geochemical effects of magmatic solitary waves ii some analysis summary as a complement to the numerical solutions of watson spiegelman 1994 hereafter known as paper i we present some analytic solutions and proofs to illustrate more generally how a single magmatic solitary wave affects the transport of trace elements in the absence of any diffusion or dispersion the equations for trace element transport can be solved by the method of characteristics this analysis shows that without diffusion a solitary wave can transport chemical signals but cannot permanently change the shape of an initial trace element distribution the solitary waves however can locally steepen trace element gradients by a distortion factor s which depends only on the ratio of initial and local transport velocities these results are quite general and are expected for any solitary wave of permanent form and constant velocity because these waves always provide a frame of reference where the melt and solid velocities are steady state

on the origin of the drumlins of the south german alpine foreland ii the sediments underneath abstract the drumlins of the south german alpine foreland have certain characteristics a distinctly limited occurrence within the formerly glaciated areas a well defined time of formation and a typical rather compact shape the character of the sediments of which they are composed and the relation between drumlin sediments and drumlin form have been a matter of discussion for more than 80 years due to the rareness of good exposures in drumlins a few individual drumlins have become better known during the past decades because they overlie interglacial deposits the observations made at these sites allow the following statements 1 1 the drumlins normally consist of sediments of the last wurm glaciation only in exceptional cases do older pleistocene strata or the pre pleistocene substratum molasse sandstone form part of the drumlin body these exceptions are important in so far as they prove that drumlin formation in principle was an erosional process in the area 2 2 the sediments are mainly till but also a gravel till sequence is not uncommon the rare interglacial beds are mainly lake deposits 3 3 the thickness of the sediments on top of the interglacial deposits varies considerably from some metres to several decametres even underneath a thin cover of younger sediments the fine grained and therefore in principle easily deformable interglacial deposits are glaciotectonically undisturbed altogether these observations allow the conclusion that 1 the process of drumlin formation shaped the glacier bed by highly selective but locally vigorous glacial erosion and 2 this process did obviously not or only poorly affect the sediments below the ice sediment interface even though it was composed of readily deformable material therefore the question is not whether there was erosion or not but why there was not much more erosion and disturbance it is suggested that the answer is likely to be found in the unevenness of the decaying permafrost table at the end of the wurm pleniglacial

converting mantle tomography into mass anomalies to predict the earth s radial viscosity abstract in this study several mantle tomography models are used as input to constrain the amplitude of mass anomalies and viscosity variations with depth in the mantle for this purpose we compute the dynamical state of an incompressible mantle overlaid with rigid plates the best profiles for the viscosity and for the seismic velocity to density conversion factor are obtained through a tarantola valette inversion by matching the predicted and observed geoid and the poloidal and toroidal surface velocities and by minimizing the dynamical topography induced by the lower mantle the recently available second generation of tomography models yields the best results i e 70 of variance reduction for the geoid an unusual trend of with depth is found in the lower mantle we show that the inversion is more dependent on a priori parameters than on the model and that there is a strong trade off between and viscosity structures in this kind of modeling finally we discuss the origin of deep mass anomalies in terms of past subduction

modelling post glacial rebound with lateral viscosity variations summary observations of isostatic adjustment of the earth s surface due to glacial loading provide important constraints on mantle viscosity structure we solve the forward problem of glacial isostatic adjustment in two complementary ways a spectral method for strictly 1 d spherically symmetric earth models and a finite element method that can accommodate 3 d viscosity structure we discuss how each method may be augmented in three ways to accommodate motion of the centre of mass to implement a gravitationally self consistent ocean load via the sea level equation and to include the influence of polar wander with all these effects implemented the two methods are benchmarked against each other we also study the influence of lateral viscosity variations upon measurements of post glacial rebound pgr in two ways first by observing the effect of viscosity perturbations in an idealized model and second by developing a realistic 3 d viscosity model and comparing it with results of related 1 d spherically symmetric models the 3 d viscosity structure is derived starting from seismic tomography models we conclude from both approaches that pgr observations are sensitive to both the local viscosity structure and to the viscosity structure beneath the loaded region even if it is removed from where the observations are made in particular pgr measurements made at hudson bay tend to reflect the local viscosity structure beneath hudson bay pgr measurements made along the east coast of north america being sensitive to both the local east coast viscosity structure as well as the loaded continental viscosity structure are not reproducible with a 1 d viscosity model

lateral variations in mantle rheology implications for convection related surface observables and inferred viscosity models summary over the past decade numerous analyses of convection related observables such as horizontal surface divergence geoid or gravity anomalies and dynamic surface topography have been carried out in the context of tomography based mantle flow models one of the major objectives of this modelling has been the inference of the rheological structure of the mantle with few exceptions these studies have been conducted in the framework of a viscous flow theory which assumes that the mantle rheology may be represented in terms of an effective viscosity which varies with depth only here we present a detailed assessment of the impact of lateral variations in viscosity on global convection related observables using forward modelling of buoyancy induced flow in a 3 d spherical shell we find that the resulting dynamic topography at the surface and the core mantle boundary as well as the gravitational response of the earth are affected relatively little by the inclusion of lateral viscosity variations lvv when compared with results for a purely 1 d radial viscosity model in particular we found that the effect of lvv on the global observables is significantly smaller than the variability due to uncertainties in the current seismic tomography models we also quantify the effect of lvv in the context of the viscosity inverse problem using two synthetic data sets generated with a 1 d viscosity profile and with a fully 3 d viscosity model in which the lvv span across three orders of magnitude we compared the 1 d viscosity profiles recovered from the inversions and found that lvv have virtually no effect on our inversion results the synthetic viscosity inversion further revealed that the effect of lvv is small in comparison to the uncertainties arising from the seismic tomography models the inversions also suggest that the 1 d viscosity profiles derived from actual surface data represent the depth variation of the horizontally averaged logarithm of the 3 d viscosity distribution in the mantle intr o duction constraining the rheological properties of the mantle using surface geophysical data has traditionally involved separate treatments of short seismic intermediate solid earth tides long postglacial rebound and very long mantle convection timescale processes in each case the initial focus historically speaking has been on the inversion of the data to determine a one dimensional 1 d purely radial variation of the relevant rheological parameter e g elastic moduli intrinsic attenuation and viscosity which provides the best fit to the data it has long been recognized particularly in the context of the seismic inverse problem that the search for a 1 d earth model is subject to possible bias due to the presence of lateral variations in structure which may be as significant as the radial variations especially at shallow depths this paper is concerned with the mantle viscosity field the earliest inferences of the radial i e horizontally averaged profile of viscosity based on glacial isostatic adjustment gia data e g mcconnell 1968 parsons 1972 were characterized by a pronounced increase of viscosity with depth in the top half of the mantle however these were followed by two decades of gia research that argued for an essentially isoviscous

role of a low viscosity zone in stabilizing plate tectonics implications for comparative terrestrial planetology 1 earth s near surface layer its lithosphere is broken into quasi rigid plates that form the upper thermal boundary layer for mantle convection since the discovery of plate tectonics it has been widely conjectured but only recently demonstrated that this peculiar style of convection may be facilitated by an upper mantle low viscosity zone lvz over which the plates glide easily the lvz or asthenosphere concept dates from 19th century investigations of isostatic support of mountain belts and is supported by modern evidence for a seismic low velocity zone and by studies of postglacial rebound and dynamic compensation of the earth s gravity field here we show in both two dimensional 2 d cartesian and 3 d spherical earth models that combining a pronounced lvz and a plastic yield stress to allow localized weakening of the cold thermal boundary layer results in a distinctly plate tectonic style of convection with 30 toroidal surface motion for the 3 d case recycling of water into the upper mantle at subduction zones is a plausible cause of earth s lvz whereas venus is dry and lacks both an lvz and plate tectonics

sediment deformation beneath glaciers rheology and geological consequences experiments beneath breidamerkurjokull in iceland have led to development of flow laws for the subglacial till relating strain rate to shear stress and effective pressure and assuming either bingham fluid or nonlinearly viscous fluid behavior water pressures in the till are less than ice pressures and it is suggested that this may lead to infiltration of ice into the sediment which inhibits sliding at the ice sediment interface where water pressures are equal or near to ice pressures infiltration does not occur and sliding may result a one dimensional theory of subglacial deformation is developed in which the empirical flow law is coupled with a model of subglacial hydrology and consolidation this predicts stable states in which subglacial sediment either does not deform or a dilatant deforming horizon forms with positive effective pressures at the ice bed interface or unstable states where zero or negative effective pressures are predicted time dependent analyses show that response times following perturbations of the system may be of the order of 103 years and thus that unsteady behavior may be normal on glaciers flowing over unlithified sediment beds it is suggested that the natural variability of material properties in subglacial sediment beds leads to the development of drumlins on the glacier bed it is suggested that unstable deformation at zero or negative effective stress leads to piping in subglacial sediments at the glacier terminus and the growth of sediment floored subglacial tunnels their frequency is that which is sufficient to draw down subglacial water pressures so as to prevent unstable deformation where they discharge large water volumes subglacial sediments flow laterally toward them producing tunnel valleys this sediment is then removed by water flowing along the axial tunnel tunnel valleys can be regarded as the equivalent in soft sediment areas of eskers in bedrock areas

compaction in a mantle mush with high melt concentrations and the generation of magma chambers abstract most compaction models in the partially molten mantle have addressed the case of low intergranular melt concentrations up to a few percent here we develop a mathematical and numerical formalism adapted to the two dimensional modeling of compaction in mushes with higher melt concentrations up to a few tens of percents experimental data on mantle like mushes olivine crystals basaltic melts suggest that the mush viscosity depends in a complex way on the melt concentration three rheological thresholds occur at melt concentrations of about 5 20 and 40 respectively the first threshold corresponds to the establishment of full interconnectivity of the intergranular melt the second to the formation of a very dense suspension of crystals and the last to the development of crystal clusters in the suspension the present models take into account the stiff and drastic viscosity drops associated with these rheological thresholds intergranular melt migration associated with an initial melt pulse generates a horizon of high melt crystal ratio if the melt concentration in the initial pulse presents a local excess the horizon becomes slightly tilted as a consequence melt percolates upslope inside the tilted horizon pools at its summit and generates a pocket like zone due to the higher melt concentration the upward darcy velocity in the pocket markedly exceeds that in the horizon the result is that the pocket like impregnation is rapidly disconnected from the horizon and a new pocket develops at the summit of the partially fragmented horizon eventually the intergranular melt contained in the horizon is completely redistributed into pockets increasing the background melt concentration in the mush from 5 20 and 40 leads to an increase of the maximum melt concentration of 10 40 and 100 in the transient horizons and of 25 60 and 100 in the pockets these models suggest that magma chambers with a kilometer extent naturally result from the compaction of a mantle mush with an initial melt concentration exceeding 5

effect of lateral viscosity variations in the top 300 km on the geoid and dynamic topography summary we have investigated the impact of lateral viscosity variations lvv in the top 300 km of the mantle on the long wavelength gravitational response of the earth in contrast to the previous studies we demonstrate that the lvv may play a crucial role if a model with imposed plate velocities and partial layering is considered assuming lvv in the top mantle associated with the continental roots and the oceanic asthenosphere we are able to explain a significant portion of the geoid 85 per cent and of the free air gravity data 55 per cent without invoking a complex radial viscosity profile or assuming a lithosphere with an unrealistically low uniform viscosity the best fit to the data is found for models in which mass anomalies located at the boundary between upper and lower mantles reduce the mass flux across the 660 km discontinuity by a factor of 3 these models are characterized by a low average value of viscosity in the asthenosphere below the oceans 10 19 pa s and a large viscosity contrast 100 between the young suboceanic mantle and the deep continental roots the viscosity in the deep upper mantle is found to be around 3 10 20 pa s while a value higher by at least two orders of magnitude is typical for the lower mantle the predicted dynamic surface topography is influenced by the surface plate velocities and its amplitude amounts to a few hundred metres besides investigating the viscosity structures that reflect the different thicknesses of the lithosphere in continental and oceanic regions we have searched for a large scale pattern of lateral viscosity variation in the top 300 km that yields the best fit to the geoid the pattern obtained by this inversion shows a good correlation with the ocean continent distribution and 90 per cent of the geoid and 67 per cent of the free air gravity can be explained

long wavelength geoid the effect of continental roots and lithosphere thickness variations summary the existence of continental roots and the gradual thickening of the cooling oceanic lithosphere give rise to large scale rheological heterogeneities in the uppermost mantle the effect of these heterogeneities on the long wavelength geoid is investigated using a 3 d mantle flow model involving a low viscosity asthenosphere beneath the oceanic lithosphere and the tectonically active continental regions and a thick highly viscous lithosphere beneath ancient continents below 400 km the mantle viscosity is laterally homogeneous with a lower mantle more viscous than the overlying layer the mantle circulation is driven by imposed surface velocities nuvel 1 hs2 gripp gordon 1990 and by the density anomalies inferred from the tomographic models p16b30 and s16b30 masters et al 1996 the geoid heights both due to plate motion and due to internal loading differ by as much as 30 per cent between the models with and without lateral viscosity variations in contrast to what was suggested in previous studies spherical harmonics 2 and 3 are strongly affected by the lateral viscosity variations these differences in the forward problem suggest that the response to the inverse problem that consists of finding the profile of viscosity as a function of depth providing the best fit to the geoid should be considerably affected by the lateral viscosity variations the shear stresses at the base of the plates induced by the imposed surface velocities and those induced by the internal loading are sensitive to the lateral viscosity variations this suggests that the lateral viscosity variations are very important for understanding the stress field or the forces acting on the plates the direction of these shear stresses which should be linked to the anisotropy direction is very different from the plate motion direction

magma migration and magmatic solitary waves in 3 d numerical studies of fluid flow in the mantle sug gest that magma migration is an inherently time dependent process that produces magmatic solitary waves from obstruc tions in melt flux previous work has considered one and two dimensional problems here we present the results of three dimensional calculations that utilize a new efficient multi grid scheme we demonstrate that one and two dimensional solitary waves are unstable and break up into sets of 3 d solitary waves which are perfectly spherical when propagat ing through a uniform porosity medium while these waves are not solirons their non linear interactions are qualitatively similar the solitary waves are highly opportunistic and es tablish efficient pathways for migration by linking up with nearby waves when the initial condition is a random dis tribution of porosity the porosity structure can organize into elongate time dependent channels formed from chains of solitary waves these results are natural consequences of the assumptions that the matrix is permeable and viscously deformable we suggest that solitary waves are likely to exist in the mantle and may contribute to the episodicity of mantle magmatism

effects of lateral viscosity variations on the geoid 1 we investigate the effects of lateral viscosity variations lvvs on mantle circulation model predictions of the global geoid the present study is motivated in part by earlier findings that lvvs due to stiff slabs in the lower mantle have a strong influence on the geoid and that slabs in the lower mantle are perhaps no stronger than the ambient mantle however more recently it has been argued based on global seismic tomography models that lvvs are a minor effect on the geoid in the light of these seemingly contradictory results we re visit the problem of slab strength in the lower mantle we substantiate that the geoid calculated from tomography is hardly affected by the presence of lvvs whereas the geoid computed from global slab models yields a poor fit to the observed geoid when lvvs are considered however this degradation of fit only occurs for very long wavelengths of flow indicating inherent differences between the slab and tomography models we also investigate the effects on the geoid due to weak plate boundaries strong cratonic keels and a low viscosity region in the d layer due to post perovskite in addition to the geoid we attempt to fit plate motions with a circulation model that has prescribed weak zones at plate boundaries motions are matched well and taking into account lvvs the geoid with appropriate surface velocity boundary conditions agrees with the observed geoid as well as for free slip cases

some mineral physics constraints on the rheology and geothermal structure of earth s lower mantle we explore the implications of recent mineral physics measurements of diffusion coefficients and melting temperatures of lower mantle materials on the rheological and geothermal structure of earth s lower mantle we show that mgsio3 perovskite is significantly stronger than mgo periclase and therefore the rheology of the lower mantle depends strongly on the geometry of a weaker phase periclase we calculate viscosities of the lower mantle for two cases 1 where periclase occurs as isolated grains and 2 where periclase occurs as continuous films using mineral physics data and models of two phase rheology we find that the effective viscosity for the former is about 10 1000 times higher than the latter we therefore suggest that the rheology of the lower mantle is structure and hence strain dependent leading to weakening at large strains due to the formation of continuous films of periclase overall depth variation of viscosity depends not only on the pressure dependence of creep but also on the geothermal gradient both mgsio3 perovskite and periclase have relatively small activation energies e g r t m with g 10 14 where r is the gas constant and t m is melting temperature and therefore the depth variation of viscosity is rather small even for a nearly adiabatic temperature gradient however the geothermal gradients consistent with the geodynamical inference of nearly depth independent viscosity are sensitive to the pressure dependence of viscosity which is only poorly understood a superadiabatic gradient of up to 0 6 k km is also consistent with mineral physics and geodynamical observations

simultaneous inversion for mantle shear velocity and topography of transition zone discontinuities summary until now modelling of three dimensional 3 d velocity variations in the mantle and topography of the transition zone discontinuities have been considered separately velocity models were obtained assuming that the radii of the discontinuities are constant then the travel time data sensitive to the topography such as the ss precursors were corrected for the effect of 3 d seismic structure and inverted for depth variations of a discontinuity such a procedure is unsatisfactory as it may introduce artefacts that could significantly affect the topographic results the opposite trade off is less likely to introduce conceptually important changes in the velocity distribution but should also be considered in this study we bring together the same set of s velocity sensitive data as used by gu et al and combine it with a large set of differential travel times of ss s400s s s670s and direct measurements of s400s s670s we formulate the inverse problem in terms of the volumetric 3 d and topographic 2 d perturbations for both the 400 and 670 km discontinuities the best fitting model of the joint inversion significantly improves the variance reduction of ss s400s and ss s670s residuals the velocity distribution in the resulting model topos362d1 is very similar to that in model s362d1 with correlation coefficients 0 9 throughout the mantle which indicates that lateral variations of discontinuity depths have only minor influence on global modelling of velocity important changes however have been made to the topography of the 400 and 670 km discontinuities with respect to those obtained earlier assuming an existing velocity model the overall undulation of the 400 km discontinuity is considerably less than that reported by earlier global studies in topos362d1 its maximum variation does not exceed 12 km the strong degree 1 component before the joint inversion has decreased such that the correlation between the velocities above the discontinuity and the shape of the discontinuity itself has substantially diminished spatially this result means a significant diminution in the strength of the earlier reported depression of the 400 km discontinuity under the pacific the power spectrum of the topography of the 670 km discontinuity has been enriched in long wavelength component especially in degree 2 the range of depth variations is 18 km and its shape correlates well with the radially averaged velocity perturbations in the transition zone at wavelengths greater than 1000 km there is little correlation between the depth perturbations of the 400 and 670 km discontinuities the topography of the 400 km discontinuity does not appear to be strongly influenced by thermal structures potentially associated with subduction processes and plumes this implies that thermal influence on the olivine to phase transformation may not fully account for the observed depth variations dynamical effects and potential variations in composition may be important near the top of the transition zone

a global geoid model with imposed plate velocities and partial layering most inversions of the long wavelength geoid in conjunction with the seismic tomographic information have so far been carried out under the assumption of either purely whole mantle or perfectly layered circulation moreover modeling the lithosphere as a spherical shell with a uniform low viscosity was found to yield the best fit to the observed geoid we have tested whether a good prediction of the geoid can also be achieved by including two constraints a semipermeable behavior of the 660 km discontinuity and surface plate velocities equal to the observed ones the mass transfer between upper and lower mantle has been changed by imposing a surface density anomaly at a depth of 660 km which is proportional to the mass anomaly needed to achieve perfectly layered circulation on the top of the mantle we assume a stiff lithosphere that moves with a velocity corresponding to the observed plate motion the viscosity only varies with depth considering a simple three layer viscosity structure and changing the permeability of the 660 km interface we have obtained a satisfactory variance reduction of the geoid data 75 for degrees 2 12 the best fit to the geoid is obtained if the mass transfer across the 660 km boundary is reduced to one third in comparison with the purely whole mantle model the best fitting viscosity profile is characterized by a clearly defined asthenosphere and a viscosity increase by at least 2 orders of magnitude in the lower mantle the amplitudes of dynamic topography predicted by our model are remarkably small 100 m thus fully compatible with the observation

melt flow in a variable viscosity matrix it is often assumed that the molten regions of planetary interiors can be modeled as a compacting viscous matrix permeated by a less viscous melt phase in order to assess the true behaviour it is important to test as many different aspects of these models as possible in the calculations presented here the matrix viscosity is made to decrease as the proportion of melt increases new results in two dimensions show that if only gravity drives the flow pockets of melt travel upwards as solitary waves and the behaviour is similar to the well known constant viscosity case however when an external shear strain is applied an instability occurs and melt flows into elongated pockets or veins perpendicular to the least compressive stress whilst veins much greater than a compaction length in width are suppressed their minimum width is not clearly constrained the growth rate of veins is directly proportional to the applied strain rate so that their degree of development is proportional to the total strain it is suggested that under mid ocean ridges the total strain may be enough for such veins to be important

a new inference of mantle viscosity based upon joint inversion of convection and glacial isostatic adjustment data we present new profiles of mantle viscosity derived on the basis of non linear occam style joint inversions of an extensive set of data associated with mantle convection and glacial isostatic adjustment gia the convection related observables include satellite derived free air gravity harmonics the geodetically inferred excess ellipticity of the cmb and tectonic plate motions the gia constraints involve two classes of observables previously shown to be relatively insensitive to errors in the late pleistocene ice history the so called fennoscandian relaxation spectrum frs and a set of site specific decay times determined from the postglacial sea level history in hudson bay and sweden the inverted viscosity profiles show a significant three orders of magnitude increase from the upper mantle mean value of f4 10 20 pa s to a high viscosity 10 23 pa s peak at

on mass transport in porosity waves abstract porosity waves arise naturally from the equations describing fluid migration in ductile rocks here we show that higher dimensional porosity waves can transport mass and therefore preserve geochemical signatures at least partially fluid focusing into these high porosity waves leads to recirculation in their center this recirculating fluid is separated from the background flow field by a circular dividing streamline and transported with the phase velocity of the porosity wave unlike models for one dimensional chromatography in geological porous media tracer transport in higher dimensional porosity waves does not produce chromatographic separations between relatively incompatible elements due to the circular flow pattern this may allow melt that originated from the partial melting of fertile heterogeneities or fluid produced during metamorphism to retain distinct geochemical signatures as they rise buoyantly towards the surface

numerical simulation of geodynamic processes with the portable extensible toolkit for scientific computation abstract geodynamics simulations are characterized by rheological nonlinearity localization three dimensional effects and separate but interacting length scales these features represent a challenge for computational science we discuss how a leading software framework for advanced scientific computing the portable extensible toolkit for scientific computation petsc can facilitate the development of geodynamics simulations to illustrate our use of petsc we describe simulations of i steady state non newtonian passive flow and thermal structure beneath a mid ocean ridge ii magmatic solitary waves in the mantle and iii the formation of localized bands of high porosity in a two phase medium being deformed under simple shear we highlight two supplementary features of petsc structured storage of application parameters and self documenting output that are especially useful for geodynamics simulations

adiabatic temperature profile in the mantle abstract the temperature at the 410 km discontinuity is re evaluated by comparing the depth of the discontinuity with the olivine wadsleyite transition pressure obtained using in situ x ray diffraction experiments by katsura et al 2004a and equation of state eos of mgo by tange et al 2009 tange scale and matsui et al 2000 the newly estimated temperature is 1830 48 k 70 k higher than that by our previous estimation the eoses of the major mantle minerals olivine wadsleyite ringwoodite and perovskite are also recalculated using the tange scale the adiabatic temperature gradient is calculated using the thermal expansion coefficient obtained from these eoses the adiabatic temperature gradient gradually decreases with increasing depth without a phase transition and abruptly increases in association with phase transitions the adiabatic temperature gradients are found to be 04 0 5 and 0 3 k km in the upper and lower parts of the mantle respectively the temperatures at a depth of 200 km the bottom of the mantle transition zone the top of the lower mantle and a depth of 2700 km are found to be 1720 40 2010 40 1980 40 and 2730 50 k the mantle potential temperature is found to be 1610 35 k

mantle dynamics and geoid green functions summary we compute green functions relating mantle mass heterogeneities to geoid undulations using both incompressible and radially compressible mantle rheologies our results differ from those previously published by forte peltier 1991 and thoraval machete1 cazenave 1994 this is due to two factors instead of taking gravity as constant throughout the mantle we compute it self consistently with the radial density profile secondly we show that in the mathematical formulation of the compressible case stresses are not continuous through a density jump we then point out that the presence of a surface ocean has no additional effect on the geoid signal associated with internal mantle mass anomalies we apply this formalism to a geodynamic model of mantle density variations and show that an excellent fit to the observed geoid can be obtained

influence of mantle compressibility and ocean warping on dynamical models of the geoid summary the influence of mantle compressibility and warping of the ocean surface on dynamical models of the geoid has been investigated topography and geoid kernels show that compressibility modifies the mantle flow pattern and hence the geoid whereas the deflection of the oceanic surface amplifies the geoid signal without affecting the global flow the combined influence of these two effects is significant and depends on the viscosity profile in the mantle comparisons with incompressible dynamical geoids show that including the effects of compressibility and ocean warping improves the fit to the observed geoid thus these effects must not be neglected in dynamical computations of the geoid

drumlins and catastrophic subglacial floods shaw j kvill d and rains b 1989 drumlins and catastrophic subglacial floods in j menzies and j rose editors subglacial bedforms drumlins rogen moraine and associated subglacial bedforms sediment geol 62 177 202 a number of lines of evidence are shown to be consistent with drumlin formation by catastrophic meltwater floods drumlins are associated with landforms related to such floods and landscapes produced by outburst floods in extragiacial areas contain drumlin like landforms some drumlins which contain mainly residual materials are compared to similar forms covering a wide range of scales and are interpreted to be scour remnant ridges produced by the action of horseshoe vortices on subgiacial materials these vortices are a product of flow separation in turbulent fluids and this interpretation implies drumlin formation by meltwater other drumlin calied cavity fill drumlins have distinctive shapes that are analogous with infilled erosional marks produced by turbulent separated flows these drumlins are interpreted as the infills of cavities eroded upwards into glacier beds by broad subgiacial meltwater sheetflows the sedimentology and internal structure of the cavity fill drumlins indicate rapid deposition from hyperconcentrated flow clast shape surface texture and lithology are consistent with the short distance of giaciofhivial transport predicted by the cavity fill hypothesis estimates of flow discharge 0 6 6 x 107 m3 s total volume of flow 84 1 103 km3 and flow duration 16 162 days are given for the catastrophic flood proposed to have produced the livingstone like saskatchewan drumlin field subgiacially derived floods are used to explain the sudden drainage of extraglacial lakes and major depositional events in proglacial lakes and it is suggested that they might have contributed to the lid of cold freshwater over the north atlantic held to have caused a late glacial cooling event the flood hypothesis requires extensive subgiacial lakes to have occurred beneath the laurentide and fennoscandian ice sheets which if they existed must have influenced the form and behaviour of these major bodies of ice

a glaciofluvial origin for drumlins of the livingstone lake area saskatchewan the livingstone lake drumlin field of northern saskatchewan is on the athabasca plains it is draped over high ground underlain by the precambrian athabasca sandstone the drumlins occur in spindle parabolic and transverse asymmetrical forms a map of individual drumlins shows that features of similar form occur together the drumlins are related on a regional scale to even larger landforms there is also an arrangement of drumlins in streams parallel to the assumed flow direction these patterns illustrate spatial organisation of the drumlin forming flows the livingstone lake drumlins are closely related to tunnel valleys large crescentic scours and eskers exposed bedrock reveals widespread scalloping and sichelwannen an argument is made that drumlins are related to these glaciofluvial forms but were created at different times and by different flows than those forming small scale flutings and other lodgment features sediments within the drumlins are mainly primary water sorted deposits some of wh

magma ascent by porous flow porous flow of buoyant liquid through partially molten rock is regarded as the initial transport process leading to magma segregation in the mantle recent work has identified the importance of matrix deformation and compaction in this process we present finite difference calculations based on a generalized form of darcy s law that includes matrix deformation in two dimensional cartesian and cylindrical coordinates we emphasize the existence of solitary wave solutions called magmons these waves are regions of locally high porosity that ascend through regions of low uniform porosity they differ from diapirs where the liquid and matrix ascend together the one dimensional waves that were previously reported are found to be unstable in two dimensions breaking down to form two dimensional waves of circular cross section both the development of the instability and the form of the two dimensional waves are supported by theoretical analysis numerical experiments in which two dimensional waves collide show that the extent to which they are conserved after collision depends on the lateral offset of the waves the conservation can be very good in other cases larger waves appear to grow at the expense of smaller waves although the quantification of the relevant permeability and rheological parameters remains uncertain geophysically plausible estimates suggest wavelengths of kilometers and velocities of centimeters per year in our preliminary assessment of the relevance of these results to igneous processes we find that magmons are unlikely to be important in regions of broad upwelling such as beneath spreading centers here the transport of liquid adjusts to match the supply by melting and compaction processes are not important if liquid is supplied from below to a stable partially molten region of the asthenosphere it is expected to ascend in magmons this may occur beneath oceanic volcanic centers or in subcontinental mantle it is possible that magma ascent in magmons leads to spatial and temporal episodicity of volcanic activity if higher level processes do not obscure this influence the waveform of a magmon ascends faster than the liquid within the magmon so new liquid is taken in from above while original liquid is lost from below consequently magmons can mobilize small degrees of partial melt and deliver it rapidly to the surface

geoframework coupling multiple models of mantle convection within a computational framework solver coupling can extend the capability of existing modeling software and provide a new venue to address previously intractable problems a software package has been developed to couple geophysical solvers demonstrating a method to accurately and efficiently solve multiscale geophysical problems with reengineered software using a computational framework pyre pyre is a modeling framework capable of handling all aspects of the specification and launching of numerical investigations we restructured and ported citcoms a finite element code for mantle convection into the pyre framework two citcoms solvers are coupled to investigate the interaction of a plume at high resolution with global mantle flow at low resolution a comparison of the coupled models with parameterized models demonstrates the accuracy and efficiency of the coupled models and illustrates the limitations and utility of parameterized models

genesis of boston harbor drumlins massachusetts abstract drumlins in boston harbor are composed of two superposed silty sandy diamicton units and subordinate sand and gravel the lower compact undifferentiated diamicton is interpreted as a pre wisconsin till based on truncated weathering profiles preserved below an erosion surface the upper less compact diamicton contains numerous discontinuous and poorly sorted lenses and stringers of sand and sandy gravel that tend to parallel the erosion surface the upper diamicton and subordinate sandy gravel lenses are interpreted to date from the late wisconsin glaciation along the exposed sections of the long island drumlin complex the preserved weathering profile on the lower diamicton is thicker beneath the drumlin axes and is either thin or missing in the interdrumlin areas this suggests that glacial erosion and streamlining of pre wisconsin deposits and their weathering profile took place after the weathering profile developed and before subsequent deposition of the overlying diamicton unit the latter drapes the erosional drumlin form without contributing substantially to relief of the drumlin form

a simple global model of plate dynamics and mantle convection cooling and thickening of lithospheric plates with age and subduction result in large scale horizontal density contrasts tending to drive plate motions and mantle flow we quantify the driving forces associated with these density contrasts to determine if they can drive the observed plate motions first two dimensional models are computed to evaluate the effects of assumed rheologies and boundary conditions we are unable to obtain platelike behavior in viscous models with traction free boundary conditions the piecewise uniform velocities distinctive of plate motion can be imposed as boundary conditions and the dynamic consistency of the models evaluated by determining if the net force on each vanishes if the lithosphere has a newtonian viscous rheology the net force on any plate is a strong function of the effective grid spacing used leading to ambiguities in interpretation incorporating a rigid plastic lithosphere which fails at a critical yield stress into the otherwise viscous model removes these ambiguities the model is extended to the actual three dimensional spherical plate geometry the observed velocities of rigid plastic plates are matched to the solution of the viscous stokes equation at the lithosphere asthenosphere boundary body forces from the seismically observed slabs from the thickening of the lithosphere obtained from the actual lithospheric ages and from the differences in structure between continents and oceans are included interior density contrasts such as those resulting from upwellings from a hot bottom boundary layer are assumed to occur on a scale small compared to plate dimensions and are not included the driving forces from the density contrasts within the plates are calculated and compared to resisting forces resulting from viscous drag computed from the three dimensional global return flow and resistance to deformation at converging boundaries the rms residual torque is 30 of the driving torque the density contrasts within the plates themselves can reasonably account for plate motions body forces from convection in the interior may provide only a small net force on the plates at converging boundaries the lithosphere has a yield stress of 100 bars drag at the base of the plates is 5 bars and resists plate motion the net driving forces from subducting slabs and collisional resistance are localized and approximately balance driving forces from lithospheric thickening are distributed over the areas of the plates as is viscous drag the approximate balance of these two forces predicts plate velocities uncorrelated with plate area as observed the model represents a specific case of boundary layer convection the dynamical results are consistent with either upper mantle or mantle wide convection

solitary waves in magma dynamics we investigate the stability of the one dimensional solitary waves solutions of the equations proposed by mckenzie to model the ascent of melts in the earth interior we show that for small porosity and two dimensional horizontal disturbances with long wavelength these solitary waves are unstable we also exhibit two and three dimensional solitary wave solutions of the mckenzie equations

de compaction of porous viscoelastoplastic media solitary porosity waves buoyancy driven flow in deformable porous media is important for understanding sedimentary compaction as well as magmatic and metamorphic differentiation processes here mathematical analysis of the viscoplastic compaction equations is used to develop an understanding of the porosity wave instability and its sensitivity to the choice of rheological model the conditions of propagation size speed and shape of the porosity waves depend strongly on the properties of the solid rock frame whereas most of the previous studies on porosity waves were focused on viscous or viscoelastic mode here we consider the ability of a solid matrix to undergo simultaneous plastic rate independent and viscous rate dependent deformation in parallel plastic yielding is identified as a cause of compaction decompaction asymmetry in porous media this is known to lead to a strong focusing of porous flow speed and amplitude of a porosity wave are given as functions of material parameters and a volume of a source region formulation is applicable to fluid flow in sedimentary rocks where viscous deformation is due to pressure solution as well as in deep crustal or upper mantle rocks deforming in a semibrittle regime

melt segregation and matrix compaction the mush continuity equation compaction segregation time implications summary two phase aggregates a special case of which is partially molten systems are commonly modelled as an interpenetrating flow of two viscous liquids and are therefore described in terms of the fluid mechanics the governing equation set of fluid mechanics describing a two phase aggregate is incomplete as it consists of nine equations momentum and mass conservation equations for each phase and an energy conservation equation in ten unknowns six velocity components two pressures temperature and melt fraction in this paper the general equation closing the governing equation set is derived it explicitly expresses the condition of the coupling between the liquid percolation and porosity volume change due to which the medium continuity is maintained therefore the equation may be referred to as the mush continuity equation the character of the closed set solutions is demonstrated using 1 d isothermal models by examples of melt segregation inside a bounded low melting degree zone and sediment compaction at the bottom of a reservoir the compaction segregation style and time are controlled by the compaction segregation parameter c l c 2 and compaction segregation length depending on the mushy layer thickness l matrix permeability k characteristic porosity 0 and matrix and fluid viscosities at low c which approximately corresponds to low viscosity liquids kimberlites carbonatites the compaction segregation time scales as l 1 which effectively constrains the molten region thickness at the moment of the segregation and appears to explain the small volume and clustering of low viscosity magma eruptions characteristic of kimberlites at high c the porosity evolves through a formation of a series of isolated waves which could provide an explanation for the rhythmicity observed in large layered plutons

geodynamic evidence for a chemically depleted continental tectosphere the tectosphere namely the portions of earth s mantle lying below cratons has a thermochemical structure that differs from average suboceanic mantle the tectosphere is thought to be depleted in its basaltic components and to have an intrinsic buoyancy that balances the mass increase associated with its colder temperature relative to suboceanic mantle inversions of a large set of geodynamic data related to mantle convection using tomography based mantle flow models indicate that the tectosphere is chemically depleted and relatively cold to 250 kilometers depth below earth s surface the approximate equilibrium between thermal and chemical buoyancy contributes to cratonic stability over geological time

plate tectonics and aspherical earth structure the importance of poloidal toroidal coupling we derive poloidal flow internal loading green functions for incompressible fluid models of the mantle consisting either of a single constant viscosity spherical shell or of two adjacent spherical shells having different viscosities from the green function we obtain kernels connecting the surface divergence the geoid and the surface topography fields to the lateral density heterogeneity inferred on the basis of the application of seismic tomographic imaging techniques and with these kernels we argue that both the surface divergence and geoid fields consisting of harmonic degrees 2 5 may be reasonably fit with only a factor of 8 viscosity increase at a depth of 1200 km we point out however that the coupling from poloidal to toroidal flow which is required to understand surface velocity spectra may allow these observations to be understood in terms of a viscosity increase at depth which is smaller than required by nonhydrostatic geoid data in the context of pure poloidal models using the observed kinetic energy in the surface plate motions as a constraint allows us to infer a value for the steady state upper mantle viscosity of 2 0 0 5 1021 pa s we comment on the implication of the difference between this number and the somewhat lower value 1 1021 pa s which has been derived on the basis of analyses of signatures of the glacial isostatic adjustment process

revising the spectral method as applied to modeling mantle dynamics 1 the observed geoid dynamic topography and surface plate velocities are controlled by various factors such as density and viscosity variations in the earth s mantle and strength of the lithosphere previous studies have shown that the geoid signal cannot be resolved in details within the framework of a simplified model of the mantle flow considering only radial viscosity variations thus a modeling technique handling both radial and lateral variations of viscosity and other parameters should be used the spectral method provides a high accuracy semianalytical solution of the navier stokes and poisson equations when viscosity is only depth radially dependent in this study we present the numerical approach built up on the substantially revised method originally proposed by zhang and christensen 1993 for solving the navier stokes equation in the spectral domain with lateral variations of viscosity lvv this approach incorporates a number of numerical algorithms providing efficient calculations of the instantaneous stokes flow in the sphere and taking into account the effects of lvv self gravitation and compressibility in contrast to the traditionally used propagator method our approach suggests a continuous integration over depth without introducing internal interfaces various numerical tests have been employed to test accuracy and efficiency of the proposed technique benchmarking of the code shows its ability to solve the mantle convection problems implying strong lvv with high resolution

effects of plate and slab viscosities on the geoid abstract the effects of plate rheology strong plate interiors and weak plate margins and stiff subducted lithosphere slabs on the geoid and plate motions considered jointly are examined with three dimensional spherical models of mantle flow buoyancy forces are based on the internal distribution of subducted lithosphere estimated from the last 160 ma of subduction history while the ratio of the lower mantle upper mantle viscosity has a strong effect on the long wavelength geoid as has been shown before we find that plate rheology is also significant and that its inclusion yields a better geoid model while simultaneously reproducing basic features of observed plate motion slab viscosity can strongly affect the geoid depending on whether a slab is coupled to the surface in particular deep high viscosity slabs beneath the northern pacific that are disconnected from the surface as a result of subduction history produce significant long wavelength geoid highs that differ from the observation this suggests that slabs in the lower mantle may be not as stiff as predicted from a simple thermally activated rheology if the slab model is accurate

geoid anomalies in a dynamic earth in order to obtain a dynamically consistent relationship between the geoid and the earth s response to internal buoyancy forces we have calculated potential and surface deformation love numbers for internal loading these quantities depend on the depth and harmonic degree of loading they can be integrated as green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts spherically symmetric self gravitating flow models are constructed for a variety of radial newtonian viscosity variations and flow configurations including both whole mantle and layered convection we demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound much less than the time scale for significant change in the convective flow pattern by calculating relaxation times for a series of spherically symmetric viscous earth models for uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads resulting in net negative geoid anomalies for positive density contrasts geoid anomalies from intermediate wavelength density contrasts are amplified by up to an order of magnitude geoid anomalies are primarily the result of density contrasts in the interior of convecting layers density contrasts near layer boundaries are almost completely compensated layered mantle convection results in smaller geoid anomalies than mantle wide flow for a given density contrast viscosity stratification leads to more complicated spectral signatures because of the sensitivity of the dynamic response functions to model parameters forward models for the geoid can be used to combine several sources of geophysical data e g subducted slab locations seismic velocity anomalies surface topography to constrain better the structure and viscosity of the mantle

pleistocene stratigraphy of the boston harbor drumlins massachusetts abstract evidence from the boston harbor drumlins indicates that two superposed tills were deposited during glacier advances which were separated by a long nonglacial interval at long and peddocks islands argillans and truncated clay filled fractures along with discontinuities in clay mineral composition define the till contacts physical indicators separating the tills are not apparent at other exposures where till boundaries were defined solely by discontinuities in clay mineral composition the weathering profile in the upper part of the lower till indicates extensive weathering under a climate similar to that of today and probably similar to that of the sangamon interglaciation the depth of the weathering profile the sequence of clay mineral alteration products and the presence of pedogenic features in the upper part of the lower till are comparable to sangamonian weathering profiles in the midwestern united states implying that the lower till is illinoian or older