glacial rebound and plate spreading results from the first countrywide gps observations in iceland iceland is one of the few places on earth where a divergent plate boundary can be observed on land direct observations of crustal deformation for the whole country are available for the first t

a method for estimating ice mass loss from relative insar observations application to the vatnajokull ice cap iceland 1 we present a new method for estimating ice mass loss from glaciers and ice sheets using interferometric synthetic aperture radar insar time series data we use a linear inversion method based on observations of nearby bedrock uplift and a solution for surface loading of an elastic half space the method assumes that mass loss is focused on lower elevation terminal regions of the glacier or ice sheet and that there is an exponential decrease in thinning rate toward the higher elevation interior we apply the method to uplift rates between 1995 and 2009 near vatnajokull iceland the data reveal up to 13 mm yr relative line of sight los velocity around the south western edge of vatnajokull we find an ice mass loss rate of 6 8 0 7 0 8 gt yr in approximate agreement with other estimates ice loss since 1995 is twice as fast as the loss rate estimated for the rest of the 20th century

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

10be inventories in alpine soils and their potential for dating land surfaces abstract to exploit natural sedimentary archives and geomorphic landforms it is necessary to date them first landscape evolution of alpine areas is often strongly related to the activities of glaciers in the pleistocene and holocene at sites where no organic matter for radiocarbon dating exists and where suitable boulders for surface exposure dating using in situ produced cosmogenic nuclides are absent dating of soils could give information about the timing of landscape evolution this paper explores the applicability of soil dating using the inventory of meteoric 10be in alpine soils for this purpose a set of 6 soil profiles in the swiss and italian alps was investigated the surface at these sites had already been dated using the radiocarbon technique or the surface exposure determination using in situ produced 10be consequently a direct comparison of the ages of the soils using meteoric 10be and other dating techniques was made possible the estimation of 10be deposition rates is subject to severe limitations and strongly influences the obtained results we tested three scenarios using a the meteoric 10be deposition rates as a function of the annual precipitation rate b a constant 10be input for the central alps and c as b but assuming a pre exposure of the parent material the obtained ages that are based on the 10be inventory in soils and on scenario a for the 10be input agreed reasonably well with the age using surface exposure or radiocarbon dating the ages obtained from soils using scenario b produced ages that were mostly too old whereas the approach using scenario c seemed to yield better results than scenario b erosion calculations can in theory be performed using the 10be inventory and 10be deposition rates an erosion estimation was possible using scenario a and c but not using b the calculated erosion rates using these scenarios seemed to be plausible with values in the range of 0 57 mm ky the dating of soils using 10be has several potential error sources analytical errors as well as errors from other parameters such as bulk soil density and soil skeleton content have to be taken into account the error range was from 8 up to 21 furthermore uncertainties in estimating 10be deposition rates substantially influence the calculated ages relative age estimates and under optimal conditions absolute dating can be carried out age determination of alpine soils using 10be gives another possibility to date surfaces when other methods fail or are not possible at all it is however not straightforward quite laborious and may consequently have some distinct limitations

short and long term delivery rates of meteoric 10be to terrestrial soils well constrained long term average meteoric 10be deposition rates are important when meteoric 10be is used as a chronometer or tracer of earth surface processes to constrain meteoric 10be delivery to terrestrial soils we estimate time integrated 10be deposition rates from meteoric 10be inventories measured in dated soils and compare these results to a new synthesis of short term measurements of 10be in precipitation comparison of these long term rates to short term measurements suggests that short term measurements likely predict long term meteoric 10be deposition rates within uncertainties of 20 in precipitation measurements it is possible to deconvolve the contribution of atmospherically produced primary meteoric 10be from recycled meteoric 10be delivered by terrestrial dust if a second isotope is measured that quantifies either the recycled or primary components of meteoric 10be deposition we use dust concentration dependent differences between 7be and 10be measurements to make new estimates of the recycled contribution to total meteoric 10be flux delivered to the earth s surface these dust corrected data show a strong linear dependence between precipitation amount and primary meteoric 10be flux concentrations of primary meteoric 10be in mid and low latitude precipitation vary predictably by latitude between 0 63 104 and 2 05 104 atoms cm3 of precipitation providing a first order estimate of primary meteoric 10be deposition for a given latitude and precipitation rate

new evidence for dislocation creep from 3 d geodynamic modeling of the pacific upper mantle structure laboratory studies on deformation of olivine in response to applied stress suggest two distinct deformation mechanisms in the earth s upper mantle diffusion creep through diffusion of atoms along grain boundaries and dislocation creep by slipping along crystallographic glide planes each mechanism has very different and important consequences on the dynamical evolution of the mantle and the development of mantle fabric due to the lack of in situ observations it is unclear which deformation mechanism dominates in the upper mantle although observed seismic anisotropy in the upper mantle suggests the presence of dislocation creep we examined the thermo mechanical erosion of the lithosphere by thermal boundary layer instabilities in 3 d dynamical models this study demonstrates that the seismically derived thermal structure of the pacific lithosphere and upper mantle imposes an important constraint on the upper mantle deformation mechanism the predominant deformation mechanism in the upper mantle is dislocation creep consistent with observed seismic anisotropy the acceptable activation energy range of 360 540 kj mol is consistent with although at the lower end of those determined from laboratory studies

moho vs crust mantle boundary evolution of an idea abstract the concept that the mohorovicic discontinuity moho does not necessarily coincide with the base of the continental crust as defined by rock type compositions was introduced in the early 1980s this had an important impact on understanding the nature of the crust mantle boundary using information from seismology and from deep seated samples brought to the surface as xenoliths in magmas or as tectonic terranes the use of empirically constrained p t estimates to plot the locus of temperature vs depth for xenoliths defined a variety of geotherms depending on tectonic environment the xenolith geotherms provided a framework for constructing lithological sections through the deep lithosphere and revealed that the crust mantle boundary in off craton regions commonly is transitional over a depth range of about 5 20 km early seismic reflection data showed common layering near the moho correlating with the petrological observation of multiple episodes of basaltic intrusion around the crust mantle boundary developments in seismology petrophysics and experimental petrology have refined interpretation of lithospheric domains the expansion of in situ geochronology especially zircon u pb ages and hf isotopes os isotopes of mantle sulfides has defined tectonic events that affected whole crust mantle sections and revealed that the crust mantle boundary can change in depth through time however the nature of the crust mantle boundary in cratonic regions remains enigmatic mainly due to lack of key xenoliths or exposed sections the observation that the moho may lie significantly deeper than the crust mantle boundary has important implications for modeling the volume of the crust mapping the crust using seismic techniques alone without consideration of the petrological problems may lead to an overestimation of crustal thickness by 15 30 this will propagate to large uncertainties in the calculation of elemental mass balances relevant to crust formation processes and the composition of the convecting mantle

ice 5g and ice 6g models of postglacial relative sea level history applied to the holocene coral reef record of northeastern st croix u s v i investigating the influence of rotational feedback on gia processes at tropical latitudes abstract fossil coral reefs along the northeastern coast of st croix in the caribbean sea provide an 8000 year record of dated and interpreted holocene sea level change we herein compare this record with the predictions of models of glacio hydro isostatic adjustment for st croix and for additional sites at similar latitudes in the greater and lesser antilles region rsl predictions are based upon the model ice 5g vm2 and with a modified model ice 6g vm5a both including and excluding the influence of rotational feedback misfits between the modeled sea levels and the local geologic data are most apparent for models without rotational feedback particularly in the prediction of a 2 to 4 m unsupported mid holocene misfit at 4 ka as well as a small amplitude highstand that extends from 2 5 to 1 5 ka incorporation of the influence of rotational feedback provides the best fit to the data largely eliminating the unsupported mid holocene misfit between the data field and the sea level histories predicted by the models without rotational feedback and fitting data older than 5 kyr more closely than a previously published latitudinally averaged sea level curve for the western atlantic the st croix data therefore demonstrate that rotational influence extends at least 27 further south from its 45 n mid latitude extremum along the us east coast and identifies tropical latitudes as influenced by proglacial forebulge collapse implications for reef based sea level reconstruction include the ability to accurately model sea levels at specific tropical sites with partial holocene chronologies using the ice 6g vm5a model with rotational feedback latitudinally averaged sea level curves are therefore of limited use in understanding the relative importance of contributing physical influences on postglacial sea level history

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

large time step numerical modelling of the flow of maxwell materials summary maxwell viscoelastic materials are commonly simulated numerically in order to model the stresses and deformations associated with large scale earth processes such as mantle convection or crustal deformation both implicit and explicit time marching methods require that the time steps used be small compared with the maxwell relaxation time if accurate solutions are to be obtained for crustal tectonic modelling where maxwell times in a ductile lower crust may be of order of a decade or less the large number of time steps required to model processes lasting many millions of years imposes a huge computational burden this burden is avoidable in this paper i show that with the appropriate formulation of the problem time steps may be taken which are much larger than the maxwell time without loss of accuracy as long as they are not large compared with the times over which strain rates vary significantly tectonic timescales in the model the method relies on explicit analytic integration of the maxwell constitutive relation for the stress over time intervals which may be longer than the relaxation time as long as they are short compared with the timescale over which crustal stresses and geometries change the validity of the formulation is also demonstrated numerically by comparison with the analytic solutions for three simple plane strain models extension of a uniform block shear of a composite layer and development of a rayleigh taylor instability

reconstruction of global 10be production over the past 250ka from highly accumulating atlantic drift sediments in this study we present a reconstruction of the global 10be production rate over the past 250 000 years from three marine sediment cores located in high accumulation environments in the north northwest and south atlantic ocean odp sites 983 1063 and 1089 the 10be records are corrected for oceanic transport processes and principal component analysis pca is used to extract the common signal from the three records which we interpreted as variations of the global 10be production rate the reconstruction presented here may serve as i a record of past flux of galactic cosmic rays gcr ii a proxy for past geomagnetic dipole strength and iii as a global matching tool to synchronize marine archives with ice cores and terrestrial records

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

calibrating a long term meteoric 10be accumulation rate in soil 1 using 13 samples collected from a 4 1 meter profile in a well dated and stable new zealand fluvial terrace we present the first long term accumulation rate for meteoric 10 be in soil 1 68 to 1 72 10 6 at cm 2 yr integrated over the past 18 ka site specific accumulation data such as these are prerequisite to the application of meteoric 10 be in surface process studies our data begin the process of calibrating long term meteoric 10 be delivery rates across latitude and precipitation gradients our integrated rate is lower than contemporary meteoric 10 be fluxes measured in new zealand rainfall suggesting that long term average precipitation dust flux or both at this site were less than modern values with accurately calibrated long term delivery rates such as this meteoric 10 be will be a powerful tool for studying rates of landscape change in environments where other cosmogenic nuclides such as in situ 10 be cannot be used

inference of mantle viscosity from grace and relative sea level data summary gravity recovery and climate experiment grace satellite observations of secular changes in gravity near hudson bay and geological measurements of relative sea level rsl changes over the last 10 000 yr in the same region are used in a monte carlo inversion to infer mantle viscosity structure the grace secular change in gravity shows a significant positive anomaly over a broad region 3000 km near hudson bay with a maximum of 2 5 gal yr 1 slightly west of hudson bay the pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ice 5g deglaciation history strongly suggesting a postglacial rebound origin for the gravity change we find that the grace and rsl data are insensitive to mantle viscosity below 1800 km depth a conclusion similar to that from previous studies that used only rsl data for a mantle with homogeneous viscosity the grace and rsl data require a viscosity between 1 4 1021 and 2 3 1021 pa s an inversion for two mantle viscosity layers separated at a depth of 670 km shows an ensemble of viscosity structures compatible with the data while the lowest misfit occurs for upper and lower mantle viscosities of 5 3 1020 and 2 3 1021 pa s respectively a weaker upper mantle may be compensated by a stronger lower mantle such that there exist other models that also provide a reasonable fit to the data we find that the grace and rsl data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle

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

10be distribution in soils from merced river terraces california abstract the distribution and residence time of cosmogenic 10 be in clay rich soil horizons is fundamental to understanding and modelling the migration of 10 be on terrestrial sediments and in groundwater solutions we have analyzed seven profiles of clay rich soils developed from terrace sediments of the merced river california the terraces and soils of increasing age are used to compare the 10 be inventory with a simple model of accumulation decay and erosion the data show that the distribution of 10 be varies with soil horizon clay content that the residence time of 10 be in these horizons exceeds 10 5 years and that to a rough approximation the inventory of 10 be in a thoroughly sampled soil profile fits the equation n q em 1 e where q is delivery rate e is erosion rate m is the concentration of 10 be in the eroding surface layer is the decay constant and t is the age of the depositional unit from which the soil has developed the general applicability of this model is uncertain and warrants further testing in well calibrated terrace sequences

quantification of soil production and downslope creep rates from cosmogenic 10be accumulations on a hillslope profile average soil transport rates over a period of 3500 yr on a convex soil mantled hillslope have been quantified using a mass balance model that incorporates the soil concentration of the cosmogenic isotope 10 be the 10 be model results support the assumption used in most geomorphic models that the soil creep rate is proportional to surface gradient the predicted diffusion coefficient is 360 55 cm 3 yr 1 cm 1 contour length and the average rate of soil production is 0 026 0 007 cm yr within the uncertainty of this technique the data do not reject g k gilbert9s hypothesis that some hillslopes may exist in a condition of dynamic equilibrium with a uniform soil production rate however the model does not require an assumption of dynamic equilibrium and may be an approach that uniquely allows the quantification of a local soil production rate law

the global average production rate of10be precipitation collected in continuously open containers for about a year at seven sites around the united states was analyzed for10be 90sr 210pb and238u based on these data and long term precipitation 90sr and210pb delivery patterns the stratospheric tropospheric and recycled10be components in the collections were estimated and the global10be production rate was assessed single station production rate estimates range from 0 52 106 atoms cm 2 yr 1 to 2 64 106 atoms cm 2 yr 1 the mean value is 1 21 106 atoms cm 2 yr 1 with a standard error of 0 26 106 atoms cm 2 yr 1

lithospheric deformation induced by loading of the hawaiian islands and its implications for mantle rheology the long term rheological properties of the lithosphere are fundamental for understanding both surface tectonics and mantle dynamics on earth in this study we have developed 3 d finite element models for computing the load induced surface deformation and stress for lithosphere and mantle with realistic nonlinear viscoelastic rheology including the frictional sliding low temperature plasticity and high temperature creep we have determined the lithospheric deformation and stress due to volcano loading in the hawaiian islands region for the last few million years by comparing model predictions with seismic observations of the depth to the top of oceanic crust and depth dependence of seismicity in the hawaiian islands region we have sought to constrain lithospheric rheology our calculations show that the load induced surface deformation is controlled by low temperature plasticity and frictional sliding but is insensitive to high temperature creep lithospheric strength predicted from laboratory derived low temperature plasticity needs to be reduced significantly and a frictional coefficient f ranging from 0 1 to 0 7 is required in order to account for the observations however f 0 1 weakens the shallow part of the lithosphere so much that it causes the minima in strain rate and stress to occur at too large depths to be consistent with the observed depth distribution of seismicity our results therefore suggest a value for f between 0 25 and 0 7 finally the maximum stress that accumulates in the deformed lithosphere beneath the hawaiian islands is about 100 200 mpa for models that match the observations and this stress may be viewed as the largest lithospheric stress on earth

postglacial rebound in a non newtonian spherical earth using finite elements we study the postglacial rebound in an axisymmetric earth with a non newtonian rheology our approach allows for the first time a self consistent study of the effect of a power law creep on the long wavelength deformations which cannot be performed using flat models we show that for a non newtonian upper mantle the time variations of the low degree stokes coefficients become largely insensitive to the viscosity of the lower mantle this is in contrast with previous evidence based on newtonian models which emphasized the importance of the low degree signatures for constraining the lower mantle viscosity

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

rheology of the upper mantle a synthesis rheological properties of the upper mantle of the earth play an important role in the dynamics of the lithosphere and asthenosphere however such fundamental issues as the dominant mechanisms of flow have not been well resolved a synthesis of laboratory studies and geophysical and geological observations shows that transitions between diffusion and dislocation creep likely occur in the earth s upper mantle the hot and shallow upper mantle flows by dislocation creep whereas cold and shallow or deep upper mantle may flow by diffusion creep when the stress increases grain size is reduced and the upper mantle near the transition between these two regimes is weakened consequently deformation is localized and the upper mantle is decoupled mechanically near these depths

on the possibility of newtonian flow in the upper mantle abstract the possibility of a linear creep newtonian viscosity upper mantle is reexamined on the basis of present knowledge on flow mechanisms in olivine including differences between activation parameters for creep and for diffusion and revised estimates of grain boundary width results of the comparison between linear superplastic creep and power law creep are presented as crossover temperature between lattice and grain boundary diffusion and crossover stress between non linear and linear creep as a function of temperature depth grain size grain boundary width grain boundary diffusion activation energy and rate controlling species silicon or oxygen for the most realistic values of the parameters linear creep is well within the range of possibilities there is no major objection from rheology to the idea of a newtonian viscosity upper mantle viscosities for the two kinds of creep are compared for laboratory upper mantle and tentatively lower mantle conditions this results in a prediction of the grain size at which coble creep could be observed in olivine polycrystals in the laboratory 10 m or less the upper mantle viscosity is in the 1020 1021 pa s range minimum estimates for the viscosity of the lower mantle are of the same order the pictures of the rheology of the mantle derived from microphysical models of flow and from geophysical observation can therefore be made compatible

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

effects of mantle flow law stress exponent on postglacial induced surface motion and gravity in laurentia summary recent studies show that power law rheology with stress exponent n 3 in the lower mantle or in a thin zone just beneath the lithosphere are consistent with the sea level observations in and around laurentia in this study the stress exponent n is varied from 2 to 4 and for each value of n a range of creep parameter a is searched to find the earth model that gives the best fit to the sea level observations in and around laurentia the effects of stress exponent on other geophysical observables namely present day uplift rate horizontal velocity free air gravity and the rate of change in gravity are also studied the model used to calculate the postglacial readjustment of the earth is a 3 d finite element model that includes realistic ice histories and eustatic water loads on stratified incompressible viscoelastic maxwell flat earths three types of earth rheology models are considered the first one has nonlinear rheology throughout the mantle and the second has a nonlinear zone at the top of the mantle below the elastic lithosphere and a linear mantle the third one has nonlinear rheology restricted to lie in the lower mantle it is found that the models with nonlinear rheology in the lower mantle give better fits to the sea level data in and around laurentia than the first two types however sea level data when taken as a whole cannot clearly discriminate between the stress exponents 2 3 or 4 present day uplift rate horizontal velocity and rate of gravity change however may be useful in further discriminating mantle rheology

coupling meteoric 10be with pedogenic losses of 9be to improve soil residence time estimates on an ancient north american interfluve we couple meteoric 10 be measurements with mass balance analysis of 9 be to estimate the soil residence time srt of a biogeomorphically stable ultisol in the southern piedmont physiographic region of the southeastern united states we estimate srt after correcting the meteoric 10 be inventory to account for observed 9 be losses which indicate that more than half of the 9 be weathered from primary minerals has been leached from the upper 18 3 m of the ultisol our estimates of minimum srt range between 1 3 1 4 ma and between 2 6 3 1 ma under high and low 2 0 and 1 3 10 6 atoms cm 2 yr 1 respectively estimates of 10 be delivery denudation rates of the physiographic region corroborate our estimates we redefine pedogenic time constraints in the southern piedmont and demonstrate that the assumption of complete meteoric 10 be retention in acidic soil systems cannot always be made the latter has far reaching consequences for soil sediment river and ocean research using meteoric 10 be

postglacial rebound in a power law medium with axial symmetry and the existence of the transition zone in relative sea level data summary this work is a continuation of the investigation of wu 1992a into understanding the effect of non linear rheology on postglacial rebound as in the previous study the finite element method is used to study the deformation of incompressible flat earth models with power law rheology however unlike the previous study where the unrealistic assumption of plane strain was used here the loads are assumed to be axially symmetrical t1 characteristic deformation pattern of some simple earth models due to these axially symmetrical loads are studied the effects of load distribution and a time dependent contracting ice model are also investigated in this paper from the characteristic deformation patterns of non linear half spaces or channels that do or do not have elastic lithospheres it is demonstrated that non linear earth models cannot explain the existence of the transition zone in the sea level data this cannot be achieved by varying the stress exponent n because increasing n only makes the effect of non linearity more prominent and will not significantly alter the pattern of deformation it is also demonstrated that a contracting parabolic ice load with diminishing load cannot explain the sea level data in the transition zone either when the observed sea level data near the centre of rebound in fennoscandia or laurentia are compared with the predicted uplift curves it is demonstrated that power law rheological models with instantaneous melting histories can fit the relative sea level rsl observations near the centre of rebound however no earth model with a completely non linear mantle that is able to match the data simultaneously in the centre near the edge or outside the ice sheet has been found thus although the rheology of the mantle maybe non linear postglacial rebound probably sees the rheology of the mantle as linear

lithospheric flexure and gravity spreading of olympus mons volcano mars the structural architecture of large volcanoes is governed substantially by gravity driven deformation that is manifest as distinct processes such as basement flexure or volcanic spreading temporal effects and the mutual interplay of these processes have been investigated only to a limited extent and so we present novel numerical models of the time dependent deformation associated with them the models simulate the combined effects of lithospheric flexure and volcanic spreading during growth increments of an elastoplastic volcanic cone different spreading scenarios are considered by a variable coupling decoupling behavior at the interface between volcano and basement we apply our models to olympus mons on mars which is characterized by upper to middle flank terraces on the shield is encircled by a basal scarp that has an average slope of 30 and is surrounded by distant deposits that resemble large scale slumping features on earth our results are consistent with the interpretation that terraces on olympus mons flanks form by thrust faulting that results from lithospheric flexure the presence and expression of terraces depend on the coupling of volcano and basement on the time of volcano growth relative to mantle relaxation and on the cohesion of the edifice the encircling scarp may be related to a very low friction detachment at the edifice base which leads to a normal fault regime on the lowermost flanks with time and volcano growth predicted stress and faulting regimes migrate only slightly indicating that the structural architecture of volcanoes is largely set in the very early stages of formation

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

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

precipitation as meteoric sediment and scaling laws of bedrock incision assessing the sadler effect abstractalthough it has been several decades since sadler 1981 first showed that sediment accumulation rates exhibit a negative power law dependence on measurement interval i e the sadler effect only recently has a manifestation of covariance in rate with duration become more widely appreciated in degradational settings because our collective understanding of rates of deposition and erosion are widely utilized to constrain the importance of active tectonism and climate forcing in shaping the surface of our planet cognizance of the dependence of rate on duration of observation is of critical importance relations between elevation change deposition erosion and rate scaling laws have often been examined by stochastic random walk simulations but this approach is generally confounded by insufficient data on amounts of land surface change on durations of land surface change and on hiatal durations separating time intervals of change deposition or erosion rates measured over short intervals suc

beryllium isotope geochemistry in tropical river basins abstract the distributions of beryllium 9 and beryllium 10 in rivers within the orinoco and amazon basins have been examined to extend our understanding of their geochemical cycles and to develop their use both in geochronometry and in studying erosional processes beryllium 9 the stable isotope is weathered from mineral lattices before entering the riverine dissolved or exchangeable phase the cosmogenic radioisotope 10be t 1 2 1 5 myr is produced primarily in the atmosphere and is brought into riverine systems via rainfall in dissolved or exchangeable form it may be used to examine the processes which affect beryllium partitioning between the dissolved and particulate phases ancillary data such as major ion distributions provide a basis for selecting regions in which riverine chemistry is dominated by a single geochemical process allowing examination of its effects on be distributions in isolation analyses of 9be in dissolved and suspended material from rivers with a wide range of chemical compositions indicate that its geochemistry is primarily controlled by two major factors 1 1 its abundance in the rocks of the watershed and 2 2 the extent of its adsorption onto particle surfaces the relative importance of these parameters in individual rivers is determined by the extent of interaction with flood plain sediments and the riverine ph this understanding of 9be geochemistry forms a basis for examination of the geochemical cycling of 10be in rivers which are dominated by interaction with sediments the riverine concentration of dissolved 10be is far lower than that in the incoming rainwater indicating that a substantial proportion of it is retained within the soils of the basin or is adsorbed onto riverine particles however in acidic rivers in which the stable dissolved be concentration is determined by the be level in the rocks of the drainage basin dissolved 10be has essentially the same concentration as in precipitation these observations imply that the soil column in such regions must be saturated with respect to 10be and that the ratio of the inventory to the flux does not represent an age as may be the case in temperate latitudes but rather a residence time

spatial and temporal variations in meteoric 10be inventories and long term deposition rates colorado front range abstract atmospherically derived cosmogenic nuclides such as meteoric 10 be offer great potential in quaternary science because they can be used as landform geochronometers and as sediment tracers use of meteoric 10 be inventories for determining landform age soil residence time or erosion rates requires knowing the long term rate of deposition for this cosmogenic nuclide to the earth s surface here we present meteoric 10 be inventories measured at 6 dated sites near the boulder creek critical zone observatory front range colorado each site lies on a relatively stable landform broad moraine or fluvial terrace at slopes between 10 be deposition precipitation dryfall and dust deposition calculated from measured inventories at these sites range from 0 4 to 5 0 10 6 atoms cm 2 yr 1 none of the inventories match expected primary meteoric 10 be deposition rates that global latitude based models or precipitation specific models predict for this region meteoric 10 be inventories and calculated deposition rates at the three older 90 ka sites fall below 0 3 0 7 model predictions inventories and rates at the three pinedale age sites lgm 21 15 ka are higher 1 5 4 than model predictions previous analysis of soils in the front range over the same timeframe as these sites indicate that long term dust accumulation rates are low and associated secondary meteoric 10 be deposition is unlikely to account for the deviation from model predictions at the pinedale age sites in particular long term dustfall would have to be 1 2 orders of magnitude higher to add the meteoric 10 be required to account for measured inventories low inventories at older sites are consistent with loss of meteoric 10 be through physical erosion or selective removal of near surface soil enriched in meteoric 10 be time averaged rates of total meteoric 10 be deposition for these sites are minima we speculate that higher inventories at pinedale age sites reflect the addition of meteoric 10 be due to snowdrifts and or interflow associated with landform location increasing the effective precipitation related primary meteoric 10 be deposition at the sampled sites given these constraints and the spatial variation observed around the front range we suggest that 1 5 0 2 10 6 atoms cm 2 yr 1 is an appropriate long term meteoric 10 be deposition rate to use across much of the front range region that receives 45 55 cm of precipitation a year this long term total meteoric 10 be deposition rate is 30 50 higher than that predicted by global or annual precipitation specific models emphasizing that local calibration of deposition rates is essential for geomorphic studies around the globe

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

application of the authigenic 10be 9be dating method to continental sediments reconstruction of the mio pleistocene sedimentary sequence in the early hominid fossiliferous areas of the northern chad basin the concentrations of atmospheric cosmogenic 10be normalized to the solubilized fraction of its stable isotope 9be have been measured in the authigenic phase leached from silicated continental sediments deposited since the upper miocene in the northern chad basin this method is validated by the systematic congruence with the biochronological estimations based on the fossil mammal evolutive degree of faunal assemblages the fifty five authigenic 10be 9be ages obtained along 12 logs distributed along two west east cross sections that encompass best representative mio pliocene outcrops including paleontological sites show a systematic stratigraphic decrease when considering all studied sedimentary facies extending from the pleistocene up to 8 ma and allow performing geologic correlations otherwise impossible in the studied area the resulting global sequence evidences and temporally specifies the succession of the main paleoenvironments that have developed in this region since the miocene under the special conditions encountered in the northern chad basin this study demonstrates that the authigenic 10be 9be ratio may be used as a dating tool of continental sedimentary deposits from 1 to 8 ma the half life of 10be theoretically allowing dating up to 14 ma it may have fundamental implications on important field research such as paleoclimatology and through the dating of fossiliferous deposits in paleontology and paleoanthropology

the depositional flux of meteoric cosmogenic 10be from modeling and observation abstract meteoric cosmogenic 10be is a powerful tracer to quantify dates and rates of earth surface processes over timescales of 103 105 yrs a prerequisite for its applications is knowledge of the flux at which 10be produced in the atmosphere is delivered to the earth surface four entirely independent approaches are available to quantify this flux 1 general circulation models gcm combined with 10be production functions and aerosol dynamics 2 10be in precipitation collections 3 10be inventories in dated soil profiles 4 riverine 10be exported in solid and dissolved forms we compiled and reprocessed published globally distributed 10be flux data from each of these methods and compared them with each other after normalization to a common atmospheric production rate based on precipitation records we propose a simple framework to discriminate between two delivery effects on 10be fluxes in the additive effect water vapor and 10be are continuously accumulating during long distance transport leading to an increase in 10be flux with precipitation rate in the dilution effect the 10be flux is delivered from proximal vapor sources limited by the rate of 10be introduction from the stratosphere and independent of precipitation rate both effects are mostly present in combination and the relative weight of either effect depends on vapor condensation rate and on the ratio of vapor condensation area to precipitation area a comparison between precipitation derived fluxes and gcm derived fluxes shows that half of the precipitation estimates are 2 times greater than gcm derived fluxes by comparison soil and gcm derived fluxes agree within a factor of 2 for more than half 57 of the dataset and the remaining soil estimates 43 are much lower than gcm derived fluxes 71 of 10be flux estimates from riverine export using 10be meteoric 9be ratios also agree with gcm derived fluxes within a factor of 2 we explain the precipitation derived fluxes that commonly exceed all other estimates by short term stochasticity in precipitation events that might introduce a measurement time interval bias towards higher fluxes this bias is not present over longer term 103 105 yrs flux estimates like those from soil profiles soil derived fluxes might still present an underestimation when retention of 10be in soil is incomplete we recommend producing more 10be depositional flux data from soil inventories with full be retention as these generate in our view the most relevant estimates for applications of meteoric 10be on millennial scale earth surface processes

the dependence of meteoric 10be concentrations on particle size in amazon river bed sediment and the extraction of reactive 10be 9be ratios abstract concentrations of meteoric 10 be extracted from detrital amazon river sediment are strongly particle size dependent such grain size dependency presents a formidable obstacle to routine applications of meteoric cosmogenic 10 be to basin wide erosion studies in this study we explore means to eliminate these grain size effects in bedload from rivers of the amazon basin by measuring 10 be 9 be ratios after selective chemical extraction of reactive authigenic phases these phases mainly comprise fe mn hydr oxides that are the main carriers of 9 be and 10 be we explore the distribution of 10 be and its stable 9 be counterpart between these phases and the partitioning of be into remaining silicate fractions this extraction procedure was carried out on bedload samples comprising the three main tectonic units of the amazon basin namely the andes the guyana and brazilian shields and the central amazonian lowlands for all samples extracted 10 be concentrations show a strong decrease with increasing particle size with up to 20 times more 10 be extracted from the finest analyzed 10 be concentrations mostly to subsequent dilution by quartz in coarse bedload however when normalized to stable 9 be concentrations that are also extracted from reactive phases grain size effects are effectively removed and the resulting reactive 10 be 9 be ratio is uniform for all particle sizes the reactive 10 be 9 be ratio thus offers important advantages over methods employing single meteoric 10 be concentrations such that this ratio can now be developed as quantitative tracer for earth surface processes

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

can observations of postglacial rebound tell whether the rheology of the mantle is linear or nonlinear it has been argued that since a power law mantle may appear to the postglacial rebound process as linear if the rebound stress is less than the ambient tectonic stress therefore observations of rebound cannot be used to determine whether the flow law in the mantle is linear or nonlinear the purpose of this paper is to show that this may not be completely true if the rebound process sees the steady state creep it will be demonstrated that for sites near the centre of rebound the relative sea level rsl observations cannot distinguish a newtonian mantle from a power law mantle with large ambient stress however for sites outside the ice margin the rsl signature for a power law mantle is clearly distinguishable from that due to deep flow in a newtonian mantle this characteristic of power law medium is independent of the ambient stress level and is unlikely to change with more complicated rebound models if these results remain valid in future work then rsl data near the ice margin can be used to argue against a steady state power law mantle

induced stresses and fault potential in eastern canada due to a realistic load a preliminary analysis summary in order to understand the causal relation between postglacial rebound and earthquakes a simple disc load model is used to 1 calculate stresses induced in the lithosphere and mantle by glacial loading melting and postglacial rebound and 2 evaluate the effect of glacial loading rebound on the failure potential for earthquakes in the upper crust the dependence of the failure potential and the actual mode of failure on the coefficient of friction the ambient tectonic stress magnitude direction the stress due to the overlying rocks and lithospheric thickness are investigated prominent features of this paper are the inclusion of 1 a viscoelastic mantle and thus the migration of stress and 2 the ambient tectonic stress and overburden stress contributions in the calculation of the total stress field it is assumed that throughout the earth there are optimally oriented pre existing virtual faults that are initially close to but not at failure thus a time dependent quantity called dfsm related to the coulomb mohr failure criterion can be defined such that a negative value of dfsm would advocate faulting or earthquake activities whereas a positive value of dfsm would promote stability the results indicate that under all combinations of tectonic stress magnitude and overburden stress crustal loading promotes fault stability directly underneath the load upon the removal of the load thrust faulting is predicted within the ice margin if the horizontal stress s induced by the overburden is greater than or equal to the vertical component s of the overburden stress 121 where sjs under this condition theory predicts that faulting or earthquake activity should have reached a maximum immediately after deglaciation if the horizontal stress induced by the overburden is less than the vertical component of the overburden stress 1 l then theory predicts fault stability within the ice margin the theory predicts fault instability both north and south of the ice margin the mode of failure however is completely determined by the value of i the trade off between the tectonic stress magnitude and the overburden stress parameter 1 is also investigated it is shown that a larger tectonic stress magnitude can be used to compensate a smaller value of 1 the results of this analysis show that variations in the coefficient of friction lithospheric thickness and a ductile zone below the upper crust do not significantly affect the above conclusions

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

a benchmark study for glacial isostatic adjustment codes the study of glacial isostatic adjustment gia is gaining an increasingly im portant role within the geophysical community understanding the response of the earth to loading is crucial in various contexts ranging from the the interpretation of modern satellite geodetic measurements e g grace and goce to the projections of future sea level trends in response to climate change modern modeling approaches to gia are based on various techniques that range from purely analytical formulations to fully numerical methods despite various teams independently investigating gia we do not have a suitably large set of explicitly validated numerical results through which they may be validated a community benchmark data set would clearly be valuable following the example of the mantle convection community here we present for the first time the results of a benchmark study of codes designed to model gia the approaches benchmarked are based on significantly different codes and different techniques this effort is performed within the working group 4 wg4 of the esf cost action es0701 improved constraints on models of glacial isostatic adjustment our aims are i testing the codes currently in use by the various teams ii establish a sufficiently large set of agreed results iii correct possible systematic errors embedded in the various physical formulations or computer implementations and iv facilitate the dissemination of numerical tools for surface loading studies to the community and to young scientists the test computations are mainly based on models with spherical symmetry and maxwell rheology and include inputs from various different methods and solution techniques viscoelastic normal modes spectral finite elements and finite elements the tests involve the loading and tidal love numbers and their relaxation spectra the deformation and gravity variations driven by surface loads characterized by simple geometry and time history and the rotational fluctuations in response to glacial unloading in spite of the significant differences in the numerical methods employed the test computations show a satisfactory agreement between the results provided by the participants most of the existing misfits have been addressed during the preparation of the manuscript some others are currently the subject of analysis within the wg4 community

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

stable runoff and weathering fluxes into the oceans over quaternary climate cycles the effect of glacial interglacial cycles on surface weathering rates has been unclear a beryllium based proxy for weathering shows minimal variations in the input of silicate weathering products to the oceans for the past two million years

viscous gravitational relaxation summary this paper is concerned with a detailed examination of the response of maxwell models of the planet to surface mass loads particular attention is devoted to an examination of the factors which determine the isostatic response since the understanding of this response is crucial in a number of different geodynamic problems one particular example which we discuss in detail is concerned with the prediction of free air gravity anomalies produced by large scale deglaciation events using the methods developed here we are able to provide the first direct assessment of the importance of initial isostatic disequilibrium on the observed relative sea level variations and free air gravity anomalies forced by the melting of the laurentide ice sheet we are therefore able to estimate the extent to which such initial disequilibrium might influence the inference of mantle viscosity from isostatic adjustment data our calculations establish that free air gravity data although they are sensitive to the degree of initial disequilibrium provide an extremely high quality constraint upon the viscosity of the lower mantle

on the interaction between small and large scale convection and postglacial rebound flow in a power law mantle abstract some consequences arising from the superposition of flows of two different kinds or scales in a non newtonian mantle are discussed and applied to the cases mantle convection plus postglacial rebound flow as well as small plus large scale mantle convection if the two flow types have similar magnitude the apparent rheology of both flows becomes anisotropic and the apparent viscosity for one flow depends on the geometry of the other if one flow has a magnitude significantly larger than the other the apparent viscosity for the weak flow is linear but develops direction dependent variations about a factorn n being the power exponent of the rheology for the rebound flow lateral variations of the apparent viscosity about at least 3 are predicted and changes in the flow geometry and relaxation time are possible on the other hand rebound flow may weaken the apparent viscosity for convection secondary convection under moving plates may be influenced by the apparent anisotropic rheology other mechanisms leading to viscous anisotropy during shearing may increase this effect a linear stability analysis for the onset of convection with anisotropic linear rheology shows that the critical rayleigh number decreases and the aspect ratio of the movement cells increases for decreasing horizontal shear viscosity normal viscosity held constant applied to the mantle this model weakens the preference of convection rolls along the direction of plate motion under slowly moving plates rolls perpendicular to the plate motion seem to have a slight preference these results could be useful for resolving the question of newtonian versus non newtonian or isotropic versus anisotropic mantle rheology

inferring radial models of mantle viscosity from gravity grace data and an evolutionary algorithm convective flow in the mantle can be thought of and modeled as exclusively driven by density heterogeneities in the mantle itself and the resulting lateral variations in the earth s gravity field with this assumption and a model of mantle rheology a theoretical relationship can be found between 3d mantle structure and flow related quantities that can be measured on the earth s surface like free air gravity anomalies this relationship can be used to set up an inverse problem with 1d mantle viscosity as a solution in the assumption that seismic velocity anomalies be of purely thermal origin and related to density anomalies by a simple scaling factor we invert the large scale length component of the above mentioned measurements jointly with seismic observations waveforms and or travel times to derive an accurate 5 layer spherically symmetric model of upper and lower mantle viscosity we attempt to account for non uniqueness in the inverse problem by exploring the solution space formed of all possible radial profiles of earth viscosity by means of a non deterministic global optimization method the evolutionary algorithm ea for each sampled point of the solution space a forward calculation is conducted to determine a map of gravity anomalies whose similarity to grace gravity recovery and climate experiment is then measured the procedure is iterated to convergence according to ea criteria the robustness of the inversion is tested by means of synthetic tests indicating that our gravity data set is able to constrain less than 6 radial layers each with uniform viscosity independently of the tomographic model or the scaling factor adopted to convert seismic velocity into density structure the ea optimization method finds viscosity profiles characterized by low viscosity in a depth range corresponding to the transition zone and relatively uniform elsewhere

glacio isostatic deformation around the vatnajokull ice cap iceland induced by recent climate warming gps observations and finite element modeling 1 glaciers in iceland began retreating around 1890 and since then the vatnajokull ice cap has lost over 400 km 3 of ice the associated unloading of the crust induces a glacio isostatic respo

coupling of tectonic loading and earthquake fault slips at subduction zones because of the viscoelastic behaviour of the earth accumulation of elastic strain energy by tectonic loading and release of such energy by earthquake fault slips at subduction zones may take place on different spatial scales if the lithospheric plate is acted upon by distant tectonic forces strain accumulation must occur in a broad region however an earthquake releases strain only in a region comparable to the size of the rupture area a two dimensional finite element model of a subduction zone with viscoelastic rheology has been used to investigate the coupling of tectonic loading and earthquake fault slips a fault lock and unlock technique is employed so that the amount of fault slip in an earthquake is not prescribed but determined by the accumulated stress the amount of earthquake fault slip as a fraction of the total relative plate motion depends on the relative sizes of the earthquake rupture area and the region of tectonic strain accumulation as well as the rheology of the rock material the larger the region of strain accumulation is compared to the earthquake rupture the smaller is the earthquake fault slip the reason for the limited earthquake fault slip is that the elastic shear stress in the asthenosphere induced by the earthquake resists the elastic rebound of the overlying plate since rapid permanent plate shortening is not observed at subduction zones there must be either strain release over a large region or strain accumulation over a small region over earthquake cycles the former can be achieved only by significant aseismic fault slip between large subduction earthquakes the most likely mechanism for the latter is the accumulation of elastic strain around isolated locked asperities of the fault which requires significant aseismic fault slip between asperities

earth surface erosion and weathering from the 10be meteoric 9be ratio abstract the isotope ratio of the meteoric cosmogenic nuclide 10 be to the mineral derived stable isotope 9 be discloses both the earth surface denudation rate and its weathering intensity we develop a set of steady state mass balance equations that describes this system from a soil column over the hillslope scale to an entire river basin the prerequisites making this new approach possible are 1 the 9 be concentration of parent rock typically 2 5 0 5 ppm in granitic and clastic sedimentary lithologies is known 2 both be isotopes equilibrate between the fluids decomposing rock and reactive solids formed during weathering and 3 a critical spatial scale is exceeded at which the fluxes of both isotopes into and out of the weathering zone are at steady state over the time scale of weathering typically 10 kyr for these cases the isotope ratios can be determined in bulk sediment or soil on leachates from the reactive adsorbed and pedogenic mineral bound phase in sediment or soil and even on the dissolved phase in river water the 10 be 9 be ratio offers substantial advantages over the single isotope system of meteoric 10 be the latter system allows to directly determine erosion rates only in the case that 10 be is fully retentive in the weathering zone and that riverine sorting has not introduced grain size dependent 10 be concentration gradients in sediments we show the feasibility of the 10 be 9 be tracer approach at the river scale for sediment and water samples in the amazon basin where independent estimates of denudation rates from in situ produced 10 be exist we furthermore calculate meaningful denudation rates from a set of published 10 be 9 be ratios measured in the dissolved load of globally distributed rivers we conclude that this isotope ratio can be used to reconstruct global paleo denudation from sedimentary records

a study of the earth s response to surface loading with application to lake bonneville summary analytical solutions are presented for the deformation of a three layered plane earth with elastic viscoelastic rheology and subject to time dependent vertical surface loads the models investigated are 1 elastic or viscoelastic layers overlying an inviscid fluid 2 viscoelastic half space 3 elastic layer over a viscoelastic layer with different boundary conditions at the base of the second layer emphasis is given to the interdependence between the dominant parameters of thickness of the elastic layer the effective viscosity of the viscoelastic layer the change in viscosity with depth and the wavelength and duration of loading the models have been applied to the loading and unloading of the late pleistocene pluvial lake bonneville using the load histories given by crittenden the studies differ from earlier analyses of the bonneville uplift in several important aspects including a rigorous treatment of the horizontal and vertical coupling between the elastic and viscoelastic media the mantle is treated as viscoelastic rather than as a viscous medium the wavelength information has been introduced by using a more realistic model for the load geometry and the effect of the wasatch fault has been considered the models indicate that the two principal parameters defining the rebound are the effective viscosity of the upper mantle and the effective thickness of the elastic layer and that those two parameters can be separated only if both wavelength and amplitude information of the deformation is available at more than one epoch observations of uplift at one epoch are not sufficient to resolve the thickness of the elastic layer and the effective viscosity of the upper mantle but upper bounds for these quantities are well established as 30km and 1 2 10 poise respectively the uplift results do not confirm or deny the possibility of a low viscosity channel in the upper mantle but this can be resolved only if the uplift data are supplemented with observations of the present uplift rate the published rates are controversial but if valid they point to a thin 15 km elastic layer and a relatively narrow 200km low viscosity channel while the models predict uplift near the centre of the former lake they also predict that the peripheral regions should be subsiding appreciably if flow is confined into a shallow channel of low viscosity observations reported by anderson bucknam suggests such behaviour likewise the present rate of uplift changes sign at some distance from the centre of the lake and detailed observations of warping of the shorelines and repeated levelling in the area may yield further constraints on the rebound model copyright