a geodynamic model of mantle density heterogeneity using cenozoic and mesozoic plate motion reconstructions we derive a model of present day mantle density heterogeneity under the assumption that subducted slabs sink vertically into the mantle the thermal buoyancy of these slabs is estimated from the observed thermal subsidence cooling of oceanic lithosphere slab velocities in the upper mantle are computed from the local convergence rate we assume that slabs cross the upper lower mantle interface and continue sinking into the lower mantle with a reduced velocity for a velocity reduction factor between 2 and 5 our slab heterogeneity model is as correlated with current tomographic models as these models are correlated with each other we have also computed a synthetic geoid from our density model for a viscosity increase of about a factor of 40 from the upper to lower mantle our model predicts the first 8 spherical harmonic degrees of the geoid with statistical confidence larger than 95 and explains 84 of the observed geoid assuming that the model c21 and s21 terms are absent due to a long relaxation time for earth s rotational bulge otherwise 73 of the geoid variance is explained the viscosity increase is consistent with our velocity reduction factor for slabs entering the lower mantle since downwelling velocities are expected to scale roughly as the logarithm of viscosity loge 40 3 7 these results show that the history of plate tectonics can explain the main features of the present day structure of the mantle the dynamic topography induced by this heterogeneity structure consists mainly of about 1 km amplitude lows concentrated along the active continental margins of the pacific basin our model can also be used to predict the time variation of mantle heterogeneity and the gravity field we find that the age of the geoid defined as the time in the past before which the geoid becomes uncorrelated with the present geoid is about 50 m y our model for the history of the degree 2 geoid which is equivalent to the history of the inertia tensor should give us a tool to study the variations in earth s rotation pole indicated in paleomagiietic studies

joint inversions of seismic and geodynamic data for models of three dimensional mantle heterogeneity the seismic models of three dimensional 3 d mantle heterogeneity may be interpreted in terms of the density perturbations which drive mantle flow and thus provide important predictions of flow related observables such as the nonhydrostatic geoid the current models of global scale shear velocity heterogeneity provide reasonably good fits to the long wavelength nonhydrostatic geoid data 60 70 variance reductions but rather poor fits to the corresponding free air gravity anomalies 30 40 variance reductions this major difference is due to two factors 1 the very different amplitude spectrum of the gravity anomalies which is nearly flat for degrees l 3 the largest mismatch between the pattern of predicted and observed gravity anomalies is in the southern hemisphere this observation suggests that one reason for the poor overall match between the two fields may be that the global seismic data are not resolving sufficiently well the heterogeneity in the southern hemisphere portion of the deep mantle in contrast the gravity data provide accurate and geographically uniform constraints on the vertically integrated heterogeneity in the mantle we therefore perform a series of experiments in which we simultaneously invert a large set of seismic data which includes long period waveforms ss s and scs s differential travel times and normal mode structure coefficients and the long wavelength gravity anomaly data we thus determine whether it is possible to derive new 3 d heterogeneity models which satisfy both data sets the gravity anomaly data are interpreted in the context of spherically symmetric viscous flow models of the mantle in these inversion experiments we test several radial viscosity and ln ln profiles and thereby assess their plausibility the joint seismic geodynamic inversions reveal that it is indeed possible to greatly improve the fit to the free air gravity anomalies with variance reductions of 80 90 readily accessible while preserving the fit to the seismic data this improvement is achieved with some adjustment to the heterogeneity in the depth range 1500 2500 km where the seismic data constraints appear to be weakest the joint inversions also reveal new structures in the southern hemisphere portion of the lower mantle which apparently are not resolved by the seismic data alone

geoid effects of lateral viscosity variation near the top of the mantle a 2d model abstract whereas the oceanic lithosphere is underlain by a low viscosity layer the asthenosphere it appears unlikely that this layer is well developed beneath continental cratons this difference could represent a lateral viscosity variation of two to three orders of magnitude near the top of the mantle previous mantle flow geoid models have typically neglected this variation to investigate the impact of such a lateral strength variation on mantle flow and the resulting geoid we solve for density driven flow in a 2d box of uniform viscosity fluid a dichotomous lateral viscosity variation near the top of the mantle is modeled by having a no slip boundary condition over a section of the top of the box while allowing the remainder of the top to be free slip for varying fractions of no slip on the upper boundary and various values of the wavenumber depth and phase of the driving density anomaly model geoids are found in contrast to viscous flow with only a depth dependent viscosity mode coupling in the geoid is observed this occurs principally at a wavelength equal to the lengthscale of the lateral viscosity structure with amplitudes as large as 20 40 in some cases thus coupling can produce a significant signal in the geoid at a wavelength longer than that of the driving load this result suggests that the accuracy of models of the geoid that assume a solely radial viscosity structure may be limited to the 60 80 level found in recent studies 1 2 we speculate that some of the earth s low order geoid is due to flow coupling resulting from the degree two to five components of lateral ocean continent structure

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

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

inferring the viscosity and the 3 d density structure of the mantle from geoid topography and plate velocities summary in a dynamic earth mantle mass heterogeneities induce gravity anomalies surface velocities and surface topography these lateral density heterogeneities can be estimated on the basis of seismic tomographic models recent papers have described a realistic circulation model that takes into account the observed plate geometry and is able to predict the rotation vectors of the present plates the relationship between the surface observables and the heterogeneities is sensitive to the viscosity stratification of the mantle here we use this model combined with a generalized least squares method in order to infer the viscosity profile of the earth from the surface observations and to get some new insight into the 3 d density structure of the mantle the computed radial viscosity profile presents a continuous increase of more than two orders of magnitude the asthenosphere has a viscosity close to 2 x lo2 pa s no sharp discontinuity is requested at the upper lower mantle interface the largest viscosity 7 x 10 pas is reached in the middle of the lower mantle at greater depth approaching the core mantle boundary the viscosity decreases by one order of magnitude the model suggests that the well known degree 2 and order 2 anomaly in the transition zone of the upper mantle is merely the signature of the slabs it also slightly increases the degree 2 and order 0 in the lower mantle and decreases it in the upper mantle in other words the inversion requests a hotter lower mantle beneath the equator and a colder upper mantle at the same latitudes

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

large scale mantle convection and the history of subduction a large scale pattern of mantle convention is evident in the shape of the earth s gravity field1 lateral variations in seismic velocity2 3 the distribution of hotspots4 and long wavelength bathv metric anomalies5 paradoxically these signals of mantle convection bear little resemblance to present day plate motions1 4 although they seem to be related to past subduction zone configurations6 here we quantify this relationship by correlating a time integrated history of subduction calculated in the hotspot reference frame for the past 180 myr with regions of the deep mantle inferred from other geophysical observations to be colder than average our results support suggestions6 9 that a direct relationship exists between large scale thermal heterogeneity in the lower mantle and subduction during the cenozoic and mesozoic

the geoid constraint in global geodynamics viscosity structure mantle heterogeneity models and boundary conditions summary the earth s non hydrostatic gravity field or geoid provides a first order constraint on mantle density structure and dynamics geodynamic models for the geoid have proliferated since the advent of seismic mapping of mantle heterogeneity structure tomography because the geoid offers perhaps the best measured independent constraint on mantle density heterogeneity however dynamic geoid models involve a number of questionable physical assumptions and uncertainties whose effects need to be evaluated before geodynamic inferences based upon the geoid can be considered sound troubling issues include the appropriate surface boundary conditions free slip no slip plates and parametrization of radial viscosity variations how many layers can be resolved in addition to lateral viscosity variations possible chemical layering of the mantle phase transitions etc there are also uncertainties in the density heterogeneity models used as input to dynamic geoid models most of which are derived from seismic tomography and require weakly constrained empirical conversion factors to go from seismic velocity variations to density variations here we address several of the most straightforward problems inherent in geoid modelling namely the issues of viscosity structure resolution uncertainties in appropriate boundary conditions and differences among mantle heterogeneity models a robust feature of all models is a lower mantle viscosity at least a factor of 30 greater than that of the upper mantle but there is little resolution with regard to finer details such as lithospheric or uppermost mantle low viscosity zone viscosity ironically free slip boundary conditions result in the best fits to the geoid in all cases but all boundary conditions exhibit predictable trade offs with the uppermost mantle viscosity models with a single viscosity layer representing the lower mantle yield similar dynamic topography estimates of the order of 700 1000 m in amplitude regardless of the finer details of upper mantle viscosity structure boundary conditions or input heterogeneity models comparing mantle heterogeneity models based on two independent seismological determinations harvard and berkeley models and on the history of subduction we find that these models are virtually indistinguishable regarding inferences of mantle viscosity structure and amplitude of dynamic topography and in terms of the effects of different boundary conditions uncertainties concerning which type of boundary condition is appropriate are much more important than which mantle heterogeneity model is chosen given other uncertainties in modelling the geoid particularly the strong effects due to lateral viscosity variations for intermediate 10 000 km wavelengths we conclude that the class of dynamic geoid models explored so far cannot reliably elucidate the details of upper mantle viscosity structure

an inversion for radial viscosity structure using seismic tomography using a uniform velocity density scaling we have inverted the seismically inferred 3 dimensional structure of the whole manfie for the radial viscosity structure which best fits the geoid we are able to obtain 60 72 variance reductions for three different s wave tomographic models the resulting viscosity structures are remarkably similar showing a high viscosity lid a low viscosity zone in the transition region and a high viscosity lower manfie a resolution analysis indcates that the viscosity structure in the upper manfie is well resolved by the data however the resolution in the lower manfie is poorer our models axe in general agreement with previous studies except that our inversions prefer a low viscosity layer at 400 670 km as opposed to 100 400 kin

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

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

kinetics of weathering and diagenesis weathering and diagenesis are discussed from a kinetic standpoint such a discussion depends upon an intimate interplay between field measurements laboratory experiments and mathematical theory because of the accessibility of soils and sediments models based on laboratory measurements and theoretical calculations can be used along with field data to calculate rate parameters which are otherwise difficult to measure in the laboratory also theoretical models can be tested in the field ways in which chemical kinetics can be applied to geological problems in the surficial environment are discussed and the author recomends extensive future study of such problems jmt

physico chemical mechanisms of weathering processes and corresponding models of dynamics of mineral zonality evolution abstract the peculiarities of weathering processes involving duration slow change of ambient conditions isothermality as well as proceeding in open systems permit to study these processes in a steady state approach d c i d t 0 where ci is concentration of intermediates and t is time the most typical quasi stationary processes for a water rock system are 1 non equilibrium step surface reaction of primary mineral dissolution and 2 non equilibrium step secondary mineral precipitation these respectively determine two extreme mechanisms of mineral formation 1 pseudomorphous replacement and 2 dissolution transfer crystallization besides non stationary weathering processes are known it is the case when a process is controlled by diffusion through a layer of secondary minerals which have been deposited on the surface of the primary mineral a mathematical model of weathering dynamics of feldspar with its metasomatic replacement by clay minerals is presented numerical simulation led to the prediction of mineral zonality development along the weathering profile at any time

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

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

mantle heterogeneities geoid and plate motion a monte carlo inversion seismic tomography in both the upper and the lower mantle as well as subducting oceanic slabs defined by seismicity has been translated into density heterogeneities to generate models of mantle circulation these models can predict both the surface velocities and the geoid which can be compared with plate tectonics and gravity data a given model is specified by 6 parameters related to the viscosities of 3 mantle layers and the absolute amplitudes of density variations in the upper and lower mantle as well as in the slabs the values of these parameters are chosen at random within an acceptable range each model is submitted to an appropriate test comparing observations with predictions the results of the most successful models selected by this monte carlo inversion are displayed they yield preferred mantle viscosity structures exhibiting large variations at depth with a physical interface between upper and lower mantle i e with the possibility for the circulation to penetrate the 650 km discontinuity two classes of viscosity profiles stand out the first one implies a regular increase of the viscosity in the sublithospheric mantle with reasonable values for the density parameters the second one is unexpected in the sense that it predicts a very stiff bottom for the upper mantle it also requires vanishingly small amplitudes for the upper mantle density heterogeneities defined by tomography which would thus have to be of lithological rather than thermal origin with a chemical interface at 650 km the outcome is very similar the same two classes of viscosity structures do yield a satisfactory geoid prediction however only the class of models with a stiff layer at midmantle depths predicts acceptable surface velocities altogether the best models out of some 60 000 which have been tested only explain one third of the geoid and two thirds of the surface divergence for spherical harmonic degrees 1 to 6 nevertheless the main features of these two observed patterns are present in the computed maps and 4 out of 6 correlation coefficients lie close to the 90 confidence level this is true for the geoid as well as for the surface divergence of the displacement velocity however as the internal viscosity structure has been assumed to have spherical symmetry the rotational component of the surface velocities cannot be predicted

cenozoic plate driving forces past studies of plate driving forces have concluded that the forces due to subducted slabs in the upper mantle and those due to the thickening of the oceanic lithosphere are the principal driving forces we reexamine the balance of driving forces for the present day and extend our analysis through the cenozoic using an analytical torque balance method which accounts for interactions between plates via viscous coupling to the induced mantle flow we use an evolving mantle density heterogeneity field based on the last 200 myr of subduction to drive plate motions an approach which has proven successful in predicting the present day mantle heterogeneity field we find that for plausible upper mantle viscosities the forces due to subducted slabs in the cenozoic and mesozoic account for in excess of 90 of plate driving forces and those due to lithospheric thickening for less than 10

understanding the effects of mantle compressibility on geoid kernels summary we develop a quasi analytical solution to compute geoid kernels for a compressible mantle with newtonian rheology by separating the stresses induced by self gravitation from the stresses resulting from viscous flow we simplify the equations and gain some insight for realistic variations in the background density field po r the solution obtained using propagator matrices converges rapidly compressibility enters into the flow problem directly through the continuity equation and indirectly by influencing parameters such as gravitational acceleration g r and density contrasts across compositional boundaries in order to understand all these effects we introduce them sequentially starting with an incompressible earth model and ending up with a realistic compressible model that includes a compressible inner and outer core phase changes in the transition zone and an ocean the largest effects on geoid kernels are from different assumptions for g r possible effects of transformational superplasticity and differences in assumptions for density contrasts at the surface and at the core mantle boundary are next in importance the effects of compressibility on the flow itself are somewhat smaller followed by the effect of compressibility of the outer core a gravitationally consistent treatment of the ocean layer yields geoid kernels that are very similar to those for a dry planet the compressibility of the inner core has a negligible impact on the geoid kernels the largest effects from compressibility are comparable to the effects of a moderate 40 per cent change in the viscosity contrast between the upper and lower mantle

parallel psm fdm hybrid simulation of ground motions from the 1999 chi chi taiwan earthquake a new technique for the parallel computing of 3 d seismic wave propagation simulation is developed by hybridizing the fourier pseudospectral method psm and the finite difference method fdm this psm fdm hybrid offers a good speed up rate using a large number of processors to show the feasibility of the hybrid a numerical 3 d simulation of strong ground motion was conducted for the 1999 chi chi taiwan earthquake mw 7 6 comparisons between the simulation results and observed waveforms from a dense strong ground motion network in taiwan clearly demonstrate that the variation of the subsurface structure and the complex fault slip distribution greatly affect the damage during the chi chi earthquake the directivity effect of the fault rupture produced large s wave pulses along the direction of the rupture propagation slips in the shallow part of the fault generate significant surface waves in coastal plain along the western coast a large velocity gradient in the upper crust can propagate seismic waves to longer distances with minimum attenuation the s waves and surface waves were finally amplified further by the site effect of low velocity sediments in basins and caused the significant disasters

cosmogenic 3he in igneous and fossil tooth enamel fluorapatite igneous fluorapatite samples from a suite of six granitic rocks from the transantarctic mountains have high 3he concentrations to 5 10 9 atoms g 1 and high 3he 4he ratios to 9 10 7 these values are far higher than those found in several hundred igneous apatites from elsewhere around the world and are higher than can be attributed to nuclear reactions on 6li this 3he is almost certainly derived from cosmic ray reactions in rocks with high exposure ages at high latitude and elevation several samples of fossil tooth enamel fluorapatite from the turkana basin of kenya are similarly rich in 3he with up to 1 10 7 atoms 3he g 1 and 3he 4he ratios up to 4 10 6 again this 3he is most logically attributed to cosmic ray reactions provided that cosmogenic 3he like radiogenic 4he is quantitatively retained in fluorapatite under earth surface conditions routine 3he exposure dating of this common phase may be possible based on its chemical composition the 3he production rate in fluorapatite is about 100 atoms g 1 yr 1 at sea level and high latitude using this rate the apatites from the transantarctic mountains have apparent exposure ages of 0 5 6 2 myr in agreement with values elsewhere in the range the fossil tooth enamel samples have apparent exposure ages ranging from a few up to 130 kyr such high exposure ages suggest some of these fossils may be lag deposits with a very long residence time at or near the earth s surface 3he exposure ages can provide insights to the depositional and reworking history of enamel bearing fossils at present the major limitations to 3he exposure dating of fluorapatite are purification of sufficient amounts of material and measurement of small amounts of 3he in the presence of large quantities of 4he in addition further work is necessary to establish the nucleogenic 3he background in fluorapatite

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

cosmogenic and nucleogenic 3he in apatite titanite and zircon cosmogenic 3he was measured in apatite titanite and zircon and cosmogenic 21 ne in quartz at 13 depth intervals in a 2 7 m long drill core in a miocene ignimbrite from the altiplano of bolivia all three 3he depth profiles as well as the 21 ne profile attenuate exponentially with depth indicating that both of these isotopes are cosmogenic in origin with no significant contribution from other sources the attenuation lengthscale for 3he production of 180 11 g cm 2 is consistent with expectations for neutron spallation and is identical to that found for the cosmogenic 21 ne in quartz by normalizing the measured 3he concentrations to 21 ne and using the independently known cosmogenic 21 ne production rate the apparent cosmogenic 3he production rates in apatite titanite and zircon were respectively found to be 112 97 and 87 atoms g yr at sea level and high latitude the formal uncertainty on these estimates is 20 2 and arises in equal parts from uncertainties in the measured 3he 21 ne ratios and the uncertainty in the 21 ne production rate however an additional factor affecting the apparent 3he production rate in these phases arises from the long stopping range of spalled 3he and tritium which decays to 3he because all three accessory phases have higher mean atomic number than major rock forming minerals they will have lower 3he production rates than their surroundings as a consequence the long stopping ranges will cause a net implantation of 3he and therefore higher apparent production rates than would apply for purely in situ production thus these apparent production rates apply only to the specific grain sizes analyzed analysis of sieved zircon aliquots suggests that a factor of 2 increase in grain size from 50 to 100 m cross section yields a 10 decrease in apparent production rate while this effect warrants further study the grain sizes analyzed here are typical of the accessory phases commonly encountered so the apparent rates provide an appropriate starting place for surface exposure dating using 3he in these minerals

continent ocean chemical heterogeneity in the mantle based on seismic tomography seismic models of global scale lateral heterogeneity in the mantle show systematic differences below continents and oceans that are too large to be purely thermal in origin an inversion of the geoid based on a seismic model that includes viscous flow in the mantle indicates that the differences beneath continents and oceans can be accounted for by differences in composition in the upper mantle superposed on mantle wide thermal heterogeneities the net continent ocean density differences integrated over depth are small and cause only a low flux of mass and heat across the asthenosphere and mantle transition zone

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

locally layered convection inferred from dynamic models of the earth s mantle the structure of convection in the mantle is still the subject of considerable debate the now standard modelling of the convective flow as driven in a viscous mantle by density anomalies derived from seismic tomography has successfully explained the longest wavelength degree 2 to 8 geoid anomalies and provided important information concerning the viscosity structure of the mantle1 8 with this approach however the predicted response of surface topography to convective stresses the dynamic topography has a typical magnitude of several kilometres which does not conform with observations9 11 a possible source of this discrepancy lies in the severe underestimation by tomography of density anomalies due to deflections of the boundary between the upper and lower mantle at 660 km depth here we model the mantle flow implied by seismically derived density heterogeneities using an empirical method to account for the 660 km boundary topography the predicted dynamic surface topography thus obtained is significantly reduced to values that conform with the observations in addition the 660 km boundary topography appears to have a strong influence on the computed mantle circulation inducing local layering of the convective flow