice sheet model bassett et al 2005 which was unconstrained from 10 kyr bp to present this new model was developed by comparing relative sea level rsl predictions from a glacial isostatic adjustment gia model to a suite of holocene sea level index points from china and malay thailand three consistent data model misfits were found using the bassett et al 2005 model an over prediction in the height of maximum sea level the timing of this maximum and the temporal variation of sea level from the time of the highstand to present the data model misfits were examined for a large suite of esl scenarios and a range of earth model parameters to determine an optimum model of holocene esl this model is characterised by a slowdown in melting at 7 kyr bp associated with the final deglaciation of the laurentide ice sheet followed by a continued rise in esl until 1 kyr bp of 5 8 m associated with melting from the antarctic ice sheet it was not possible to identify an earth viscosity model that provided good fits for both regions with the china data preferring viscosity values in the upper mantle of less than 1 5 10 20 pa s and the malay thailand data preferring greater values we suggest that this inference of a very weak upper mantle for the china data originates from the nearby subduction zone and hainan plume the low viscosity values may also account for the lack of a well defined highstand at the china sites

vertical gps ground motion rates in the euro mediterranean region new evidence of velocity gradients at different spatial scales along the nubia eurasia plate boundary we use 2 5 to 14 years long position time series from 800 continuous global positioning system gps stations to study vertical deformation rates in the euro mediterranean region we estimate and remove common mode errors in position time series using a principal component analysis obtaining a significant gain in the signal to noise ratio of the displacements data following the results of a maximum likelihood estimation analysis which gives a mean spectral index 0 7 we adopt a power law white noise stochastic model in estimating the final vertical rates and find 95 of the velocities within 2 mm yr with uncertainties from filtered time series 40 smaller than from the unfiltered ones we highlight the presence of statistically significant velocity gradients where the stations density is higher we find undulations of the vertical velocity field at different spatial scales both in tectonically active regions like eastern alps apennines and eastern mediterranean and in regions characterized by a low or negligible tectonic activity like central iberia and western alps a correlation between smooth vertical velocities and topographic features is apparent in many sectors of the study area glacial isostatic adjustment and weathering processes do not completely explain the measured rates and a combination of active tectonics and deep seated geodynamic processes must be invoked excluding areas where localized processes are likely or where subduction processes may be active mantle dynamics is the most likely process but regional mantle modeling is required for a better understanding

on post glacial sea level i general theory summary modern analyses of sea level changes due to glacial isostatic adjustment gia are based on the classic sea level equation derived by farrell clark 1976 geophys j r astr soc 46 647 667 the connection between global sea level variations and changes to ocean height that is assumed within this equation breaks down in the presence of a time varying shoreline geometry we present a generalized sea level equation that overcomes this difficulty we also derive analytic expressions for and present schematic illustrations of the error in the ocean height change over finite time intervals introduced in published efforts to incorporate shoreline evolution into the theory of gia induced sea level change this comparison includes studies of shoreline migration due to either local sea level changes or the growth and ablation of marine based ice we conclude that the theories applied by johnston 1993 geophys j int 114 615 634 milne 1998 phd thesis university of toronto toronto and co workers are more accurate than the procedure advocated by peltier 1994 science 265 195 201 1998a geophys res lett 25 3955 3958 1998b rev geophys 114 615 634 although an improvement in the latter has recently been reported peltier drummond 2002 geophys res lett 29 10 1029 2001gl014273 our generalized theory is valid for any earth model in a companion paper we derive the equations necessary to treat the special case of a spherically symmetric linear viscoelastic and rotating earth and we quantify errors associated with previous work

eustatic sea level fluctuations induced by polar wander the observation of apparently simultaneous episodes of deposition or non deposition of marine sediments in different parts of the world has led to the proposal that at least some sea level rises and falls must be global or eustatic in character1 3 here we show that polar wander of a viscoelastic stratified earth can induce global sea level fluctuations comparable to the short term component in the eustatic sea level curves the sign of these fluctuations which are very sensitive to the rheological stratification depends on the geographical location of the observation point rises and falls in sea level can thus be coeval in different parts of the world this finding is in distinct contrast to the main assumption underlying the reconstruction of eustatic curves namely that global sea level events produce the same depositional sequence everywhere this apparent contradiction is due to the poor time resolution of the stratigraphie records in the distant past which is comparable to the timescale of polar motion4 6 and to non uniform data coverage we propose that polar wander should be added to the list of geophysical mechanisms the others are glacial instabilities plate tectonic mechanisms sea floor spreading and thermal and compaction induced subsidence that can control the third order cycles in sea level

measurement requirements for glacial uplift detection of nonadiabatic density gradients in the mantle recent isotope studies have rekindled interest in the possibility that the mantle may be chemically stratified and therefore nonadiabatic previous calculations of the last ice age are compatible only with a 1022p mantle calculations of the isostatic response of an adiabatic partially nonadiabatic and fully nonadiabatic 1022p mantle to the load cycle of the last ice age show that the uplift responses of an adiabatic and even partially nonadiabatic mantle are very different however geoid perturbations mask these differences and the emergence curves of the two mantle types are nearly identical except in the regions near and under the ice loads at the early stages of isostatic readjustment the calculations suggest that we must seek shoreline emergence data around glaciated areas more than 6000 years before present if nonadiabatic density gradients in the mantle are to be detected from emergence data

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

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

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

using commercial finite element packages for the study of earth deformations sea levels and the state of stress summary modifications to commercial finite element fe packages must be applied before they can be used for geophysical studies involving long wavelength deformation or viscoelasticity this paper provides in detail how and why the commercial codes have to be modified when incompressibility is assumed both the non self gravitating flat earth and self gravitating spherical earth will be considered the latter involves an iterative procedure which converges within 5 iterations this is demonstrated both analytically and numerically in addition implementation of the gravitationally self consistent sea level equation on a self gravitating spherical earth is also described good agreement between numerical results obtained with this coupled finiteelement method and the conventional spectral method is also demonstrated in all cases the interpretation of the outputs of fe models are particularly important in modelling the state of stress

on postglacial sea level iii incorporating sediment redistribution we derive a generalized theory for gravitationally self consistent static sea level variations on earth models of arbitrary complexity that takes into account the redistribution of sediments the theory is an extension of previous work that incorporated into the governing equations shoreline migration due to local sea level variations and changes in the geometry of grounded marine based ice in addition we use viscoelastic love number theory to present a version of the new theory valid for spherically symmetric earth models the love number theory accounts for the gravitational deformational and rotational effects of the sediment redistribution as a first illustrative application of the new theory we compute the perturbation in sea level driven by an idealized pulse of sediment transport into the gulf of mexico we demonstrate that incorporating a gravitationally self consistent water load in this case significantly improves the accuracy of sea level predictions relative to previous simplified treatments of the sediment redistribution

total meltwater volume since the last glacial maximum and viscosity structure of earth s mantle inferred from relative sea level changes at barbados and bonaparte gulf and gia induced j2

the viscoelastic relaxation of a realistically stratified earth and a further analysis of postglacial rebound summary we discuss the isostatic adjustment of the earth in response to pleistocene deglaciation and derive constraints on the earth s viscosity profile we model the earth as viscoelastic self gravitating realistically stratified and spherically symmetric it is shown that the earth s relaxation eigenspectrum besides possessing a small set of well known discrete modes also includes infinitely dense sets of modes a continuous spectrum which separate into classes that depend on the principal restoring force of the mode methods for estimating the continuous spectrum are discussed and the effects on the predicted uplift are assessed we find that the effects of the continuous spectrum are far less important than those of the discrete modes though the presence of the continuous spectrum can make the discrete modes more difficult to identify the continuous spectrum does become important when computing the rebound due to more recent loading such as might be associated with present day changes in polar ice we use our model to refine predictions of the earth s response to pleistocene glacial loading with particular emphasis on implications for mantle viscosity we have used time histories that are consistent with the recently recalibrated 14c time scale a special effort is made to match the geologic records of sea level at sites in the vicinity of hudson bay we find consistent with the results of other authors that the curvatures of the records are sensitive indicators of lower mantle viscosity but that there are inconsistencies between the records at different sites however we find we are also able to change the predicted curvatures by modifying the temporal and spatial distribution of the ice loads if we assume a factor of 50 increase in viscosity between the upper and lower mantles and if we assume that the ice on the eastern side of hudson bay melted a few thousand years later than the ice on the western side a result consistent with recent geologic evidence we are able to match the observed sea level data about as well as we are able to if we use instead a uniform mantle viscosity profile a model with a factor of 50 jump in viscosity predicts a large free air gravity anomaly over northern canada that is reasonably consistent with what is observed whereas a uniform viscosity model does not though some authors have argued that the observed north american gravity anomaly may be mostly a consequence of mantle convection and largely unrelated to postglacial rebound our objective here is not to present a preferred ice model or viscosity profile rather we conclude only that the interpretation of the data is ambiguous and that the mantle viscosity profile can not yet be uniquely inferred from them

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

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

uplift rates from a new high density gps network in palmer land indicate significant late holocene ice loss in the southwestern weddell sea the measurement of ongoing ice mass loss and associated melt water contribution to sea level change from regions such as west antarctica is dependent on a combination of remote sensing methods a key method the measurement of changes in earth s gravity via the grace satellite mission requires a potentially large correction to account for the isostatic response of the solid earth to ice load changes since the last glacial maximum in this study we combine glacial isostatic adjustment modelling with a new gps dataset of solid earth deformation for the southern antarctic peninsula to test the current understanding of ice history in this region a sufficiently complete history of past ice load change is required for glacial isostatic adjustment models to accurately predict the spatial variation of ongoing solid earth deformation once the independently constrained effects of present day ice mass loss have been accounted for comparisons between the gps data and glacial isostatic adjustment model predictions reveal a substantial misfit the misfit is localized on the southwestern weddell sea where current ice models under predict uplift rates by approximately 2 mm yr 1 this under prediction suggests that either the retreat of the ice sheet grounding line in this region occurred significantly later in the holocene than currently assumed or that the region previously hosted more ice than currently assumed this finding demonstrates the need for further fieldwork to obtain direct constraints on the timing of holocene grounding line retreat in the southwestern weddell sea and that grace estimates of ice sheet mass balance will be unreliable in this region until this is resolved

the influence of sediment isostatic adjustment on sea level change and land motion along the u s gulf coast sea level rise presents a hazard for coastal populations and the mississippi delta md is a region particularly at risk due to the high rates of land subsidence we apply a gravitationally self consistent model of glacial and sediment isostatic adjustment sia along with a realistic sediment load reconstruction in this region for the first time to determine isostatic contributions to relative sea level rsl and land motion we determine optimal model parameters earth rheology and ice history using a new high quality compaction free sea level indicator database using the optimal model parameters we show that sia can lower predicted rsl in the md area by several meters over the holocene and so should be taken into account when modeling these data we compare modeled contemporary rates of vertical land motion with those inferred using gps this comparison indicates that isostatic processes can explain the majority of the observed vertical land motion north of latitude 30 7 n where subsidence rates average about 1 mm yr however subsidence south of this latitude shows large data model discrepancies of greater than 3 mm yr indicating the importance of nonisostatic processes this discrepancy extends to contemporary rsl change where we find that the sia contribution in the delta is on the order of 10 1 mm yr we provide estimates of the isostatic contributions to 20th and 21st century sea level rates at gulf coast permanent service for mean sea level tide gauge locations as well as vertical and horizontal land motion at gps station locations near the md

sea level changes since the last glacial maximum an appraisal of the ipcc fourth assessment report the ipcc fourth assessment report ar4 stated that global sea level rose by about 120 m between the last glacial maximum lgm and 3 2 ka and did not rise again until the late 19th century a review of relevant literature demonstrates that the rise may have been larger by 10 15 m that the timing of stabilisation is poorly constrained within the last 7 ka bp and that the onset of modern rates of sea level rise is not synchronous and uniform across the globe the lgm lowstand as defined in the ar4 is based on the classic barbados sea level history but the sea level curve from this island may not be an accurate eustatic approximation if glacial isostatic adjustment gia processes were significant as suggested by various authors the barbados sea level curve revealed the existence of meltwater pulse mwp 1a at around 14 000 cal a bp questions about the source and causal mechanism of mwp 1a are still being explored by field scientists and gia modellers these problems have direct relevance for contemporary measurements of ice mass changes because space geodetic measurements rely on information provided by gia models to separate land motion from ice mass changes global patterns of holocene sea level change are controlled by regional sea level variability not only through isostatic and tectonic processes but also through steric effects longer wavelength gravitational changes produced by changing ice ocean mass flux and hemispheric scale perturbations in the earth s rotation eustasy is therefore merely a concept not a measurable quantity constraining the late holocene ice melt contribution to global sea level rise and determining regional sea level rise patterns in the 18th and 19th centuries are important future tasks for sea level scientists these will establish the baseline contributions to 20th and 21st century sea level rise and will help to determine the causes of modern rates of sea level rise constraining historical sea level accelerations and short term ice mass flux will aid models of ice sheet dynamics and help to reduce current uncertainties in future sea level predictions the ar4 shows that regional sea level variability is clearly present in sea level change patterns for the past 50 a and an important challenge for the next ipcc assessment is to incorporate this variability into regional future sea level rise scenarios copyright 2009 john wiley sons ltd

the effect of spatially non uniform water loads on prediction of sea level change summary numerical modelling of postglacial rebound predics a spatially variable pattern of sea level change yet many previous models predicting late pleistocene sea level change either neglect the load of water added to the oceans or assume a spatially uniform time dependent load over the whole ocean this is a poor approximation of the load near the former ice sheet since sea level change varies geographically in addition the coastline goemetry changes through time a spectral technique has been used to solve the sea level equation on an earth model with axisymmetric distribution of ice and oceans and also for a realistic ice ocean configuration the axisymmetric model is useful for demonstrating the fundamental physics involved in sea level changes caused by changes in surface loads in particular it can be seen that the elastic and gravitational response to the load is spread over a great distance whereas the viscous response is more localized a realistic ice ocean configuration has been used to demonstrate that neglect of the melt water load underestimates the amount of uplift in fennoscandia and other regions where rebound occurs in the ocean as previously noted by wu peltier 1983 in hudson bay and that movement of the coastlines and spatially varying water loads must both be included in calculations for the north sea and other near field regions with shallow seas sea level calculations including these effects and careful analysis of the sea level and ice melting record are required to determine modifications to the viscosity profile and ice model inferred by previous inaccurate models of the ocean load in the near field

postglacial sea level change on a rotating earth summary we present a complete derivation of the equation governing long term sea level variations on a spherically symmetric self gravitating maxwell viscoelastic planet this new sea level equation extends earlier work by incorporating in a gravitationally self consistent manner both a time dependent ocean continent geometry and the in uence of contemporaneous perturbations to the rotation vector of the planet we also outline an e cient pseudo spectral numerical methodology for the solution of this equation and present a variety of predictions based on a suite of earth models of relative sea level rsl variations due to glacial isostatic adjustment gia these results show that the contribution to the predicted rsl signal from gia induced perturbations to the rotation vector can reach 7 8 m over the postglacial period in geographic regions where the rotationally induced signal is a maximum this result is sensitive to variations in the adopted lower mantle viscosity and is relatively insensitive to variations in the adopted lithospheric thickness we also show that the rotationally induced component of rsl change is su cient to in uence previous estimates of late holocene melting events and ongoing sea level change due to giawhich were based on a rsl theory for a non rotating earth in particular estimates of antarctic melting over the last 5 kyr based on the amplitude of sea level highstands from the australian region may require an adjustment downwards of the order of 0 5 m of equivalent sea level rise furthermore present day rates of sea level change are perturbed by as much as 0 2 mm yr 1 by the rotational component of sea level change and this has implications for gia corrections of the global tide gauge record over the period from the last glacial maximum to the present we predict a distinctly non monotonic variation in the rotation induced component of rsl this is in agreement with our previous preliminary study milne mitrovica 1996 but contrasts signi cantly with predictions presented by han wahr 1989 and bills james 1996 we demonstrate that the disagreement arises as a consequence of approximations adopted in the latter studies we furthermore refute an assertion by bills james 1996 that previously published constraints on mantle viscosity and ice sheet histories which did not incorporate a rotation induced rsl component are largely invalidated by this omission

influence of glacial isostatic adjustment on tide gauge measurements of secular sea level change modem tide gage records of secular sea level change are strongly contaminated by the ongoing influence of glacial isostatic adjustment in this paper we employ an accurate high resolution model of the glacial isostatic adjustment process to filter this signal from time series consisting of annual mean heights observed on over 500 tide gages from which records of duration longer than 10 years are available these records are all contained in the archive of the permanent service for mean sea level at bidston in the united kingdom prior to removal of the isostatic adjustment contamination from these records the secular sea level change signal is seen to exhibit both rising and falling levels depending upon geographic location with regions of falling level corresponding to those that were ice covered during the last glaciation event of the present ice age after filtering the geographic heterogeneity in rates is considerably reduced so much so that a globally coherent component consisting of a rise of sea level at a rate of 2 4 0 9 mm yr 1 is revealed this could conceivably be driven by the greenhouse effect although no particular mechanism has been unambiguously identified by our analyses we investigate the impact of a number of different variants of the analysis procedure upon the inferred global signal

the gravitationally consistent sea level fingerprint of future terrestrial ice loss 1 we solve the sea level equation to investigate the pattern of the gravitationally self consistent sea level variations fingerprints corresponding to modeled scenarios of future terrestrial ice melt these were obtained from separate ice dynamics and surface mass balance models for the greenland and antarctic ice sheets and by a regionalized mass balance model for glaciers and ice caps for our mid range scenario the ice melt component of total sea level change attains its largest amplitude in the equatorial oceans where we predict a cumulative sea level rise of 25 cm and rates of change close to 3 mm yr from ice melt alone by 2100 according to our modeling in low elevation densely populated coastal zones the gravitationally consistent sea level variations due to continental ice loss will range between 50 and 150 of the global mean this includes the effects of glacial isostatic adjustment which mostly contributes across the lateral forebulge regions in north america while the mid range ocean averaged elastic gravitational sea level variations compare with those associated with thermal expansion and ocean circulation their combination shows a complex regional pattern where the former component dominates in the equatorial pacific ocean and the latter in the arctic ocean

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

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

material versus isobaric internal boundaries in the earth and their influence on postglacial rebound summary most previous earth models used to calculate viscoelastic relaxation after the removal of the late pleistocene ice loads implicitly assume that there is no exchange of mass across the mantle density discontinuities on periods of tens of thousands of years the material boundary formulation in the present study simple incompressible models are used to determine the earth s behaviour in the case where the density discontinuity remains at a constant pressure rather than deforming with the material the isobaric boundary formulation the calculation of the movement of the boundary is more rigorous than in earlier studies and uses the local incremental pressure calculated at the depth of the boundary and allows for the vertical deformation caused by the change in volume as material changes phase it is shown that the buoyancy modes associated with the density discontinuities decrease in strength and increase in relaxation time analogous to what results when the density contrast is reduced also two viscoelastic modes arise from an isobaric boundary which is also predicted when there is a contrast in rigidity or viscosity across a material boundary the difference in predicted radial deformation between the isobaric boundary model and the material boundary model is largest for long wavelength loads for which the material incremental pressure at depth is largest if the isobaric boundary model is appropriate for the treatment of the mineral phase changes in the mantle on glacial rebound timescales then previous inferences of the deep mantle to shallow mantle viscosity ratio based on large scale deformation spherical harmonic degree lo of the earth and including data from the early part of the glacio isostatic uplift are too small

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

glacial isostatic adjustment and the anomalous tide gauge record of eastern north america sea level variations as recorded by the global network of tide gauges represent a rich data set for studying a wide range of natural and anthropogenic phenomena such as the sea level rise induced by possible global warming for this purpose long term sea level trends must be corrected for the contaminating effects of continuing glacial isostatic adjustment1 5 gia the numerical correction procedure has for sites on the east coast of north america yielded a set of highly anomalous sea level rates characterized by systematic geographical trends2 4 5 we demonstrate that these trends are a consequence of inadequacies in the previous standard numerical prediction for gia in particular we find that the well known trends in the gia corrected tide gauge rates are eliminated if the lower mantle viscosity of the earth model used in the gia prediction is increased this result obviates the need to explain the anomalous trend as a manifestation of gulf stream ocean circulation4 or neotectonic processes2

regional biases in absolute sea level estimates from tide gauge data due to residual unmodeled vertical land movement the only vertical land movement signal routinely corrected for when estimating absolute sea level change from tide gauge data is that due to glacial isostatic adjustment gia we compare modeled gia uplift ice 5g vm2 with vertical land movement at 300 gps stations located near to a global set of tide gauges and find regionally coherent differences of commonly 0 5 2 mm yr reference frame differences and signal due to present day mass trends cannot reconcile these differences we examine sensitivity to the gia earth model by fitting to a subset of the gps velocities and find substantial regional sensitivity but no single earth model is able to reduce the disagreement in all regions we suggest errors in ice history and neglected lateral earth structure dominate model data differences and urge caution in the use of modeled gia uplift alone when interpreting regional and global scale absolute geocentric sea level from tide gauge data

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

pleistocene deglaciation and the earth s rotation a new analysis summary this paper is concerned with an analysis of the effect of the pleistocene glacial cycle upon the earth s rotation we demonstrate that two important geophysical observables may be explained as aspects of the rotational response to surface mass loading by ice sheets these are the astronomically observed non tidal component of the acceleration of planetary rotation and the secular drift of the rotation pole relative to the surface geography which is evident in the ils pole path the former observation is shown to provide an unambiguous constraint upon the viscosity of the planetary mantle and requires a depth dependence of this parameter which is the same as that which has previously been inferred in studies of the relative sea level variations and free air gravity anomalies associated with post glacial rebound the observed secular drift of the pole cannot provide an independent estimate of the viscosity of the mantle because it depends jointly upon mantle viscosity and lithospheric thickness with the viscosity profile fixed by the rebound data the observed speed of polar wander suggests a continental lithospheric thickness which is in excess of that appropriate for old ocean basins but nevertheless in accord with independent constraints

on postglacial sea level summary an exact method is presented for calculating the changes in sea level that occur when ice and water masses are rearranged on the surface of elastic and viscoelastic non rotating earth models the method is used to calculate the instantaneous elastic and delayed vi scoelastic sea level changes following the partial melting of late quaternary ice sheets we find that there can be large errors in the usual assumption that changes in sea level are uniform over the ocean basins if a quantity of ice equivalent to a uniform 100 m rise in sea level melts from the laurentide and fennoscandian ice sheets then in the south pacific the instantaneous rise in sea level can be as large as 120m in the north atlantic the instantaneous rise is always less than 100 m there is a zone in the north atlantic with almost no sea level change and near greenland and norway the sea level falls rather than rises by over 100 m one thousand years after the melting a forebulge migrating towards the ice loads causes water to flow from the south pacific into the north pacific suggesting that raised beaches should occur in the south pacific the gravitational attraction of an ice mass upon a nearby ocean tends to hold sea level high in the vicinity of the ice this extra load near the ice may have a significant influence on postglacial isostatic adjustment

uncertainties in elevation changes and their impact on antarctic temperature records since the end of the last glacial period abstract this study presents a sensitivity analysis considering the influence of elevation changes associated with both ice thickness and land height changes on water stable isotope temperature proxies from antarctic ice cores we compare results from three different ice sheet models and three different earth viscosity models at a 10 ice core sites as expected the ice thinning signal at west antarctic sites is the largest contributor to elevation induced temperature changes the signal predicted by the ice models considered produced 100 200 of the total glacial to interglacial signal in d indicating that the deglacial ice thinning is overestimated by an amount approaching an order of magnitude at some locations this indicates that the total volume loss in these models is considerably overestimated furthermore the predicted rate of this change is not supported by the isotope data and so again most likely reflects inaccuracies in the adopted ice models estimates of contemporary ice mass changes inferred from satellite gravity data corrected using any of these models with therefore be biased as a result the isostatic signal acts to reduce the total elevation change at most sites and has a relatively small magnitude a few to 20 of that due to the ice thickness change so is secondary at most sites and for most of the time however our results indicate that it could be the dominant control on elevation at some west antarctic sites during the holocene resulting in a secular cooling signal of 10 20 in d none of the models capture the holocene isotopic depletion trend present at several sites in east antarctica

near field hydro isostasy the implementation of a revised sea level equation summary we describe how the existing sea level equation incorrectly predicts the change in sea level and thus the ocean load in ice covered subgeoidal geographic regions during periods of deglaciation we go on to present a new sea level equation that overcomes this problem and we describe how this equation can be solved in a gravitationally self consistent manner by employing a well known spectral technique application of the new theory to predict relative sea level rsl histories and present day 3 d solid surface deformation rates in northeastern canada based on a single earth model characterized by a lithospheric thickness of 100 km and upper and lower mantle viscosities of 5 1020 and 5 1021 pa s respectively demonstrates that a significant error is introduced when the original theory is employed to predict the oceanic component of the surface load predictions of rsl curves show a discrepancy of 40 per cent at sites where data have been obtained and employed to constrain models of earth viscosity structure and ice sheet histories this error will significantly bias estimates of mantle viscosity structure and ice thicknesses that are based on the original theory in addition predictions of 3 d deformation rates differ by up to 25 per cent in some regions and so future applications that employ these data to constrain models of the glacial isostatic adjustment process should adopt the improved sea level theory in contrast estimates of inverse decay times from the predicted rsl curves are insensitive to within the observational error to the improvement in the surface load introduced by the new theory thus viscosity structure inferences based on this parametrization and the original sea level equation are unaffected by the error in the ocean load finally the new theory predicts a eustatic i e globally uniform rise in sea level over the postglacial period that is 11 m lower than that determined via the original theory therefore estimates of the global ice budget at the last glacial maximum based on far field rsl data and the original sea level theory will be too small by 10 per cent

coral indicators of past sea level change a global repository of u series dated benchmarks fossil corals provide valuable data for reconstructing past sea levels as they are often well preserved in the fossil record and can be dated with u series methods here we present a global and internally consistent database of usingle bondth dated fossil coral sea level indicators including full consideration of all known associated uncertainties both vertical and chronological we include carefully determined taxon specific depth distributions rather than blanket depth uncertainty terms as used in most previous work this is based on a synthesis of extensive modern ecological information on depth ranges these ranges are found to be spatially variable between ocean basins between regions and on sub regional scales because depth itself is not limiting instead depth distributions arise from complex physical chemical and biological interactions with coral reef growth distribution and composition one of the main causes for recognition of the greater depth variability of coral taxa has been the routine inclusion of deep diving and rov surveys in coral ecological studies over the past few decades which has broken through the shallow water bias of early surveys by adding frequent observations on deeper occurrences although more are needed it is also clear from our assessment that coral habitat depth distributions must be determined on the species level to reduce uncertainties in reconstructions of past sea levels and that application to sea level studies then requires these studies also to identify fossil corals to the species level samples identified only to the genus level give rise to wide uncertainties in habitat depth and hence sea level our database contains extensive metadata to assist evaluations of dating quality as well as geomorphic and stratigraphic metadata we demonstrate with examples how such metadata can help to evaluate sea level reconstructions for example by identifying outlier points one example discusses the last interglacial lig where we use the available data with their uncertainties to assess probabilistically the time at which local sea levels exceed that of the present which yields a mean age of 124 6 ka with 95 probability bounds at 118 5 and 129 5 ka we conclude with identification of key outstanding issues relating to i current incomplete understanding of tectonic setting including the current lack of independent verification of uplift subsidence rates and reliance of somewhat unsatisfactory and circular use of the elevation of last interglacial deposits ii the depth distributions of coral taxa and iii the complete documentation of stratigraphic geomorphological and other contextual information with suggestions for strategies to address these issues

on transient rheology and glacial isostasy theoretical predictions from analytical self gravitating layered earth models with maxwell burgers body and standard linear solid rheologies are employed to explore the extent to which transient creep may have influenced the inference of long term mantle viscosity from analysis of the various signatures derived from the process of glacial isostatic adjustment the compatibility of the various models is checked by their ability to fit simultaneously the relative sea level free air gravity and the rotational data we conclude that transient creep cannot operate throughout the entire mantle on account of the extreme sensitivity of the uplift and gravity data to any significant departures of the steady upper mantle viscosity from 1021 pa s transient rheology would most likely be unimportant in the upper mantle restricting transient rheology to the lower mantle we find that models with an adiabatic density jump at 670 km depth are not satisfactory because of their inability to produce sufficiently large gravity anomalies and polar wander speeds our calculations show that the preferred models with transient creep in the lower mantle are chemically stratified with a nonadiabatic density change of around 10 the long term viscosities in the lower mantle associated with compatible transient rheological models lie between 5 1022 and 1023 pa s these values are consistent with viscosity estimates derived from correlation of long wavelength geoid anomalies and the density perturbations in the deep mantle

glacial rebound of the british isles ii a high resolution high precision model summary observations of ice movements across the british isles and of sea level changes around the shorelines during late devensian time after about 25 000 yr bp have been used to establish a high spatial and temporal resolution model for the rebound of great britain and associated sea level change the sea level observations include sites within the margins of the former ice sheet as well as observations outside the glaciated regions such that it has been possible to separate unknown earth model parameters from some ice sheet model parameters in the inversion of the glaciohydro isostatic equations the mantle viscosity profile is approximated by a number of radially symmetric layers representing the lithosphere the upper mantle as two layers from the base of the lithosphere to the phase transition boundary at 400 km the transition zone down to 670 km depth and the lower mantle no evidence is found to support a strong layering in viscosity above 670 km other than the high viscosity lithospheric layer models with a low viscosity zone in the upper mantle or models with a marked higher viscosity in the transition zone are less satisfactory than models in which the viscosity is constant from the base of the lithosphere to the 670 km boundary in contrast a marked increase in viscosity is required across this latter boundary the optimum effective parameters for the mantle beneath great britain are a lithospheric thickness of about 65 km a mantle viscosity above 670 km of about 4 5 lo2 pa s and a viscosity below 670 km greater than 4 x lo2 pas

predictions of secular geoid changes from late pleistocene and holocene antarctic ice ocean mass imbalance summary estimates on ice volume changes in antarctica from both contemporary mass imbalance during the last hundred to thousand years and ice volume changes during the last glacial cycles are difficult to obtain future satellite gravity missions monitoring secular changes in gravity as a proxy of mass changes of the antarctic ice sheet will therefore provide an additional important constraint on the antarctic ice sheet history we assess the contributions from both past ice volume changes during the last glacial cycles and present ice imbalances over antarctica using a variety of published ice models model predictions of secular changes of the geoid anomaly based on plausible mantle viscosity profiles enable us to discuss the importance of past and present ice volume changes and their characteristic signatures while uncertainties arising from the viscosity profile are of secondary importance for model predictions of the secular change of the geoid anomaly we expect significant bias of the observed signal from uncertainties in the timing of the end of deglaciation which is in agreement with previous studies hence the benefit of inferring present day antarctic ice imbalance from satellite gravity missions will depend on improvements to ice models for the last glacial cycle

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

an assessment of the ice6g_c vm5a glacial isostatic adjustment model the recent release of the next generation global ice history model ice6g c vm5a is likely to be of interest to a wide range of disciplines including oceanography sea level studies space gravity mass balance studies glaciology and of course geodynamics earth rheology studies in this paper we make an assessment of some aspects of the ice6g c vm5a model and show that the published present day radial uplift rates are too high along the eastern side of the antarctic peninsula by 8 6 mm yr and beneath the ross ice shelf by 5 mm yr furthermore the published spherical harmonic coefficients which are meant to represent the dimensionless present day changes due to glacial isostatic adjustment gia contain excessive power for degree 90 do not agree with physical expectations and do not represent accurately the ice6g c vm5a model we show that the excessive power in the high degree terms produces erroneous uplift rates when the empirical relationship of purcell et al 2011 is applied but when correct stokes coefficients are used the empirical relationship produces excellent agreement with the fully rigorous computation of the radial velocity field subject to the caveats first noted by purcell et al 2011 using the australian national university anu groups calsea software package we recompute the present day gia signal for the ice thickness history and earth rheology used by peltier et al 2015 and provide dimensionless stokes coefficients that can be used to correct satellite altimetry observations for gia over oceans and by the space gravity community to separate gia and present day mass balance change signals we denote the new data sets as ice6g anu

new relative sea level insights into the isostatic history of the western mediterranean abstract a recent suite of relative sea level rsl data for the past 12 ka bp has provided new insights into the sea level histories of the western mediterranean region our analysis of the chronostratigraphic context of sea level indicators from spain catalonia the balearic islands and the gulf of valencia france corsica island and italy sardinia island has yielded 162 new sea level index and limiting points these data have considerably enhanced previous rsl compilations in addition to improving the quality of spatio temporal sea level reconstructions and our capacity to estimate isostatic related vertical motions in the western mediterranean basin the glacial and hydro isostatic adjustment gia pattern elucidated by the new database shows discrepancy with respect to those predicted by the available gia models in particular the new results underscore a non coherent isostatic response of the central portion of the western mediterranean with the balearic islands manifesting significant departures from the sea level histories of corsica sardinia and more generally along most of the western mediterranean coast our results are a crucial contribution to defining both the pattern and the magnitude of the isostatic signal along the western mediterranean coast in fact vertical isostatic motions represent a key to better assess any possible post industrial acceleration in sea level rise and to define future scenarios of coastal inundation in the context of global change

postglacial sea level change on a rotating earth first results from a gravitationally self consistent sea level equation we present and solve a gravitationally self consistent sea level equation which governs postglacial sea level variations on a spherically symmetric self gravitating viscoelastic and rotating earth we find that the inclusion of a glacio isostatically induced rotational excitation can significantly affect previous predictions of both present day sea level rates and postglacial sea level histories which were based on a theory that assumed a non rotating earth model to illustrate we consider present day sea level rates and tide gauge corrections along the us east coast and relative sea level curves in the far field of the late pleistocene ice sheets

reassessment of the potential sea level rise from a collapse of the west antarctic ice sheet theory has suggested that the west antarctic ice sheet may be inherently unstable recent observations lend weight to this hypothesis we reassess the potential contribution to eustatic and regional sea level from a rapid collapse of the ice sheet and find that previous assessments have substantially overestimated its likely primary contribution we obtain a value for the global eustatic sea level rise contribution of about 3 3 meters with important regional variations the maximum increase is concentrated along the pacific and atlantic seaboard of the united states where the value is about 25 greater than the global mean even for the case of a partial collapse

present day secular variations in the low degree harmonics of the geopotential sensitivity analysis on spherically symmetric earth models 1 we predict present day rates of change of the long wavelength components of the earth s geopotential due to the late pleistocene glacial cycles hereinafter referred to as glacial isostatic adjustment or gia these predictions are generated using spherically symmetric self gravitating maxwell viscoelastic earth models previous studies have generally considered only zonal i e azimuthally independent harmonics or the so called coefficients we extend these efforts to focus on the nonzonal harmonics and explore the sensitivity of our predictions to changes in a variety of model inputs as an example we examine the influence on the gia predictions of ignoring rotational perturbations and assuming an elastically incompressible model and find that these assumptions can have a significant impact on the degree 2 order 1 coefficients while the other harmonics are generally affected by 10 though the gia predictions are generally insensitive to variations in lithospheric thickness and upper mantle viscosity reasonable variations in either lower mantle viscosity or the late pleistocene ice history will have a more significant effect mindful of upcoming dedicated gravity missions we show that predictions of the gia induced changes of the geoid can vary by at least 0 5 mm yr 1 over a plausible range of earth and ice models

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

decoding last interglacial sea level variations in the western mediterranean using speleothem encrustations from coastal caves in mallorca and sardinia a field data model comparison u th ages of phreatic overgrowths on speleothems in coastal caves of the western mediterranean record high sea level positions during marine isotope stage mis 5e of the last interglacial while relative sea level rsl on the southeastern coast of mallorca stood 2 6 m above present sea level apsl during mis 5e it stood 4 3 m apsl at this time in northwestern sardinia the difference between the two sites during mis 5e and the deviation from the eustatic sea level trend during the holocene was investigated using the numerical code selen the offset between the eustatic curve and those pertaining to the two sites principally reflect the vertical deformations and geoidal variations in response to meltwater loading as sardinia is closer to the center of the mediterranean basin the hydro isostatic component of rsl is enhanced here compared to mallorca which results in a modeled offset of 60 cm between the two sites this result is qualitatively useful as it provides a partial reconciliation for the site differences however the need for refinement in the model is also recognized as it does not match the observation based on u th dating of speleothem overgrowths in mallorca that sea level there has remained stable for the past 2800 years overall the results of the study first suggest that both sites largely track the eustatic sea level curve and second suggest that glacial isostatic adjustment is a viable mechanism to reconcile some if not most of the relatively small elevation difference of mis 5e sea level observed at mallorca and sardinia although minor tectonic adjustments cannot be ruled out in explaining some low amplitude local variations