is the rotation real earth9s interior consists of a mantle liquid core and at the very center a solid inner core made of iron one of the inner core9s most peculiar properties is its anisotropy seismic waves travel slightly faster if they are parallel to earth9s rotation axis in her perspective souriau describes recent seismic studies that suggest the inner core rotates faster than earth9s mantle and comments on the current dilemma in interpreting the experimental findings

imaging the inner core under africa and europe abstract the inner core under africa is thought to be a region where the nature of inner core texture changes from the strongly anisotropic western part of the inner core to the weakly anisotropic or isotropic eastern part of the inner core additionally observations of a difference in isotropic velocity between the two hemispheres have been made a very large new dataset of simultaneous pkpdf and pkpbc observations on which differential travel times have been measured is used to examine the upper 360 km of the inner core under europe africa and the surrounding oceans inversion of the differential travel time data for laterally varying inner core anisotropy reveals that inner core anisotropy is stronger under central africa and the atlantic ocean than under the western indian ocean no hemispherical pattern is present in voigt isotropic velocities indicating that the variation in anisotropy is due to differing degrees of crystal alignment in the inner core not material differences when anisotropy is permitted to change with depth the upper east most part of the study region shows weaker anisotropy than the central and western regions when depth dependence in the inner core is neglected the hemisphere boundary is better represented as a line at 40 e than one at 10 e however it is apparent that the variation of anisotropy as a function of depth means that one line of longitude cannot truly separate the more and less anisotropic regions of the inner core the anisotropy observed in the part of the inner core under africa which lies in the western hemisphere is much weaker than that under central america showing that the western hemisphere is not uniformly anisotropic as the region of low anisotropy spans a significant depth extent it is likely that heterogeneous heat fluxes in the core which may cause variations in inner core anisotropy have persisted for several hundred million years

latest spin on the core during the 1990s evidence has emerged from seismic data that the earth s inner core may be rotating slightly faster than the mantle and crust estimates of the rate have been as high as 3 per year the conclusion of the latest study however is that there is no or very little differential rotation

harmonic excitation of mantle rayleigh waves by the 1991 eruption of mount pinatubo philippines an unusually long at least two hours seismic wave train having periods of about 230 sec was recorded at many worldwide seismic stations during the major eruption of mount pinatubo in the philippines on june 15 1991 this wave train exhibits two sharp spectral peaks at 228 and 270 sec the group velocity phase velocity and the particle motion of this wave train indicate that it is a rayleigh wave the most probable excitation mechanism is acoustic coupling of atmospheric oscillations that were set off by continuous thermal energy flux from the volcano the two spectral peaks correspond to the characteristic periods of acoustic and gravity modes of the earth s atmosphere the magnitude of the vertical single force equivalent to the acoustic coupling is 1 6 10 17 dynes over a frequency band of 0 003 to 0 01 hz the results suggest the possibility of using acoustically coupled rayleigh waves for detection characterization and quantification of volcanic eruptions acoustic coupling of the atmosphere and the solid earth provides a unique seismic source with long duration

axial and equatorial rotations of the earth s cores associated with the quaternary ice age abstract the differential axial and equatorial rotations of both cores associated with the quaternary glacial cycles were evaluated based on a realistic earth model in density and elastic structures the rheological model is composed of compressible maxwell viscoelastic mantle inviscid outer core and incompressible maxwell viscoelastic inner core the present study is however preliminary because i assume a rigid rotation for the fluid outer core in models with no frictional torques at the boundaries of the outer core the maximum magnitude of the predicted axial rotations of the outer and inner cores amounts to 2 year 1 and 1 year 1 respectively but that for the secular equatorial rotations of both cores is 0 0001 at most however oscillating parts with a period of 225 years are predicted in the equatorial rotations for both cores then i evaluated the differential rotations by adopting a time dependent electromagnetic em torque as a possible coupling mechanism at the core mantle boundary cmb and inner core boundary icb in a realistic radial magnetic field at the cmb estimated from surface magnetic field the axial and equatorial rotations couple through frictional torques at the cmb although these rotations decouple for dipole magnetic field model the differential rotations were evaluated for conductivity models with a conductance of 10 8 s of the lowermost mantle inferred from studies of nutation and precession of the earth and decadal variations of length of day lod the secular parts of equatorial rotations are less sensitive to these parameters but the magnitude for the axial rotations is much smaller than for frictionless model these models however produce oscillating parts in the equatorial rotations of both cores and also in the axial rotations of the whole earth and outer and inner cores these oscillations are sensitive to both the magnitude of radial magnetic field at the cmb and the conductivity structure no sharp isolated spectral peaks are predicted for models with a thin conductive layer 200 m at the bottom of the mantle in models with a conductive layer of 100 km thickness however sharp spectral peaks are predicted at periods of 225 and 25 years for equatorial and axial rotations respectively although these depend on the strength of radial magnetic field at the cmb while the present study is preliminary in modelling the fluid outer core and coupling mechanism at the cmb the predicted axial rotations of the whole earth may be important in explaining the observed lod through interaction between the equatorial and axial rotations

normal mode coupling due to hemispherical anisotropic structure in earth s inner core summary we present illustrative calculations of the effect of hemispherical variation in inner core anisotropy on earth s normal modes of oscillation body wave studies show that the anisotropy in the inner core is not simple cylindrical anisotropy which is often portrayed in models derived from normal mode data but varies with longitude hemispherical or odd degree structure has to be studied by cross coupling normal modes as the self coupling technique is sensitive only to even degree earth structure a completely general definition of inner core anisotropy would require a prohibitive number of degrees of freedom however we show that any existing cylindrical anisotropy model can be confined to only one part of the inner core using our new theory we find that hemispherical anisotropy causes significant changes in the frequency and quality factor of several inner core sensitive normal modes the effect of hemispherical inner core anisotropy can also be seen in synthetic seismograms radial pkikp and pkjkp modes all respond to the presence of hemispherical variation in inner core anisotropy if the variations in inner core anisotropy seen in body wave data are part of a gross large scale pattern then this structure should also affect normal mode data on an observable scale

localized temporal change of the earth s inner core boundary compressional waves of an earthquake doublet two events occurring in the south sandwich islands on 1 december 1993 and 6 september 2003 recorded at three seismic stations in russia and kyrgyzstan and reflected off earth s inner core boundary arrived at least from 39 to 70 milliseconds earlier in the 2003 event than in the 1993 event such changes indicate that earth s inner core radius enlarged locally beneath middle africa by 0 98 to 1 75 kilometers between the times of these two events changes of the inner core radius may be explained by either a differential motion of the inner core assuming that irregularities are present at the inner core boundary and fixed to the inner core or a rapid growth of the inner core by this amount

examination of systematic mislocation of south sandwich islands earthquakes using station pairs implications for inner core rotation 1 one of the most robust observations for the inner core rotation is that the differential pkp bc df traveltimes from south sandwich islands ssi earthquakes to college alaska and some other stations in alaska have increased systematically over the past 50 years the time shift in the differential time residuals is some 0 3 s over 30 years this temporal change is thought to result from a shift of the inner core structure from a superrotation of the inner core however the observation has been hotly debated and has been suggested to be an artifact of systematic earthquake mislocation here we examine this issue using three mutually independent approaches with a goal to quantify the amount of the systematic mislocation if any all three approaches involve differencing data between north stations at a similar azimuth as the ssi alaska azimuth and south stations at nearly the opposite azimuth mislocation along this azimuth has greatest impact on the pkp differential times in approach 1 we examine how the double difference of p traveltimes between a north station and a south station changes with time because the differential apparent slowness between the p traveltimes of the pairs is 8 to 16 times that of the differential bc df times mislocation would cause a time shift in the double difference an order of magnitude larger than that of bc df times in approach 2 we compare directly difference in p arrival times between two ssi events that are close by and between a north and a south stations which avoids using earthquake locations and earth models entirely in approach 3 we compare pkp traveltime residuals between a group of north and south stations because pkp traveltimes are generally not used for location in earthquake bulletins they provide an independent data set to check earthquake location errors the results from approaches 1 and 2 both of which use p data are generally consistent the mislocation is up to 3 6 4 2 km one standard deviation explaining less than 10 of the observed col temporal change the results from approach 3 using pkp data show a larger mislocation but with a larger error 14 4 10 8 km over 30 years it can explain about 30 22 of the observed col temporal change therefore inner core superrotation is still the best explanation for the observed temporal change in the differential traveltimes

neoproterozoic earth moon dynamics rework of the 900 ma big cottonwood canyon tidal laminae the tidal rhythmites in the proterozoic big cottonwood formation bcc of utah the neoproterozoic elatina formation of the flinders range of southern australia and the lower pennsylvanian mansfield formation of indiana indicate that the rate of retreat of the lunar orbit has been approximately constant since the late precambrian and closely matches the present epoch value determined from apollo lasers examination of a new bcc core leads to a slightly revised length of day lod and modified values for other earth moon dynamical parameters thus implying the length of day 900 million years ago reported earlier by sonett et al 1996 should be modified to 18 9 hrs

normal mode splitting due to inner core attenuation anisotropy the earth s inner core displays transverse velocity anisotropy with cylindrical symmetry which causes the anomalous zonal splitting of inner core sensitive normal modes in this paper we extend existing theory for calculating normal mode splitting from models of cylindrical velocity anisotropy to include models of anelastic attenuation anisotropy furthermore we derive the equations that can be used to rewrite the attenuation anisotropy parameters natural to normal mode considerations in terms of body wave attenuation anisotropy for compressional and shear waves

75 plus years of anisotropy in exploration and reservoir seismics a historical review of concepts and methods the idea that the propagation of elastic waves can be anisotropic i e that the velocity may depend on the direction is about 175 years old the first steps are connected with the top scientists of that time people such as cauchy fresnel green and kelvin for most of the 19th century anisotropic wave propagation was studied mainly by mathematical physicists and the only applications were in crystal optics and crystal elasticity during these years important steps in the formal description of the subject were made at the turn of the 20th century rudzki stressed the significance of seismic anisotropy he studied many of its aspects but his ideas were not applied research in seismic anisotropy became stagnant after his death in 1916 beginning about 1950 the significance of seismic anisotropy for exploration seismics was studied mainly in connection with thinly layered media and the resulting transverse isotropy very soon it became clear that the effect of layer induced anisotropy on data ac

pkp travel times at near antipodal distances implications for inner core anisotropy and lowermost mantle structure abstract previous studies from pkp ab df differential travel times at large distances suggest that the central part of the inner core is very anisotropic these differential times however can be affected greatly by strong heterogeneity in the lowermost mantle here we examine a unique data set of pkp travel times from global digital and analog stations at near antipodal distances where the effects of both inner core anisotropy and mantle heterogeneity are the greatest our results show that the ab df residuals for the polar paths are consistently larger than those of the equatorial paths by over 3 4 standard deviations we also measured df and ab absolute times and found that the df residuals are negatively correlated with the ab df residuals while the ab residuals have a much weaker correlation with the ab df residuals we compare several mantle models with the data our results suggest that the mantle structure can explain part of the residuals of the equatorials paths but cannot explain the polar path anomalies these results strongly suggest that most of the ab df anomalies for the polar paths are likely from the inner core anisotropy and not from mantle heterogeneity assuming a uniform cylindrical anisotropy model the average inner core anisotropy amplitude is about 2 5 on the other hand equatorial paths from events in the west pacific and recorded at south america show a steep azimuthal change in ab df times about 4 s over a 60 azimuthal range the sharp change is well predicted by existing p and s tomographic models the azimuthal change occurs as the ab paths sweep across the great slow anomaly in the central pacific the high correlation between the p and s velocities suggests that the central pacific slow anomaly may be of thermal origin

coupled dynamics of earth s geomagnetic westward drift and inner core super rotation this phd work focuses on the rotational dynamics of the coupled inner core outercore mantle system the conservation of the angular momentum our coupled earth model indeed involves two direct electromagnetic torques at the fluid core boundaries and a remote gravitational torque between the inner core and the mantle the rotational dynamics is described by four typical shears and studied in convective numerical simulations of the geodynamo which are able to reproduce the main characteristics of the geomagnetic field and its secular variation this secular variation is mainly embodied by the westward drift of magnetic flux patches at the cmb concentrated on the equator of the atlantic hemisphere and is well documented for the last four centuries we provide constrains on the inner core differential rotation by expressing its link to the geomagnetic westward drift this is performed through the formulation and the validation of dynamical electromagnetic torque models which are then introduced in the conservation of the angular momentum of the system in the long term state the global shear in the fluid outer core is distributed between the westward drift and the differential rotation of the inner core in proportions controlled by the state of couplings as a present day estimate of this shear is close to the observed westward drift we conclude there is no differential rotation of the inner core on time average in the time dependent state we observed that the strength of gravitational coupling is the dominant parameter this places limit on the decadal fluctuations of the inner core differential rotation which should not exceed a few hundredths of degree per year

geodynamic estimates of the viscosity of the earth s inner core recent seismological studies1 2 have suggested that the inner core is rotating relative to the bulk of the earth a situation which according to numerical simulations3 may be sustained by convective flow in the liquid outer core on the other hand large gravitational forces due to the heterogeneous distribution of mass in the earth s mantle should be sufficient to keep the inner core aligned with the mantle4 here i show that the differential rotation of the inner core can be reconciled with these strong gravitational forces by allowing the shape of the inner core to adjust as it rotates so permitting an estimate of the effective viscosity of this innermost region of the earth the inferred rotation rate constrains the viscosity of the inner core to be less than 1016 pa s or greater than 1020 pa s as two different dynamical regimes are possible the viscosity estimates for these two regimes have very different implications for the origin of seismic anisotropy in the inner core

seismic anisotropy of the earth s inner core resulting from flow induced by maxwell stresses seismological observations indicate that the inner core of the earth is elastically anisotropic1 anisotropic structures are likely to be formed by dynamic processes and therefore such observations have the potential to provide constraints on flow in the inner core and on the geodynamo itself but in addition to the difficulties in estimating the relevant physical properties of iron under inner core conditions2 3 4 even the macroscopic processes responsible for generating seismic anisotropy in this region have yet to be determined5 6 7 8 9 as a result the geodynamic significance of seismic anisotropy in the inner core has remained unknown here i propose based on geodynamic and mineral physics considerations that flow induced by the stress due to the magnetic field the maxwell stress near the inner core boundary produces an axisymmetric fabric responsible for the observed seismic anisotropy the resultant seismic anisotropy reflects the geometry of the magnetic field near the inner core boundary and therefore seismological observations might provide constraints on the geodynamo this flow also causes non uniform release of energy at the inner core boundary associated with solidification and melting which may affect the pattern of convection in the outer core

wide scale detection of earthquake waveform doublets and further evidence for inner core super rotation summary we report on more than 100 earthquake waveform doublets in five subduction zones including an earthquake nest in bucaramanga colombia each doublet is presumed to be a pair of earthquakes that repeat at essentially the same location these doublets are important for studying earthquake physics as well as temporal changes of the inner core particularly our observation from one south sandwich islands ssi doublet recorded at station ink in canada shows an inner core traveltime change of 0 1 s over 6 yr confirming the innercore differential motion occurring beneath central america observations from one aleutian islands doublet recorded at station bosa in south africa and from one kuril islands doublet recorded at station bdfb in brazil show an apparent inner core traveltime change of 0 1 s over 7 yr and 6 yr respectively providing evidence for the temporal change of inner core properties beneath central asia and canada respectively on the other hand observations from one tonga fiji solomon islands doublet recorded at station ptga in brazil and from one bucaramanga doublet recorded at station wrab in australia and station chto in thailand show no little temporal change no more than 0 005 syr 1 if any of inner core traveltimes for the three corresponding ray paths for which the path in the inner core is nearly parallel to the equatorial plane such a pattern of observations showing both presence and possible absence of inner core traveltime change can be explained by the geometry and relative directions of ray path lateral velocity gradient and inner core particle motion due to an eastward super rotation of a few tenths of a degree per year

evidence for inner core super rotation from time dependent differential pkp traveltimes observed at beijing seismic network summary in an effort to confirm and constrain inner core rotation we examine earthquakes from the south sandwich islands recorded at the beijing seismic network we obtained a total of 109 high quality measurements of pkp bc pkp df differential traveltimes by waveform cross correlations from earthquakes spanning over 30 years the results show robust temporal changes in pkp bc pkp df residuals along this pathway providing new support for the differential inner core hypothesis we also observed evidence for a lateral velocity gradient in this part of the inner core assuming that the temporal changes result from a shift of a lateral structure due to an inner core rotation we estimate the inner core rotation rate to be about 0 41 0 12 yr 1 faster than the mantle

core geophysics the deep interior of earth is inaccessible directly yet determining our planet s structure and composition is critical for understanding the origin and evolution of our planet in recent years important advances have been made using indirect methods to infer the nature of the earth s deep interior these advances have been made by applying an interdisciplinary approach using seismic geochemical and geomagnetic methods on the basis of seismic wave propagation through the earth we divide the planet into the crust 10 70 km thick the mantle which extends down to 2 900 km the liquid outer core from 2 900 km to 5 080 km and a solid inner core 5 080 km to 6 371 km the composition of the earth is estimated by assuming that the planets and the sun formed from a parent nebula of gas and dust therefore the elemental abundances in the sun together with those in chondritic meteorites which are considered remnants of the early material that accreted to form the planets can be used to infer the bulk composition of the earth the result is that the outer core must be composed of an iron and nickel alloy 80 wt fe 5 wt ni along with a smaller percentage of a less dense

variability of fault slip behavior along the san andreas fault in the san juan bautista region an improved understanding of the time history of fault slip at depth is an essential step toward understanding the underlying mechanics of the faulting process using a waveform cross correlation approach we document spatially and temporally varying fault slip along the northernmost creeping section of the san andreas fault near san juan bautista sjb california by systematically examining spatiotemporal behaviors of characteristically repeating earthquakes cres the spatial distribution of pre 1998 sjb earthquake 1984 1998 fault slip rate inferred from the cres reveals a 15 km long low creep or partially locked section located near the 1998 mw 5 1 sjb earthquake rupture a finite fault slip inversion reveals that the rupture of the 1998 sjb earthquake is characterized by the failure of a compact 4 km2 asperity with a maximum slip of about 90 cm and corresponding peak stress drop of up to 50 mpa whereas the mean stress drop is about 15 mpa following the 1998 earthquake the cre activity was significantly increased in a 5 10 km deep zone extending 2 7 km northwest of the main shock which indicates triggering of substantial aseismic slip the postseismic slip inferred from the cre activity primarily propagated to the northwest and released a maximum slip of 9 cm in this 5 10 km depth range the estimated postseismic moment release is 8 6 1016 n m which is equivalent to mw 5 22 the aseismic slip distribution following the 1998 earthquake is not consistent with coseismic stress driven afterslip but represents a triggered long lasting slow earthquake

using earthquake doublets to study inner core rotation and seismicity catalog precision 1 we report our search for doublets in the south sandwich islands ssi region among 906 earthquakes from january 1982 to december 1998 event pairs with source separation less than 40 km which was calculated using pde locations were checked using vertical component short period and broadband digital records cross correlation coefficients of p or pkp waveforms were computed for similarity comparison whole waveforms of those event pairs with correlation coefficients larger than 0 8 were checked by eye by this process 17 doublets were found some of which form multiplets however only one doublet event pair 14 august 1995 and 28 march 1987 has clear pkp df phases on both records at college alaska col the pkp df travel time change measured by cross correlation is a decrease by 0 15 s with standard deviation 0 02 s over a time period of about 8 years this result strongly supports differential rotation of the earth s inner core relative to the mantle and the crust the estimated rotation rate ranges from 0 4 to 1 per year eastward the special case of a locked inner core can then be ruled out we also checked the precision of pde and isc locations using the 17 doublets results show that both catalogs have relatively high location precision standard deviations in latitude longitude and depth are less than 4 km 6 km and 10 km respectively supporting prior claims of detection of inner core rotation song and richards 1996

seismological evidence for differential rotation of the earth s inner core the travel times of seismic waves that traverse the earth s inner core show a small but systematic variation over the past three decades this variation is best explained by a rotation of the inner core that moves the symmetry axis of its known seismic anisotropy the inferred rotation rate is on the order of 1 per year faster than the daily rotation of the mantle and crust

evidence for small scale heterogeneity in earth s inner core from a global study of pkikp coda waves abstract recent seismic observations have provided evidence that the inner core contains strong heterogeneity at a scale length of tens of kilometers the corresponding lateral variations in elastic properties could be caused by pockets of partial melt alignment of iron crystals or variations in chemistry however the relevant seismic observations precritical pkikp coda waves were subtle and were made using historic seismic data furthermore it has been suggested that the seismic data might be explainable by scatterers in the lower mantle or by a complex inner core boundary to address these issues we investigate a preexisting global database of precritical pkikp waveforms at distances of 10 50 and a second newly generated global data base of pkikp waveforms at distances of 50 90 we analyze the data using standard array processing techniques and identify pkikp coda waves based on travel time ray parameter amplitude and coherence although it remains unclear whether the scattered energy is being created within the inner core or along its boundary we find three lines of evidence which support the idea that it is in fact related to the inner core at smaller distances the decay rate of pkikp coda is significantly lower than the decay rates of the corresponding pcp and scp codas at larger distances we find examples of emergent spindle shaped pkikp coda waves that exist without the parent pkikp phase and at larger distances we infer a pkikp coda decay rate similar to that determined from the data at the smaller distances it is likely that many more pkikp coda observations can be made with existing data sets and hence seismologists possess a new extraordinarily fine probe for inferring inner core structure

s diffusivity in fe ni s p melts soret diffusion rise times were observed and resolved for fe ni s p melts at 10 kbar in thermal gradients between 1300 and 1450 c a steady state separation of s rich components to the hot end of the 2 mm long liquid charges is achieved in about 20 minutes chemical diffusivities of about 10 5 cm2 s are consistent with these observations and those of the compaction velocity of aggregates of crystalline fe metal against the cold end of our experiments these rapid diffusivities are not rapid enough for diffusion to be an important agent of bulk mass transfer in the addition or extraction of light elements in the earth s core

seismology inner core takes another turn the degree of rotation of the earth s inner core relative to the mantle has been under study for several years the techniques concerned becoming ever more refined the best resolution yet comes from a method involving seismic waves scattered by the core the answer it gives is 0 15 per year

depth dependence of anisotropy of earth s inner core both body wave pkp travel times creager 1992 song and helmberger 1993a mcsweeney and creager 1993 shearer 1994 and fits to the splitting of core modes tromp 1993 show general agreement that the top 300 km of inner core is very anisotropic the anisotropy displays axial symmetry around the earth s spin axis with the polar direction 3 faster than the equatorial direction one key problem now is the depth dependence of the inner core anisotropy here we extend our polar path studies to include both long period and short period modeling for the pkp phases at ranges 120 to 173 arrivals from the top of the inner core pkikp and reflections from the inner core boundary pkikp can be observed distinctly in short period records at ranges 130 to 140 and as waveform distortions in the long period records at ranges 130 to 146 these waveforms provide a new set of data for examining the topmost 150 km of the inner core which is not well sampled by the previous body wave travel times record sections of waves traversing the inner core nearly parallel to the earth s spin axis polar paths from three events two beneath the south sandwich islands and one along the macquarie ridge recorded at world wide standardized seismograph network canadian network and long range seismic measurements stations are analyzed our results suggest that the top 150 km of the inner core is only weakly anisotropic less than 1 with strong evidence indicating that the top 60 km is not anisotropic at all

estimate of inner core rotation rate from united kingdom regional seismic network data and consequences for inner core dynamical behaviour abstract we analyse over 12 500 records of southwest pacific earthquakes recorded by the uk network for pkpbc and pkpdf phases to seek constraints on the inner core s rotation rate careful analysis and strict rejection criteria yield 655 pkpbc pkpdf differential travel time residuals computed with respect to the ak135 reference model densely sampling a small region of the inner core over a time period of 15 years the data images both lateral and radial velocity heterogeneity in the inner core located geographically beneath the north pacific between radii of 870 and 1080 km the dominant feature is a longitudinal wave speed gradient centred at about 180 longitude in combination with different earthquake catalogues and inner core anisotropy models we explore different techniques to use this gradient to constrain the rotation rate our estimates range from 0 45 0 25 to 0 74 0 29 yr relative to the mantle with two of four estimates including zero rotation at the 95 2 confidence level indicating that rotation is marginally detectable as an alternative to monotonic rotation we find weak evidence for rotational oscillation of the inner core on time scales of about 280 days in consequence these observations suggest that 1 viscous coupling between the outer and inner core simulated using viscous hyperdiffusivity is not appropriate for modelling inner core rotation 2 temperature gradients between the interior and exterior of the tangent cylinder in the core are also small 3 gravitational torques coupling the inner core to the mantle are large on the order of 2 1021 nm and 4 the inner core s viscosity is high 3 9 1019 pas

tomographic inversion for three dimensional anisotropy of earth s inner core abstract seismological studies generally suggest that the earth s inner core is anisotropic and the anisotropic structure changes significantly both laterally and with depth previous body wave studies of the inner core have relied on ray tracing or waveform modeling using one dimensional 1d models here we present non linear tomographic inversions of the inner core anisotropy using three dimensional 3d ray tracing spline parameterization and a large collection of pkp differential travel times we adapt a pseudo bending ray tracing pbr method in spherical coordinates for seismic rays that traverse the inner core pkp df phase the method iteratively perturbs each discontinuity point and continuous segment of the ray through 3d earth structure so that its travel time is minimum the 3d anisotropic structure of the inner core is approximated to the first order as 3d heterogeneous but isotropic structure for a given ray the data are corrected using a scaled mantle tomographic model the inner core anisotropy model obtained has the following major features 1 the model has strong hemispherical and depth variation the isotropic velocity in the topmost inner core is greater in quasi eastern hemisphere qeh 40 160 e than in quasi western hemisphere qwh other longitudes the anisotropy is weak in qeh to the depth of 600 700 km below the inner core boundary icb while in qwh the anisotropy increases at much shallower depth about 100 200 km below the icb to about 3 4 then remains at about 2 4 throughout the rest of the inner core 2 the anisotropy form changes abruptly over a depth range of about 150 km at the radius of about 600 km slightly less than half of the inner core radius forming a distinct inner inner core iic the velocity in the iic has maximums at equatorial and polar directions and minimum at an angle of about 40 from the equatorial plane the velocity in the outer inner core oic however changes little for ray directions 0 40 from the equatorial plane 3 despite large variation of the anisotropy the isotropic velocity voigt average throughout the inner core is nearly uniform the results suggest that the oic is likely composed of the same type of iron crystals with uniform chemistry but the iic may be composed of a different type of crystal alignment a different iron phase or a different chemical composition our tests on model parameterization mantle correction and linear and non linear inversion suggest the main features of our model are very robust however fine scale structures are likely to differ particularly in the major transition zones e g in the topmost qwh isotropy to anisotropy between oic and iic change in the form of anisotropy and between qeh and qwh in oic difference in anisotropy strength searches for possible waveform complications from these boundaries need to be aware of the directional dependence and geographical variation to be successful

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

the structure of the base of the outer core inferred from seismic waves diffracted around the inner core 1 we systematically searched for seismograms of waves diffracted around the inner core pkpcdiff from all the temporary seismic arrays with data currently available at the iris dmc as well as some permanent regional seismic arrays including f net in japan and grf in germany to assemble the largest high quality pkpcdiff database ever created pkpcdiff waves preferentially sample the base of the outer core and so contain important clues about earth structure in this region we measured pkpdf pkpcdiff differential traveltimes and pkpcdiff pkpdf amplitude ratios in the distance range of 154 160 and modeled the observations using grid searches and full wave theory synthetic seismograms the optimum model found by fitting the differential traveltimes has relatively low velocity at the base of the outer core as in ak135 which is consistent with many previous traveltime studies however the optimum model found by fitting the amplitude ratios pkpcdiff pkpdf does not exhibit this feature and instead is closer to prem the discrepancy may be explained by two likely causes one is that small scale topography or roughness on the icb tends to scatter energy away from pkpcdiff waves by generating trailing coda waves the other is that there exists a thin layer with relatively low q at the base of the outer core this might be expected if there are suspended solid particles at the base of the outer core as proposed decades ago both mechanisms could generate smaller pkpcdiff amplitudes without significantly affecting pkpcdiff traveltimes

planet within a planet rotation of the inner core of earth the time dependence of the orientation of earth9s inner core relative to the mantle was determined using a recently discovered 10 degree tilt in the axis of symmetry of the inner core9s seismic velocity anisotropy two methods of analyzing travel time variations for rays traversing the inner core on the basis of 29 years of data from the international seismological centre 1964 1992 reveal that the inner core appears to rotate about 3 degrees per year faster than the mantle an anomalous variation in inner core orientation from 1969 to 1973 coincides in time with a sudden change jerk in the geomagnetic field

joint inversion for inner core rotation inner core anisotropy and mantle heterogeneity observational evidence for differential rotation of the inner core has recently been reported from time dependent travel times of the seismic inner core phase pkp df these analyses are hindered by potential biases from the mantle heterogeneity and systematic earthquake location errors which have raised doubts about the reality of the inferred differential rotation here we report time dependent pkp df pkp bc differential travel times of a total of 611 measurements obtained from 92 earthquakes in the south sandwich islands ssi over the past nearly half a century recorded at the college alaska station col and alaska seismic network asn the events are relocated using the joint hypercenter determination jhd technique dewey 1971 travel time residuals at col from ssi earthquakes over a period of 45 years and at three additional stations from ssi earthquakes over periods of about 22 years show steady increases with time the temporal trends are demonstrated to be statistically very significant with dense samples of the pathway at different time periods we use a joint inversion technique that allows us to separate the time dependent inner core structure from the time independent mantle biases surprisingly the inner core rotation seems resolvable even from digital data observed at asn in the 1990s spanning over 8 years alone in such a joint inversion the results provide strong support for a differential inner core rotation the inferred rotation rate ranges from 0 3 to 1 1 per year faster than the mantle when we take into account the uncertainty in the tilt of the anisotropy axis of the patch of the inner core that was sampled a westward inner core rotation can be ruled out

constraints on inner core anisotropy from pkp df travel times pkp df travel times reported by the international seismological centre isc are analyzed to study the depth dependence of inner core anisotropy plots of pkp df travel time residuals versus range for different subsets of the data clearly show large anomalies at ranges beyond about 149 for those paths with inner core ray angles within 30 of the rotation axis on average the times are about 3 to 5 s earlier for these paths than for rays at other angles consistent with recent waveform measurements of anomalous pkp df times by creager 1992 and song and helmberger 1993 and indicative of inner core anisotropy in which the p velocity is about 3 faster for n s paths than e w paths the size of these apparent anomalies in the isc data are much larger than those inferred from several previous analyses of isc pkp df data which indicated 0 5 to 2 s anomalies at these ranges the earlier studies applied binning and averaging schemes to the data using windows that were overly tight thus excluding some of the most anomalous data points and biasing the results toward smaller anomalies to avoid this problem i apply a method for computing summary ray residuals that finds the maxima in smoothed histograms of the residuals and does not rely on a fixed interval to window the data points standard errors on each summary ray residual are estimated using a bootstrap technique that randomly resamples the data plots of the summary ray residuals for several range intervals reveal a small number of independent paths nearly parallel to the rotation axis for which the arrivals are 3 to 5 s early although the data are sparse for paths within 30 of the rotation axis anisotropy does not appear to diminish with depth within the inner core and may cause a much larger anomaly near 180 than the 2 s value obtained in several prior studies of isc data the uniform anisotropy models of creager 1992 and song and helmberger 1993 fit the bulk of the data reasonably well however the observed residuals at ranges between 132 and 140 are smaller than those predicted by most anisotropy models suggesting that the anisotropy may diminish within the outermost 50 km of the inner core

stable regions in the earth s liquid core summary slow cooling of the whole earth can be responsible for the convection in the core that is required to generate the magnetic field previous studies have assumed the cooling rate to be high enough for the whole core to convect here we study the effects of a low rate of cooling by assuming the temperature at the base of the mantle to remain constant with an initially entirely molten adiabatic core we argue that in such a situation convection would stop at the top of the core and calculate the consequent thermal evolution a stable density stratified layer grows downwards from the core mantle boundary reaching a thickness of 100 1000 km in a few thousands of millions of years there is some geomagnetic evidence to support belief in the existence of such a stable layer

tidal despinning of the mantle inner core superrotation and outer core effective viscosity dissipation of tidal energy in the oceans causes a net transfer of angular momentum from the spin of the earth to the relative orbital motions of the moon and sun these torques couple directly to the mantle and cause it to despin viscous coupling across the outer core is an effective means of communicating this change to the inner core the ekman time scale for dissipation of transient fluid motions associated with unsteady torques is much shorter than the time scale for adjustment of inner core and mantle rotational velocities in the steady couette flow regime the relative amplitude and phase of rotational variations in this system with respect to the applied torques are given in terms of core viscosity and torque variation frequency any short period variations in mantle torques will leave the inner core largely unchanged and the influence of long period and secular torques applied to the mantle is efficiently transmitted to the inner core the system response to a steady tidal torque applied to the mantle leaves the inner core with a small excess rotational velocity relative to the mantle proportional to the product of outer core viscosity and the applied mantle torque recent estimates of an inner core super rotation of 1 degree year imply an effective outer core viscosity of 10 3 pa s glacial cycle variations in tidal torques somewhat complicate this picture but do not yield significantly different viscosity estimates however they do imply that the differential rotation velocity varies by roughly a factor of 2 over a 100 kyr glacial cycle the tidal shear strain may also contribute to development of anisotropy in the inner core

whole earth structure estimated from seismic arrival times the arrival times of 10 compressional and shear phases p s pp pcp ss scs pk pab pk pbc pk pdf sk sac and two sets of differential times ss s410s and ss s660s are used to infer the earth s three dimensional structure with the exception of ss sds the raw data are composed of arrival times from the international seismological centre isc catalogue the isc events have been relocated using p and s phases and the ak135 radial earth model a total of 818 655 summary arrival times constrain lateral velocity variations in the crust mantle and core we also determine relocation parameters for all events stations corrections for each phase boundary topography 410 km 660 km core mantle boundary inner core boundary and inner core anisotropy variations our model of p and s velocity variations in the crust and mantle contains the general features observed in other body wave inversions a low velocity ring around the pacific ocean basin in the depth range 35 400 km high velocity anomalies associated with subducting slabs most prominent in the depth range 660 1070 km and high velocity anomalies surrounding the pacific basin just above the core mantle boundary in the outer core there is evidence of a latitudinal variation in velocity approaching 0 6 in magnitude with lower p velocities at the poles and higher velocities near the equator this pattern is observed throughout the outer core but is most prominent in the depth range 3671 4071 km and near the inner core boundary synthetic tests indicate that outer core features are moderately resolvable and inversions of random arrival times indicates that the anomalies are a factor of 2 above the estimated parameter noise level lateral heterogeneity in the inner core trades off with anisotropy resulting in poor resolution of isotropic velocity variations anisotropy in the inner core is predominantly subparallel to the earth s axis and of the order of 3 but this value can decrease if more inner core isotropic lateral heterogeneity is allowed a comparison of structure above and below the core mantle boundary cmb indicates that velocity heterogeneity is uncorrelated across the cmb but there is a moderate correlation between cmb topograpy and outer core heterogeneity an inversion in which the pk pdf residuals were absent indicates that the latitudinal pattern of outer core velocity variations is not due to the influence of inner core velocity structure

possible heterogeneity of the earth s core deduced from pkikp travel times the core of the earth is usually described by spherically symmetrical velocity models the core is made of two main spherical layers the fluid outer core with a radius close to 3 480 km and a p velocity increasing with depth from 8 km s 1 to 10 3 km s 1 and the solid inner core with a radius of 1 220 km and a p velocity close to 11 km s 1 refs 1 2 station residuals of the seismic core phase pkikp have been computed for 400 seismological observatories worldwide using 5 yr of the international seismological centre isc bulletins pkikp travel times can be corrected for upper mantle propagation by subtracting p delays thus pkikp p residuals are a measurement of the average vertical travel times in the lower mantle and in the core of the earth beneath seismic stations a spherical harmonic development of pkikp p delays up to degree 4 explains 58 of the variance in the data pkikp p exhibit a latitudinal dependence polar stations tend to be faster than equatorial stations we show here that this pattern may reflect a departure from spherical symmetry in the p velocity distribution in the vicinity of the inner core boundary of the earth

earth s core and the geodynamo earth s magnetic field is generated by fluid motion in the liquid iron core details of how this occurs are now emerging from numerical simulations that achieve a self sustaining magnetic field early results predict a dominant dipole field outside the core and some models even reproduce magnetic reversals the simulations also show how different patterns of flow can produce similar external fields efforts to distinguish between the various possibilities appeal to observations of the time dependent behavior of the field important constraints will come from geological records of the magnetic field in the past

on the observation of high frequency pkikp and its coda in australia the seismic phase pkikp reflected from the inner core and its coda give information on the short scale heterogeneities at and below the inner core boundary icb of the earth we have collected pkikp recorded at short distances 45 at broadband stations in australia and at the warramunga seismic array wra despite potential complications from a dual passage through d pkikp is frequently observed on single traces in the frequency band 1 5 hz pkikp usually has a sharp onset but sometimes its waveforms have multiple pulses separated by times of the order of 1 s at wra the coda of pkikp initially decays very rapidly after the main pulse thereafter its amplitude is nearly constant and more than three times smaller than pkikp with duration longer than 200 s our observations differ from those of nature 404 2000 273 275 at rather greater distances who found that the coda is larger than pkikp and increases slowly we suggest that the pkikp coda is generated near the inner core boundary by complex reverberation effects rather than scattering through the volume of the inner core 2004 elsevier b v all rights reserved

inner core anisotropy in three dimensions the purpose of this paper is the investigation of cylindrical anisotropy in the inner core based on the travel time anomalies of the pkikp phase we use the arrival times reported in the international seismological centre bulletins for years 1964 1990 we select only earthquakes which have a good azimuthal coverage and a sufficiently large number of reporting stations the earthquakes are relocated using corrections for lateral heterogeneity computed for our most recent three dimensional mantle model we use a total of 313 422 observations of the df branch of pkp travel time anomalies within the epicentral distance ranges of 120 140 and 150 180 reported by 2335 stations for 26 377 earthquakes we process the data using an averaging procedure which we call cylindrical anisotropy stacking that enhances the effects of anisotropy but is expected to suppress those due to lateral heterogeneity and random errors the processed residuals show a remarkably consistent pattern this confirms the dominance of the cylindrical elastic anisotropy in the inner core with approximately a constant axis of symmetry this axis of symmetry is found to be tilted 10 5 1 from the earth s rotation axis in the direction 160 e 5 in the northern hemisphere in this new coordinate system we determine a four layer axisymmetric model of transverse anisotropy with each layer approximately 300 km thick the model shows that the anisotropy is strongest 3 within the innermost part of the core the travel time anomalies show significant 1 5 s longitudinal variations even when the tilt of the axis of symmetry is considered there is a substantial increase in the amplitude of the longitudinal variations which are dominated by the second and fourth harmonics for rays with bottoming depths exceeding 400 km below the inner core boundary the measurable tilt of the axis of symmetry and the presence of significant nonaxisymmetric signal may provide important clues with respect to the possible causes of anisotropy the increase in the anisotropy in the innermost part of the core departs from earlier inferences that anisotropy may be limited to the outermost 200 300 km of the earth s inner core

hemispherical structure in inner core velocity anisotropy 1 we investigate the hemispherical pattern in inner core velocity anisotropy using a new and independent high quality data set of pkpbc pkpdf and pkpab pkpdf body wave observations our data show no evidence for a tilted anisotropy axis with respect to the earth s rotation axis and is significantly better fit by a model with 4 4 anisotropy in the western hemisphere and only 1 0 in the eastern hemisphere than by a model of uniform anisotropy we carry out variance minimization and find the boundaries between the hemispheres at lines of constant longitude at 14 e and 151 w variance minimization enables us to extract the imprint of hemispherical structure from all of the data and not just polar paths resulting in boundaries which are nearly 30 from the results of previous studies the high quality of the data allows us to provide robust evidence that the isotropic velocity in the eastern hemisphere is 0 2 lower than in the western hemisphere in the top 660 km of the inner core our data set also suggests an increase in inner core anisotropy in the eastern hemisphere from 1 to around 6 at depths deeper than 660 km indicating that the hemispherical pattern in anisotropy may disappear at greater depths the presence of hemispherical structure rules out mechanisms for creating anisotropy which are unable to sustain longitudinal variations in the inner core furthermore steady inner core superrotation of the order of 0 1 year would eradicate the hemispherical differences though inner core oscillation would still be permissible

dynamic earth system and ecological controls of rainfall initiated landslides abstract rainfall initiated landslides continue to inflict damages and loss of life throughout the world processes and mechanisms revealed from hydrological geomorphic geotechnical pedological geological hydrochemical and biological investigations have advanced our understanding of these effects on slope stability however the interactions amongst these processes and attributes as they affect the initiation and propagation of landslides are not as well understood too often landslide studies are conducted from only one or at most two of these perspectives moreover while precipitation and hydrology are recognized as dynamic influences the earth system and ecological effects are often assumed to be static we assess the interplay of these processes related to landslides triggered by positive pore water accretion and loss of soil suction each of these conditions arguably requires a different view on the processes that cause slope failure and predictive approaches this review starts from the perspective of dynamic adapting earth and ecological systems and discusses how these attributes relate to landslide initiation mode location and timing specifically the role that large and small scale preferential flow plays in both contributing to and mitigating instability is elucidated including effects of bedrock exfiltration we also examine how and under what conditions these pathways manifest in different soils lithology and landforms the multiple effects of rhizosphere processes on slope stability are discussed including root reinforcement evaporation from canopies and litter layers transpiration and the role of root structure affecting preferential flow paths rainfall initiated landslides involve highly dynamic hydrologic earth surface and ecological processes that persist over a range of spatial and temporal scales however guidance for overcoming these challenges has been elusive a conceptual framework is presented to shed light on these dynamic and interactive processes that should lend insights into why and when certain slopes fail during storms while other seemingly similar slopes do not fail such advances will benefit landslide hazard assessments and disaster responsiveness protocols

inner core differential rotation inferred from antipodal seismic observations abstract the earth s inner core may rotate at a different speed than earth s crust mantle we use observations for antipodal earthquake and station pairs to examine the arrival time shift of the whispering gallery wave which propagates tangentially along the top of the inner core observations of these waves for earthquakes which occurred at the same location reveal that travel times vary by 0 2 s over the past 20 years we propose that these time shifts are caused by the interaction of a zero rigidity patch lateral heterogeneity at the inner core surface with the inner core differential rotation the simplest interpretation infers a rotation rate of 0 05 year which is one order of magnitude smaller than those reported by previous studies our result may also give constraint to the provenance of a zero rigidity patch at the inner core surface the fresnel zone coverage of whispering gallery pkiikp antipodal measurements beneath the inner core boundary extend over 60 of the boundary surface in contrast to pkikp pkp paths which individually measure specular reflections 1 hz from the top of the icb over fresnel zones each encompassing 0 002 of the inner outer core boundary

earth s inner core variable rotation different measurements of inner core rotation have delivered inconsistent results an analysis of seismic data provides a resolution of this discrepancy by suggesting decadal variations in inner core rotation rate

on waveform correlation measurement uncertainty with implications for temporal changes in inner core seismic waves abstract we address the uncertainty related to cross correlation waveform time shift measurements particularly related to temporal changes in inner core seismic waves details of the cross correlation measurement including data processing window length pick time sampling rate and the algorithm itself all affect the calculated time shift by systematically varying measurement parameters for a set of earthquake doublets we find time shift uncertainties of 0 01 s and 0 02 s for differential times and double differential times respectively the uncertainty is of a similar magnitude to reported double differential times of pkikp and pkikp inner core phases accounting for measurement uncertainty results in 80 of values published in a recent study being below the measurement resolution yang and song 2020a while the temporal variations in inner core phases is not in dispute properly accounting for uncertainties is needed for robust data interpretation a re assessment for the origin of inner core temporal changes is therefore warranted and future studies should account for measurement uncertainty

a comparison of geodetic and seismic estimates of inner core rotation seismological observations suggest the inner core has been rotating faster than the mantle during the past 30 50 years differential rotation can produce large gravitational torques on the mantle which if not balanced by other torques would be detectable as changes in the rotation rate of the mantle length of day or lod we compare seismological estimates of inner core rotation with estimates derived by inverting lod observations using models of gravitational coupling model predictions depend on several parameters but for the expected range of parameter values the seismological estimates of relative rotation are at least an order of magnitude larger than those predicted by the lod data furthermore the lod data predict oscillation in the angular alignment of the inner core and mantle during the past 30 50 years while the seismological data seem to require a component of steady rotation we show that steady rotation of the inner core implies a steady torque on the mantle this torque is not accelerating the rotation rate of the mantle so it must be opposed by another torque the required torque is consistent with a frictional electromagnetic stress on the base of the mantle due to a westward flow at the top of the core

inner core rotation a test at the worldwide scale abstract in order to determine the angular velocity of a possible inner core differential rotation with respect to the mantle we analyse travel times of waves sampling the inner core at the worldwide scale over a period of about 30 years for situations in which the inner core heterogeneities are dominant with respect to the mantle heterogeneities travel times of summary rays i e bunches of seismic rays with the same geometry must have smaller mean standard deviations when computed in the inner core reference frame than when computed in the mantle reference frame thus we build summary rays by applying a backward rotation of the inner core at angular velocity in order to sum residuals which sample the same inner core region at different times the mean standard deviation of the summary ray residuals computed for different values of should exhibit a minimum for the effective value this method has been applied to absolute pkp df residuals in considering only polar paths for which inner core heterogeneities are dominant with respect to mantle heterogeneities the data used come from a high quality file derived by engdahl et al engdahl e r van der hilst r buland r 1998 global teleseismic earthquake relocation with improved travel times and procedures for depth determination bull seismol soc am 88 722 743 from the catalogs of the international seismological centre isc for the period 1964 1995 the minimum standard deviation is obtained for the null rotation rate a similar analysis on the absolute pkp bc residuals which correspond to paths that do not sample the inner core shows that mantle heterogeneities are not at the origin of the observed minimum the same method has also been applied to a set of more than 1200 worldwide distributed pkp bc pkp df differential travel time residuals hand picked by ourselves or gathered by different authors for specific core studies here again the minimum standard deviation is obtained for the null rotation implying a synchronous rotation of the inner core with the mantle however the limited number of very old data and the geographic distribution of the paths prevent us from obtaining a resolution better than 1 year in particular a small super rotation with 1 year cannot be ruled out with the presently available data the problem of the level of the inner core heterogeneities compared to that of the mantle which is another possible limitation of the method is also discussed

pkp bc versus pkp df differential travel times and aspherical structure in the earth s inner core pkp bc versus pkp df differential travel times show coherent patterns of residuals indicating aspherical structure within the earth s inner core using a waveform correlation method we measure 318 differential pkp bc versus pkp df travel times from 5 years of global digital seismograph network gdsn short period data at ranges between 145 and 155 in addition we obtain 19 470 probable bc versus df travel times at these ranges by searching through 23 years of the international seismological centre isc catalog plots of residuals versus turning point location and residuals versus ray direction show clear patterns which indicate that the differential travel times are highly correlated along similar ray paths this pattern is robust with respect to range and source depth these anomalies are almost certainly due to aspherical inner core structure since pkp bc and pkp df have nearly coincident ray paths in the mantle and outer core the gdsn and isc residual patterns are in general agreement but the isc residuals underpredict the gdsn residuals by about a factor of 2 the isc data have better spatial coverage particularly for n s ray paths within the inner core these n s ray paths show positive residuals of about 0 5 s indicating faster inner core p velocities in this direction a result consistent with previous studies of absolute pkp df travel times but derived from an independent data set due to the sparse ray coverage of our data either heterogeneity or anisotropy within the inner core with about 1 velocity variations could explain these residual patterns however inversions of the isc data for heterogeneity require many more free parameters to achieve the same variance reduction as a simple two parameter anisotropy model

inner core differential motion confirmed by earthquake waveform doublets we analyzed 18 high quality waveform doublets with time separations of up to 35 years in the south sandwich islands region for which the seismic signals have traversed the inner core as pkp df the doublets show a consistent temporal change of travel times at up to 58 stations in and near alaska and they show a dissimilarity of pkp df coda using waveform doublets avoids artifacts of earthquake mislocations and contamination from small scale heterogeneities our results confirm that earth s inner core is rotating faster than the mantle and crust at about 0 3 degrees to 0 5 degrees per year

global earth structure inference and assessment summary a suite of compressional and shear phase arrival times p s pp pcp ss scs pkpab pkpbc pkpdf sksac and two sets of differential times ss s410s ss s660s are used to infer lateral variations in p and s velocity structure in the entire earth crust mantle and core volumetric heterogeneity is parametrized by 22 depth layers each of which is subdivided into a grid of cells in addition to volumetric hetero geneity we determine topography on the major internal velocity discontinuities station corrections event relocation parameters and inner core anisotropy a total of 96 300 unknowns the model parameters are estimated using an iterative lanczos algorithm to obtain a partial singular value decomposition a total of 5000 lanczos values and vectors are used to construct model parameter estimates as well as measures of model parameter resolution and covariance the lanczos resolution estimates provide lower bounds on conventional svd based measures throughout most of the mantle we find that regions beneath the continents particularly in the northern hemisphere are well resolved with the exception of africa velocity variations are moderately well resolved in that portion of the outer core lying beneath the continents velocity heterogeneity is poorly resolved in the inner core where cell dimensions are small and deviations in velocity heterogeneity trade off with variations in anisotropy variations in the uppermost mantle 2 3 per cent are correlated with surface tectonics while at greater depths high velocity variations coincide with regions of past and present subduction the high velocity anomalies extend into the lower mantle although with a reduced amplitude 0 5 1 0 per cent until the lowest mantle 2 5 per cent at the base of the outer core a large scale pattern of heterogeneity 0 8 per cent is observed slower at the poles in the inner core we infer a peak anisotropy of 2 3 per cent which varies laterally and with depth however the magnitude and distribution of the anisotropy trades off strongly with velocity heterogeneity

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

the existence of an inner core super rotation questioned by teleseismic doublets abstract the first evidence for a differential rotation of the earth s inner core with respect to the mantle comes from the detection of a variation over 30 years of the differential travel time anomalies of seismic core phases song x richards p g 1996 seismological evidence for differential rotation of the earth s inner core nature 382 221 224 the comparison of teleseismic doublets provides a powerful means to measure such differential travel times and to test their temporal variation contrary to direct measurements of differential travel times this technique does not require to have an accurate location of the seismic events this method is first checked on examples of doublets for which no differential travel time is expected these tests allow us to point out the difficulties such as polarity reversals which may be encountered in the use of the doublet method it is then applied to deep tonga events recorded in france and to the south sandwich islands events recorded at station college col alaska which led song and richards to propose an inner core rotation for the first path we find no time variation in agreement with previous studies for the path from south sandwich island to col the doublet analysis shows that no significant temporal change in pkp travel time can be detected within the resolution of the method which is about 0 05 s the variation of the residuals observed by song and richards about 0 3 s over 30 years is in a large extent ascribable to hypocenter mislocations consequently present seismological observations do not detect the inner core differential rotation because if it exists it is smaller than about 0 2 year the present detection capacity of seismology

fine scale heterogeneity in the earth s inner core the seismological properties of the earth s inner core have become of particular interest as we understand more about its composition and thermal state1 2 observations of anisotropy and velocity heterogeneity in the inner core are beginning to reveal how it has grown and whether it convects3 4 the attenuation of seismic waves in the inner core is strong and studies of seismic body waves5 6 have found that this high attenuation is consistent with either scattering or intrinsic attenuation5 the outermost portion of the inner core has been inferred to possess layering and to be less anisotropic than at greater depths7 8 9 10 here we present observations of seismic waves scattered in the inner core which follow the expected arrival time of the body wave reflection from the inner core boundary the amplitude of these scattered waves can be explained by stiffness variations of 1 2 with a scale length of 2 kilometres across the outermost 300 km of the inner core these variations might be caused by variations in composition by pods of partial melt in a mostly solid matrix or by variations in the orientation or strength of seismic anisotropy

reconciling the hemispherical structure of earth s inner core with its super rotation earth s solid inner core grows through solidification of material from the fluid outer core onto its surface at rates of about 1 mm per year1 freezing in core properties over time and generating an age depth relation for the inner core a hemispherical structure of the inner core is well documented an isotropic eastern hemisphere with fast seismic velocities contrasts with a slower anisotropic western hemisphere2 3 4 independently the inner core is reported to super rotate at rates of up to 1 per year5 6 7 considering the slow growth steady rotation rates of this magnitude would erase frozen in regional variation and cannot coexist with hemispherical structure here we exploit the age depth relation using the largest available pkikp pkikp seismic travel time data set to confirm hemispherical structure in the uppermost inner core and to constrain the locations of the hemisphere boundaries we find consistent eastward displacement of these boundaries with depth from which we infer extremely slow steady inner core super rotation of 0 1 1 per million years our estimate of long term super rotation reconciles inner core rotation with hemispherical structure two properties previously thought incompatible it is in excellent agreement with geodynamo simulations8 9 while not excluding the possibility that the much larger rotation rates inferred earlier5 6 7 correspond to fluctuations in inner core rotation on shorter timescales10

a local crossing path study of attenuation and anisotropy of the inner core 1 we report results from studying a region under the north pacific using 46 ray paths along east west and north south directions to study the nature of inner core anisotropy and find an anisotropy signal in differential pkpbc pkpdf at about the resolution of the data with north south paths faster than east west but no dependence of attenuation on wavespeed or depth in this part of the inner core inner core q is 130 52 255 between 140 340 km depth the observations also provide constraints on the degree of homogeneous meridional anisotropy possibly present in the core to between 0 1 and 0 6 velocity differences in the fast and slow directions significantly smaller than the 2 4 axi symmetric anisotropy in the inner core the small meridional component to anisotropy argues against significant contributions to anisotropy from low order inner core convection or stresses imposed on the inner core by the outer core field

structure of the inner core inferred from observations of its spheroidal shear modes spheroidal modes of elastic gravitational oscillation that have an energy partition dominated by shear energy in the inner core are called core modes recordings from the ida gravimeter network of an earthquake in the tonga region on june 22 1977 have provided the first unambiguous observations of core modes they conclusively show that at low frequencies the inner core has a very high q about 3500 they also tightly constrain the ratio of the inner core radius to the mean shear velocity to be 345s with an uncertainty of 0 5

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

inner core rotation and its variability from nonparametric modeling 1 we present a new approach for studying the inner core rotation and its variability by separating the underlying structure from its time evolution this is achieved by fitting a large set of existing seismic bc df traveltime data with a smoothing spline analysis which is implemented in the statistics package r this method allows us to separate the time independent mantle contribution from the time dependent core contribution without any a priori constraints and to also estimate the error of the fit we add our newly acquired seismic data from the passcal experiment arctic in northern alaska to pkp differential traveltime measurements previously obtained from south sandwich islands earthquakes and recorded at college col and the alaskan seismic network this nearly doubles the number of measurements to a total of 1165 and increases the data coverage of the inner core structure and our time coverage to about 55 years the large number of measurements allows us to use the standard statistical method of bootstrapping to derive the rotation rate and thus to further separate the core structure from its time evolution this approach has been successfully tested with synthetic data sets that feature both a nonlinear structure and variable rotation rates while sharing the same earthquakes and stations geometry as our real data applying this method to the real data yields an average rotation rate of 0 39 0 090 22 yr 1 at 68 confidence level our results also suggest a nonzero acceleration of the inner core with an apparent change in the rotation rate from 0 24 to 0 56 yr 1 within the last 55 years the minimum torque acting on the inner core is estimated 1 19 1016 n m which could result from the imbalance of the electromagnetic and gravitational torques

the shuffling rotation of the earth s inner core revealed by earthquake doublets earth s inner core rotates at a different rate than the mantle and discrepancies exist between rotation rates derived from geophysical observations and geodynamical simulations an inverse analysis of seismic data from repeating earthquakes over the past 50 years suggests that the rotation rate of the inner core fluctuates on decadal timescales