validating earth and ocean tide models using tidal gravity measurements summary o1 and m2 observations from well calibrated spring gravimeters and superconducting gravimeters from the global geodynamics project ggp are used to test models of the earth s body tide and 10 ocean tide models it is shown that some of the ocean tide models give anomalous results in various parts of the world for example the schwiderski ocean tide model gives discrepancies in several areas and the fes series of ocean tide models have problems in the western pacific china japan and australia the majority of the high quality tidal gravity measurements in europe are in close agreement with the dehant defraigne and wahr ddw elastic and inelastic body tide models the gravimetric factors for the ddw elastic and inelastic models only differ by 0 12 per cent and the present calibration accuracy does not allow us to distinguish between these models but does reduce the previous upper bound on inelastic gravimetric factors the european observations give a phase lag of a few hundredths of a degree for the o1 body gravity tide which is consistent with the mathews inelastic body tide model at some european and worldwide stations the gravimetric factors differ by up to 0 3 per cent from the ddw model and it is suggested that further checks on the gravimeter calibrations are required accurate determinations of instrumental phase lags are now easier to achieve and the imaginary out of phase component of tidal gravity can be used for accurate tests of this component of ocean tide models

new transfer functions for nutations of a nonrigid earth there are differences between the observed values of nutation and the computed ones based on the international astronomical union iau 1980 adopted nutation series these differences can be expressed in the frequency domain where they may reach several milliarc seconds a level that is too large for practical use this paper aims to resolve part of these differences by computing a new theoretical model accounting for additional geophysical effects a new transfer function is computed based on an earth initially in a nonhydrostatic equilibrium corresponding to the steady state associated with the present mantle convection the mantle mass anomalies are deduced from seismic tomography data and the flow induced boundary deformations are computed from internal loading for an earth made up of a viscous inner core a liquid outer core a viscous mantle and a solid lithosphere in this way a new core mantle boundary cmb flattening is obtained which gives the observed free core nutation fcn period furthermore the global earth dynamical flattening induced by the mass anomalies in the mantle associated with tomography and by the mass anomalies due to the computed boundary deformations is in agreement with the j2 form factor or the observed precession constant in addition to this nonhydrostatic initial state the rheology of the mantle is considered as inelastic the transfer function for nutation is then obtained by numerical integration of motion equations from the earth s center up to the surface to provide a model which is completely self consistent in order to validate our model the transfer function is convolved with new rigid earth nutations ocean corrections are applied and the final results are then compared with the observed nutations or with the international earth rotation service iers nutation series the residuals between our model and the observation are about 3 times smaller than those between the iau 1980 adopted model and the observation however our model still presents residuals above the observational error this is particularly true for the out of phase part of the residuals while the in phase part gives very small residuals improvement of about 1 order of magnitude a further step in this study is a refinement of the modeling of geophysical fluids core ocean and atmosphere

long period variations in gravity field caused by mantle anelasticity a numerical perturbation approach is used to assess the effect of mantle anelasticity on the earth s zonal response coefficient the zonal geopotential coefficient j2 and the orbital node of geodetic satellites the theoretical predictions are used to compare solutions of elastic ocean tide models and tides observed by geodetic satellites for mr m m ssa and s a the discrepancies between the satellite observed tides and the solution from schwiderski and recent altimetric ocean tide models can be partly explained by the predicted effect of mantle anelasti city at mf and m m frequencies approximately 80 of the observed semiannual variation in 2 by geodetic satellites can be attributed to the tidal deformation from anelasticity and from the classical equilibrium ocean the predicted for the 18 6 year tide was computed for an earth with an anelastic mantle and a nonequilibrium ocean the range of the lower and upper bounds of for the 18 6 year tide is from 0 345 to 0 377 in amplitude and from 6 o to 3 o in phase with preferred amplitude of 0 365 and phase of 0 o8

geometrical determination of the love number h2 at four tidal frequencies the love number h2 is determined at the m2 n2 o1 and k1 frequencies by combining satellite altimetry with in situ ocean tidal measurements topex poseidon altimetry is used to measure the ocean earth tide while gauges at 114 island and ocean bottom sites determine the ocean tide the difference sets constraints on h2 our h2 standard errors are somewhat larger than recent vlbi estimates but they clearly delineate the resonance in k1 at the 6 level

constraints on mantle anelasticity from geodetic observations and implications for the j2 anomaly summary we use geodetic observations of the earth to constrain anelasticity in the earth s mantle at periods between 12 hr and 18 6 yr the observations include satellite laser ranging slr measurements of 12 hr and 18 6 yr tides in the j 2 component of the gravity field spacebased observations of tidal variations in the earth s rotation rate and optical and space based measurements of the chandler wobble period and damping these geophysical signals are mostly sensitive to the lower mantle the results suggest the dissipative process could consist of a single absorption band that extends across seismic periods out at least as far as 20 yr the results also require values of the anelastic parameter q that are smaller than those required by seismic observations we interpret this as evidence that q in the lower mantle is frequency dependent the frequency dependence suggested by the geodetic observations is reasonably consistent with laboratory measurements though those measurements have only been done on rocks at upper mantle conditions after fitting and removing the 18 6 yr tide from the slr j 2 results we find that the 1998 2002 anomaly present in the original j 2 observations is no longer a singular anomaly in the j 2 residuals but becomes one of a series of maxima in a quasi decadal oscillation

body tides on a 3 d elastic earth toward a tidal tomography abstract the deformational and gravitational response of the earth to the tide generating potential has generally involved 1 d i e depth varying earth models progressive improvement in observational constraints on body tides generated from both ground and space based surveys suggests that an examination of the potential impact of lateral variations in earth structure is warranted we present a suite of predictions of the body tide response within the semi diurnal diurnal and long period tidal bands computed using a finite volume numerical code the calculations adopt 3 d density and elastic structure taken from seismic inferences and in a subset of the calculations dynamic topography on the surface and internal interfaces we find that perturbations in the radial displacement and surface gravity within the semi diurnal band reach 1 mm and 0 15 gal respectively the perturbations in the diurnal band are comparable to these values and within the long period band they are a factor of 3 5 smaller we also demonstrate that lateral variations in the elastic moduli which have been ignored in recent work contribute greater than 50 of the total perturbation the level of perturbation associated with 3 d structure exceeds the current observational uncertainty obtainable using space geodetic methods and this suggests the possibility of performing tidal tomographic inversions of such data

on the nutations of a more realistic earth model summary the last adopted nutation series corresponds to an elliptical uniformly rotating earth it is now well known that when comparing the theory with very long baseline interferometry vlbi lunar laser ranging llr or astronomical observations relatively large residuals appear this paper reviews and evaluates different possibilities to explain these differences i new rigid nutations are used in the convolution for computing nutations series the elastic nutation amplitudes are computed at each frequency by multiplying the ratios with rigid earth results ii the mantle inelasticity is introduced in the earth model iii the core flattening and thus the free core nutation fcn is changed among these effects the only very significant one is the effect of a change in the core flattening it explains the discrepancy between recent data and the amplitude adopted by the international astronomical union iau for the annual component these are still some differences to be explained for the semi annual and the fortnightly components

the devonian of the parana basin brazil sequence stratigraphy paleogeography and sw gondwana interregional correlations abstract the devonian period is characterized by an overall mean sea level higher than is observed today this pattern is recognized in several basins worldwide and permitted for example the flooding of the rheic ocean through sw gondwana s cratonic domain nonetheless this flooding was not purely eustatic the ordovician devonian geodynamic famatinian episode also played its role this tectonic eustatic interplay favored shallow marine deposition recorded in several sw gondwana basins such as the parana basin in brazil even so the evolution of the parana basin through the devonian and the factors responsible for the accommodation space remain speculative which leads to bias regarding the correlation of transgressive regressive events in sw gondwana this work aims by integrating outcrop and subsurface data to provide a basin scale stratigraphic framework and a paleogeographical reconstruction of the ponta grossa early devonian and sao domingos formations middle to late devonian of the parana basin it also correlates the studied interval with adjacent basins to identify the impact of tectonic and eustatic processes on the evolution of sw gondwana tectono sedimentary cycles we identified two 2nd order transgressive regressive sequences that correspond to the lithostratigraphic occurrence of ponta grossa and sao domingos formations respectively and whose maximum transgressive and regressive surfaces and high hierarchy unconformities are traceable through adjacent basins the ponta grossa sao domingos boundary also delineates an important tectonic event associated with far field stresses probably caused by precordilleran orogeny related phenomena the ponta grossa and sao domingos formations share several similarities with coeval strata in sw gondwana basins indicating that they can be extrapolated and correlated to contemporaneous processes of interregional scale the first namely precordilleran i early devonian was dominated by tectonics and encompasses the ponta grossa and las pavas composite sequence set the second precordilleran ii middle to late devonian was mostly eustatic and encompasses sao domingos and aguarave composite sequence sets both intervals are part of the famatinian geodynamic cycle

spore diversity trends in the middle devonian of the chaco salteno plain northwestern argentina abstract devonian deposits in northwestern argentina were historically studied with stratigraphical purposes since these layers conform the source rocks of the producing basins of the region a fairly well preserved palynomorph assemblage from the tonono formation provides an opportunity to perform the first quantitative analysis to study the evolution of diversity in the succession two associations are here defined by both stratigraphic distribution of species and cluster analysis ranging from the lower eifelian to the lower givetian rarefaction analysis reveals the existence of a relatively rich miospore population species richness increases while there is a drop in diversity and evenness towards the top of the column the increment of the marine components towards the latter section indicates shifts in the shoreline the influx of warmer water into higher latitudes as highlighted by the arrival of the brachiopod tropidoleptus could have favored the inception of new spore species in the settled community these results add to evidence that some groups build up the number of species in disturbed settings and evenness is reduced with each new species introduced

an analysis of tidal variations in the length of day observations of the length of day lod corrected for the effects of variations in the angular momentum due to changes in wind velocity and atmospheric pressure ocean tide heights and currents and solid earth zonal tides were analyzed the apparent effect of atmospheric angular momentum aam on the astronomically determined lod is found to be much less at the highest frequencies than at lower frequencies for periods shorter than ten days there appears to be essentially no correlation between aam and lod the international earth rotation service iers standards 1992 model for the effects of zonal tides on the earth s rotation which includes ocean tidal effects adequately accounts for the observations of the variations in the length of day with periods between five and 180 days at the present level of accuracy a currently unexplained semi annual variation in the length of day remains but this may be due to the unmodeled effects of stratospheric winds the power spectrum of the remaining variations with periods less than twenty days is essentially that of a white noise process the amplitudes of the remaining unexplained variations in length of day are less than thirty microseconds this paper has been accepted by geophysical journal international for publication

constraints on short term mantle rheology from the j observation and the dispersion of the 18 6 y tidal love number abstract the nature of short term mantle rheology for timescales between the seismic frequency band and a few hundred years remains relatively unknown we have made use of two pieces of information which have emerged as a consequence of the recent acquisition of data from the lageos satellite to place some contraints on the rheological parameters of short term mantle rheology the first is the secular variation of the gravitational harmonic j the second is the amount of dispersion of the tidal love number for the 18 6 y tide which has been inferred to be 20 two types of rheology have been considered the first is a frequency dependent q rheology an analytical expression for the transformed shear modulus has been developed from the truncated retardation spectrum explicitly for this purpose the second anelastic rheology we have used is a standard linear solid where the parameters of importance are the relaxation strength and the short term viscosity 2 rheological parameters of the frequency dependent q model previously proposed by lambeck and nakiboglu to explain the dispersion of the tidal love number for a 18 6 y period are found to produce too much dispersion for the chandler wobble and to yield seismic q s between o 103 and o 104 for fundamental toroidal modes which are not compatible with the data we have used instead a three layer model consisting of an elastic lithosphere a mantle with a standard linear solid rheology whose debye peak lies beyond the long time cutoff of the retardation spectrum and an inviscid core for relaxation strength of around 1 and short term viscosity 2 j would result from earthquake excitation a sharp decrease of the tidal dispersion takes place for 2 5 1020 p and 1 0 for smaller values of relaxation strength 0 15 the maximum tidal dispersion is only 9 and decreases gradually as 2 is increased beyond 5 1020 p we have found that the maximum dispersion caused by the maxwell rheology is small around 5 even for asthenospheric viscosities of o 1018p these results suggest that the datum of 18 6 y tidal dispersion can be utilized eventually to place constraints on potential candidates of short term mantle rheology

long period lunar earth tides at the geographic south pole and recent models of ocean tides for many years the ocean tide models of schwiderski 1980 were the standards used by the earth tide community to interpret deviations of observed earth tides from predictions on the basis of earth models constructed by seismologists recently the topex poseidon altimeter mission provided new and improved information on pelagic ocean tides which led several research groups to generate new models of the major oceanic tides this in turn renewed our own interest in the observations of long period lunar tides at the geographic south pole that were reported many years ago with an attempt to interpret the deviation from predictions using the schwiderski models we used four different models of the fortnightly mf and monthly mm ocean tides to calculate their attraction and loading effects at the south pole and compared the results with the observed gravity tides in our earlier interpretation we did not realize that for long period ocean tides the so called greenwich phase does not refer to the phase of these tides at the latitude of greenwich but to the phase at the equator this resulted in a mistake in the relative phases of earth tide and ocean effect at the south pole for mf we now find that all models predict the phase lead of the observed versus theoretical tides within the formal uncertainties however the amplitude is still underpredicted by 1 5 2 per cent this could be due to several reasons instrument calibration errors in the body and or ocean tide models relaxation of the earth s elastic properties and the huge ice sheet of antarctica these possibilities are discussed for the mm tide the observed amplitude is well predicted within error however the uncertainties in the measurements are rather large

oceanic tidal angular momentum and earth s rotation variations abstract luni solar tides affect earth s rotation in a variety of ways we give an overview of the physics and focus on the excitation of earth rotational variations by ocean tides under the conservation of angular momentum various models for diurnal and semidiurnal tidal height and tidal current fields have been derived following a legacy of a number of theoretical tide models from the topex poseidon t p ocean altimetry data we review the oceanic tidal angular momenta otam predicted by these t p models for the eight major tides q1 o1 p1 k1 n2 m2 s2 k2 and their excitations on both earth s rotational speed variation in terms of length of day or ut1 and polar motion prograde diurnal semidiurnal components and retrograde semidiurnal components these small high frequency effects have been unambiguously observed in recent years by precise earth rotation measurements via space geodetic techniques here we review the comparison of the very long baseline interferometry vlbi data with the t p otam predictions the agreement is good with discrepancies typically within 1 2 microseconds for ut1 and 10 30 microarcseconds for polar motion the eight tides collectively explain the majority of subdaily earth rotation variance during the intensive vlbi campaign cont94 this establishes the dominant role of otam in exciting the diurnal semidiurnal polar motion and paves the way for detailed studies of short period non otam excitations such as atmospheric and oceanic angular momentum variations earthquakes the atmospheric thermal tides earth librations and the response of the mantle lateral inhomogeneities to tidal forcing these studies await further improvements in tide models and earth rotation measurements

devonian sea level change in bolivia a high palaeolatitude biostratigraphical calibration of the global sea level curve article i nfo available online xxxx during the devonian period the cool water malvinokaffric realm was located at high palaeolatitudes in the southern hemisphere the realm is defined by its highly endemic marine benthic fauna which makes extra malvinokaffric correlations problematic investigation of the devonian palynomorphs from an extensive regional sub surface dataset 24 wells in the chaco basin bolivia reveals the presence of a number of stratigraphically restricted and regionally correlative epiboles peak abundances of the distinctive palynomorphs bimerga bensonii crucidia camirense evittia sommeri petrovina connata and ramochitina magnifica these palynomorph epiboles were then located at outcrop by a high resolution palynological investigation 225 samples of two bolivian outcrop localities in the chaco basin bermejo santa cruz department and campo redondo chiquisaca department the important evittia sommeri epibole in the basal los monos formation is related to a marine transgression that is present in both these outcrop sections additional chronostratigraphic control on this marine transgression comes from the occurrence of rare goniatites in the base of the huamampampa formation at campo redondo which are at least early eifelian in age post chot c event based on the goniatite together with spore data the marine transgression with evittia sommeri in the basal los monos formation can be tentatively assigned to the mid devonian mid late eifelian kacak event the presence of a datable malvinokaffric goniatite has shown that key spore taxa which are used zonally in both laurussia and gondwana do not all have coincident first occurrences in both areas furthermore despite the appearance of some cosmopolitan elements in the microflora mid and late devonian spore assemblages in bolivia are distinct from other regions in being relatively impoverished in both progymnosperm and lycopod spores this floral difference is attributable to the malvinokaffric realm continuing to retain a distinctive cool climatic signature throughout this interval however the sporadic occurrences of extra malvinokaffric macrofauna in restricted stratigraphic intervals of the middle devonian in south america and south africa are significant the oldest known occurrence of the extra malvinokaffric brachiopod tropidoleptus in bolivia is coincident with the late eifelian basal los monos formation transgression hence there was a relationship between influxes of this fauna and marine transgressions i e temporary periods of reduced climatic gradient the migration of devonian spores and particularly heterosporous spores between gondwana and laurussia clearly occurs during the mid and late devonian this is at variance with models claiming a wide rheic ocean during much of the devonian

tides for a convective earth in this paper we give values of the tidal gravimetric factor as well as of the love numbers for the tidal surface displacement and for the tidal mass redistribution potential that are consistent with the presently adopted definitions we present analytical expressions for these quantities and compute numerical values for two rotating nonspherical earth models in the first model the earth is everywhere in hydrostatic equilibrium and the inner core and mantle are both elastic in the second model the earth is ellipsoidal with an inelastic mantle and with a nonhydrostatic initial state for which the effects of mantle convection and its associated boundary deformations are considered this latter model is constrained to reproduce the observed free core nutation period and global earth dynamical flattening

review of the earth tidal models and contribution of earth tides in geodynamics the attraction of the moon and the sun on the earth induces deformations of the earth body at the surface of the earth these effects are described using tidal parameters which are observed by tidal instruments and estimated using an earth model these tidal parameters are indeed computed from a linear combination of the displacement field the stress field and the potential due to the mass readjustment associated with the tides the theoretical tidal parameter values depend crucially on the model used for the interior of the earth the system of equations used in the computation contains a stress strain relationship this equation is the only one which changes when considering mantle inelasticity instead of elasticity for an inelastic mantle the stress strain relationship is a hooke law with complex and frequency dependent rheological parameters the numerical values of these rheological parameters depend on the hypotheses formulated on the earth body even after the introduction of mantle inelasticity in the equations there are still some differences between the theory and the observations by increasing the complexity of the model scientists want to decrease the difference between the theory and the observations this comparison brings answers to very important points in geophysics in particular the resonances at the free core nutation frequency and at the free inner core nutation frequency in the tidal response give the values of these earth normal mode periods and the comparison between the observed and the computed period constrains the core flattening and the jump in the density at the inner core outer core boundary respectively

a discussion of world wide measurements of tidal gravity with respect to oceanic interactions lithosphere heterogeneities earth s flattening and inertial forces abstract by the end of 1981 the international center of earth tides icet had collected and evaluated a considerable amount of data from 180 stations including those of the trans world profile which ensure for the first time a world wide distribution including the tropical areas and the southern hemisphere in 1979 80 new oceanic cotidal maps of high quality established by schwiderski became available these maps fit on land tidal gravity measurements quite successfully a new theoretical approach developed by wahr in 1981 has resulted in a set of theoretical formulae establishing the latitude dependence of the classical elastic amplitude factors for tidal deformations we calculate here for six tidal waves the correlations between the observed gravity variations and those resulting from a calculation based upon the schwiderski maps these correlations are highly significant after subtraction of these oceanic effects we calculate the latitude dependences of the experimentally determined amplitude factors which are found to fit wahr s theoretical formulae there remains however a serious discrepancy in the constant terms of the various formulae the effects of heterogeneities in the lithosphere on tidal deformations are also clearly identified

time variability of the earth s gravity field hydrological and oceanic effects and their possible detection using grace the grace satellite mission scheduled for launch in 2001 is designed to map out the earth s gravity field to high accuracy every 2 4 weeks over a nominal lifetime of 5 years changes in the gravity field are caused by the redistribution of mass within the earth and on or above its surface grace will thus be able to constrain processes that involve mass redistribution in this paper we use output from hydrological oceanographic and atmospheric models to estimate the variability in the gravity field i e in the geoid due to those sources we develop a method for constructing surface mass estimates from the grace gravity coefficients we show the results of simulations where we use synthetic grace gravity data constructed by combining estimated geophysical signals and simulated grace measurement errors to attempt to recover hydrological and oceanographic signals we show that grace may be able to recover changes in continental water storage and in seafloor pressure at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer with accuracies approaching 2 mm in water thickness over land and 0 1 mbar or better in seafloor pressure

does the moon possess a molten core probing the deep lunar interior using results from llr and lunar prospector 1 it is the main purpose of this study to examine the deeper structure of the moon in the light of four numbers these are lunar mass m mean moment of inertia i second degree tidal love number k2 and the quality factor q accounting for tidal dissipation within the solid body of the moon the former two have been measured by lunar prospector to high precision and more than 30 years of lunar laser ranging llr data have led to an estimate of the second degree tidal love number and quality factor the inverse problem dealt with here of obtaining information on the lunar density and s wave velocity profile from the four numbers follows our earlier investigations by employing an inverse monte carlo sampling method we present a novel way of analyzing the outcome using the bayes factor the advantage lies in the fact that rather than just looking at a subset of sampled models we investigate all the information sampled in different runs i e take into account all samples in order to estimate their relative plausibility the most likely outcome of our study based on the data their uncertainties and prior information is a central core with a most probable s wave velocity close to 0 km s density of 7 2 g cm3 and radius of about 350 km this is interpreted as implying the presence of a molten or partially molten fe core in line with evidence presented earlier using llr regarding the dissipation within the moon

phanerozoic transgressions and regressions on the continents a quantitative approach based on areas flooded by the sea and areas of marine and continental deposition

geophysical analysis of zonal tidal signals in length of day summary the earth s zonal response coefficient k is estimated from the tidal signals in the observed length of day lod data its magnitude and phase are functionals of the earth s internal structure and dynamics in this paper an analysis of 13 years of precise lod data 1980 1992 reveals strong signals for nine zonal tidal groups ranging from 5 to 35 days in period numerical estimates of k for 27 major tides are thus obtained 11 among which are considered sufficiently high in signal to noise ratio to provide meaningful geophysical constraints on the earth s rotational dynamics the results favour a k magnitude close to but somewhat smaller than 0 315 which is the theoretical value for an elastic mantle completely decoupled from the fluid core plus equilibrium oceans a small amount of dispersion is also detectable where shorter periods tend to have lower k magnitude and larger phase lag our k magnitude estimates are consistent with two recently published non equilibrium ocean tide models and an anelastic response in the mantle although an equilibrium response in the ocean and a purely elastic response in the mantle is not disallowed phase lags of a few degrees are required by both ocean tide models and by our data

stacking gravity tide observations in central europe for the retrieval of the complex eigenfrequency of the nearly diurnal free wobble summary we have used tidal gravity measurements from six stations in central europe to investigate the resonance in the diurnal tidal band caused by inertial coupling between the mantle and outer core of the earth by the use of stacking it was possible to determine the eigenfrequency and quality factor of this eigenmode commonly called the nearly diurnal free wobble we assessed the effect of systematic errors from the ocean correction to the tidal measurements employing a monte carlo method the observed eigenfrequency is 1 1 434 f 7 cycles per sidereal day and is significantly higher than predicted by theories the observed quality factor is 2 8 0 5 x 10

long term evaluation of ocean tidal variation models of polar motion and ut1 recent improvements in the development of vlbi very long baseline interferometry and other space geodetic techniques such as the global navigation satellite systems gnss require very precise a priori information of short period daily and sub daily earth rotation variations one significant contribution to earth rotation is caused by the diurnal and semi diurnal ocean tides within this work we developed a new model for the shortperiod ocean tidal variations in earth rotation where the ocean tidal angular momentum model and the earth rotation variation have been setup jointly besides the model of the short period variation of the earth s rotation parameters erp based on the empirical ocean tide model eot11a we developed also erp models that are based on the hydrodynamic ocean tide models fes2012 and hamtide furthermore we have assessed the effect of uncertainties in the elastic earth model on the resulting erp models our proposed alternative erp model to the iers 2010 conventional model considers the elastic model prem and 260 partial tides the choice of the ocean tide model and the determination of the tidal velocities have been identified as the main uncertainties however in the vlbi analysis all models perform on the same level of accuracy from these findings we conclude that the models presented here which are based on a reexamined theoretical description and long term satellite altimetry observation only are an alternative for the iers conventional model but do not improve the geodetic results

viscoelastic mantle density heterogeneity and core mantle topography summary starting with the model of mantle density heterogeneity derived by ricard et al 1993 which uses plate motion reconstructions under the assumption that subducted slabs sink vertically into the mantle we model the temporal evolution of these internal loads we investigate the viscoelastic deformation of the earth due to this time dependent excitation source using a love number formalism for a linear viscoelastic mantle with a maxwell model of rheology we are especially interested in the deep earth viscoelastic deformation such as the radial displacement that appears at the core mantle boundary and we compare the calculated topography with that proposed by seismologists

low viscosity of the bottom of the earth s mantle inferred from the analysis of chandler wobble and tidal deformation abstract viscosity of the d layer of the earth s mantle the lowermost layer in the earth s mantle controls a number of geodynamic processes but a robust estimate of its viscosity has been hampered by the lack of relevant observations a commonly used analysis of geophysical signals in terms of heterogeneity in seismic wave velocities suffers from major uncertainties in the velocity to density conversion factor and the glacial rebound observations have little sensitivity to the d layer viscosity we show that the decay of chandler wobble and semi diurnal to 18 6 years tidal deformation combined with the constraints from the postglacial isostatic adjustment observations suggest that the effective viscosity in the bottom 300 km layer is 1019 1020 pa s and also the effective viscosity of the bottom part of the d layer 100 km thickness is less than 1018 pa s such a viscosity structure of the d layer would be a natural consequence of a steep temperature gradient in the d layer and will facilitate small scale convection and melt segregation in the d layer

a new approach to computing accurate gravity time variations for a realistic earth model with lateral heterogeneities we have developed a new elasto gravitational earth model able to take into account lateral variations deviatoric pre stresses and topographies as a first application we assume an el lipsoidal earth with hydrostatic pre stresses and validate and discuss our numerical model by comparison with previous studies on the m 2 body tide we then study the response of the ellipsoidal earth to zonal atmospheric loads and find that global lateral variations within the earth such as ellipticity have a weak impact about 1 per cent on the elasto gravitational deformations induced by atmospheric loading at low frequencies the earth is deformed mainly by luni solar tides and by surface loads including ocean atmosphere ice volumes and post glacial rebound in this work we focus our attention on the earth s body tides and atmospheric loadings the most accepted earth body tide models presently deal with an ellipsoidal rotating earth containing a liquid core and an anelastic mantle with hydrostatic pre stresses wahr 1981 wahr bergen 1986 the earth however is not an exact ellipsoid but presents lateral variations and deviatoric pre stresses there are long wavelength density anomalies within the mantle as shown by geoid anomalies and tomography studies e g romanowicz gung 2002 wang 1994 and dehant et al 1999 studied the influence of lateral heterogeneities on earth tides and showed that this effect is small but not necessarily negligible they did not however take into account possible deviatoric pre stresses these effects on the earth s body tides are totally unknown in addition to tidal forces mass changes in the atmosphere also cause deformation and mass redistribution inside the planet involving both local and global surface motions and variations in the gravity field which may be observed in geodetic experiments for several decades satellite geodesy has provided information on the temporal variation of the earth s geopotential and especially on the low degree zonal harmonics j 2 j 3 gegout cazenave 1993 which are essentially controlled by surface loads these hydrological atmospheric or oceanic effects on the earth s gravity field are usually modelled assuming a spherical earth with hydro static pre stress e g farrell 1972 wahr et al 1998 with the advent of the new generation of gravity measurements one of the challenges of the coming decade will be to provide more realistic earth models that show the variation of gravity with time in particular global studies based on gravity data from satellites such as grace goce and future grace goce follow on ones require accurate body tide deformation models more realistic gravity variation models are also needed for local and ground measurements particularly for the very accurate superconducting gravimeters and the associated gravimetric observatory network such as the global geodynamic project crossley et al 1999 the formalism developed to compute this elasto gravitational model is usually based on spherical harmonic analysis the addition of lateral variations leads to couplings between spherical harmonics i e to a more complex formalism that requires a large numerical effort e g wang 1994 plag et al 1996 we develop here a new approach for a non radially symmetrical earth model using a finite element method known as the spectral element method the efficiency of this method is less dependent on the shape of the lateral heterogeneities than the spherical harmonic method our method is therefore well adapted to studying the impact of global and local lateral variations on the earth deformation we solve the elasto gravitational equations taking into consideration the lateral variations within the earth by using a first order perturbation theory smith 1974 dahlen tromp 1998 this new model allows us to take into account lateral variations of density and rheological parameters deviatoric pre stresses and interface topography in order to validate our calculations we tackle a well known problem the impact of the hydrostatic ellipticity on the earth body tides an analytical solution for this problem can be derived for a simple model in which the earth is assumed to be homogeneous and incompressible the gravitational potential and the vertical displacement on the surface of the deformed ellipsoid were first derived by love 1911 and then corrected by wang 1994 we have recently extended these analytical results to the tangential surface displacement greff lefftz et al 2005 we first validate our model with our analytical solutions and then compare our results with

test of theoretical solid earth and ocean gravity tides summary data from three superconducting gravimeters at four different locations are analysed for agreement with theoretical computations of gravity tides and of the influence of ocean tides on gravity the absolute value of the measured tide is determined by an independent absolute calibration of the gravimeters the method differs from previous tests of tide theories in that it compares the entire predicted time series rather than specific harmonic constituents in this way it is possible to test the solid earth and ocean tide effects independently we find that the ratios of observed to predicted solid earth tides at different locations are the same within an uncertainty of about ko 2 per cent however the magnitude of the tides deduced by the absolute calibration of the gravimeters is 0 6 per cent larger than the theoretical solid earth tide we point out that an accurate determination of the solid earth tide in this way provides a direct comparison between the gravitational constant g at laboratory scales and at the distance to the moon

constraints on magnetic energy and mantle conductivity from the forced nutations of the earth observations of the earth s nutations are used to explore the possible presence of a conducting layer at the base of the mantle the existence of such a layer is suggested by recent experiments on iron and silicate mixtures at high pressures and temperatures knittle and jeanloz 1986 1989 which indicate that iron may react with silicate minerals to produce metallic compounds nutations provide an ideal tool for investigating the existence of such a layer because they are sensitive to the electrical properties within a thin magnetic boundary layer along the core mantle boundary cmb evidence in favor of a conducting layer is found in the effects of ohmic dissipation which cause the amplitude of the earth s nutation to be out of phase with tidal forcings although out of phase components in the earth s nutations are conventionally attributed to the dissipative influences of ocean tides and mantle anelasticity these effects appear incapable of explaining nutation amplitudes determined from very long baseline interferometry vlbi observations the additional effects of ohmic dissipation enhanced by the presence of a thin conducting layer at the cmb are sufficient to reconcile theory and observation the largest mismatch between observations and theory taking account of ocean tides and mantle anelasticity is a discrepancy of 0 39 0 04 milliarcseconds in the out of phase component of the retrograde annual nutation this discrepancy can be eliminated if the lowermost 200 m of the mantle has a conductivity of 5 105s m 1 and the magnetic energy in the spherical harmonic components of the field at the cmb in degrees l 12 is approximately 4 times greater than the energy inferred in degrees l 12 from surface observations unfortunately the vlbi observations do not uniquely resolve the mantle conductivity and magnetic energy so that trade offs exist between these two parameters nevertheless a high mantle conductivity is favored on the grounds that the alternative involving high levels of magnetic energy yields an excessive amount of ohmic heating other interpretations of the vlbi discrepancy are also discussed one such alternative involves viscous dissipation at the cmb requiring a kinematic viscosity of 0 1m2s 1

long period tidal variations in the length of day a new model of long period tidal variations in length of day is developed the model comprises 80 spectral lines with periods between 18 6 years and 4 7 days and it consistently includes effects of mantle anelasticity and dynamic ocean tides for all lines the anelastic properties follow wahr and bergen experimental confirmation for their results now exists at the fortnightly period but there remains uncertainty when extrapolating to the longest periods the ocean modeling builds on recent work with the fortnightly constituent which suggests that oceanic tidal angular momentum can be reliably predicted at these periods without data assimilation this is a critical property when modeling most long period tides for which little observational data exist dynamic ocean effects are quite pronounced at shortest periods as out of phase rotation components become nearly as large as in phase components the model is tested against a 20 year time series of space geodetic measurements of length of day the current international standard model is shown to leave significant residual tidal energy and the new model is found to mostly eliminate that energy with especially large variance reduction for constituents sa ssa mf and mt

middle devonian microfloras and megafloras from western argentina and southern bolivia their importance in the palaeobiogeographical and palaeoclimatic evolution of western gondwana the study of microfloras and megafloras from western argentina and southern bolivia presented here extends our knowledge of the biodiversity and succession of floristic events during the middle devonian and hence improves the current biostratigraphy among floral remains species attributable to haplostigma are mostly recorded from the same grandispora pseudoreticulata and other palynomorph bearing sections at balapuca southern bolivia and del chaco and la cortadera creeks in the precordillera of argentina the northernmost record of grandispora pseudoreticulata is recorded from a third palynoassemblage from the pando x 1 corehole of northern bolivia a great similarity among all these assemblages notably abundant grandispora pseudoreticulata suggests the identification of terrestrial connections or at least proximity of these local areas and other regions in south america during the givetian comparison with other contemporary gondwanan palynofloras shows cosmopolitan species e g geminospora lemurata samarisporites triangulatus archaeozonotriletes variabilis chelinospora concinna along with some others with more restricted distribution e g grandispora pseudoreticulata leiotriletes balapucensis acinosporites ledundae this pattern defines an afro south american subrealm which most likely results from the effects of palaeolatitude and in a lesser way local palaeoenvironmental conditions on the other hand such a level of cosmopolitanism supports previous palaeogeographical reconstructions where a narrow rheic ocean was developed between euramerica and the northern parts of africa and south america

fortnightly earth rotation ocean tides and mantle anelasticity summary this study of the fortnightly mf tide comprises three main topics 1 a new determination of the fortnightly component of polar motion and length of day lod from a multidecade time series of observed space geodetic data 2 the use of the polar motion determination as one constraint in the development of a hydrodynamic ocean model of the mf tide and 3 the use of these results to place new constraints on mantle anelasticity at the mf tidal period our model of the mf ocean tide assimilates more than 14 years of altimeter data from the topex poseidon and jason 1 satellites because the mf altimetric signal to noise ratio is very small it is critical that altimeter data not be overweighted the polar motion data plus tidegauge data and independent altimeter data give useful additional information with only the polar motion putting constraints on tidal current velocities the resulting ocean tide model plus the dominant elastic body tide leaves a small residual in observed lod caused by mantle anelasticity the inferred effective tidal q of the anelastic body tide is 90 and is in line with a frequency dependence with in the range 0 2 0 3

variations in the earth s oblateness during the past 28 years 1 analysis of satellite laser ranging slr data indicates that the earth s dynamic oblateness j2 has undergone significant variations during the past 28 years the dominant signatures in the observed variations in j2 are 1 a secular decrease with a rate of approximately 2 75 10 11 yr 1 2 seasonal annual variations with a mean amplitude of 2 9 10 10 3 significant interannual variations with timescales of 4 6 years and 4 a variation with period of 21 years and an amplitude of 1 4 10 10 with minimum in december 1988 two large interannual variations are related to the strong el nino southern oscillation events during the periods of 1986 1991 and 1996 2002 and it appears that another interannual cycle may have started in late 2002 the superposition of the decadal variation on the interannual signal makes the j2 fluctuation appear to be anomalously large during the 1996 2002 period contemporary models of the mass redistributions in the atmosphere ocean and surface water can explain a major part of the 4 to 6 year fluctuations however the cause of the decadal variation remains unknown

mantle lateral variations and elastogravitational deformations ii possible effects of a superplume on body tides summary the body tides response deformation and gravity of the earth is generally computed assuming radial symmetry in stratified earth models at the hydrostatic equilibrium we present in this paper numerical experiments with the aim to evaluate the impact of very large mantle heterogeneities of density on body tides in a companion paper we have developed a new earth elasto gravitational deformation model able to take into account the heterogeneous structure of the mantle we use this model to calculate the theoretical perturbation induced by three types of spherical heterogeneities in the mantle on m2 body tides response the heterogeneities are 1 our limit case a heterogeneity of 1000 km of radius in the lower mantle 2 a heterogeneity of 500 km of radius at the bottom of the lower mantle and 3 a heterogeneity of 285 km of radius in the upper mantle the density variation has been set to 50 kg m 3 f or each experiment we first calculate the equilibrium state of the earth when it contains a heterogeneity including non hydrostatic prestresses dynamical topography and lateral variation of density then we compute the m2 tidal perturbation we find that the surface tidal displacement perturbation is smaller than 1 mm and that the gravity perturbation has a maximum amplitude of 525 nanogal ngal regarding to the present precision in position measurement the displacement is too small to be detected the gravity perturbation should be measurable with superconducting gravimeters which have a ngal instrumental precision in experiment 2 the maximum gravity perturbation is about 120 ngal and in experiment 3 the maximum perturbation is about 33 ngal finally we investigate the maximum theoretical impact of the pacific and the african superplumes on the m2 body tide the superplumes have been modelled as two spherical heterogeneities with a radius of 1000 km in the lower mantle we find that these superplumes induce a maximum perturbation in gravity of about 370 ngal with a large part corresponding to a mean variation of gravity we conclude that we can expect to have a gravity perturbation of body tide with an order of magnitude of about hundred of ngal induced by the biggest mantle heterogeneities of density this perturbation in gravity should be measurable with superconducting gravimeters if all other contributions in the signal could be extracted with a sufficient precision

significant and vertically coherent seismic anisotropy beneath eastern tibet 1 shear wave splitting measurements using teleseismic sks and skks phases recorded by the indepth iv arrays has revealed a strong upper mantle anisotropic fabric in northeastern tibet with large delay times of up to 2 2 s suggesting that anisotropy exists in both the lithospheric and asthenospheric mantle the coherence among fast polarization orientations of split core phases and the left lateral slip on eastern striking southern striking faults in eastern tibet and the surface deformation fields calculated from both gps observations and quaternary fault slip rates support the idea that left lateral shear strain is the predominant cause of the orientation of the upper mantle petrofabrics we suggest the bending of the eastern himalayan syntaxis around the foundering burma andaman sumatra slab also contributes to the observed seismic anisotropy in the eastern himalayan syntaxis region two plausible competing processes are proposed for the flow of asthenosphere in eastern tibet in the first the deforming lithosphere glides over the passive asthenosphere inducing flow in the asthenospheric mantle in the second the asthenosphere beneath northeastern tibet is squeezed between the advancing indian continental lithosphere and the thick tarim and qaidam lithospheric blocks to the north a westward retreat of the burma slab from eurasia may induce flow that is toroidal and located exclusively around the northern edge of the slab the rotation of fast orientations for stations in the eastern himalayan syntaxis region are consistent with the toroidal flow pattern as well as the rotational deformation of the overlying lithosphere

reconstructing the terrestrial flora and marine plankton of the middle devonian of spain implications for biotic interchange and palaeogeography a rich and well preserved palynomorph assemblage from the middle devonian of northern spain is analysed with regard to palaeobiogeography and palaeocontinental reconstruction the communities of terrestrial plants dispersed spores marine zooplankton chitinozoans and marine phytoplankton acritarchs and prasinophytes all show significant endemism they are depauperate in some respects missing common species found elsewhere but also containing many endemic taxa measures of similarity and cluster analysis reveal little relatedness to other contemporary assemblages with both the spore and phytoplankton communities being sister groups to all other communities except one attempted correlation with local regional and global sea level and transgression regression schemes is complicated by the absence of key index palynomorphs in this unusual assemblage the distinctive sedimentary sequence of northern spain may reflect an increased clastic input to the marine shelf resulting from an increasingly monsoonal climate possibly connected to the kacak extinction event the assemblage9s unusual endemic character requires restrictions on dispersal the terrestrial spore assemblage suggests that large tracts of ocean existed without appreciable land bridges between the armorican terrane assemblage and laurussia to the north and gondwana to the south the phytoplankton communities support existing evidence for significant east to west ocean currents through the rheic ocean supplementary material supplementary tables 1 3 contain presence absence data for spores chitinozoans and phytoplankton respectively in various assemblages used to construct the dendrograms in figures 4 6 the tables are available at https doi org 10 6084 m9 figshare c 4726862

the period and q of the chandler wobble summary we have extended our calculation of the theoretical period of the chandler wobble to account for the non hydrostatic portion of the earth s equatorial bulge and the effect of the fluid core upon the lengthening of the period due to the pole tide we find the theoretical period of a realistic perfectly elastic earth with an equilibrium pole tide to be 426 7 sidereal days which is 8 5 day shorter than the observed period of 435 2 day using rayleigh s principle for a rotating earth we exploit this discrepancy together with the observed chandler q to place constraints on the frequency dependence of mantle anelasticity if q in the mantle varies with frequency u as u between 30 s and 14 months and if q in the lower mantle is of order 225 at 30 s we find that 0 04 5 a 5 0 1 1 if instead q in the lower mantle is of order 350 near 200 s we find that 0 11 5 a 0 19 in all cases these limits arise from exceeding the 68 per cent confidence limits of 2 6 day in the observed period since slight departures from an equilibrium pole tide affect the q much more strongly than the period we believe these limits to be robust

a chronology of paleozoic sea level changes sea levels have been determined for most of the paleozoic era 542 to 251 million years ago but an integrated history of sea levels has remained unrealized we reconstructed a history of sea level fluctuations for the entire paleozoic by using stratigraphic sections from pericratonic and cratonic basins evaluation of the timing and amplitude of individual sea level events reveals that the magnitude of change is the most problematic to estimate accurately the long term sea level shows a gradual rise through the cambrian reaching a zenith in the late ordovician then a short lived but prominent withdrawal in response to hirnantian glaciation subsequent but decreasingly substantial eustatic highs occurred in the mid silurian near the middle late devonian boundary and in the latest carboniferous eustatic lows are recorded in the early devonian near the mississippian pennsylvanian boundary and in the late permian one hundred and seventy two eustatic events are documented for the paleozoic varying in magnitude from a few tens of meters to 125 meters

long period tidal factors at antarctica syowa station determined from 10 years of superconducting gravimeter data 1 we determined long period gravimetric tidal parameters from 10 years of superconducting gravimeter observations at syowa station in antarctica the obtained amplitude and phase lead for the mm wave were 6 106 0 030 gal gal 10 8 m s 2 0 32 0 28 respectively and those for the mf wave were 11 657 0 018 gal 0 78 0 09 respectively we also determined the parameters of other tidal constituents with periods of 6 to 32 days mqm msqm mtm mstm msf msm and their frequency dependence was estimated by means of a weighted least squares method the observed values corrected by the four ocean tide models of schwiderski nao 99l fes99 and tpxo6 0 were compared with the theoretical values calculated from the elastic and inelastic solid earth tide models by dehant et al even though the values of the ocean tide corrections have relatively large discrepancies between the four models and it is still difficult to discuss the degree of inelasticity of the earth for this frequency band we can say that the observations favor the inelastic earth model rather than the elastic model

stratigraphic evidence for the hirnantian latest ordovician glaciation in the zagros mountains iran abstract high latitude hirnantian diamictites dargaz formation and lower silurian kerogenous black shales sarchahan formation are locally exposed in the zagros mountains the glaciogenic dargaz deposits consist of three progradational retrogradational cycles each potentially controlled by the regional advance and retreat of the hirnantian ice sheet glacial incisions of sandstone packages change laterally from simple planar to high relief

seismic geodynamic determination of the origin of excess ellipticity of the core mantle boundary we demonstrate that the excess dynamic ellipticity of the core mantle boundary cmb inferred from the period of the earth s retrograde free core nutation rfcn may be explained in terms of viscous stresses generated by mantle convective flow the 3d elastic structure and radial viscosity profile which define the model used in the viscous flow calculations are constrained to simultaneously reconcile a large set of seismic and geodynamic data

the geological evolution of the tibetan plateau the geological evolution of the tibetan plateau is best viewed in a context broader than the india eurasia collision zone after collision about 50 million years ago crust was shortened in western and central tibet while large fragments of lithosphere moved from the collision zone toward areas of trench rollback in the western pacific and indonesia cessation of rapid pacific trench migration 15 to 20 million years ago coincided with a slowing of fragment extrusion beyond the plateau and probably contributed to the onset of rapid surface uplift and crustal thickening in eastern tibet the latter appear to result from rapid eastward flow of the deep crust probably within crustal channels imaged seismically beneath eastern tibet these events mark a transition to the modern structural system that currently accommodates deformation within tibet

tidal gravity and ocean tide loading in europe b the results are presented from tidal gravity measurements at five sites in europe using lacoste and romberg et gravimeters improvements that we have made to the accuracies of these gravimeters are discussed it is shown that the standard calibration of the international center for earth tides used for worldwide tidal gravity profiles is 1 2 per cent too high the m2 and o1 observations are compared with model calculations of the earth s body tide and ocean tide loading and it is shown that there is a very significant improvement in the agreement between observations and models compared to that obtained with previous tidal gravity measurements for o1 where the ocean tide loading and attraction in central europe is only 0 4 per cent of the body tide our measurements verify that the dehant wahr anelastic body tide model gravimetric factor is accurate to 0 2 per cent it is also shown that the effects of lateral heterogeneities in earth structure on tidal gravity are too small to explain the large anomalies in previously published tidal gravity amplitudes the observations clearly show the importance of conserving tidal mass in the schwiderski ocean tide model for sites in central europe the m2 and o1 observations and the models are in agreement at the 0 1 gal 10 9 m s 2 level and tidal corrections to this accuracy can now be made to absolute gravity measurements

anelasticity from seismic to tidal timescales theory and observations abstract we examine strain energy dissipation of earth s normal modes and body tides in order to compare these observations with predictions from an experimental model of intrinsic dissipation for this comparison we employ a recently developed self consistent treatment of modes and tides that includes the separation of dynamical processes self gravity and inertia from intrinsic attenuation we select a set of normal modes and tides with similar depth sampling centered on the lower mantle without contributions from the core this dataset ranges from 7 min to 18 6 yr or about 6 decades in frequency the results show that the attenuation of the higher frequency modes defines a broad plateau in dissipation inferred experimentally to occur at the transition from elastic to anelastic behavior whereas the attenuation of lower frequency tides falls on a frequency dependent absorption band this reconciles published seemingly contradictory models of dissipation for modes versus tides the absorption band for modes terminates at periods where tidal models infer its onset microphysically the experimental data can be explained by elastically accommodated grain boundary sliding producing a broad plateau at short periods transitioning to diffusionally assisted grain boundary sliding at longer periods corresponding to an absorption band extrapolation of the fit to the experimental data with parameters adopted for the lower mantle can reconcile the seismological and geodetic observations

the response method applied to the analysis of superconducting gravimeter data abstract the response method a technique used in ocean tide analysis to separate linear and nonlinear components is applied to the analysis of superconducting gravimeter data a response analysis is shown to be capable of resolving small non tidal signals of a few nanogal amplitude arbitrarily close in frequency to large amplitude tidal signals a synthetic example in which a small signal is injected into a spectrally rich tidal signal is used to demonstrate how the method is applied and its advantages compared to a conventional analysis the technique is also applied to the analysis of degree 3 diurnal and semi diurnal tides in short records the degree 3 waves are easily separated and a reasonable ocean loading effect for these waves is recovered despite the fact the open ocean tide is only a few mm in amplitude finally a response analysis is used to separate gravitational tides from the radiation tides at coincident frequencies in both the diurnal and semi diurnal bands

long period tides observed with a superconducting gravimeter at syowa station antarctica and their implication to global ocean tide modeling abstract the long period tides mf and mm waves were analyzed with the 2 years data obtained with a superconducting gravimeter sg installed at syowa station 69 0 s 39 6 e antarctica the observed amplitudes phase lags and amplitude factors factors were 11 642 0 035 gal 0 12 0 17 and 1 1218 0 0034 for the mf wave and 6 143 0 058 gal 0 33 0 54 and 1 1205 0 0106 for the mm wave respectively 1 gal 10 8 m s 2 the ocean tide effects effects of the attraction and loading due to the ocean mass at the observation site were estimated using the five global ocean tide models equilibrium ocean tide model schwiderski model schwiderski e w 1980 on charting global ocean tides rev geophys space phys 18 243 268 dickman model dickman s r 1989 a complete spherical harmonic approach to luni solar tides geophys j int 99 457 468 csr model eanes r j 1995 private communication and desai and wahr model desai s h wahr j m 1995 empirical ocean tide models estimated from topex poseidon altimetry j geophys res 100 25205 25228 the averages of the five estimates are 0 433 gal and 0 244 gal in amplitude and 192 9 and 179 5 in phase for the mf and mm waves respectively the five estimates differ by a maximum of 0 104 gal in amplitude and 18 8 in phase for the mf wave and by 0 033 gal and 6 4 for the mm wave the estimated mm phases are nearly 180 for the five models and the variation of their values among the models is relatively small compared with that of the mf phases these indicate that the mm wave is much closer to an equilibrium tide than the mf wave due to the variation of the ocean tide corrections the corrected factors were scattered within the ranges of 1 158 to 1 169 for the mf wave and of 1 163 to 1 169 for the mm wave however it is noted that the mean factors of the five ocean models i e 1 162 0 023 for the mf wave and 1 165 0 014 for the mm wave prefer slightly larger value rather than those estimated from the theory of the elastic tide

the effects of mantle anelasticity on nutations earth tides and tidal variations in rotation rate summary we model the effects of mantle anelasticity on luni solar nutations on tidal deformation on tidal variations in rotation rate and on the eigenfrequency of the free core nutation our results can be used to invert observations to solve for the anelastic contributions to the shear and bulk moduli of the upper and lower mantle we use specific anelastic models to numerically estimate the effects of anelasticity on these geodetic observables we compare our nutation estimates with observational results among our conclusions 1 mantle anelasticity is likely to be the most important source of damping for the free core nutation 2 present vlbi nutation results are in principle accurate enough to usefully bound anelasticity at diurnal periods but the discrepancy between the vlbi observed nutations and the 1984 iau nutation model cannot be explained by anelasticity and is not yet well enough understood to allow anelasticity to be determined from the data

a new test of earth tide models in central europe new improved ocean tide models allow a corresponding improvement in ocean tide loading computations during recent years various groups have made more accurate tidal gravity observations in central europe using gravimeters carefully calibrated on various calibration lines this progress with tidal gravity measurements and ocean loading corrections now allows a more comprehensive test of body tide models than was possible previously it is shown that the o1 and m2 gravimetric factors corrected using the latest ocean tide models are very consistent between the sites despite the different instruments and gravity calibration lines that have been used these observations allow constraints to be put on the anelasticity of the earth at tidal frequencies the corrected gravimetric factors are consistent with recent model results for both the elastic prem model and with 0 09 for an anelastic prem model with the q for dissipation in shear varying as frequency to the power

significant seismic anisotropy beneath the southern lhasa terrane tibetan plateau 1 shear wave splitting measurements using teleseismic pks skks and sks phases recorded by station lsa on the southern part of the lhasa terrane of the tibetan plateau reveal significant azimuthal anisotropy with a splitting time of up to 1 5 s a conclusion that is contradictory to previous studies which suggested isotropy or weak anisotropy in addition systematic variations of the splitting parameters fast polarization direction and splitting time with the arriving azimuth of the seismic ray path are observed suggesting a model of anisotropy that is more complicated than a single layer with horizontal axis of symmetry the measurements are consistent with a model with two layers of anisotropy the top layer has a ne sw fast direction which is consistent with gps revealed direction of surface movement and can be associated with lattice preferred orientation of middle lower crustal minerals such as amphibole the lower layer has a nearly e w fast direction and can be the consequence of either the n s directed compressional stress originated from the india eurasia collision or flow in the asthenosphere related to the absolute motion of eurasia this study underlines the importance of a long duration of deployment of seismic stations in resolving complex anisotropy

chemical stratification at the top of earth s core constraints from observations of nutations abstract dissipation due to tidally driven flow in the earth s liquid core is detected in observations of nutations one source of dissipation is due to electromagnetic core mantle coupling but this mechanism requires a high electrical conductivity on the mantle side of the boundary and a strong radial magnetic field an alternative mechanism is viable in the presence of fluid stratification at the top of the core stratification causes the fluid close to the core mantle boundary to be trapped by the effects of topography further from the boundary the stratified fluid is swept past the mantle with the underlying tidal flow shear in the flow induces electric currents where the fluid is permeated with a radial magnetic field the resulting dissipation is only weakly dependent on the electrical conductivity of the mantle and the required strength of the radial magnetic field can be lowered for a representative calculation we explain the observed dissipation with a radial field of 0 5 mt and a mantle conductivity of 1000 s m provided the buoyancy frequency in the stratified layer is 0 09 s 1 such a strong stratification has recently been proposed on the basis of chemical interactions between the core and the mantle nutation observations support the presence of stratification to the extent that the resulting dissipation mechanism is more compatible with conventional estimates for the radial magnetic field and the mantle conductivity

determination of long term changes in the earth s gravity field from satellite laser ranging observations temporal changes in the earth s gravity field have been determined by analyzing satellite laser ranging slr observations of eight geodetic satellites using data spanning an interval of over 20 years the satellites used in the analysis include starlette lageos 1 and 2 ajisai etalon 1 and 2 stella and be c geophysical parameters related to both secular and long period variations in the earth s gravity field including the geopotential zonal rates and and the 18 6 year tide parameter were estimated the estimated values for these parameters are centimeters and s18 6 20 0 1 0 2 centimeters the amplitude and phase for the 18 6 year tide are in general agreement with the effects predicted by the earth s mantle anelasticity the solution accuracy was evaluated by considering the effects of errors in various non estimated dynamical model parameters and by varying the data span and data sets used in the solution estimates for from individual lageos 1 and starlette slr data sets are in good agreement the lumped sum values for and are very different for lageos 1 and starlette the zonal rate determination is limited to degree 6 with the current slr data sets analysis of the sensitivity of the solution for the zonal rates to the satellite tracking data span suggests that the temporal extension of the current slr data sets will enhance the solution of zonal rates beyond degree 6

a parametrized solid earth tide model and ocean tide loading effects for global geodetic baseline measurements summary an observation model for earth tide displacements in application to very long baseline interferometry and similar precise geodetic techniques is developed it incorporates effects from anelasticity ellipsoidal figure and fluid core resonance based on a harmonic development of the external potential the model follows the familiar love number concept the transfer function of the earth to each harmonic is formulated in terms of coupled harmonics in the space domain and fulfils the causality condition in the time domain solve for parameters can be chosen flexibly the guideline however has been to provide a minimum set of well defined and well resolvable tide response parameters for analysis of observations the aim of accuracy for tide displacements prediction is below 1 mm being the major perturbation of the solid earth tide ocean tide loading effects are computed and the accuracy of the models involved is discussed it appears that the major error source relates to those ocean tide frequencies for which global models are not available these frequencies form a continuum with a power spectrum being largely a result of non linear tide interaction the associated loading effects cannot be reliably interpolated from global tide models which are available only for a few distinct frequencies and which disregard tidal intermodulation thus an accuracy of 1 mm for computed loading tide displacements cannot always be achieved

the variation with frequency of the long period tides the oceanic response to long period tidal forcing in closed basins approaches equilibrium for periods much longer than a month for moderate values of dissipation at a given frequency the response is closest to equilibrium near the eastern wall of the basin global calculations of the mf and mm tides made using a 2 2 grid are presented changes in the length of day have also been computed for these tides

verification of the ellipsoidal earth model with an inelastic and convective mantle using tidal gravity variations revisited summary tidal gravity observations can be used to validate theoretical estimation for inelastic response of the earth and its latitude dependence using gravimetric factors we used superconducting gravimeter sg data at five sites mets ahovi strasbourg sutherland canberra and syowa to validate theoretical estimation based on an existing method for the correction of ocean loading effect we tested eight global ocean tide models four old csr4 0 got99 2b nao 99b and fes2004 and four new tpxo7 atlas eot11a dtu10 and hamtide11a were tested we selected an optimal ocean tide model based on the criterion of the smallest misfit for the three main waves o1 k1 and m2 at each station as determinedbytheresidualbetweentheobservedloadingeffectandthemodelledoceanloading effect large discrepancies among the results of ocean tide models remained at mets

the rotation of the earth studies of the earth s rotation provide one of the best means of probing the interactions of the atmosphere oceans and solid earth as well as the structure of the core and mantle since the last report of the u s national report to the iugg tapley 1983 two developments have led to significant improvement in the measurement of the rotation the upgrading of the laser network of the national aeronautics and space administration nasa and the expansion of vlbi observations coordinated by the national geodetic survey ngs with the support of nasa and the u s naval observatory both of these developments have been complemented by strong contributions from other countries the availability of more accurate measurements together with healthy research support in this field by federal agencies has also created a ripe environment for progress in theoretical studies of the rotation

stacking global gps verticals and horizontals to solve for the fortnightly and monthly body tides implications for mantle anelasticity the availability of long term position measurements from permanent gps stations distributed around the earth makes it feasible to extract small globally coherent long period geophysical signals from the data using 11 years of daily vertical and horizontal positions from over 600 permanent gps stations worldwide we solve for the amplitude and phase of the fortnightly and monthly body tides by stacking the surface displacements against spherical harmonics and isolating the fortnightly and monthly signals in the stacks we use our solutions to help constrain the earth s anelastic properties which are not well understood within the tidal frequency band our error estimates include the effects of the following 1 random noise across the fortnightly and monthly tidal bands 2 fortnightly and monthly ocean tide model errors 3 errors in the diurnal and semidiurnal ocean tide models that alias into the fortnightly and monthly frequency bands 4 errors in the solid earth green s functions used to compute ocean tidal loading corrections and 5 leakage from gps draconitic signals at periods close to the fortnightly and monthly frequencies the mantle anelasticity coefficients we infer from our solutions are consistent with a frequency dependence of mantle q with in the range 0 1 0 3

elasto gravitational deformation relative gravity changes and earth dynamics summary we consider the elasto gravitational deformation of an earth model with fluid parts core ocean atmosphere a love number formalism is used in order to express the global deformation induced by volume potentials tides variations in the earth s rotation or boundary conditions in pressure transverse stress load at the interfaces between the fluid layers and the solid mantle the induced disturbances in gravity are expressed with the help of generalized gravimetric factors and special attention is paid to resonance processes various applications related to global earth dynamics are developed and numerically quantified the surface gravity changes caused either by a variation in the direction of the earth s rotational axis polar motion or in the rotation rate length of the day are compared with the lunisolar gravimetric tides the loading effect due to the oceans is found to increase the oceanless gravimetric factor by about 2 5 per cent two simplified approaches are proposed to model the gravity perturbations originating in the fluid core e g due to buoyancy core modes it is shown that a degree 2 planetary scale pressure field acting at the core mantle boundary of about 80 pa is able to induce a 10 ngal surface signal similarly gravity contributions from the atmosphere or oceans are derived using outer pressure load or spheroidal shear stress gravimetric factors a degree 2 surface pressure and transverse traction of 100 pa causes a gravity change of 0 27 and 0 14 pgal respectively finally we point out that in addition to the solar gravitational tide there are several other contributions rotational meteorological appearing in the annual gravity signal by different gravimetric factors we therefore conclude that high precision relative gravimetry can provide useful information not only about the earth s physical properties but also about its dynamical behaviour

a comparison of annual vertical crustal displacements from gps and gravity recovery and climate experiment grace over europe 1 we compare approximately 3 years of gps height residuals with respect to the international terrestrial reference frame with predictions of vertical surface displacements derived from the gravity recovery and climate experiment grace gravity fields for stations in europe an annual signal fit to the residual monthly heights corrected for atmospheric pressure and barotropic ocean loading effects should primarily represent surface displacements due to long wavelength variations in water storage a comparison of the annual height signal from gps and grace over europe indicates that at most sites the annual signals do not agree in amplitude or phase we find that unlike the annual signal predicted from grace the annual signal in the gps heights is not coherent over the region displaying significant variability from site to site confidence in the grace data and the unlikely possibility of large amplitude small scale features in the load field not captured by the grace data leads us to conclude that some of the discrepancy between the gps and grace observations is due to technique errors in the gps data processing this is evidenced by the fact that the disagreement between gps and grace is largest at coastal sites where mismodeling of the semidiurnal ocean tidal loading signal can result in spurious annual signals