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

three dimensional finite element modelling of earth s viscoelastic deformation effects of lateral variations in lithospheric thickness summary we have developed a 3 d spherical finite element model to study the dynamic response to surface loads of a self gravitating and incompressible earth with 3 d viscoelastic structure we have forced our model with the ice 3g deglaciation history of tushingham peltier to study the effects of laterally varying lithospheric thickness on observations of post glacial rebound pgr the laterally varying lithospheric thicknesses are derived from estimates of the thermal structure of the oceanic lithosphere and from elastic thicknesses on continents as estimated from studies of long term geological loads our calculations show that the effects of lithospheric structure on the relative sea level change rslc depend on the locations of the observation sites and on the size of loads the rslc at the centre of the north american ice sheet is significantly less sensitive to lithospheric thickness compared with the rslc at the centre of the fennoscandian ice sheet at the peripheral bulges the rslc tends to be more sensitive to lithospheric thickness the rslc is controlled by local lithospheric thickness the rslc at a given location as predicted using models with laterally varying lithospheric thickness can be reproduced using a 1 d model with a uniform lithospheric thickness equal to the local lithospheric thickness coupled with efficient parallel computing we believe that the finite element model that we present here can be used to address a variety of viscoelastic deformation problems in geodynamics

viscoelastic versus viscous deformation and the advection of pre stress summary the heaviside response of an incompressible viscous half space is compared to that of a viscoelastic half space that may or may not be compressible elastically it will be shown that the difference between viscous and viscoelastic response is detectable from uplift data provided that the age of the data goes back far enough it is also possible to resolve using the post glacial rebound data whether the viscous model or the viscoelastic model is preferred provided that the ice model is better constrained moreover the rate of solid fluid transition is wavenumber k dependent and the transition is not as rapid nor as small as was previously predicted finally the advection of pre stress is shown to be required in viscoelastic deformation problems of the earth and that it is responsible for viscoelastic gravitational relaxation

the south scandinavian crust structural complexities from seismic reflection and refraction profiling abstract pioneering work on mapping the scandinavian crust commenced in the early 1960s and since then numerous profiling surveys have been undertaken particularly as part of the on going eugeno s project however the most significant contribution to mapping crustal structural details came from the m v mobil search cruises in the skagerrak and off the west coast of norway 16 s twt reflection profiling all past and present crustal profiling results have been integrated to produce detailed maps of moho depths and crustal thicknesses for south scandinavia the thinnest crust is found in the north sea and skagerrak approximately 20 km while east central sweden features very thick crust approximately 50 km other interesting features are the apparent correlation between crustal thinning and sedimentation subsidence magmatic activity earthquake occurrences and the tectonic age of the crust moho depths and the crustal thicknesses clearly reflect the tectonic evolution and the present structural features of the region investigated

rainfall thresholds for landsliding in the himalayas of nepal landsliding of the hillslope regolith is an important source of sediment to the fluvial network in the unglaciated portions of the himalayas of nepal these landslides can produce abrupt increases of up to three orders of magnitude in the fluvial sediment load in less than a day an analysis of 3 years of daily sediment load and daily rainfall data defines a relationship between monsoonal rainfall and the triggering of landslides in the annapurna region of nepal two distinct rainfall thresholds a seasonal accumulation and a daily total must be overcome before landslides are initiated to explore the geomorphological controls on these thresholds we develop a slope stability model driven by daily rainfall data which accounts for changes in regolith moisture the pattern of rainfall thresholds predicted by the model is similar to the field data including the decrease in the daily rainfall threshold as the seasonal rainfall accumulation increases results from the model suggest that for a given hillslope regolith thickness determines the seasonal rainfall necessary for failure whereas slope angle controls the daily rainfall required for failure d 2004 elsevier b v all rights reserved

heat flow and thermal structure of the lithosphere across the baltic shield and northern tornquist zone abstract terrestrial heat flow data from archean and proterozoic provinces of the baltic shield its southwestern margin and the tectonic transition to the younger tectonic units of central europe northern segment of the european geotraverse are compiled and examined for local and regional variations a 2 d numerical lithospheric temperature and heat flux model is presented covering 1800 km of the deep seismic fennolora profile across the baltic shield and 500 km of eugeno s northern eugemi seismic lines across the northern tornquist zone and the danish and north german basins thermal lithosphere defined as the outer layer with relatively low temperatures t c in which heat transfer is dominantly by conduction is found to vary markedly in thickness from 85 110 km beneath basins and tornquist zone to about 150 km in central shield areas and 200 250 km in areas of low heat flow along the northern shield profile these results are in very good agreement with seismological information from surface wave dispersion analysis and the refraction wide angle seismic interpretation of fennolora data the combined thermal and seismologic evidence indicates that the uppermost mantle region stratified in seismic velocity is restricted to the upper relatively cold thermal layer which is interpreted to constitute shield lithosphere local and to some extent regional variations in surface heat flow are found to be closely related to variations in near surface radiogenic heat production for the southern baltic shield a heat flow heat production relationship of q 0 32 8 7 6 h 0 is derived regional increase in heat flow from northern and central shield provinces to the shield margin and the tornquist zone is interpreted to be related partly to differences in upper crustal heat generation partly and in southernmost areas mainly to an increased heat flux from the upper mantle upper mantle heat flux is estimated at 20 25 mw m 2 along the northern and central shield transect increasing to 30 40 mw m 2 beneath the shield margin basins and tornquist zone lithospheric thickness variations in this region of northern europe are found to be closely associated with variations in heat flux from the uppermost mantle and perhaps to a large extent controlled by geodynamically determined lateral differences in upper mantle heat flux earthquake focal depth data and information on crustal strength show baltic shield seismicity to be limited generally to the upper 20 25 km brittle part of the crust at temperatures less than 300 400 c maximum source depth of magnetic anomalies at temperatures near 600 c is in the deepest part of the crust near the crust mantle boundary in the southern region about 25 km depth along the tornquist zone and about 35 40 km in southern shield areas and in the uppermost mantle 60 70 km depth in the northern shield areas some petrologic implications are discussed the present deep crust is supposed to be at lower temperature pressure conditions than at early stages of formation however also the present deepest parts of the shield crust 35 40 km are within the stability field of eclogites the general absence of significant gravity anomalies in areas of marked crustal thickness variations indicate high density eclogites to be present in significant amounts in the deep shield crust

recent postglacial rebound gravity change and mantle flow in fennoscandia summary the recent postglacial rebound of fennoscandia is investigated using sea level data levelling data and gravity data in particular an analysis is made of the repeated data obtained hitherto on the fennoscandian land uplift gravity line along latitude 63 methods for this analysis include an iterative procedure for computing the relation between gravity change and absolute land uplift the mass flow parameter and the geoid rise the remaining land uplift is also estimated the mass flow parameter c is used to characterize the relation between additional mass and additional volume due to rebound it is a number between 0 and 1 1 corresponding to full inflow of mantle below the rising crust and 0 to no inflow but some kind of decompression the main result is that c is significantly different from 0 at the 99 per cent level we find c 0 8 this means that models proposed of the present uplift based on pure decompression must be ruled out and that a viscous inflow of mantle is a necessary part of the ongoing uplift process on the other hand this process might be more complicated than a pure viscous flow

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

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

early paleozoic ca 465 ma eclogites from beishan nw china and their bearing on the tectonic evolution of the southern central asian orogenic belt abstract the beishan orogen is situated in the southern margin of the central asian orogenic belt caob it is connected with the tianshan orogen to the west and the mongolia xing anling orogen to the east this orogen exhibits a well preserved neoproterozoic to late paleozoic sequence containing ophiolites accretionary complexes and eclogites in this paper we provide new geochronological data for eclogites and their country paragneiss to constrain the tectonic evolution of the beishan orogen u pb zircon dating of eclogites yielded two concordant ages 886 4 ma for the cores and 465 10 ma for the rims the zircon cores display bright luminescence with homogeneous or planar sector zoning intermediate th u ratios 0 17 0 47 and hree enriched patterns with negative eu anomalies eu eu 0 16 0 58 these features coupled with their formation temperatures of 680 710 c suggest that the core age represents the time of an earlier upper amphibolite facies metamorphic episode by contrast the zircon rims have dark luminescence with homogeneous or fir tree zoning low th u ratios 12 kbar for the eclogite facies metamorphism on the other hand zircon dating of a paragneiss near the eclogite produced two major groups of ages ca 1450 ma for a magmatic event and ca 900 ma for a metamorphic event it seems that eclogites and their country rocks have suffered the same earlier metamorphic episode based on the available age data obtained for eclogites ophiolites and granitoids from the beishan area a tectonic scenario can be constructed as follows the ca 1000 ma oceanic crust representing by protoliths of the eclogites was involved in early neoproterozoic orogenesis to have formed a microcontinental block during the early paleozoic island arcs and microcontinental blocks were progressively accreted to the northern margin of the tarim craton dunhuang block this was followed by the closure of paleoasian ocean and final amalgamation between the tarim craton and kazakhstan block in the late paleozoic

predominance of long wavelength heterogeneity in the mantle analysis of travel time anomalies of long period shear waves recorded by the global digital seismographic network indicates that mantle heterogeneities which probably reflect patterns of mantle convection occur most prominently on length scales greater than about 6 000 km when projected onto a two dimensional map at the earth s surface models of mantle convection will need to be able to produce a similar power spectrum

earth s gravitational field seismic tomography resolves the enigma of the laurentian anomaly we demonstrate that the negative free air gravity anomaly over hudson bay is not due to glacial isostatic disequilibrium but rather to the influence of large scale mantle convection

crust and upper mantle structure along the dss baltic profile in se finland summary the 430 km long dss baltic profile in se finland runs through the rapakivi intrusion the svecokarelian geosynclinal complex including the ladoga bothnian bay zone and the archean basement complex a brief description of field operations in 1982 is presented record sections of p and s waves were used for the interpretations a starting model was constructed by inverse methods and improved by dynamic ray tracing modelling three blocks are indentified on the cross section from sw to ne these are the southern associated with the rapakivi massif depth to moho m about 40 km the central ladoga bothnian bay zone with m of approximately 55 60 km and the northern archean crystalline basement with m about 40 45 km the average crustal velocity is 6 6 6 7 kms the crustal structure along the baltic profile is compared with the surrounding dss profiles finnish sveka and soviet kern tulos and ladoga profiles the eastern border of the ladoga bothnian bay zone was located and specific features of the crust and uppermost mantle along the profile area are discussed

some effects of lateral heterogeneities in the upper mantle on postglacial land uplift close to continental margins summary we investigate the effects of lateral heterogeneities in the upper mantle on the calculation of postglacial land uplift for the model calculations we use a commercial finiteelement code which enables us to solve the equations governing a layered isotropic incompressible maxwell viscoelastic half space with laterally varying layer thicknesses and physical properties following previous investigations performed by sabadini yuen portney 1986 and gasperini sabadini 1989 we extend their results using a more realistic loading history and different earth models we then focus our attention on the question whether lateral heterogeneities in the upper mantle can be modelled correctly using a set of homogeneous earth models to this end a comparison of model calculations using both laterally homogeneous and heterogeneous earth models is performed we find that lateral heterogeneities in the upper mantle significantly influence the calculated postglacial land uplift the resolving power of relative sea level observations for the prescribed lateral heterogeneities used in this study is mainly focused on observations around the load margin and outside the glaciated areas where differences in predicted land uplift between individual models are large enough to be resolved by observations we can qualitatively determine lateral heterogeneities in the upper mantle using a set of laterally homogeneous earth models if the geological structure for example a continental margin is known however in order to infer the correct values of lithospheric thickness and asthenospheric viscosity we need to use laterally heterogeneous models

glacial isostasy and the interplay between upper and lower mantle lateral viscosity heterogeneities from the analysis of sea level data near the centre of the former fennoscandian ice sheet and the theoretical predictions of vertically and laterally stratified earth models we explore the extent to which lateral viscosity variations could have influenced the estimate of long term mantle viscosity we follow a finite element scheme in cylindrical symmetry focusing on the effects of lateral viscosity contrasts of different magnitudes and wavelengths sea levels are consistent with long wavelength lateral viscosity contrasts of at most 2 orders of magnitude short wavelength variations comparable with the lateral extension of the surface load should be ruled out differences in the average viscosities inferred from laterally stratified and uniform mantle models may be as high as 1 order of magnitude if we allow for different lateral viscosity patterns in the upper and lower mantle we find that sea levels are consistent with short wavelength variations in the upper mantle of around 2 orders of magnitude coupled with smoother lateral viscosity contrasts in the lower mantle

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

viscoelastic perturbations of the earth significance of the incremental gravitational force in models of glacial isostasy summary the incremental gravitational force igf arises from perturbations of the earth s gravitational potential in glacial isostasy its sources are the surjicial and internal mass redistributions associated with the growth and decay of the continental ice sheets we examine the errors caused by the neglect of the igf using closed form solutions of the equations governing surface load induced perturbations of two types of incompressible spherical earth models 1 maxwellian viscoelastic mantle enclosed by elastic lithosphere and 2 maxwellian viscoelustic mantle enclosing inviscid core calculations in the legendre domain of the radial surface displacement for these models show that neglecting the igf causes enhancement of the elastic response and acceleration of the viscous relaxation in the space domain these changes entail corresponding modifications of the calculated land adjustment the magnitude of the error caused by the neglect of the igf strongly depends on the deglaciation history and load radius adopted assuming a typical deglaciation history the error reaches a maximum of less than 20 m at the end of the deglaciation phase for loads comparable in size to the canadian or the fennoscandian ice sheets we also compare sphericul earth models with igf and plane earth models without igf calculations of the radial surface displacement show that the errors due to the neglect of sphericity and the igf partially compensate each other taking the uncertainties of the observational data into account we conclude that the majority of the canadian and fennoscandian glacial isostatic adjustment data can be modelled with sufficient accuracy using a plane earth model without igf

lateral heterogeneities in mantle viscosity and post glacial rebound summary seismic tomographic results and convection calculations support the evidence of horizontal temperature variations in the mantle on the basis of commonly accepted rheological laws we thus expect lateral variations in the viscosity of several orders of magnitude this paper is concerned with the effects of lateral viscosity variations on vertical displacement induced by pleistocenic deglaciation a finite element scheme in axial symmetry mimics the relaxation process of a flat earth model characterized by a linear maxwell rheology we follow a spectral approach to analyse the impact of lateral viscosity variations with different amplitudes and wavelengths the potential impact of lithospheric thickening and viscosity increase in stable continental regions on the interpretation of sea level data is also analysed lateral viscosity heterogeneities are found to have strong influence on ground deformations induced in deglaciated areas from the analysis of sea level data near the centre of the former fennoscandian ice sheet and the theoretical predictions of radially and laterally stratified earth models we explore the extent to which lateral viscosity contrasts may have influenced the inference of long term mantle viscosity while radially stratified models predict a rather uniform mantle viscosity we show that lateral viscosity contrasts of 1 or 2 orders of magnitude are consistent with sea level data if the wavelength of the heterogeneity is comparable with the dimension of a convecting cell in this case the average viscosity can deviate by around an order of magnitude from the canonical value of 1021 pa s predicted by rebound models in the past viscosity values close to 1021 pa s are found to be appropriate for the mantle region underlying the load long wavelength viscosity variations of 3 or 4 orders of magnitude degrade our ability to reproduce the observed uplift in the centre of the ice sheet and must be ruled out for wavelengths comparable with the horizontal extension of the surface load and viscosity contrasts of 1 or 2 orders of magnitude model results are found to be inconsistent with sea level data these findings suggest that rebound modelling can become a useful tool to constrain the magnitude and wavelength of viscosity contrasts comparison between horizontally and vertically varying models indicates that lateral viscosity heterogeneities could have been interpreted as radial variations in previous rebound studies

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

a consistent map of the postglacial uplift of fennoscandia a consistent map of the recent postglacial rebound of fennoscandia is constructed on the basis of sea level records lake level records and repeated high precision levellings the uplift rates calculated from the sea level series form a consistent framework of the map the sea level stations used are 56 reliable stations in the baltic sea and adjacent waters with series spanning 60 years or more many of them about 100 years using a reference station in the baltic sea and another one outside the baltic all results are reduced to a common time span the 100 year period 1892 1991 in order to eliminate oceanographic changes inland uplift differences are obtained from the repeated national levellings and in four of the large lakes from long water level series in pairs the levellings however yield less accurate land uplift values than the sea level and lake level data the resultant map shows a fairly smooth phenomenon with a maximum apparent uplift in the gulf of bothnia of 9 0 mm yr 1 the standard error is typically 0 2 mm yr i close to the sea level stations larger inland finally the pattern of the present uplift as determined here is observed to be very similar to that of the past uplift as determined from ancient shore lines of the litorina sea however the ratio between the past uplift and the present uplift rate tends to increase somewhat towards the uplift centre this might reflect a non uniform mantle viscosity also the uplift maximum seems to have migrated towards nne

holocene relative sea level change isostatic subsidence and the radial viscosity structure of the mantle of northwest europe belgium the netherlands germany southern north sea abstract a comprehensive observational database of holocene relative sea level rsl index points from northwest europe belgium the netherlands northwest germany southern north sea has been compiled in order to compare and reassess the data collected from the different countries regions and by different workers on a common time depth scale rsl rise varies in magnitude and form between these regions revealing a complex pattern of differential crustal movement which cannot be solely attributed to tectonic activity it clearly contains a non linear glacio and or hydro isostatic subsidence component which is only small on the belgian coastal plain but increases significantly to a value of ca 7 5 m relative to belgium since 8 cal ka bp along the northwest german coast the subsidence is at least in part related to the post glacial collapse of the so called peripheral forebulge which developed around the fennoscandian centre of ice loading during the last glacial maximum the rsl data have been compared to geodynamic earth models in order to infer the radial viscosity structure of the earth s mantle underneath nw europe lithosphere thickness upper and lower mantle viscosity and conversely to predict rsl in regions where we have only few observational data e g in the southern north sea a very broad range of earth parameters fit the belgian rsl data suggesting that glacial isostatic adjustment gia only had a minor effect on belgian crustal dynamics during and after the last ice age in contrast a narrow range of earth parameters define the southern north sea region reflecting the greater influence of gia on these deeper older samples modelled rsl data suggest that the zone of maximum forebulge subsidence runs in a relatively narrow wnw ese trending band connecting the german federal state of lower saxony with the dogger bank area in the southern north sea identification of the effects of local scale factors such as past changes in tidal range or tectonic activity on the spatial and temporal variations of sea level index points based on model data comparisons is possible but is still complicated by the relatively large range of earth model parameters fitting each rsl curve emphasising the need for more high quality observational data

effects of removing concentric positioning on postglacial vertical displacement in the presence of lateral variation in lithospheric thickness in order to understand the effects of non concentric positioning on postglacial rebound in the presence of lateral lithospheric thickness variations vertical displacements are calculated for disc like loads placed on non axisymmetric earth models results show that removal of concentric positioning do not produce significant effects that can be resolved by relative sealevel data and the edge of the ice load remains most sensitive to the effects of lateral heterogeneities this implies that earlier results of axisymmetric models can be extended to fully 3d laterally heterogeneous models

deformation of an incompressible viscoelastic flat earth with powerlaw creep a finite element approach summary extrapolating experimental creep data to mantle conditions indicates that the upper mantle may deform as a power law medium in all of the previous models of loading unloading in a power law medium some simplifying assumptions were made to keep the calculation tractable unfortunately some of these assumptions are invalid while others are too restrictive in this paper the finite element method is used to study the deformation of incompressible linear and non linear rheological earth models that are subject to constant gravitational acceleration the advantage of this new approach is that none of these simplifying assumptions has to be made thus the solution is much more rigorous the deformation of a non linear half space due to heaviside loading and unloading of a boxcar load is shown to be characterized by i ubiquitous updoming sinking outside the load ii a very high initial rate of deformation followed by a much slower rate inside the load and iii the load history is fully coupled with the rheology of the earth because the state of stress caused by the magnitude of the load and the sequence of loading or unloading events determines the effective viscosity and thus the deformation it is also demonstrated that the usual assumption of self similarity and proportional relaxation are invalid moreover the relaxation time is a function of both space and time the effect of an elastic lithosphere on a linear or non linear channel is shown to be much larger than that for a half space even at small t the effects of a non linear channel a parabolic load and a depth dependent creep parameter a are also studied when the observed uplift data near the rebound centre in fennoscandia are compared to the predicted uplift curves it is demonstrated that for the instantaneous removal of a 15 mpa boxcar load power law rheological models cannot fit the observations as well as the linear models can however more work has to be done before one can decide whether the rebound process actually involves a mantle with linear rheology or power law rheology

deglacial land emergence and lateral upper mantle heterogeneity in the svalbard archipelago ii extended results for high resolution load models summary in paper i breuer wolf 1995 a preliminary interpretation of the postglacial land emergence observed at a restricted set of six locations in the svalbard archipelago was given the study was based on a simple model of the barents sea ice sheet and suggested increases in lithosphere thickness and asthenosphere viscosity with increasing distance from the continental margin in the present paper the newly developed high resolution load model barents 2 and land uplift observations from an extended set of 25 locations are used to study further the possibility of resolving lateral heterogeneity in the upper mantle below the northern barents sea a comparison of the calculated and observed uplift values shows that the lithosphere thickness is not well resolved by the observations although values above 110 km are most common for this parameter in contrast to this there are indications of a lateral variation of asthenosphere viscosity whereas values in the range 10 8 1020 pa s are inferred for locations close to the continental margin 1020 102 pa s are suggested further away from the margin a study of the sensitivity of the values found for lithosphere thickness and asthenosphere viscosity to modifications of load model barents 2 shows that such modifications can be largely accommodated by appropriate changes in lithosphere thickness whereas the suggested lateral variation of asthenosphere viscosity is essentially unaffected an estimate of the influence of the fennoscandian ice sheet leads to the conclusion that its neglect results in an underestimation of the thickness of the barents sea ice sheet by about 10 per cent

lateral asthenospheric viscosity variations and postglacial rebound a case study for the barents sea the effect of lateral asthenospheric viscosity variations on observable signatures related to postglacial rebound in the barents sea is studied using a finite element approach to discretize the problem a comparison between a laterally homogeneous reference earth model and a laterally heterogeneous earth model is performed the results indicate that a change in asthenospheric viscosity of about three orders of magnitude influences predictions of land uplift up to 10 20 m present day velocities up to 0 5 1 5 mm a and present day gravity anomalies up to 0 4 0 8 mgal in the northwestern part of the barents sea region

a spectral formalism for computing three dimensional deformations due to surface loads 2 present day glacial isostatic adjustment using a spherically symmetric self gravitating linear viscoelastic earth model we predict present day three dimensional surface deformation rates and baseline evolutions arising as a consequence of the late pleistocene glacial cycles in general we use realistic models for the space time geometry of the final late pleistocene deglaciation event and incorporate a gravitationally self consistent ocean meltwater redistribution the predictions of horizontal velocity presented herein differ significantly in both their amplitude and their spatial variation from those presented in an earlier analysis of others which adopted simplified models of both the late pleistocene ice history and the earth rheology an important characteristic of our predicted velocity fields is that the melting of the laurentide ice sheet over canada is capable of contributing appreciably to the adjustment in europe the sensitivity of the predictions to variations in mantle rheology is investigated by considering a number of different earth models and by computing appropriate frechet kernels these calculations suggest that the sensitivity of the deformations to the earth s rheology is significant and strongly dependent on the location of the site relative to the ancient ice sheet the effects on the predictions of three dimensional deformation rates of altering the ice history or adopting approximate models for the ocean meltwater redistribution have also been considered and found to be important the former especially so finally for a suite of earth models we provide predictions of the velocity of a number of baselines in north america and europe we find that in general both radial and tangential motions contribute significantly to baseline length changes and that these contributions are a strong function of the earth model we have furthermore found a set of earth models which together with the ice 3g deglaciation chronology produce predictions of baseline length changes that are consistent with very long baseline interferometry measurements of baselines within europe

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

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

lateral viscosity variations and post glacial rebound effects on present day vlbi baseline deformations by means of a finite element algorithm we investigate the effects of lateral viscosity variations upon the horizontal motions currently detected by vlbi techniques in europe our axisymmetric flat models appropriate to describe the rebound due to the melting of the fennoscandia ice sheet are characterized by a layered compressible mantle with linear maxwell rheology we have first computed the time evolution of theoretical baselines characterized by a simple geometry in agreement with previous results the rates of horizontal deformation have been found to be greatly sensitive to both lateral viscosity variations and deep mantle stratification especially for baselines located in the vicinity of the ice sheet margin to complete our study we have compared our numerical results with the observed time evolutions of relevant european baselines onsala wettzell and onsala eflsberg are fitted by a laterally varying asthenosphere and sharp viscosity increase in the lower mantle longer baselines connecting these sites to medicina northern italy indicate that post glacial rebound is responsible only for a fraction of the vlbi observations the residual being thus attributable to continental collision in the mediterranean sea

the lithosphere asthenosphere system in fennoscandia abstract we present a summary of the available information on rayleigh wave dispersion data for the fennoscandian region the observations have been combined to produce regional dispersion relations which have then been subjected to the hedgehog inversion procedure the results are presented on a map outlining the thickness of the lid and the shear velocities in both the lid and the asthenosphere channel lid thickness up to around 135 km is found in the bothnia north central finland area with if any weak shear velocity contrast to the underlying layer the surrounding areas are characterized by lid thickness up to around 75 km a stronger low velocity zone to lid contrast may be found in the caledonian and baltic sea area 0 25 0 45 km s taking into account moho depth data and the aforementioned results a map of the lithosphere asthenosphere system was derived

global mantle shear velocity model developed using nonlinear asymptotic coupling theory we present a three dimensional shear velocity model of the whole mantle developed using s h waveform data the model is expressed horizontally in terms of spherical harmonics up to degree 12 and vertically in terms of legendre polynomials up to degrees 5 and 7 in the upper and lower mantle respectively what distinguishes this model from other tomographic models published to date is 1 the theoretical normal mode based wave propagation approach where we include across branch mode coupling terms in order to model the body wave sensitivity to structure along the path more accurately 2 the wave packet weighting scheme which allows to balance contributions from high amplitude and low amplitude phases increasing the resolution in some parts of the mantle we also relax the constraints on the moho depth which is allowed to vary in the inversion thus absorbing some uncertainties in crustal structure the resulting model is generally in good agreement with other recent global mantle s velocity models and with some regional models the rms profile with depth has more power than other models in the upper mantle lower mantle transition region and the zone of increased power and low degree structure near the base of the mantle is confined to the last 500 km in depth this model provides a particularly good fit to the non hydrostatic geoid through harmonic degree 12 79 variance reduction as well as good fits to observed splitting functions of s velocity sensitive mantle modes indicating that both large scale and small scale features are really well constrained