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

deformation induced crystallographic preferred orientation of hcp iron an experimental study using a deformation dia apparatus abstract shear and uniaxial deformation experiments on hexagonal close packed iron hcp fe was conducted using a deformation dia apparatus at a pressure of 13 17 gpa and a temperature of 723 k to determine its deformation induced crystallographic preferred orientation cpo development of the cpo in the deforming sample is determined in situ based on two dimensional x ray diffraction using monochromatic synchrotron x rays in the shear deformation geometry the 0001 and 11 2 0 axes gradually align to be sub parallel to the shear plane normal and shear direction respectively from the initial random texture in the uniaxial compression and tensile geometry the 0001 and 11 2 0 axes respectively gradually align along the direction of the uniaxial deformation axis these results suggest that basal slip 0001 11 2 0 is the dominant slip system in hcp fe under the studied deformation conditions the p wave anisotropy for a shear deformed sample was calculated using elastic constants at the inner core condition by recent ab initio calculations strength of the calculated anisotropy was comparable to or higher than axisymmetric anisotropy in earth s inner core

the computation of body wave synthetic seismograms in laterally homogeneous media synthetic seismograms computed for realistic horizontally stratified media are now routinely used as an aid to seismic interpretation this paper reviews the theoretical background to these methods and presents comparisons of the two popular algorithms reflectivity and wkbj seismograms for a variety of earth models the transformed wave equations are developed from the equations for a spherical gravitating medium in a symmetric form suitable for body wave calculations four methods of solving these equations in general inhomogeneous layers are described the wkbj and langer asymptotic expansions and the wkbj and langer iterative solutions together with the earth flattening transformation and the ray expansion transformed solutions for body waves can then be obtained for realistic layered media four methods of inverting the frequency and wave number transformations are also described the real and complex spectral and slowness methods although realistic seismic models are normally sufficiently complicated that numerical calculations are essential before proceeding with numerical comparisons we have included a review of the canonical signals included in body wave seismograms these analytic results for direct rays partial and total reflections turning rays on forward and reversed branches head waves interface waves airy caustics and fresnel and interface shadows are useful to anticipate and understand numerical problems and results finally a comparison of green s functions for crustal mantle and whole earth models calculated using the wkbj and reflectivity algorithms is included

ocean tide model obtained from topex poseidon altimetry data tidal corrections are very important for oceanographic study of altimetry because tidal signals contaminate the low frequency part of raw altimetric signals accurate tidal predictions are also necessary for geophysical research such as with the superconducting gravimeter scg which needs to distinguish very weak signals from the overwhelming tidal signals the aim of this paper is to derive accurate global ocean tide models from the topex poseidon sea surface height data of 5 cm accuracy more accurate than any other previous altimeter data topex geophysical data records of cycles 9 94 were processed and analyzed we describe response analysis of tidal waves at crossover points and application of hydrodynamical interpolation the tidal solutions with 0 5 grid system are obtained for eight major constituents i e m2 s2 n2 k2 k1 o1 p1 and q1 and compared with the schwiderski 1980a b c model the cartwright and ray 1991 model and the eight constituent version of the egbert et al 1994 model or tpxo 2 the accuracy of the models is checked using island and bottom tide gauge data in open ocean and using scg data in antarctica and japan

seismic tomography of the uppermost inner core abstract seismic body wave and normal mode analyses have revealed that the inner core is solid strongly anisotropic and characterized by dramatic quasi hemispherical differences in elastic structure and attenuation yet despite these discoveries the highly heterogeneous and incomplete data coverage of the inner core has impeded the development of tomographic models even at the longest wavelengths here we use a probabilistic and transdimensional tomographic approach tbi on a newly expanded dataset of p wave travel times sensitive to the upper 120 km of the inner core the tbi approach yields a ensemble of parsimonious models that simultaneously capture both the dominant hemispheric dichotomy and laterally abrupt velocity variations analysis of the model ensemble allows us to determine the locations of the hemisphere boundaries and rule out the presence of hemispheric dichotomy in anisotropy instead we robustly map regional variations in anisotropy beneath africa and the eastern pacific and detect variations at high latitudes suggesting that cylindrical anisotropy may not be adequate for describing the uppermost inner core

the ocean tide gravimetric loading reconsidered in 1994 95 a set of new global ocean tide models computed by different teams was made available to the scientific community these models were derived from the analysis of satellite altimetric data numerical hydrodynamics or a combination of both the task is now to evaluate their relative accuracy in particular with independent data the data bank prepared by the international center for earth tides icet melchior 1994 gives us a unique opportunity to compare the tidal models by testing their capability to predict the induced gravimetric loading effects the more recent versions released in 1995 of the models by ma et al 1994 and by schrama and ray 1994 both completed at high latitudes by the le provost et al 1994 fes94 1 model have the best scores for the semidiurnal m2 wave with a standard deviation sd of the gravimetric data residues less than 0 540 gal schwiderski 1980 and egbert et al 1994 models give the smallest residual sd about 0 370 gal for the diurnal o1 component however the ordering of the models may change when we focus on some particular regions of the globe

intercomparison of recent ocean tide models one of the tremendous achievements of the topex poseidon t p satellite mission is the release of 12 new global ocean tide models during 1994 virtually all of these models are based on the high precision altimetry obtainable from the t p satellite and all of the models are superior to both the cartwright and ray 1990 1991 model as well as to the schwiderski 1980a b model when compared to tide gauges in the present intercomparison only global ocean tide models released during 1994 have been tested as t p continues to operate new ocean tide models will continue to be released and existing ocean models will be updated hence this intercomparison can only present a snapshot of the state of the art within ocean tide modeling however the intercomparison demonstrates the high accuracy and consistency of all these recent ocean tide models from a comparison with a common 104 tide gauge data set compiled by le provost and others unpublished data the general result is that six of the new ocean tide models have rms agreement better than 3 cm the obtainable accuracy with different tide gauge types raises the question about the accuracy of ground truth as ocean tide models become increasingly more accurate the accuracy of the harmonic constants derived from the tide gauge recordings becomes significant generally the rms agreement between models based on 2 years of t p altimetry is significantly better than the agreement between models based on 1 year of t p altimetry for models based on two years of t p altimetry the rms agreement has values around 2 0 1 4 1 0 and 0 7 cm for the m2 s2 k1 and o1 constituents respectively as a preliminary evaluation these values might be taken as a measure of the consistency of ocean tides estimated from the first part of the t p mission which is extremely promising for future ocean tide models derived from t p altimetry using 3 or more years of data this also suggests that further improvement using 3 or more years of data will only be marginal the differences arise when studying the ocean tides on continental shelves surrounding the ocean major differences are seen especially on the patagonian shelf as the continental shelves are critical for tidal dissipation it will be very important to improve tide models on the shelves in future global ocean tide models

multiple phase analysis of the shear velocity structure in the d region beneath alaska a large data set more than 990 total waveforms comprised of north american station recordings of a variety of long period s phases s scs sdiff ss sscs sks skks from 36 earthquakes in western pacific subduction zones is analyzed to determine characteristics of the shear velocity structure in the d region beneath alaska three hypotheses that have been proposed to explain observed scs precursors and s waveform distortions for this region are appraised with the multiple phase data set and the radial and lateral variations of the shear velocity structure in the 1500 km broad portion of d sampled are also assessed the observed travel time and waveform variations may result from diffraction by near source slab structure scattering by low velocity heterogeneity in the lower mantle or interaction with complex velocity gradients in d associated with a deep mantle velocity discontinuity we utilize waveform modeling and differential time analysis to resolve greater detail of the structure than can presently be obtained by standard travel time tomography techniques and find that the discontinuity model is most consistent with the data subdivision of the data by source region and source to receiver azimuth establishes that the observations exhibit fairly stable behavior which is consistent with extensive local stratification of d the data show sufficient coherence over the 1500 km broad region that we find it useful to present a local average radial model the preferred model sylo has a 2 75 velocity increase 243 km above the core mantle boundary and a negative velocity gradient within the d layer analysis of sks s sks scs and sks skks differential times also indicates that the outermost 100 km of the core below the fast d region underlying alaska must be slower than the prem structure the observations exhibit significant scatter most of which can be attributed to unmodeled heterogeneity in the midmantle and near source regions as well as lateral variations in the d region the complex structure of d that we prefer may be associated with large scale downwelling in the lower mantle but it is not certain whether it is a purely thermal or a combined chemical and thermal effect

accuracy assessment of recent ocean tide models over 20 global ocean tide models have been developed since 1994 primarily as a consequence of analysis of the precise altimetric measurements from topex poseidon and as a result of parallel developments in numerical tidal modeling and data assimilation this paper provides an accuracy assessment of 10 such tide models and discusses their benefits in many fields including geodesy oceanography and geophysics a variety of tests indicate that all these tide models agree within 2 3 cm in the deep ocean and they represent a significant improvement over the classical schwiderski 1980 model by approximately 5 cm rms as a result two tide models were selected for the reprocessing of topex poseidon geophysical data records in late 1995 current ocean tide models allow an improved observation of deep ocean surface dynamic topography using satellite altimetry other significant contributions include theft applications in an improved orbit computation for topex poseidon and other geodetic satellites to yield accurate predictions of earth rotation excitations and improved estimates of ocean loading corrections for geodetic observatories and to allow better separation of astronomical tides from phenomena with meteorological and geophysical origins the largest differences between these tide models occur in shallow waters indicating that the current models are still problematic in these areas future improvement of global tide models is anticipated with additional high quality altimeter data and with advances in numerical techniques to assimilate data into high resolution hydrodynamic models

a comparison of tidal ocean loading models using superconducting gravimeter data 1 errors in global ocean models have been shown to be larger than the accuracy of surface gravity measurements baker and bos 2001 and also new space gravity missions ray et al 2001 in this paper we compare the tidal loading estimated using 10 different ocean tide models to the surface gravity variations observed with 12 superconducting gravimeters sg belonging to the global geodynamics project crossley et al 1999 worldwide network ocean tidal gravity variations are shown to be mostly dependent on tidal sea height variations within a radius of 5000 km precise surface gravity measurements are therefore another tool for validating ocean tidal models from short to long wavelengths in addition for example to tide gauge data in this study we also compute the tidal loading using several different available computer codes as for ocean tidal models we show that the differences between tidal loading programs are frequently larger than the error estimates of sg measurements compared to previous models both recent hydrodynamical and topex poseidon derived tidal models allow a significant reduction of discrepancies between ocean tidal observations using sg and tidal loading estimates there still remains however a nonnegligible in phase discrepancy between ocean tidal loading estimates and surface gravity observations whereas the out of phase component is much smaller we have shown that the in phase disagreement does not seem to be caused by an inaccurate determination of the sg calibration

global charts of ocean tide loading effects global ocean tide loading charts of the radial displacement the potential divided by g gravity acceleration and the gravity effect have been computed using the 11 constituents m2 s2 n2 k2 k1 o1 p1 q1 mf mm ssa of schwiderski s tidal model these new charts have a resolution of 1 1 on the continents as well as on the oceanic area a description of farrell s convolution method to compute the loading effects is given and an estimate of the numerical errors leads to the conclusion that these global charts have a precision better than 2 5 independent of the accuracy of schwiderski s maps the current approximation of the loading effects by a proportionality relation with the local oceanic tides is also compared with farrell s convolution method departures of several centimeters systematically appear in particular over the continental shelves we then show that the maps of the oceanic tides deduced from satellite altimetry could be corrected for the loading effect by an iterative computational procedure based on our algorithm of farrell s convolution

equatorial anisotropy in the inner part of earth s inner core from autocorrelation of earthquake coda the speed of seismic waves passing through the earth s inner core varies with direction analysis of earthquake seismic data suggests that this directional dependence differs between innermost and outer inner core

test of the innermost inner core models using broadband pkikp travel time residuals 1 two different innermost inner core imic models have recently been proposed each with different radii and different orientation and strength of anisotropy in order to test these imic models we have systematically assembled a high quality dataset of broadband pkikp data in the epicentral distance range of 150 to 180 our new dataset consists of 1 100 individually measured absolute pkikp arrival times also pkikp bottoming points and ray paths in the inner core are well distributed in the east west and north south hemispheres we invert this dataset for two layer models of anisotropy in the inner core and compare the fits obtained with those predicted from the existing imic models our results show that if there is an imic its radius is most likely around 500 km rather than the 300 km originally proposed and is in better agreement with the layering in the inner core based on pkikp waveform modeling

upper mantle slab under alaska contribution to anomalous core phase observations on south sandwich to alaska paths abstract observations of travel time anomalies of inner core sensitive pkpdf seismic body waves as a function of path orientation with respect to the earth s rotation axis have been interpreted as evidence of anisotropy in the inner core paths from earthquakes in the south sandwich islands to stations in alaska show strongly anomalous travel times with a large spread that is not compatible with simple models of anisotropy here we assess the impact of strong velocity heterogeneity under alaska on the travel times directions of arrival and amplitudes of pkpdf we use 3d ray tracing and 2 5d waveform modelling through a new high resolution tomography model of the upper mantle beneath alaska we find that the structure beneath alaska notably the subducting slab is reflected in the patterns of these pkpdf observations and this can be replicated by our model we also find similar patterns in observed teleseismic p waves that can likewise be explained by our slab model we conclude that at least 2 s of the travel time anomaly often attributed to inner core anisotropy is due to slab effects in the upper mantle beneath alaska

is inner core seismic anisotropy a marker for plastic flow of cubic iron this paper investigates whether observations of seismic anisotropy are compatible with a cubic structure of the inner core fe alloy we assume that anisotropy is the result of plastic deformation within a large scale flow induced by preferred growth at the inner core equator based on elastic moduli from the literature body centered cubic or face centered cubic fe produces seismic anisotropy well below seismic observations 0 4 a monte carlo approach allows us to generalize this result to any form of elastic anisotropy in a cubic system within our model inner core global anisotropy is not compatible with a cubic structure of fe alloy hence if the inner core material is indeed cubic large scale coherent anisotropic structures incompatible with plastic deformation induced by large scale flow must be present

anisotropy in the deep earth abstract seismic anisotropy has been found in many regions of the earth s interior its presence in the earth s crust has been known since the 19th century and is due in part to the alignment of anisotropic crystals in rocks and in part to patterns in the distribution of fractures and pores in the upper mantle seismic anisotropy was discovered 50 years ago and can be attributed for the most part to the alignment of intrinsically anisotropic olivine crystals during large scale deformation associated with convection there is some indication for anisotropy in the transition zone particularly in the vicinity of subducted slabs here we focus on the deep earth the lower mantle and core where anisotropy is not yet mapped in detail nor is there consensus on its origin most of the lower mantle appears largely isotropic except in the last 200 300 km in the d region where evidence for seismic anisotropy has been accumulating since the late 1980s mostly from shear wave splitting measurements recently a picture has been emerging where strong anisotropy is associated with high shear velocities at the edges of the large low shear velocity provinces llsvps in the central pacific and under africa these observations are consistent with being due to the presence of highly anisotropic mgsio 3 post perovskite crystals aligned during the deformation of slabs impinging on the core mantle boundary and upwelling flow within the llsvps we also discuss mineral physics aspects such as ultrahigh pressure deformation experiments first principles calculations to obtain information about elastic properties and derivation of dislocation activity based on bonding characteristics polycrystal plasticity simulations can predict anisotropy but models are still highly idealized and neglect the complex microstructure of polyphase aggregates with strong and weak components a promising direction for future progress in understanding the origin of seismic anisotropy in the deep mantle and its relation to global mantle circulation is to link macroscopic information from seismology and microscopic information mineral physics through geodynamics modeling anisotropy in the inner core was proposed 30 years ago to explain faster p wave propagation along the direction of the earth s axis of rotation as well as anomalous splitting of core sensitive free oscillations there is still uncertainty about the origin of this anisotropy in particular it is difficult to explain its strength based on known elastic properties of iron as it would require almost perfect alignment of iron crystals indeed the strongly anomalous p travel times observed on paths from the south sandwich islands to alaska may or may not be due to inner core anisotropy and will need to be explained before consensus can be reached on the strength of anisotropy in the inner core and its origin

waveform search for the innermost inner core abstract waveforms of the pkikp seismic phase are inconsistent with the effects of a sharp boundary at 300 km radius of an inner most inner core seismograms synthesized for the distance range 150 to 180 in models having a discontinuity at 300 km radius in the inner core exhibit focused diffractions around the innermost sphere at antipodal range that are inconsistent with observed pkikp waveforms a few examples however can be found of pkikp complexity near 165 consistent with a triplication created by a 475 km radius discontinuity a rapid change in the magnitude and variance of seismic attenuation of pkikp whose rays turn between 400 and 600 km radius is also observed consistent with an innermost sphere of low regionally uniform seismic attenuation models predicting waveforms in agreement with observed waveforms have either a transition in elastic and anelastic properties spread over a depth interval greater than 100 km or an innermost sphere of differing elastic properties that exceeds 450 km radius the weak but suggestive evidence for an innermost inner core may simply represent a transition in fabric spread over 100 km or more centered near 500 km radius this change may signify the end stage of solidification flow and re crystallization resulting in the highest ordering and largest grain sizes of intrinsically anisotropic crystals

laterally varying reflector at the top of d beneath northern siberia summary we analyse p wave data from the french laboratoire de dctection et gcophysique l d g network of digital short period seismic stations whereas our previous paper houard nataf 1992 showed a few promising kurd events and depicted the methods we proposed to apply an extensive analysis of 32 earthquakes from the kurivkamchatka region has now been carried out by using the deconvolution technique previously described houard nataf 1992 clear and quantitative evidence of intermediate arrivals between the p and pcp waves is shown in the 75 82 distance range our approach is complementary to previous studies in the same region which used broad band data recorded at a dense narrow aperture array weber davis 1990 weber 1993 or long period data recorded at the wwssn stations gaherty lay 1992 for each station record sections of deconvolved signals from different earthquakes are built and lead us to eliminate crustal reverberations beneath l d g stations as a major explanation for these secondary arrivals a compilation of the most conclusive signals has been made it is perhaps one of the most complete pdp wave record sections since the move out with distance can be followed clearly with a good sampling over more than 5 the move out with distance of this extra pdp arrival its residual slowness value eliminates source complexities diffraction or multipathing through the kuril subduction slab as possible explanations the extra arrivals indicate the existence of a lower mantle reflector the structure of the lay discontinuity is investigated using tpdp tp residual traveltimes two different residual time versus distance tendencies are found which correlate to different geographical bounce point regions indicating the existence of lateral variations of the structure the d region is also sampled further south at distances well beyond the theoretical triplication cross over by analysing events from the honshu ryukyu islands region but only one p wave branch is observed the hodochrones and p a curves of the first p arrival are used as a complementary analysis the global prem model dziewonski anderson 1981 predicts correct p wave slownesses though its smooth lower mantle structure does not account for pdp observations this may be an indication that the lay discontinuity is a global feature however the hodochrones of the first p arrival do not allow us to test the existence of the discontinuity in the 82 85 cross over distance range

a continuing discussion about the correlation of tidal gravity anomalies and heat flow densities on the basis of several objections rydelek et al phys earth planet inter 68 215 219 1991 hereafter noted rzh denied the existence of a correlation between residuals of tidal gravity r and heat flow h suggested by other workers to re examine the whole matter on safe grounds we previously revised and reanalysed all the original tidal data from 300 stations taking care of the rzh objections by eliminating what they considered as the important sources of errors in the data essentially calibration errors of the instruments in amplitude and phase using this new data base we meet here one by one the other criticisms not related to the original tidal measurements and show that most of them are not valid in particular those concerning oceanic load and attraction corrections the findings are as follows 1 no correlation between diurnal tide and semi diurnal tide residuals is normal 2 distance from the sea is not a valid criterion for elimination of several excellent stations 3 unexpected residues at the south pole are not due to imperfections of the cotidal schwiderski maps but to ice shelf tides not considered by rzh 4 the correlation of the tidal gravity residues with the age of tectonic provinces is proposed as an alternative to the correlation with heat flow the data used in 1991 having been corrected are recalculated for comparison with 1986 1991 statistics the correlation is confirmed with the same degree of probability also new tidal gravity data obtained since 1990 with nullified instruments as recommended by rzh in africa 31 stations and latin america 34 stations are included in new statistics which also confirm the correlation the global result obtained from 174 revised and new stations on all continents gives a correlation coefficient k 0 691 with a linear regression r 0 0201 h 57 0 063 0 0013 where r is in microgals and h is in mw m 2 as there is at present no practical or theoretical means to take into account the role of fluids lubrication and stress corrosion owing to deep seated saline waters or fluids in crustal processes such as tidal deformations such small tidal gravity anomalies cannot be correctly calculated the use of a correlation technique therefore remains the only way to treat unexplained residues even if this does not constitute an unequivocal proof other arguments have to be found to deny the existence of this correlation

a new data bank for tidal gravity measurements db 92 abstract tidal gravity parameters are now available in 352 permanent or temporary stations all over the world previous tentative interpretations of these data were made on the basis of a data bank created in 1980 1982 which contained all available results without any discrimination which could have appeared as arbitrary these interpretations were criticized on the basis of the different qualities of instruments null instruments or not data calibration and necessary corrections for ocean continent interactions as we agree that a careful re examination of the basic data is needed before any geophysical discussion we have built this new data bank which contains only those 211 stations where rigid control of every step in the observations calibrations and reduction could be made either because the original data are stored in the world data center c or because the published results give enough information to permit checks and revisions as a result the scattering in the tidal parameters is reduced by a factor of 2 with respect to the previous data while the mean values of the amplitude factors of the two main waves o 1 diurnal m 2 semi diurnal calculated continent by continent agree with the best available earth model it is expected that this new data bank will be used for renewed discussions of the results

lateral variations near the core mantle boundary differential travel times between s and sks ts sks and skks and sks tskks sks along with amplitude behavior have been used to study lateral variations at the core mantle boundary the data were recorded by the world wide seismographic station network wwssn and the canadian seismograph network csn from source regions in south america and the fiji tonga area a core mantle boundary region traversed by sks and s beneath the mid pacific from the fiji tonga area to north american stations shows the most anomalous behavior in ts sks sks and s are anomalously separated by up to 8 seconds in addition to ts sks anomalies sks and skks are anomalously separated by 2 to 3 seconds a model fitting ts sks for this anomalous region requires one or more of the following 1 up to 5 increase in the top 300 km of outer core velocity 2 a large scale high vs region 2 increase in the lower mantle ne of tonga 3 lateral variations in d shear wave velocities of up to 3 however 1 above predicts a decrease in tskks sks contradicting the observations this suggests that 2 and 3 are more likely explanations in modeling this data set

testing recent global ocean tide models with loading gravimetric data as soon as altimetric data from topex poseidon satellite were available several ocean tide models were able to be constructed by different teams in response to the scientific community request here we present a complement to a first comparison study made with ten tidal models llubes and mazzega 1996 we use five more models of which some are updated versions computed using longer time series of altimetric data the loading tide effects predicted by these models are compared to a data base of 228 gravimetric stations provided by the international center for earth tides melchior 1994 global statistical tests provide us with the relative performances of the models merging the five new models with the ten previous models allows us to make more general conclusions csr3 0 eanes 1994 remains the best of the fifteen models for the m2 constituent standard deviation of 0 425 gal for the o1 constituent schwiderski schwiderski 1980 with a standard deviation of 0 298 gal gives the best results when considering only regional subsets of gravimetric data no ocean tide model systematically performs better than any other

seismic anisotropy in the earth s innermost inner core testing structural models against mineral physics predictions using an updated data set of ballistic pkikp travel time data at antipodal distances we test different models of anisotropy in the earth s innermost inner core imic and obtain significantly better fits for a fast axis aligned with earth s rotation axis rather than a quasi equatorial direction as proposed recently reviewing recent results on the single crystal structure and elasticity of iron at core conditions we find that an hcp structure with the fast c axis parallel to earth s rotation is more likely but a body centered cubic structure with the 111 axis aligned in that direction results in very similar predictions for seismic anisotropy these models are therefore not distinguishable based on current seismological data in addition to match the seismological observations the inferred strength of anisotropy in the imic 6 7 implies almost perfect alignment of iron crystals an intriguing albeit unlikely situation especially in the presence of heterogeneity which calls for further studies

stability of iron crystal structures at 0 3 1 5 tpa abstract ab initio molecular dynamics simulations carried out for tetragonal and orthorhombic distortions of iron closely follow the results of static lattice electronic structure calculations in revealing that the body centered cubic bcc phase of fe is mechanically unstable at pressures of 0 3 1 5 tpa and temperatures up to 7000 k crystal structural instabilities originate in the static lattice for the bcc configuration and are consistent with recent results from both static and dynamic high pressure experiments both theory and experiment thus show that the close packed hexagonal hcp and face centered cubic fcc crystal structures of iron are those relevant to the cores of earth like planets

the innermost inner core of the earth evidence for a change in anisotropic behavior at the radius of about 300 km since the discovery of the inner core in 1936 no additional spherical subshell of the earth has been observed based on an extensive seismic data set we propose the existence of an innermost inner core with a radius of 300 km that exhibits a distinct transverse isotropy relative to the bulk inner core specifically within the innermost inner core the slowest direction of wave propagation is 45 from the east west direction in contrast the direction of the slowest wave propagation in the overlying inner core is east west the distinct anisotropy at the center of the earth may represent fossil evidence of a unique early history of inner core evolution

phase relations in the fe fesi system at high pressures and temperatures the earth s core is comprised mostly of iron and nickel but it also contains several weight percent of one or more unknown light elements which may include silicon therefore it is important to understand the high pressure high temperature properties and behavior of alloys in the fe fesi system such as their phase diagrams we determined melting temperatures and subsolidus phase relations of fe 9 wt si and stoichiometric fesi using synchrotron x ray diffraction at high pressures and temperatures up to 200 gpa and 145 gpa respectively combining this data with that of previous studies we generated phase diagrams in pressure temperature temperature composition and pressure composition space we find the b2 crystal structure in fe 9si where previous studies reported the less ordered bcc structure and a shallower slope for the hcp b2 to fcc b2 boundary than previously reported in stoichiometric fesi we report a wide b2 b20 two phase field with complete conversion to the b2 structure at 42 gpa the minimum temperature of an fe si outer core is 4380 k based on the eutectic melting point of fe 9si and silicon is shown to be less efficient at depressing the melting point of iron at core conditions than oxygen or sulfur at the highest pressures reached onlymore the hcp and b2 structures are seen in the fe fesi system we predict that alloys containing more than 4 8 wt silicon will convert to an hcp b2 mixture and later to the hcp structure with increasing pressure and that an iron silicon alloy in the earth s inner core would most likely be a mixture of hcp and b2 phases less

structure and dynamics of earth s inner core abstract the seismological exploration of the earth s inner core has revealed unexpected and puzzling structural complexities its elastic anisotropy is now well established and has been shown to vary spatially there is a well defined hemispherical dichotomy in anisotropy and attenuation and significant variations in the radial direction with weaker anisotropy in the uppermost regions and possibly different properties in an innermost inner core of radius 300 600 km perhaps even more puzzling is the observation of a stably stratified layer at the base of the outer core which has recently been proposed to result from melting of inner core material if confirmed the presence of this layer has major implications for our understanding of convection in the outer core inner core differential rotation with respect to the mantle remains controversial we will review here recent progress in understanding the dynamics of the inner core a number of different models have been proposed for the development of the inner core s structure and formation of the stable layer at the base of the outer core and particular care will be taken to clarify under which conditions the proposed mechanisms can be active

ocean load tides at the south pole a validation of recent ocean tide models small diurnal and semidiurnal gravity tides are seen at the south pole because of the loading by and attraction of the ocean tides these data provide a check on the quality of ocean tide models especially in the southernmost ocean which has historically been the most lacking in tidal data ocean tide models developed in the 1980 s did not predict the gravity tides at this location very well recently developed models based on the topex poseidon altimetric data and improved hydrodynamical modeling agree much better with the observations provided that the tides beneath the ice shelves are included the level of agreement at this remote location suggests that loads from very local tides aside the new generation of ocean tide models can predict the loading tides to very high accuracy

global ocean tides from ers 1 and topex poseidon altimetry ocean tide models representing all major diurnal and semidiurnal tidal constituents with a spatial resolution of 0 75 0 75 have been estimated using the first 1 5 years of ers 1 and topex poseidon altimetry the ocean tide model was derived from the combined use of ers 1 and topex poseidon data by using a modified orthotide formulation that simultaneously solves for all diurnal and semidiurnal constituents as well as the annual signal an additional adjustment of the solar semidiurnal harmonic of the gravitational potential was applied in order to account for radiational forcing particularly in the s2 constituent topex poseidon provides excellent ocean tide estimates in the open ocean however especially in coastal regions the track spacing of topex poseidon 315 km at the equator is too coarse to determine large parts of the ocean tide signal for these regions the inclusion of data from the ers 1 35 day repeat mission provides a valuable supplement as the ers 1 satellite has a track spacing which is around 3 6 times better than that of the topex poseidon satellite the combined ers 1 and topex poseidon ocean tide solution exhibits distinct sectoral geographical pattern of highs and lows when compared with the cartwright and ray 1990 1991 ocean tide model this indicates the presence of small but fundamental orbit errors present in the cartwright and ray ocean tide solution compared with a new set of 104 tide gauge readings compiled by le provost the rms differences of the combined ers 1 and topex solution are 2 51 1 67 1 58 and 1 13 cm for the m2 s2 k1 and o1 constituents respectively the increased spatial resolution of the combined ers 1 and topex model as compared to a topex alone model is seen to reduce rms differences from 37 to 22 cm for the m2 constituent when compared to a selection of 90 pelagic and coastal tide gauges in the northwest european shelf region

ab initio calculations of the elasticity of hcp fe as a function of temperature at inner core pressure ab initio finite temperature molecular dynamics simulations have been used to calculate the elastic constants of hexagonal close packed hcp fe as a function of temperature at similar to 300 gpa the longitudinal modulus c 1 1 decreases with temperature in stark contrast to previous calculations but in agreement with experimental observations on other transition metals at ambient pressures c 33 and c 44 also decrease with temperature while c 12 and c 23 slightly increase when these moduli are used to calculate p wave velocities through the crystal the sense of the anisotropy is such that v p is fastest along the c axis up to 5000 k however by 5500 k the anisotropy reverses with v p becoming faster in the a b plane this suggests that for an inner core dominated by crystals of hcp fe aligned with the c axis in the polar direction the observed isotropic outer inner core could result from the hcp fe being at a temperature close to melting where the axial wave velocities parallel and perpendicular to the c axis become similar while at greater depths in the inner inner core where iron is further from melting stronger anisotropy is achieved with the faster p wave velocities parallel to the polar axis no other mechanisms such as changes in composition or crystal alignment are therefore required to account for the observed change in seismic anisotropy of the earth s inner core with depth c 2009 elsevier b v all rights reserved

tidal loading in south western europe a test area the gravity attraction and loading effects computed on the basis of recent ocean tide models still present non negligible discrepancies for the principal tidal lunar wave m2 the installation of new tidal gravity stations in these regions would be useful to assess the accuracy of these new ocean tide models in particular for the atlantic ocean this investigation clearly proves that there is a real scientific interest to set up a new earth tides gravity profile along the coasts from belgium to portugal

the structure of fe si alloy in earth s inner core abstract phase relations of iron silicon alloy fe 6 5 wt si and fe 9 wt si were investigated up to 407 gpa and 5960 k in a laser heated diamond anvil cell which likely covers the entire pressure and temperature conditions of the earth s inner core synchrotron x ray diffraction measurements show that fe 9 wt si with a hexagonal close packed hcp structure is stable to 4800 k at 330 gpa corresponding to the pressure at the inner outer core boundary and decomposes into a mixture of si poor hcp and si rich cscl type b2 phases at higher temperatures we also found that the solubility of silicon in solid iron is relatively insensitive to temperature decreasing from 9 to 6 5 wt over a range of 1500 k at 70 gpa these suggest that the inner core is composed solely of the hcp phase when the silicon content is up to 7 wt that likely accounts for the inner core density deficit as well as for the mg si ratio and the si isotopic composition of the mantle additionally the present experiments demonstrate that the incorporation of silicon in iron expands the stability of hcp with respect to that of fcc

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

tomographic imaging of the lowermost mantle with differential times of refracted and diffracted core phases pkp pdiff the mapping of variations in p wave speed in the deep mantle is restricted by the uneven sampling of p waves in particular beneath the southern hemisphere to enhance data coverage we augmented the 1 6 million summary rays of p pp and pwp that we used in previous studies with differential travel times of diffracted and refracted core phases for the core refracted differential travel time residuals pkpab pkpdf and pkpab pkpbc we used 1383 cross correlated digital waveforms as well as 27 000 routinely processed bulletin data we used the waveform data to define quality criteria for the selection and reduction of the bulletin pkp data for pkpdf pdiff we only considered 543 records derived from waveform cross correlation no pcp data were used in this study we used optical ray theory to calculate the ray paths associated with the p pp pwp and pkp data which are measured at 1 hz however to account for the large fresnel zones of the low frequency 50 mhz pkpdf pdiff data we estimated the three dimensional shape of the frechet sensitivity kernels from kernels calculated by normal mode summation the use of these kernels allows us to properly distribute the sensitivity for a given seismic phase over a large mantle volume while allowing the high frequency data to constrain small scale structure the differential times are relatively insensitive to source mislocation and to structure in the shallow mantle beneath source and receivers and they have previously been interpreted exclusively in terms of lateral structure directly above the core mantle boundary cmb however images thus obtained can be contaminated by effects of small scale structure elsewhere in the mantle here we do not make a priori assumptions about the mantle source of anomalous time differentials from test inversions we conclude that both upper and lower mantle structures that are poorly resolved by p data can be mapped into the core along pkp paths but that the effect of outer core structures if any on the mantle model is small compared to the inversion of the p pp and pwp alone the inclusion of the pkpab pkpdf and pkpab pkpbc and pkpdf pdiff data improves the resolution of structure beneath 2200 km depth in particular the joint inversion puts better constraints on the long wavelength variations in the very deep mantle and yields an increase in the amplitude of velocity perturbations near the cmb that is in agreement with but still smaller than inferences from shear wave studies resolution tests indicate that in some regions the enhanced definition of structure is significant but in most regions the improvements are subtle and structure remains poorly resolved in large regions of the mantle

the earth s coda correlation wavefield rise of the new paradigm and recent advances abstract seismology has come a long way in providing insights into earth s internal structure and dynamics among many forward and inverse geophysical techniques developed full waveform modelling seismic tomography and receiver based studies enabled detailed imaging of earth s subsurface the invention of ambient noise tomography within the last two decades revolutionized studies of earth s subsurface based on the cross correlation of the earth s ambient noise that method in particular enabled imaging of earth structure in places where earthquakes or receivers do not exist at the same time progress in imaging the earth s deepest shells has been impeded by the lack of geometric coverage of body waves due to uneven global distribution of seismic sources and receivers and the fact that the ambient noise studies cannot reach deeper than the uppermost earth s shells near its surface in seeking the ways forward global seismologists started experimenting with cross correlating the part of the seismograms recorded many hours after the first arrivals of body waves the so called earthquake coda as in many science disciplines initial work on this topic resulted in controversies but also led to new realisations and discoveries that all contributed to the rise of a new paradigm the earthquake coda correlation wavefield which is the focus of this review paper we do not attempt here to provide a review of ambient noise correlation although we use some familiar concepts to introduce coda correlation our main goal is to review theoretical and observational work to date that resulted in a better understanding of the coda correlation wavefield both as a phenomenon and a powerful method the features in global correlograms exist due to many cross terms of reverberating body waves a principle fundamentally different from the reconstruction of surface waves in the ambient noise correlograms once the coda correlation wavefield is fully understood through theoretical developments the method becomes a powerful way to study earth s deep structure apart from providing a review of the most important results to date we scrutinise the process of making global correlograms and analyse their characteristics while taking into consideration various aspects such as the time after the earthquake the source receiver geometries the level of seismicity and the type of earthquake mechanism furthermore we provide practical examples on how to build correlograms and interpret correlogram features using programming language python our review seeks to promote the topic of coda correlation among already experienced researchers as well as students who embark on this interesting research which may play a central role in global and planetary seismology in the coming decades

qualitative comparisons of global ocean tide models by analysis of intersatellite ranging data 1 four global ocean tide models are compared in terms of their contribution to gravity recovery and climate experiment grace satellite to satellite tracking residuals the residuals are computed relative to a comprehensive model of earth s time varying gravity including allowance for mass motions in the atmosphere ocean terrestrial hydrology and mantle in addition to tides for each analyzed tide model 4 years of grace range rate data are processed range and range acceleration residuals are tidally analyzed by geographic location all four global tide models are shown to be error prone in various ways leaving tidally coherent residuals especially in polar regions but also in some lower latitude regions considerable power in the solar semidiurnal s2 tide in low latitudes suggests errors in our adopted model of atmospheric tides which is based on 3 hourly european centre for medium range weather forecasts operational analyses anomalies in the 2 tidal constituent over some shallow seas suggest the presence of unmodeled nonlinear compound tides in this case 2ms2 similarly anomalies in the nonlinear m4 tide are seen if this constituent is omitted from the models errors in assumed seawater density may be contributing to some residuals

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

a search for anomalies in the lowermost mantle using seismic bulletins abstract for deep events and epicentral distances around 75 the bulletins of the international seismological centre bisc contain many secondary arrivals between p and pcp the reflection from the core mantle boundary cmb which cannot be explained by current spherical symmetric earth models assuming that these arrivals in the p coda are reflections from p velocity anomalies in the lower mantle we calculate the associated reflection points geographical coordinates and distance from the cmb and map both strength relative density of reflection points in bins in the lower mantle and distance of the reflectors from the cmb on a global scale the regions with these anomalous bins cover 3 of the 50 of the lowermost mantle that can be analysed with this data set the most significant regions with anomalous bins values in parentheses give a preliminary estimate of the distance of the reflector from the cmb are under the north atlantic ridge 250 km northern central siberia 230 km japan 180 km the central mid atlantic ridge 310 and 260 km and off the coast of ecuador 340 km the presence of reflectors in one of these regions has already been confirmed by detailed seismic studies using waveform data from arrays and networks a slight 2 3 p velocity contrast is sufficient to produce measurable reflection amplitudes in the distance range of 70 80 ten percent of the lower mantle sampled by this study is covered by bins with no or very few secondary arrivals in the p coda the most significant regions with such a normal lower mantle are under central america the caroline and marshall islands in the eastern pacific the area of hawaii and the easter islands and the northern atlantic identification of the regions with anomalous bins serves to locate the areas of the lowermost mantle which should be analysed further by using the full information content of seismograms the study of the travel time the amplitude and the form of the wavefield recorded preferably at seismic arrays dense networks will allow the determination of the anomalous velocity structure of the core mantle transition zone in more detail the most promising areas for such a study are given here but further anomalies are likely to exist

convection and anisotropy of the inner core estimation of the rayleigh number of the inner core suggests that this region is convecting the flow pattern is likely to produce crystallographic preferred orientation of the elastically anisotropic hexagonal closest packed phase of iron such that compressional wave velocities would be greater in the axial relative to the equatorial direction by roughly 1 percent this result is in agreement with seismological evidence that the inner core is elastically anisotropic

polymorphic nature of iron and degree of lattice preferred orientation beneath the earth s inner core boundary deciphering the polymorphic nature and the degree of iron lattice preferred orientation in the earth s inner core holds a key to understanding the present status and evolution of the inner core a

further evidence for the lay discontinuity beneath northern siberia and the north atlantic from short period p waves recorded in france abstract we analyze data from the french laboratoire de detection geophysique ldg network of digital short period seismic stations the p waves from several earthquakes in the kuril okhotsk region display clear secondary arrivals in the 75 85 range which are not explained by smooth lower mantle models the move out of the arrivals across the network indicates a deep mantle origin we interpret them as waves reflected off or transmitted at the lay discontinuity about 300 km above the core mantle boundary the bounce points at this discontinuity are located beneath northern siberia slightly to the northwest of the region for which a similar structure has been reported we propose tools for investigating the lateral variations of the d structure on the scale 100 1000 km the method we propose is based on the deconvolution of the data or convolution of synthetics by a source time function derived from the data we show that the method helps identification of the waves that interact with the lay discontinuity and enables a more objective mapping of its lateral variations evidence for bumps a few kilometers high on the lateral scale of a few tens of kilometers is proposed we also probe a spot of the lower mantle beneath the north atlantic a detailed analysis of the waveforms from a chiapas earthquake suggests that the lay discontinuity is also present in that part of the world

wave propagation effects and the earth s structure in the lower mantle lay and helmberger and their co workers have recently proposed models of earth structure in which the s velocity increases discontinuously with depth by about 3 at the bottom of a postulated region of abnormally low near zero gradient between depths of about 2300 and 2600 km in the lower mantle such models involve drastic departures from previously proposed models of earth structure in this region by use of kirchhoff wave theory it is shown that the pertinent data may be interpreted alternatively as an effect of wave propagation in an inhomogeneous lower mantle on this alternative interpretation the s velocity need nowhere sharply increase with increasing depth at any level in the lower mantle

support for equatorial anisotropy of earth s inner inner core from seismic interferometry at low latitudes abstract anisotropy of earth s inner core provides a key role to understand its evolution and the earth s magnetic field recently using autocorrelations from earthquake s coda we found an equatorial anisotropy of the inner inner core iic in apparent contrast to the polar anisotropy of the outer inner core oic to reduce the influence of the polar anisotropy and reduce possible contaminations from the large fresnel zone of the pkikp 2 and pkiikp 2 phases at low frequencies we processed coda noise of large earthquakes 10 000 40 000 s after magnitude 7 0 from stations at low latitudes within 35 during 1990 2013 using a number of improved procedures of both autocorrelation and cross correlation we extracted 52 array stacked high quality empirical green s functions egfs an increase of over 60 from our previous study the high quality data allow us to measure the relative arrival times by automatic waveform cross correlation the results show large variation 10 9 s in the differential times between the pkikp 2 and pkiikp 2 phases the estimated influence of the fresnel zone is insignificant

constraints on inner core anisotropy using array observations of p p author s frost da romanowicz b abstract 2017 american geophysical union all rights reserved recent studies of pkpdf travel times suggest strong anisotropy 4 or more in the quasi western inner core hemisphere however the availability of paths sampling at low angles to the earth s rotation axis the fast axis is limited to augment this sampling we collected a travel time data set for the phase p p df pkppkpdf for which at least one inner core leg is quasi polar at two high latitude seismic arrays we find that the inferred anisotropy is weak on the order of 0 5 to 1 5 confirming previous results based on a much smaller p p data set while previous models of inner core anisotropy required very strong alignment of anisotropic iron grains our results are more easily explained by current dynamic models of inner core growth we observe large travel time anomalies when one leg of p p df is along the south sandwich to alaska path consistent with pkpdf observations and warranting further investigation

validation of ocean tide models around antarctica using onshore gps and gravity data 1 ocean tide models around antarctica are presently only sparsely tested against independent data ocean tide modeling errors along with subsequent ocean tide loading otl displacement modeling errors alias into altimetry and time variable gravity e g gravity recovery and climate experiment grace time series for example to validate various ocean tide models around antarctica gps data from 15 sites have been used to derive three dimensional displacement estimates at eight diurnal and semidiurnal tidal frequencies using hundreds of days of gps data harmonic parameters were estimated on a daily basis then combined these were then compared with otl displacement estimates derived from global and regional ocean tide models in east antarctica where the tides are well defined submillimeter differences are demonstrated in each coordinate component with the lunar n2 and q1 constituents in closest agreement as found in other studies k1 and especially k2 agree less well the spatial variation in the misfits for these two constituents indicates a site dependency with the k2 errors also suggesting an interaction with satellite dependent effects in west antarctica where sites are nearer the largest ice shelves agreement with the older models csr3 and tpxo 2 and nao 99b is poor for all constituents modeled tidal gravity variations were also compared with gravity measurements at the south pole overall the gps and gravity data agree best with newer tide models namely tpxo 6 cada00 10 fes99 and cats02 01 however validation data are lacking at the southern extents of the large ice shelves and hence some uncertainty still exists in all ocean tide models in these regions