effects of lateral viscosity variations on postglacial rebound implications for recent sea level trends global sea level changes have been occurring since the last pleistocene deglaciation recently the contribution of current postglacial rebound to local sea level variations has been removed by means of a radially stratified earth model in order to assess the amount of sea level rise due to recent climatic changes the authors have studied the effects of lateral variations in the viscosity structure on the postglacial uplift rates along the continental margins finite element calculations in cylindrical geometry show that the spread in the cumulative vertical displacement may be affected by 20 in the presence of lateral rheological contrasts but the vertical rates of deformation can attain differences of up to 50 for the different models horizontal deformation rates along continental margins are much more affected by the lateral variations in viscosity and can be used in the future as constraints on mantle rheology

generalized maxwell bodies and estimates of mantle viscosity summary three generalized maxwell bodies gmbs are discussed whose transient creep properties make them interesting alternatives to the classical maxwell body cmb in interpretations of post glacial uplift the first gmb is defined by its relaxation spectrum the second by its quality factor and the third by its stress strain relation in each case the gmb is characterized by three parameters only the unrelaxed modulus the steady state viscosity or a time constant and a dimensionless parameter representative of the transient creep properties this is one parameter less than needed for the burgers body which has mainly been used so far to model transient creep the gmb models are described in some detail and numerical results for their viscoelastic moduli relaxation spectra and relaxation and creep functions are given for practical applications it is most important that the viscoelastic moduli can be calculated at arbitrary frequencies in the second part of the paper post glacial uplift data from canada and fenno scandia are interpreted with the gmb rheologies described otherwise the earth model used and the assumptions on the form and history of the ice load are very simple effective viscosities of the successful models i e inverse creep rates at times representative of mantle convection fall in the range 1022 1024p 1021 1023pas and are in part considerably larger than mantle viscosities derived under the assumption of a cmb rheology hence post glacial uplift data constrain mantle viscosity less than has been believed until recently

anelastic response of the earth to a dip slip earthquake the deformation of the earth s surface immediately following an earthquake is well modeled by a dislocation in an elastic half space some time after the event however the elastic stresses begin to relax due to flow in the more fluid regions of the upper mantle the asthenosphere this relaxation causes further slow displacements observable at the earth s surface this paper examines the pattern and timing of these postseismic motions for a vertical dip slip fault and a 30 dip thrust fault a variety of rheological models are studied these models encompass variations in asthenosphere thickness mesosphere viscosity fault depth and most important power law flow both newtonian n 1 and non newtonian n 3 maxwell rheologies are considered for the asthenosphere and mesosphere the results for a vertical dip slip fault show that a peripheral upwarp develops within a distance of a few lithosphere thicknesses from the rupture zone on the downthrown side of the fault a comparable downwarp develops on the upthrown side these peripheral warps grow to a maximum height of about 5 of the total fault slip some time after the earthquake event and then collapse at much greater times the vertical motions for a 30 dip thrust fault show that after the earthquake a general uplift occurs in the region near the rupture zone horizontal displacements propagate asymmetrically away from the rupture zone the largest displacements occurring in the overthrust plate the principal result of the comparison of n 1 and n 3 rheological laws is that the basic pattern of uplifts and horizontal motions is very similar the major difference is the time dependence of the development of the pattern in spite of the complex geometrical structure of the subduction zone the displacements ui 1 t for newtonian rheology are nearly the same as ui 3 t for the non newtonian rheology if t t3 thus although the qualitative pattern of the displacements is not diagnostic of power law flow the great difference in time dependence allows a clear discrimination of the two flow laws

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

sensitivity of relative sea levels and crustal velocities in laurentide to radial and lateral viscosity variations in the mantle summary sensitivity kernels are normally used in the inversion of mantle viscosity profile from postglacial rebound observations in this paper they are used for the planning of geodetic sites to find the optimal location that is most sensitive to the viscosity in a certain region of a laterally and radially heterogeneous mantle thus the kernels are presented in a slightly different format these kernels are computed for a spherical self gravitating laterally heterogeneous incompressible viscoelastic maxwell earth with self gravitating oceans and induced by cyclic glaciation of a simple parabolic ice sheet with size comparable to the laurentide ice sheet it is shown that the kernels for relative sea level data are age dependent different age of the data at a fixed location can be sensitive to the viscosity at different depth or lateral position in the mantle for radial velocity data sensitivity to radial and lateral viscosity changes as a function of location from the ice load and the anomalous viscosity region are investigated present day tangential velocity data are found to display drastically different sensitivity from present day radial velocity or geoid rate data with more emphasis on the shallow part of the mantle and directly underneath the ice load in particular regions of anomalous viscosity lying under the ice sheet can influence tangential velocities at far away sites

influence of lithospheric thickness variations on 3 d crustal velocities due to glacial isostatic adjustment 1 predictions of 3 d crustal velocities driven by glacial isostatic adjustment gia have generally been based on spherically symmetric earth models we adopt a finite volume formulation to explore the impact of lateral variations in elastic plate strength including lithospheric thickness changes across the continent ocean interface and plate boundary weak zones on these predictions weak zones introduce horizontal rate perturbations with a plate scale coherency and amplitudes reaching 1 2 mm yr radial velocity perturbations can be as large but are geographically isolated to the weak zones specifically the north atlantic ridge a discontinuity in ocean continent lithospheric thickness significantly impacts rates along continental margins order 1 mm yr for radial rates and generally about half this for tangential rates we conclude that lateral variations in lithospheric strength should be included in future gia analyzes of space geodetic survey results and in assessing the impact of gia on the stability of geodetic reference frames

unmixing of stable isotope signals using single specimen δ18o analyses 1 the resolution at which foraminiferal stable isotopes are applied in paleo environmental studies is ever increasing resulting in continuous sampling of sediment cores the resolution of such continuously sampled records depends on the rate of sedimentation of foraminiferal shells in its relation to the intensity of bioturbation bioturbation essentially mixes sediment layers of different age altering the primary climate signal thereby impacting the accuracy of both the timing and magnitude of reconstructed climate changes a new approach to assess and correct the impact of bioturbation is investigated here based on the 18o of individual specimens of planktonic foraminifera globorotalia inflata from a series of boxcore samples in the eastern north atlantic average 18o values decrease southward from 1 62 to 1 07 with the exception of site t86 11 1 35 the 18o distribution of each station can be fitted with a uni to polymodal distribution a nonunimodal distribution strongly suggests admixing of bioturbated individuals quantification of these distributions allows deconvolving the original and bioturbated signals and subsequently provides a correction for bioturbation

haskell 1935 revisited the haskell 1935 value of 1021 pa s for mantle viscosity is a classic and enduring constraint on the rheology of the earth s interior we revisit this inference using spherically symmetric self gravitating maxwell viscoelastic earth models our inference is based on both forward and inverse analyses of decay times associated with uplift at two sites considered by haskell angerman river sweden and oslo norway rather than the raw relative sea level rsl data at these sites we demonstrate that predictions of the decay time associated with the angerman river data are insensitive to variations in both the late pleistocene ice load history and the lithospheric thickness of the earth model the predictions at oslo are sensitive to both these inputs and hence decay times at this site provide a remarkably robust constraint on mantle viscosity we derive a constraint on the average viscosity of the mantle of 0 65 1 10 1021 pa s where the average resolved by the data encompasses a region which extends from the base of the lithosphere to a depth of near 1400 km this indicates that many previous analyses which have invoked the haskell value of 1021 pa s as a constraint on the average upper mantle i e above 670 km depth viscosity alone have misinterpreted the resolving power of the inference furthermore our analysis indicates that a number of apparently contradictory inferences of viscosity based on fennoscandian data satisfy the new rigorous interpretation of the haskell constraint finally we demonstrate how the ambiguity in the upper mantle lower mantle viscosity contrast associated with the haskell average may be reduced by invoking decay time constraints estimated from rsl curves in hudson bay a preliminary inversion of decay times at angerman river and richmond gulf in hudson bay suggests a contrast of approximately an order of magnitude between the average viscosities of the upper mantle and the top 1000 km of the lower mantle however a conclusive analysis in this regard must await the determination of consistent decay time estimates for the hudson bay region

planktic foraminiferal sedimentation and the marine calcite budget 1 the vertical flux and sedimentation rate of planktic foraminiferal tests are quantified and a global planktic foraminiferal cac0 3 budget is presented test and calcite flux rates are calculated according to the distribution of species obtained from multinet and sediment trap samples modern planktic foraminiferal population dynamics are discussed as a prerequisite for the quantification of the calcite budget highlighting the importance of ecological autecological e g reproduction and biogeochemical conditions that determine the presence or absence of species to complete the open marine particulate caco 3 inventory the contribution of coccolithophores pteropods and calcareous dinophytes is discussed based on the studied regions the global planktic foraminiferal calcite flux rate at 100 m depth amounts to 1 3 3 2 gt yr 1 equivalent to 23 56 of the total open marine caco 3 flux the preservation of tests varies on a regional and temporal scale and is affected by local hydrography and dissolution during most of the year off peak periods many tests dissolve above 700 m water depth while settling through the water column with on average only 1 3 of the initially exported caco 3 reaching the deep seafloor pulsed flux events mass dumps of fast settling particles yield a major contribution of tests to the formation of deep sea sediments on average 25 of the initially produced planktic foraminiferal test cac0 3 settles on the seafloor the total planktic foraminiferal contribution of caco 3 to global surface sediments amounts to 0 36 0 88 gt yr 1 32 80 of the total deep marine calcite budget

deglacial land emergence and lateral upper mantle heterogeneity in the svalbard archipelago i first results for simple load models summary the glacial isostatic adjustment following the removal of the pleistocene ice sheets furnishes basic information on the thickness of the earth s lithosphere and the viscosity of the subjacent mantle paper i is concerned with an elementary interpretation of the post glacial land emergence observed at a restricted set of six locations in the svalbard archipelago the interpretation is based on a three layer incompressible maxwell viscoelastic earth model which is forced by a time dependent load distribution simulating the deglaciation history of the svalbard archipelago and the barents sea in view of inconclusive geomorphological evidence suggesting either total or partial glaciation of the area at glacial maximum two simple load models barents t1 and barents p1 are considered in the first instance a comparison between the calculated and observed values of land emergence suggests increases in lithosphere thickness and asthenosphere viscosity with increasing distance of the location from the continental margin the trends are qualitatively insensitive to the load model load thickness or load cross section used for load model barents t1 with parabolic cross section an initial load thickness of 1 50 km and a relaxed fitting criterion the lateral variations are only weak if a more restrictive fitting criterion is employed the variations become more prominent and suggest increasing values of lithosphere thickness from below 80 km to above 140 km and of asthenosphere viscosity from below 3 1018 pa s to above 2 1019 pa s over a distance of about 300 km in paper ii kaufmann wolf 1995 a high resolution load model and an extended set of land emergence observations are used to study further the possibility of resolving lateral heterogeneity in the upper mantle below the svalbard archipelago

effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced surface motion on a spherical self gravitating maxwell earth abstract the effects of lateral variations in lithospheric thickness and mantle viscosity on surface motions on a spherical self gravitating incompressible viscoelastic earth are investigated using the coupled laplace finite element method the ice 4g deglaciation model is used together with gravitationally self consistent sea levels in realistic oceans to describe the load lateral variations in mantle viscosities and lithospheric thickness are inferred from seismic tomography model s20a using well known scaling relationships the laterally homogeneous background viscosity has viscosity increases across 670 km and 1330 km depths and is a simplification of peltier s vm2 model the effect of interaction between ice complexes in north america greenland eurasia and antarctica are investigated and found to be significant for tangential motion the predicted motion in laurentide and antarctica are also compared with results obtained with flat earth models and found that there is general agreement between the two types of modeling although spherical earth models are more realistic because they take into account the interaction between ice complexes and there is no problem with edge effects the effects of lateral heterogeneity on uplift rate are found to be large enough to be resolved by current gps technology it confirms that the effect of the reverse viscosity contrast in the transition zone under the laurentian and fennoscandian craton may mask the effect of lateral heterogeneity in the neighboring layers on uplift rate for tangential motion lateral heterogeneity is found to be able to overprint the divergent motion from the centers of rebound predicted in laterally homogeneous models this finding is new for laurentide and is due to the contribution from the deep part of the lower mantle although the contribution from the upper mantle is also important on tangential motion its effects are compromised by the effects from the other layers

steady state secondary convection beneath lithospheric plates with temperature and pressure dependent viscosity we have constructed a thermomechanical model for upper mantle convection such that the thickness and structure of the lithosphere are determined self consistently by the heat transported by convection in this study of the interaction between the lithosphere and upper mantle strongly temperature and pressure dependent rheologies for both newtonian and non newtonian creep mechanisms are employed for a strictly temperature dependent rheology an insignificant amount of heat less than 12 5 mw m2 can be transported convectively for an interior viscosity 0 1021 pas compatible with postglacial rebound on the other hand for similar values of the interior viscosity steady heat fluxes between 20 and 40 mw m2 are produced by introducing pressure dependence into the rheology for the temperature and pressure dependent flow law the horizontally averaged interior temperature displays very little variation with the amount of heat evacuated once all of the rheological parameters are fixed this finding may have important ramifications for parameterized convection we employ both the single mode mean field approximation and the complete two dimensional equations using finite elements to obtain solutions for the various types of rheologies from evaluating the geophysically relevant observables such as topography free air gravity anomalies surface heat flow and stress fields in the lithosphere we find that the lateral variations of these quantities predicted by a non newtonian rheology are much smaller than those derived from a linear rheology these results suggest that surface variations of geophysical observables are more compatible with a non newtonian rheology in the upper mantle

glacial isostatic adjustment in fennoscandia with a three dimensional viscosity structure as an inverse problem abstract glacial isostatic adjustment data are commonly used to invert for the radial viscosity structure of the mantle however the effects of lateral variations in mantle viscosity in such inversions are not yet accounted for here we analysed synthetic sea level data for the fennoscandian region which are derived from a three dimensional 3d earth model with realistic lateral and vertical viscosity variations deduced from seismological and geological information the inversion of the 3d synthetic data for a best fitting 1d viscosity profile reveals that i lateral lithospheric thickness variations can be detected with 1d model predictions if the data are grouped into regional subsets ii combined lateral variations in lithospheric thickness and asthenospheric viscosity are not properly resolved with 1d model predictions and iii the spatial and temporal distribution of observational data strongly affects the resulting 1d viscosity profile

modelling postglacial sea levels with power law rheology and a realistic ice model in the absence of ambient tectonic stress previous studies of postglacial rebound with power law rheology and simple ice models over laurentia have found that sea level data in the transition zone e g boston cannot be easily explained unless non linear rheology is restricted to lie within a thin layer between the lithosphere and the upper mantle the reason is the existence of a viscously stationary zone which is characteristic of non linear mantles in this study the simple ice model is replaced by a realistic ice history adapted from the ice 3g model which takes into account important effects such as retreating ice margins and eustatic ocean loading a 3 d finite element model is used to calculate the deformation and the relative sea levels in eastern canada and along the us east coast the purpose is to investigate whether the realistic load model allows sea level data near the centre of rebound and along the atlantic east coast of canada and the usa to be explained by non linear rheology simultaneously the assumptions made are that 1 postglacial rebound sees the steady state creep and not the transient creep 2 either ambient tectonic stresses do not interact with rebound stress or the ambient stress level is low 3 lateral heterogeneity of rock properties and anisotropic flow can be neglected results indicate that the retreating ice margin does make it easier for non linear rheology in the mantle to explain the sea level data in the transition zone around boston however reconciling all the sea level data near the centre of rebound and along the atlantic east coast simultaneously is still difficult for a non linear rheology so far two types of models with non linear rheology have been found to be able to explain the sea level data inside and outside laurentia simultaneously they are 1 earth models with a thin 270 km non linear zone overlying a 1021 pa s lower mantle 2 earth models with a linear upper mantle with an average viscosity of 1021 pa s overlying a non linear lower mantle with a 3 10 35 pa 3 s 1 and n 3

mineralogy and composition of the upper mantle seismic velocities are calculated for two petrological models of the upper mantle an olivine rich assemblage pyrolite and a garnet clinopyroxene rich olivine bearing assemblage piclogite these are compared with recent seismic profiles for various tectonic provinces the shield data is most consistent with a cold olivine and orthopyroxene rich lid the seismic lithosphere extending to 150 km followed by a high temperature gradient and or a change in mineralogy that serves to decrease the velocity from 200 to 400 km the velocities follow a 1400 c adiabat the rise tectonic mantle is much slower presumably hotter and is likely to be above the solidus to depths of at least 300 km the high v p v s ratio of the lower oceanic lithosphere in the western pacific is most consistent with eclogite

the effects of upper mantle lateral heterogeneities on postglacial rebound we have investigated the potentially important effects arising from lateral heterogeneities on postglacial uplifts time dependent solutions for maxwell rheology with lateral variations in the upper mantle are obtained by finite element techniques in cylindrical geometry the displacements in the central portion of the ice sheet are not at all influenced by these lateral variations whereas the uplifts near the edge of the ice load are extremely sensitive to lateral heterogeneities in the upper mantle for ice sheets characteristic of the laurentide ice sheet deformations around the peripheral bulge can still be affected by an asthenosphere as far as twenty five degrees away the continental lithosphere under the former ice load would appear to be thicker with the presence of a neighboring asthenosphere recent estimates of the north american plate thickness would exceed 250 km under these circumstances

stable oxygen isotope composition is biased by shell calcification intensity in planktonic foraminifera planktonic foraminifera are widely used for environmental reconstructions through measurements of their shell s geochemical characteristics including its stable oxygen and carbon isotope composition using these parameters as unbiased proxies requires a firm knowledge of all potential confounding factors influencing foraminiferal shell geochemistry one such parameter is the shell calcification intensity shell weight normalized for shell size that may influence the shell delta 18o value either bioenergetically by reducing energy available and required for equilibrium isotope fractionation during faster calcification or kinetically by influencing calcification depth through the shell s density contrast with seawater specimens from the globigerinoides ruber elongatus compound from a sediment trap in the north atlantic have been used to quantify the influence of shell calcification intensity on shell delta 18o values shell calcification intensity was found to have a significant effect on the shell stable oxygen isotope composition in all species through model fitting it is suggested that the effect size may be in a range of 1 to 2 depending on species depth migration and local oceanographic conditions we show that the confounding effect of shell calcification intensity on stable oxygen isotope composition can be of importance depending on the anticipated precision of the derived reconstructions a framework is provided to quantify this effect in future studies

mg ca ratios of two globigerinoides ruber white morphotypes implications for reconstructing past tropical subtropical surface water conditions 1 tests of the planktonic foraminifer globigerinoides ruber white d orbigny have become a standard tool for reconstructing past oceanic environments paleoceanographers often utilize the mg ca ratios of the foraminiferal tests for reconstructing low latitude ocean glacial interglacial changes in sea surface temperatures sst we report herein a comparison of mg ca measurements on sample pairs n 20 of two g ruber white morphotypes g ruber sensu stricto s s and g ruber sensu lato s l from surface and downcore samples of the western pacific and indian oceans g ruber s s refers to specimens with spherical chambers sitting symmetrically over previous sutures with a wide high arched aperture whereas g ruber s l refers to a more compact test with a diminutive final chamber and small aperture the g ruber s s specimens generally show significantly higher mg ca ratios compared to g ruber s l our results from the mg ca ratio analysis suggest that g ruber s l specimens precipitated their shells in slightly colder surface waters than g ruber s s specimens this conclusion is supported by the differences in 18o and 13c values between the two morphotypes although it is still unclear if these two morphotypes represent phenotypic variants or sibling species our findings seem to support the hypothesis of depth and or seasonal allopatry within a single morphospecies

effects of lateral viscosity variations on long wavelength geoid anomalies and topography models for the earth s geoid and dynamically supported topography usually account only for radial vertical variations in mantle rheology and flow structure however expected lateral variations in viscosity due to temperature or stress dependent rheology can degrade our ability to infer mantle structure from geoid models based on seismically determined density contrasts in the mantel theoretically the main difficulty is that the harmonic components of the flow stress deformation field are no longer independent and exact analytical methods cannot account for this mode coupling for large thermal density contrasts of small lateral dimension e g subducted slabs it is difficult to form any general theory for these effects however we believe that the largest geoid anomalies which occur at the lowest harmonic degrees l 2 3 are due to a global pattern of relatively mild temperature variations for convection with mainly broadscale thermal and rheological changes some relatively straightforward ideas can be developed combining results from simple perturbation theory and numerical models for convective flow we find the following 1 if we are correct in inferring viscosity variations of less than one order of magnitude globally the longest wavelength geoid anomalies l 2 3 are not seriously contaminated by lateral viscosity variations 2 contamination of the higher degrees l 4 is expected and in particular self coupling between l 2 heterogeneity and viscosity variations may be observable at degree 4 the most severe contamination occurs at the doubled harmonic l 4 of the dominant heterogeneity harmonic l 2 3 perturbation techniques are adequate to model global scale lateral viscosity variations of an order of magnitude or less 4 the steady state surface deformation problem at the heart of our geoid models may be more robust with respect to broadscale lateral viscosity variations than are models for transient deformations e g postglacial rebound 5 for loading by broadscale density heterogeneity the effects of stress dependent rheology are probably secondary to the effects of radial viscosity stratification

rheological models and interpretation of postglacial uplift accepted 1989 february 1 received 1989 january 28 in original form 1988 september 26 summary paper investigates four generalized maxwebl bodies gmbs and the classical maxwell body cmb with respect to their potential to explain postglacial uplift the gmbs are the lomnitz body defined by a logarithmic creep law the q power law body defined by a power law dependence of the quality factor on frequency the caputo body defined by a special stress strain relation with memory and the burgers body the burgers body is a 4 parameter model the other gmbs have 3 and the cmb has only 2 parameters theoretical uplift curves are calculated for simple space time models of the canadian and fennoscandian deglaciations and hedgehog inversion yields the successful model parameters the gmbs explain the data better than the cmb the parameters of the burgers body are only rather weakly constrained because of trade offs among them from the success of the gmbs we conclude that long time scale transient creep is a possible rheological behaviour of mantle rocks viscosity extrapolation from the time constant of postglacial uplift about 10 ka to the time constant of mantle convection roughly 100 ma is made with the effective viscosity and yields approximately ld2 pas q power law body loz3 pas caputo body and loz5 pas lomnitz body hence postglacial uplift does not strongly constrain the long time scale mantle viscosity it provides only a lower bound about loz1 pas this value follows from data interpretation with the cmb model in which steady state creep is present alone rayleigh number estimates for whole mantle convection are clearly supercritical for the cmb the q power law body and the caputo body but only about critical or even subcritical for the lomnitz body both postglacial uplift and mantle convection is satisfactorily explained by the cmb the q power law body and the caputo body

linear or non linear rheology in the earth s mantle the prevalence of power law creep in the postglacial isostatic readjustment of laurentia summary the great majority of postglacial rebound computations carried out during the last three decades assumed a purely linear rheological relation for the mantle experimental data on high temperature creep deformation and modelling of other tectonic processes however might also support the existence of non linear creep mechanisms we addressed postglacial rebound in north america through an axially symmetric finite element model with a composite linear plus non linear mantle rheology in such a formulation the transition stress t governs the balance between linear and non linear creep components while the term b added to the effective shear stress accounts for the background ambient stress induced by convection and other tectonic processes by varying t and b in the ranges 0 10 mpa and 0 5 mpa respectively we found that composite models fit relative sea level rsl variations at 29 north american sites better than the purely linear model on the basis of the effective shear stress induced in the mantle by glacial forcing 1 3 mpa our results indicate that power law creep accounts for the majority of the strain rate

effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced relative sea levels and long wavelength gravity field in a spherical self gravitating maxwell earth the effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced relative sea level rsl changes and the secular rate of change of the earth s long wavelength gravity field in a spherical self gravitating incompressible visco elastic earth are investigated using the coupled laplace finite element method the ice 4g deglaciation model is used with gravitationally self consistent sea levels in realistic oceans to describe the load lateral variations in mantle viscosity and lithospheric thickness are inferred from seismic tomography model s20a the full 3 d earth model which includes all the lateral heterogeneities in the lithosphere and mantle gives a better fit to the global rsl data than the related laterally homogeneous model however the situation is less clear for the observed secular drift of the low degree geopotential coefficients j l because of the uncertain contribution of recent melting but the full 3 d model can fit the j 2 observation if recent melting contributes about 1 0 mm a of equivalent sea level rise it predicts that the gia induced secular gravity rate of change to be detected by the grace mission in the southern part of hudson bay is about 1 2 to 1 6 gal a moreover the contributions of lateral heterogeneities from individual layers in the mantle or in the lithosphere are studied the contribution from the transition zone 420 670 km is generally opposite to that from its neighboring layers and thus can mask their effects as a consequence the effects from the deep lower mantle become dominant for rsl and secular rate of change of gravity over laurentide for the secular rates of change for degrees 2 4 geopotential coefficients the contribution is mostly from lateral heterogeneities in the deeper mantle the effects of background viscosity profiles are also investigated and are found to be significant for all these observables

dynamic models of subduction geophysical and geological evidence in the tyrrhenian sea summary predictions based on a 2 d finite element model for subduction underneath the calabrian arc in southern italy are compared with a variety of geophysical and geological data such as the present day stress pattern within the slab uplift from the elevation of marine terraces in calabria and subsidence in the tyrrhenian marsili basin from odp leg 107 we model the behaviour of the slab driven by slab pull in agreement with the present tectonic style in this part of the mediterranean as suggested by several investigators the model accounts for the crustal lithospheric and mantle structures in a vertical cross section perpendicular to the calabrian subduction zone the shape of the slab is constrained on the basis of new tomographic images in the southern tyrrhenian sea which were obtained from the regional seismic stations of the istituto nazionale di geofisica while the rheological properties of the mantle are taken from global dynamic models density contrasts between the subducted slab and the surrounding mantle based on petrological models drive the flow in our viscoelastic model stress values displacements and vertical velocities at the surface are sampled at different times after loading until dynamic equilibrium is reached our estimates are appropriate for a time window of 100 kyr the validity of our comparison with the geological record is based on the assumption that the tectonic configuration in the past was not substantially different from that of the present day two families of models with unlocked and locked subduction faults are considered the unlocked models allow for roll back of the trench of about 20 mm yr in agreement with some geological estimates the same family of models predicts uplift of the calabrian arc of about 1 mm yr l and subsidence in the marsili basin of 1 2 mm yr in agreement with geological surveys the deviatoric stress obtained from the unlocked model is consistent with the continuous distribution of deep seismicity in the southern tyrrhenian sea with minor concentration within the lithospheric wedge locked models fail to reproduce these geophysical and geological observations predictions derived from a detached slab model are not consistent with the continuous hypocentral distribution of deep seismicity in the southern tyrrhenian sea deformation at the surface and the stress patterns at depth for a detached slab differ substantially from those of a continuous plate dynamic topography and horizontal motions are reduced when compared with the continuous plate with deviatoric stresses concentrated within the relict slab our results indicate that subduction is a major tectonic process in the southern tyrrhenian sea

an intensity ratio calibration method for the accurate determination of mg ca and sr ca of marine carbonates by icp aes an inductively coupled plasma atomic emission spectroscopy icp aes method for the accurate and precise simultaneous measurement of the mg ca and sr ca content of carbonates was established while a precision of 0 3 1 standard deviation sd is easily obtainable for both mg ca and sr ca analysis a ca matrix effect complicates achieving similar levels of accuracy with conventional calibration procedures an alternative ratio calibration procedure is proposed which overcomes the ca matrix effects and ensures the accuracy of the mg ca and sr ca analysis of marine carbonates to 0 3 almost an order of magnitude better than conventional calibration methods the longer term precision is 0 1 if the batch run average values are corrected for longer term drift the method is suitable for analysis of foraminiferal calcite and coral aragonite and can easily be adjusted for the analysis of other carbonates or microsamples

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

the role of hydro isostasy for holocene sea level changes in the british isles abstract the last deglaciation of the british ice sheet in combination with melting of more distant ice sheets gives the nearby region a complicated sea level history with post glacial rebound occurring over scotland and northern england eustatic sea level rise much further away and more complex changes in the intermediate regions like southern england at the glacial maximum most of the present north sea floor was above sea level and it has subsequently been covered by water in most previous sea level calculations the meltwater load has usually been modelled without allowing for the change in ocean shape as sea level changes and frequently without including spatial variability of the meltwater load by assuming the shoreline was at its present position throughout the period of deglaciation of the late pleistocene ice sheets the amount of tilting of the british isles by the meltwater load is reduced since such a model erroneously applies loads both to the east and west of the british isles a review of the various meltwater models is included and it is shown that errors in predictions of sea level change of up to 10 m at 10 kyr b p are made along the east coast of england and along the coastlines on the southern edge of the north sea the most important effect of the meltwater load is to tilt the continent normal to the continental margin this pattern is modified by the unloading brought about by glacial rebound of scotland and the norwegian coast and the recent filling with water of the north sea

postglacial rebound with a non newtonian upper mantle and a newtonian lower mantle rheology we have employed a composite rheology consisting of both linear and nonlinear creep mechanisms which are connected by a transition stress background stress due to geodynamical processes is included for models with a non newtonian upper mantle overlying a newtonian lower mantle the temporal responses of the displacements can reproduce those of newtonian models the average effective viscosity profile under the ice load at the end of deglaciation turns out to be the crucial factor governing mantle relaxation this can explain why simple newtonian rheology has been successful in fitting the uplift data over formerly glaciated regions

mode coupling in a viscoelastic self gravitating spherical earth induced by axisymmetric loads and lateral viscosity variations the importance of mode coupling in a viscoelastic self gravitating spherical earth with lateral variations in linear or nonlinear rheology is investigated with a finite element model coupled to poisson s equation both the lateral viscosity variations and the harmonic load are axisymmetric the effects of self gravitation viscosity contrast and the location of the abrupt lateral change in viscosity in a linear mantle are studied and are found to be significant in determining the strength of mode coupling it is demonstrated that a larger number of harmonics than generally assumed is required to give accurate description of the induced deformation mode coupling is also found to be important in a nonlinear mantle especially when the harmonic degree l is large

the effects of transient rheology on the interpretation of lower mantle viscosity we have reexamined the role played by transient rheology in the interpretation of mantle viscosity this investigation has been carried out by comparing the amplitude responses with the data of secular variation of the relative sea level histories at sites well within the ice margins and at the ice margin like the city of boston a linear burgers body rheology has been assumed in the lower mantle the data near the edge of the ice load proves most sensitive to the transient viscosity structure the non monotonic behavior of sea level data near boston can be explained both by a steady state lower mantle viscosity of 1022p with a thick lithosphere and also by a transient lower mantle rheology but with a thin lithosphere the long term viscosity of the lower mantle in this second model has a steady state value of around 5 1023p

inferences of mantle viscosity based on ice age data sets the bias in radial viscosity profiles due to the neglect of laterally heterogeneous viscosity structure inferences of mantle viscosity using glacial isostatic adjustment gia data are hampered by data sensitivity to the space time geometry of ice cover a subset of gia data is relatively insensitive to this ice history the fennoscandian relaxation spectrum frs postglacial decay times in canada and scandinavia and the rate of change of the degree 2 zonal harmonic of the geopotential urn x wiley 21699313 media jgrb53014 jgrb53014 math 0001 these geographically limited data have been inverted to constrain the radial one dimensional 1d mantle viscosity profile we explore potential biases in these 1d inversions introduced by neglecting a three dimensional 3d viscosity structure we perform 1d bayesian inversions of synthetic gia data generated from earth models with realistic 3d variations in mantle viscosity and lithospheric thickness and compare results to the 1d viscosity profile associated with the 3d model used to generate the synthetics differences between these two 1d profiles reflect gia data resolution and biasing introduced by neglecting in the inversions a 3d viscosity structure we focus on the second issue demonstrating that the largest bias occurs within the upper mantle in particular the transition zone this remains consistent when varying inversion parameters e g prior starting models and the 1d 3d viscosity fields adopted in generating the synthetics inversions of individual data sets show 3d biasing increases for data exhibiting shallower thus more localized sensitivity to viscosity of the data considered herein inversions of the frs are subject to the largest bias followed by decay time data the bias is minimal for urn x wiley 21699313 media jgrb53014 jgrb53014 math 0002 as its deeper sensitivity is accompanied by broader averaging of structure in radial and lateral directions

core top calibration of mg ca in tropical foraminifera refining paleotemperature estimation 1 optimal use of mg ca as a paleotemperature proxy requires establishing calibrations for different species of foraminifera and quantifying the influence of dissolution to achieve this goal we have measured mg ca and 18o in a series of tropical and subtropical core tops including four depth transects the ceara rise the sierra leone rise and the rio grande plateau in the atlantic and the ontong java plateau in the pacific focusing on spinose mixed layer dwelling species globigerinoides ruber and globigerinoides sacculifer and nonspinose thermocline dwelling neogloboquadrina dutertrei shell mg ca in g sacculifer is 5 15 lower than in g ruber while n dutertrei mg ca is 49 55 lower than in g ruber this statistically significant offset has allowed us to establish different calibrations for each species multilinear regression analysis was used to develop calibration equations that include a correction term for the dissolution effect on mg ca in foraminiferal calcite presented in this paper are two sets of calibrations one set using core depth as a dissolution correction and another using co32 as a dissolution parameter the calibrations suggest that g ruber is the most accurate recorder of surface temperature while g sacculifer records temperatures below the surface at 20 30 m the depth habitat of n dutertrei is more uncertain owing to the wide range in habitat depths depending on hydrographic conditions but on average mg ca and 18o data suggest it is at 50 m of the three species n dutertrei is the most sensitive to dissolution up to 23 decrease in shell mg ca per km while g sacculifer is the most resistant

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

mapping the upper mantle three dimensional modeling of earth structure by inversion of seismic waveforms a method is presented for the inversion of waveform data for the three dimensional distribution of seismic wave velocities the method is applied to data from the global digital networks international deployment of accelerometers global digital seismograph network the selected data set consists of some 2000 seismograms corresponding to 53 events and 870 paths the moment tensors of the earthquakes are determined through an iterative procedure which minimizes the corrupting influence of lateral heterogeneity a global model is constructed for shear wave velocity expanded up to degree and order 8 in spherical harmonics and described by a cubic polynomial in depth for the upper 670 km of the earth s mantle although no a priori information is incorporated the model predictions reproduce much of what is known about the dispersion of mantle waves for example high phase velocities for shields low velocities at ridges and a strong degree 2 pattern for rayleigh waves since the method makes use of complete waveforms overtone data are also included it is shown that the model is reproducible in that substantially the same model can be constructed from each half of the total data set considered independently the model shows that shields and ridges are major features in the depth interval 25 250 km the ridges of the southern pacific and the larger shields persist to 350 km but the southeast indian rise is underlain by a high velocity anomaly at this depth as is much of the mid atlantic ridge at 450 650 km the major features are a broad region of high velocities incorporating south america much of the south atlantic and parts of west africa a broad region of low velocities in the central and eastern pacific high velocities in the western pacific and a low velocity anomaly beneath the red sea and the gulf of aden in the absence of a crustal correction degrees 2 and 3 show a high positive correlation with the geoid paradoxically this is largely destroyed when the distribution in crustal thickness is taken into account spherical harmonic degrees 4 7 show a significant negative correlation

new constraints on transient lower mantle rheology and internal mantle buoyancy from glacial rebound data a model of mantle rheology which has an explicit transient component of its relaxation spectrum is shown to reconcile two apparently conflicting inferences of lower mantle viscosity if recent analyses of isostatic geoid anomalies are correct in requiring a large increase of viscosity with depth then the weak viscosity stratification demanded by postglacial rebound data implies the importance of such rheological behaviour at least in the earth s lower mantle

can the 1d viscosity profiles inferred from postglacial rebound data be affected by lateral viscosity variations in the tectosphere we have tested the impact of lateral viscosity variations lvv in the top 200 km of the mantle tectosphere on the interpretation of fennoscandian postglacial uplift data in terms of 1d viscosity models our test consists of two steps in the first step we simulate the postglacial uplift for a given 2d viscosity structure involving a cratonic lithospheric root below the ice sheet and an asthenosphere below oceanic areas in the second step we interpret the result of this simulation in terms of a 1d viscosity model the resultant 1d viscosity model shows a lower viscosity in the lower mantle a higher viscosity in the shallow sublithospheric mantle and a smaller thickness of the lithosphere than the synthetic model of viscosity

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

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

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

three dimensional finite element modeling of the glacial isostatic adjustment in fennoscandia abstract during the last ice age cycles large ice sheets have covered north america northern eurasia greenland and antarctica the earth s crust and mantle has been depressed by the weight of these ice sheets by several hundreds of meters at the end of the last ice age cycle the ice sheets have vanished around 6000 yr ago and the earth s surface rebounded however due to the time dependent viscoelastic relaxation of the earth s mantle the rebound also termed glacial isostatic adjustment gia is still observable today in fennoscandia a key region of gia numerous observations such as paleo strandlines present day crustal deformations monitored by gps observations and present day changes in the gravity field seen by satellite missions provide a detailed picture of the past and ongoing deformation we model the gia process in fennoscandia by means of the finite element technique we employ a three dimensional viscosity structure in the earth s mantle derived from seismic shear wave tomography models and we use thermodynamic considerations to convert the shear wave perturbations into viscosity variations we then compare the results based on the three dimensional earth s structure with a simpler earth model where viscosity depends on the vertical direction only our results indicate significant differences between three and one dimensional modeling the vertical crustal velocities reveal differences up to 7 mm yr and horizontal crustal velocities are effected even stronger the typical divergent motions of the latter observed for one dimensional earth models are no longer present for three dimensional viscosity models instead a regional velocity field with movements away from the norwegian coast towards the old baltic shield is observed in a sensitivity analysis we show that the dramatic change in the horizontal flow pattern has its origin deeper in the upper mantle between 450 and 670 km depth we also confirm that the observed gia process in fennoscandia is not very sensitive to the viscosity structure in the lower mantle however a comparison with bifrost data reveals a best fit with the simple one dimensional model which requires a revision of our three dimensional models in a future analysis

spectral finite element approach to postseismic deformation in a viscoelastic self gravitating spherical earth summary theoretical models of the viscoelastic relaxation of a spherical earth are derived to model large scale postseismic deformation resulting from great earthquakes m 7 over decadal timescales most existing models of postseismic deformation do not consider strong lateral heterogeneities in mantle viscosity in particular in the subducting slab where such events occur in addition the self gravitation effect is often treated only approximately both effects become important when observations from space geodetic techniques such as gps and grace are interpreted in this paper we present a spectral finite element approach that allows these two effects to be considered in a rigorous way in this way much larger lateral viscosity variations can be handled than by perturbation techniques we derive interface conditions for an arbitrary shear fault in the form of double couple forces that are equivalent to a prescribed dislocation and simulate a relaxation process for an incompressible maxwell earth with a 3 d viscoelastic structure computational results are validated for a spherically symmetric model by an independent method based on the inverse laplace integration and good agreement is obtained as an example we apply this approach to the 2004 sumatra andaman earthquake and simulate a large scale postseismic gravity potential variation by a forward calculation in the presence of a slab the secular variation in geoid height change decreases by 30 per cent for wavelengths longer than 500 km with respect to the case excluding the slab the effect of the slab can exceed 0 3 mm yr 1 for short term variations when the asthenosphere viscosity is 10 19 pa s which are larger than the observation errors of grace for a displacement field a decrease in deformation rates can amount to 70 per cent due to the inclusion of a slab which is detectable with geodetic observations such as gps the effect of the slab is attenuated in the gravity field for such longer wavelengths since horizontal scales of the slab are smaller than its spatial resolution lateral heterogeneities in viscosity due to a slab should therefore be considered for interpreting observed postseismic relaxation due to a large thrust event in a subduction zone

postglacial rebound and lateral viscosity variations a semi analytical approach based on a spherical model with maxwell rheology accepted 1997 march 10 received 1997 february 20 in original form 1996 june 10 s u m m a r y a spectral method is employed to study the response to surface loads of a maxwell earth including lateral viscosity variations in particular we focus on the effects of lithospheric cratons on the long wavelength time dependent displacement field for simple earth models the viscosity contrast of the craton with respect to the surrounding mantle is kept fixed whereas its thickness is allowed to vary we show that the longwavelength vertical displacement is not greatly affected by the presence of a lithospheric craton while the tangential displacement is severely modified for the case of a homogeneous mantle with increasing harmonic degree and thickness of the craton the load deformation coefficients deviate from those pertaining to a homogeneous mantle with a viscosity of 10 pa s these deviations are particularly enhanced on timescales larger than a few hundred years these findings indicate that the interpretation of the viscosity structure of the mantle inferred from postglacial rebound signatures based on radially stratified models is affected by the presence of lateral viscosity variations

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

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

tomography the geoid and plate motions the dynamics of the earth s mantle and its relationship to mantle structure as revealed by seismic tomography the geoid and plate motions are discussed in a critical review of u s research from the period 1987 1990 sections are devoted to plates and mantle convection seismic anomalies flow and the geoid subducted slabs and the 670 km discontinuity the physical properties of the mantle plumes and computational and experimental modeling efforts also included is a comprehensive bibliography for the period 248 refs

modelling of mantle postglacial relaxation in axisymmetric geometry with a composite rheology and a glacial load interpolated by adjusted spherical harmonics analysis summary although studies on glacial isostatic adjustment usually assume a purely linear rheology we have previously shown that mantle relaxation after the melting of laurentide ice sheet is better described by a composite rheology including a non linear term this modelling is however based on axially symmetric geometry and glacial forcing derived from ice 3g and suffers from a certain amount of arbitrariness in the definition of the ice load in this work we apply adjusted spherical harmonics analysis to interpolate the ice thicknesses of ice 3g and ice 1 glaciological models this filters out the non axisymmetric components of the ice load by considering only the zonal terms in the spherical harmonics expansion the resulting load function is used in finite element simulation of postglacial rebound to compare composite versus purely linear rheology our results confirm that composite rheology can explain relative sea level rsl data in north america significantly better than a purely linear rheology the performance of composite rheology suggests that in future investigations it may be better to use this more physically realistic creep law for modelling mantle deformation induced by glacial forcing

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

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

postglacial sealevels on a spherical self gravitating viscoelastic earth effects of lateral viscosity variations in the upper mantle on the inference of viscosity contrasts in the lower mantle abstract previous studies of lateral viscosity variations on postglacial rebound often neglect the spherical shape of the earth and the self gravity of the solid earth and oceans in this paper the consistent sealevel equation is solved by the coupled laplace finite element method for a spherical self gravitating incompressible maxwell earth it confirms the importance of self gravity in the oceans on sealevel computation near the ice margin where the data are most sensitive to the existence of lateral variations in lithospheric thickness and asthenospheric viscosity the effects of lateral variations in lower mantle viscosity asthenospheric viscosity and lithospheric thickness are investigated this paper confirms the finding of earlier investigations the combined effect of lateral viscosity variations in the lower mantle with reverse viscosity contrasts in the upper mantle is also investigated for sealevel data near the center of rebound the effect of lateral viscosity contrast in the lower mantle can be masked by the existence of a reverse lateral viscosity contrasts in the upper mantle however this is not the case for sealevel data just outside the ice margin

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

the tectosphere and postglacial rebound large lateral variations in the thickness of the lithosphere and viscosity of the mantle may be associated with continental roots the effects of continental roots or the tectosphere on postglacial rebound are calculated using an axisymmetric flow model in which both the mantle and lithosphere are described as newtonian fluids continental roots are shown to have a measurable effect on postglacial rebound in particular on the evolution of the peripheral bulge effects of continental roots are concentrated near the edge of the tectosphere and thus often near ocean continent boundaries where many relative sea level histories are measured the pattern and distribution of tectonic and seismic activity associated with deglaciation are affected by a tectosphere

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

effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced surface motion in laurentia abstract the effects of lateral variations in lithospheric thickness and mantle viscosity on surface motions in laurentia are investigated using the finite element method both a simple axisymmetric ice model and a more realistic ice deglaciation model ice4g are used to investigate the effects of lateral heterogeneity beside the laterally homogeneous reference model six laterally heterogeneous models are used the lateral heterogeneity in the lithosphere upper mantle transition zone and lower mantle are inferred from seismic tomographic model s20a in general the magnitude of the effect of lateral heterogeneity is found to depend on the deglaciation history and the relative position between the ice center and the lateral heterogeneity it is shown that lateral heterogeneity does affect horizontal motion in laurentia however because the effects of lateral heterogeneity from different depths give different orientations to the incremental velocity vector the total effect is not large enough to overwhelm the divergent motion but just weaken it in southern laurentia for land uplift rate the effect of lateral viscosity variation in the transition zone between 425 and 700 km depth is opposite to that of the upper or lower mantle thus the net effect of lateral heterogeneity on uplift rate is not very large but enough to change the shape of the uplift pattern

mantle rheology and satellite signatures from present day glacial forcings we study the changes of the long wavelength portion of the earth s gravity field as a result of present day gladal discharges and the possible growth of the antarctic ice sheet we employ both maxwell and burgers body rheologies and find that there are significant differences in the responses between the two rheologies for time spans less than a century both present day gladal forcing and the ice buildup on antarctica can cause non negligible perturbations in j 2 of about one third the observed amount the contributions from the two mechanisms have opposite signs in j 2 only for i 3 and 6 do these cryospheric contributors act in concert with one another in disturbing the gravity field ali other degree harmonics up to 1 9 have opposite signs from these two excitations for a steady state lower mantle viscosity of 1022 pa s j 3 can attain a maximum value of around 1 5 x lo i1 yr 1 and j a value of 1 3 x io il yr i for current forcings these have signs opposite to those predicted for pleistocene deglaciation ali harmonics up to i 9 are sensitive to variations of the steady state vis cosity in the lower mantle even for time scales shorter than 100 years it is proposed that detailed satellite monitoring of present day ice movements in conjunction with geodetic satellite missions will eventually pro vide a viable alternative for estimating deep mantle viscosity useful in mantle convection models

mapping the lower mantle determination of lateral heterogeneity in p velocity up to degree and order 6 the data from the international seismological centre bulletins for the years 1964 1979 are used to derive a three dimensional model of lateral variations of the p velocity in the lower mantle unlike previous studies in which such perturbations were represented by a blocklike parameterization we seek the solution in the form r k 0k l 0l m 0l k r kalm cos m kblm sin m plm cos some 500 000 travel time residuals for teleseismic distances from 5000 earthquakes are used in an iterative procedure to derive the coefficients a and b the maximum k and l used are 4 and 6 respectively in each iteration in addition to solving for the three dimensional structure we also relocate all the earthquakes perturb the average travel time curve and determine station corrections for over 1000 stations particular attention is given to the problem of weighting the individual observations in order to avoid as much as possible the bias due to the uneven distribution of sources and receivers the resulting model shows a high level of perturbations just below the 670 km discontinuity and just above the core mantle boundary where the maximum perturbations reach 1 1 5 of the average velocity even for this highly smoothed model at a depth of 2000 km the rms perturbations are some 3 to 4 times lower than at either of the two boundaries the model predicts well the large scale pattern of observed travel time residuals for various source regions except for the distinct effects of the subduction zones the most striking large scale three dimensional feature of the model is a ring of high velocities circumscribing the pacific basin within a depth range from 1000 km to the core mantle boundary if the proportionality between perturbations in the velocity and temperature is assumed the derived pattern of anomalies could be consistent with a two boundary layer model of convection in the lower mantle some caution however should be exercised in interpreting the results near the 670 km discontinuity where the resolving power of our data set is limited by the lack of adequate control of the upper mantle structure at the same time a significant global increase in the level of perturbations in the lowermost mantle is established beyond question the results of dziewonski et al 1977 on the correlation between the equivalent geoid and the observed geoid for the angular order numbers 2 and 3 is confirmed but there is no significant correlation for degrees from 4 to 6 these calculations are made for the rigid earth richards and hager this issue show that introduction of finite viscosity can change the sign of a geoid anomaly in addition recent studies of lateral variations in the shear velocity reveal the presence of large scale anomalies in the upper mantle thus while the inferences made here with respect to the origin of the gravest orders of the geopotential field are not conclusive they point the way in which results from seismology can be used to address some of the basic questions of geodynamics

temperature distribution in the crust and mantle in an attempt to understand the temperature distribution in the earth experimental constraints on the geotherm in the crust and mantle are considered the basic form of the geotherm is interpreted on the basis of two dominant mechanisms by which heat is transported in the earth 1 conduction through the rock and 2 advection by thermal flow data reveal that 1 the temperature distributions through continental lithosphere and through oceanic lithosphere more than 60 million years old are practically indistinguishable 2 crustal uplift is instrumental in modifying continental geotherms and 3 the average temperature through the archean crust and mantle was similar to that at present it is noted that current limitations in understanding the constitution of the lower mantle can lead to significant uncertainties in the thermal response time of the planetary interior

tomographical mapping of the lithosphere and asthenosphere beneath southern scandinavia and adjacent areas abstract in this paper we report on a seismic tomographical survey of the lithosphere asthenosphere beneath southern scandinavia and adjacent areas the ach inversion technique has been used and the observational data in the form of p wave travel time residuals have been obtained from seismogram records from networks in denmark southern norway and southern sweden the volume under investigation subdivided into four levels layers of 7 7 knots blocks each for estimation of velocity perturbations covers the area 54 62 n and 7 20 e and depth range 0 600 km major findings are as follows level 1 0 100 km pronounced velocity lows beneath southern jutland zealand the variscan foredeep and the sveco norwegian province of southeastern norway 1500 ma old the svecofennides of southeastern sweden exhibit relatively high velocities while the sveco norwegian province of southwestern sweden 1700 ma old is characterized by moderately high velocities the transition between velocity highs and lows coincides with the tornquist teisseyre line ttl or fennoscundian border zone level 2 100 300 km velocity anomalies are less pronounced at this level although velocity lows are found beneath the northern jutland zealand area and slightly northwestwards of the oslo rift the only velocity high is found beneath the southeasternmost part of sweden the ttl does not appear to have a clear counterpart in the velocity anomaly pattern in this depth range although a clearly unambiguous answer here would require far more extensive observational data a research goal of the future level 3 300 500 km and level 4 500 600 km velocity anomalies are weak which is not unexpected for the upper mantle beneath shield areas

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

thermally induced phase changes lateral heterogeneity of the mantle continental roots and deep slab anomalies pressure induced solid solid phase changes are responsible for most of the increase of density and seismic velocity with depth in the upper mantle lateral variations in temperature cause a similar effect abrupt changes of density and seismic velocity due to phase changes are superposed on smaller changes associated with thermal expansion temperature induced isobaric phase changes are as important in explaining various recent geophysical data as are the more familar pressure induced phase changes in cold slabs the equilibrium mineral assemblage contains high density high velocity phases which are not stable in hotter mantle in particular the ilmenite form of mgsio 3 and the spinel form of mg 2sio 4 have broad stability fields in cold mantle which increase the density and velocity of deep slabs to values in excess of those which have been used in geoid and seismic travel time modeling recent arguments for slab penetration into the lower mantle and whole mantle convection are based on thermal models of the slab which ignore the large density and seismic velocity anomalies associated with temperature induced phase changes when these effects are taken into account the geoid and seismic anomalies associated with subducted slabs are consistent with slab confinement to the upper mantle and layered models of mantle convection the seismicity cutoff and evidence for slab thickening at 670 km also favor this style of convection mantle seismic velocities between 200 and 400 km depth in tectonic and young oceanic regions are lower than in shield regions and this is due to the presence of a melt phase and lower velocity high temperature phase assemblages deep 200 km long lived continental roots differing in chemistry from normal mantle are not required when isobaric phase changes are taken into account high velocity subshield mantle is closer to normal subsolidus mantle than is suboceanic mantle which is affected by the presence of high temperature phase assemblages the whole mantle convection thick continental root and deep slab penetration hypotheses are not supported by seismic and geoid data when isobaric phase changes are included in the analysis phase changes are more effective in changing density and seismic velocity than are lateral variations in temperature and composition the lack of correlation of the geoid with ridges shields heat flow and upper mantle velocity variations suggests a low geoid sensitivity to the upper mantle consistent with layered convection

plate motion and dragging of the upper mantle lateral variations of lithospheric thickness and their implications for intraplate deformation the impact of lateral variations in the thickness of the lithosphere on surface topography horizontal intraplate deformation and stress accumulation is studied for plates that drift with respect to the highly viscous lower mantle and the transition zone the lithosphere and upper mantle are de scribed by a viscoelastic maxwell rheology within the frame work of a finite element scheme which allows the modeling of heterogeneous lithospheric structures in 2d vertical cross sections the geophysical signatures are found to be extremely sensitive to lateral viscosity contrasts which interact with the upper mantle flow this mechanism can contribute to a certain extent and in concert with the other driving forces of plate tec tonics to the evolution of back arc basins to the explanation of the largest angle of subduction in west dipping slabs and to the initiation of subduction of an oceanic lithosphere undemeath a stable continental one

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

glacial isostatic adjustment and relative sea level changes the role of lithospheric and upper mantle heterogeneities in a 3 d spherical earth summary the response of the earth to the melting of the late pleistocene ice sheets is commonly studied by spherically layered models based on well established analytical methods in parallel a few models have been recently proposed to circumvent the limitations imposed by spherical symmetry and to reproduce the actual structure of the lithosphere and of the upper mantle their main outcome is that laterally varying rheological structures may significantly affect various geophysical quantities related to glacial isostatic adjustment gia and particularly post glacial relative sea level rsl variations and 3 d crustal velocities in formerly ice covered regions in this paper we contribute to the ongoing debate about the role of lithospheric and mantle heterogeneities by new 3 d spherical newtonian finite elements models and we directly compare their outcomes with publicly available global rsl data this differs from previous investigations in that have mainly focused on extensive sensitivity analyses or have considered a limited number of rsl observations from formerly glaciated regions and their periphery in our study the lithospheric thickness mimics the global structure of the cratons based on geological evidence and the upper mantle includes a low viscosity zone beneath the oceanic lithosphere we use two distinct global surface loads based upon the ice1 and ice3g deglaciation chronologies respectively our main finding is that using all of the available rsl observations in the last 6000 years it is not possible to discern between homogeneous and heterogeneous gia models this result which holds for both ice1 and ice3g suggests that the cumulative effects of laterally varying structures on the synthetic rsl curves cancel out globally yielding signals that do not significantly differ from those based on the 1 d models we have also considered specific subsets of the global rsl database sharing similar geographical settings and distances from the main centres of deglaciation when we consider the data from the margins of the baltic region a laterally varying lithospheric thickness improves significantly the agreement with the observations this is not observed in other relevant situations including the hudson bay region in the regions where the disagreement between predictions and observations is particularly evident further investigations are needed to improve the geometry of the heterogeneous structures and of the surface ice sheets distribution

planktonic foraminiferal area density as a proxy for carbonate ion concentration a calibration study using the cariaco basin ocean time series 1 biweekly sediment trap samples and concurrent hydrographic measurements collected between march 2005 and october 2008 from the cariaco basin venezuela are used to assess the relationship between co32 and the area densities a of two species of planktonic foraminifera globigerinoides ruber pink and globigerinoides sacculifer calcification temperatures were calculated for each sample using species appropriate oxygen isotope 18o temperature equations that were then compared to monthly temperature profiles taken at the study site in order to determine calcification depth ambient co32 was determined for these calcification depths using alkalinity ph temperature salinity and nutrient concentration measurements taken during monthly hydrographic cruises the a which is representative of calcification efficiency is determined by dividing individual foraminiferal shell weights 0 43 g by their associated silhouette areas and taking the sample average the results of this study show a strong correlation between a and ambient co32 for both g ruber and g sacculifer r2 0 89 and 0 86 respectively confirming that co32 has a pronounced effect on the calcification of these species though the a for both species reveal a highly significant p 0 001 relationship with ambient co32 linear regression reveals that the extent to which co32 influences foraminiferal calcification is species specific hierarchical regression analyses indicate that other environmental parameters temperature and po43 do not confound the use of g ruber and g sacculifer a as a predictor for co32 this study suggests that g ruber and g sacculifer a can be used as reliable proxies for past surface ocean co32

abundance and geochemical significance of c2n dialkylalkanes and highly branched c3n alkanes in diverse meso and neoproterozoic sediments several series of branched alkanes with quaternary carbon centers have been detected by gc ms in the saturated hydrocarbon fractions of neoproterozoic sedimentary rocks associated with fossilised microbial mats officer basin south australia and of shallow water carbonates spitsbergen east greenland and baffin island canada a series of 5 5 diethylalkanes was predominant in most of these sediments and was typically accompanied by related series in lower abundance which based on mass spectral characteristics are tentatively assigned as 6 6 diethylalkanes 5 butyl 5 ethylalkanes and 6 butyl 6 ethylalkanes each series displays strong odd or even carbon number preferences several of the sediments contained additional series of structurally undefined c3n alkanes notable for very negative retention time factors which become more negative with increasing molecular weight indicating that branching increases with each c3 addition the strongly sequential carbon preference of the respective c2n and c3n branched alkane series and a predominantly light 13c signature of the 5 5 diethylalkanes cf co occurring n alkanes are consistent with an origin from organisms with a distinct physiology and or carbon source the relatively wide occurrence and high abundance of these branched alkanes in proterozoic sediments containing benthic microbial mats suggests a relationship with specific paleoenvironmental conditions for example strong water column redox gradients that may have been more prevalent than in the phanerozoic

effects of lateral viscosity variations on postglacial rebound an analytical approach summary so far interpretations of postglacial rebound have usually been based on the assumption of laterally homogeneous earth models however in view of the increasing evidence of the 3 d structure of the earth s mantle several studies on the effects of lateral variations of the viscosity on postglacial rebound have been completed during the last decade in the present study we consider load induced viscoelastic and viscous perturbations of incompressible and vertically homogeneous flat earth models with lateral variations of the shear modulus and viscosity the solution is obtained using a perturbation method and given in analytical form our results show that sinusoidal variations of the parameters of less than one order of magnitude can modify the vertical surface displacement associated with a model of the fennoscandian ice sheet by several tens of metres the modifications increase approximately in proportion to the amplitude of the lateral variations the overall increase of the modifications with increasing wavelength is complicated in detail and also results in changes of the spatial and temporal distributions of the vertical surface displacement