chaotic subduction like downflows in a spherical model of convection in the earth s mantle numerical models of three dimensional nonlinear thermal convection of very viscous fluids have recently been developed in rectangular1 4 and spherical5 12 geometries as analogues of convection in the earth s mantle here we describe model calculations for a compressible fluid in a three dimensional spherical shell with 80 of the surface heat flow generated within the model mantle in agreement with estimates for the earth s mantle13 the rayleigh number and the numerical resolution for these calculations are greater than those of our previous studies9 10 of internally heated convection in a spherical shell our numerical solutions are strongly chaotic with surface planforms dominated by long curvilinear downflows reminiscent of the descending slabs in the earth s mantle although analogy to the earth s mantle is necessarily imperfect owing to for example the absence of variable viscosity and rheology and hence of lithospheric plates our results suggest that descending slabs play an important part in driving mantle convection and that their chaotic evolution may influence the spatial and temporal behaviour of plates and thus the dispersal and aggregation of continents

slabs hotspots cratons and mantle convection revealed from residual seismic tomography in the upper mantle to further investigate the fate of slabs the structure of hotspots and the style of mantle convection we calculate residual tomographic maps in the upper mantle by excluding from the tomography the first order effects of conductive cooling of oceanic plates deep cratonic roots and cooling or partial melting associated with subducted lithosphere no correlation is found between residual tomography in the upper mantle and the 30 130 ma subduction the good correlations between residual tomography in the transition zone 400 650 km and 0 30 ma subduction at spherical harmonic degree l 2 can be explained either by slab accumulation in the transition zone beneath some subduction zones or by the poor lateral resolution of seismic tomography hotspots correlate with the residual tomography in the shallow 100 400 km and the lowermost mantle at degree l 2 however correlations of hotspots and seismic velocities in the middle mantle and correlations between residual tomography at shallow depths and lowermost mantle tomography are poor therefore the connection between residual tomography at shallow depths and seismic tomography in the lowermost mantle is not clear craton distribution correlates with distribution of hotspots and residual topography very well at degree l 6 this might indicate that cratonic roots may affect the locations of upwellings and thus modulate upper mantle convection or that the degree l 6 could be intrinsic in upper mantle convection with cratons and and other near surface features establishing the pattern

the potential influence of radiative heat transfer on the formation of megaplumes in the lower mantle abstract recent seismic tomographic models have revealed broad low velocity anomalies in the lower mantle beneath africa and the central pacific which suggest a break in the symmetry between hot and cold regions in lower mantle dynamics we have considered the possible impact from radiative heat transfer which can be described by a nonlinear temperature dependent coefficient in the thermal conductivity in 2d numerical simulations results for rayleigh numbers up to 106 show a strong stabilizing influence from radiative heat transfer on mantle upwellings and the production of extremely hot thermal anomalies in the interior this nonlinearity is responsible for producing a strong attractor in the mantle convective system which greatly simplifies its time dependent dynamics the possible link of the simplified lower mantle time dependent dynamics with polar wander is discussed the main point here is that slow time dependence of the huge anomalies in the lower mantle can be the main mechanism controlling long term rotational dynamics

long wavelength s wave velocity structure throughout the mantle summary long wavelength s wave velocity anomalies are obtained for the entire mantle by inverting 6ooo long period 40 100s sh body waves and lo00 long period 100 500 s love waves in the shallow mantle the patterns of fast and slow velocity anomalies correlate well with age and tectonics in the depth range of 400 1000 km we find two antipodal fast velocity anomalies one in the western pacific and the other in south america they form a fairly strong i 2 anomaly moreover the 1 2 anomaly is the largest spherical harmonic component throughout the entire mantle except for in the layer of 1000 1300 km depth a fast velocity anomaly near the caribbean previously reported by several other investigators is found between the depths of 1000 and 1300km with diminishing amplitudes it can be traced to canada and the aleutians and may be related to old subducted slabs in the same depth interval similar size anomalies can be found in the middle of the pacific and in the indian ocean these could be checked by more detailed studies to judge the reliability of this study heterogeneity power has a peak at the surface and a secondary peak at the bottom of the mantle d consistent with the existence of chemical and or thermal boundary layers at the base of the mantle we also find a fast velocity anomaly which surrounds the pacific ocean this feature has been found by other researchers previously but its interpretation is difficult due to the trade off between velocity anomaly and core mantle boundary deformation

lidar based quantification of lava flow susceptibility in the city of auckland new zealand abstract lava flows represent one of the most significant volcanic hazards from basaltic monogenetic volcanoes such as spatter cones scoria cones maars and tuff rings they are common features emanating from parasitic vents on the flanks of polygenetic volcanoes and in dominantly flat lying intraplate volcanic fields the auckland volcanic field avf is a volcanic field that has been active for the last ca 250 ka hosting at least 50 monogenetic volcanoes morphometric parameters of lava flows such as volume length thickness and area were used to quantify the potential lava flow inundation susceptibility to new zealand s most densely populated area the city of auckland based on an airborne light detection and ranging lidar digital surface model dsm the morphometric parameters of fifteen studied flows included average length of 2 5 km range 0 7 6 5 km overall average thickness of 14 8 m range 3 4 43 8 m average of maximum thicknesses of 48 2 m range 18 3 180 5 m average area occupied of 5 1 km 2 range 0 4 25 1 km 2 and average volume of 0 12 km 3 range 0 005 1 km 3 based on these parameters and a lidar derived dsm the present topography was classified into sea topographic depressions low lying areas prone to inundation by an average lava flow buffer zones prone to inundation only by extremely thick lava flows and peaks or ridges which are unlikely to be overtopped in monogenetic fields each new vent occurs in a new location creating uncertainty around the spatial location of the volcanic hazard thus this research provides a general vent location independent approach to describe the lava flow susceptibility for a potentially active monogenetic volcanic field what this analysis reveals is that the city of auckland can be divided into two distinct areas with strongly different susceptibility to lava flow inundation the southern part of the city is predominantly flat without hindrance to lava flow whereas the hilly northern and central part has many ridges that can limit or channelise lavas these contrasting properties must be accounted for in scenario based or probabilistic hazard and risk models developed for the avf

the effect of post pangea subduction on global mantle tomography and convection there is an excellent correlation between tomographic patterns and global tectonics in the upper 200 km of the mantle below this depth there is little relationship with present tectonic provinces most of the power in the tomography is in the longest wavelengths l 1 3 with l 2 generally dominant this is quite different from expectations based on mantle convection models the question then arises what causes the long wavelength variations mapped by seismic techniques we investigate the hypotheses that past locations of supercontinents and subduction may control temperature variations in the mantle we look for correlations between pangea and post pangeatic subduction and seismic velocity variations at various depths the best correlations with time integrated slab locations occur near the base of the uppermantle suggesting that slabs bottom out in the mesosphere the pangea hemisphere has a colder than average uppermantle probably due to circum and intra pangea subduction hotspots and ridges avoid regions cooled by subduction over the past 180 ma the presence of large continents at the surface and large areas of cold slab at depth explain the dominance of long wavelengths in the mantle s thermal structure despite the high rayleigh number

the geological origin of long wavelength lateral heterogeneity at depths of 300 400km on the basis of two three dimensional 3 d models of s wave velocity pumo hara et at 1993 and sh425 2 su and dziewonski 1991 we show that the deep roots of cratons and mid ocean ridges provide a satisfactory explanation of the pattern and amplitude of the earth s long wavelength lateral heterogeneity in the depth range from 300 to 400km

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

aspherical earth structure from fundamental spheroidal mode data free oscillation data reveal heterogeneity in the earth s mantle whose geographical pattern is dominated by spherical harmonics of angular degree two and correlates well with the hydrostatically referenced geoid the heterogeneity can be modelled as localized in the transition zone 420 670 km depth and may be related to a large scale component of mantle convection

moment tensors of ten witwatersrand mine tremors ground motions recorded both underground and on the surface in two of the south african gold mining districts were inverted to determine complete moment tensors for 10 mining induced tremors in the magnitude range 1 9 to 3 3 the resulting moment tensors fall into two separate categories seven of the events involve substantial coseismic volumetric reduction v together with normal faulting entailing shear deformation ad where the summation is over fault planes of areaa and average slipd for these events the ratio v ad ranges from 0 58 to 0 92 with an average value of 0 71 for the remaining three events v is not significantly different from zero these events are largely double couple sources involving normal faulting surprisingly the two types of source mechanism appear to be very distinct in that there is not a continuous distribution of the source mix from v 0 to v ad presumably the coseismic closure indicates substantial interaction between a mine stope and adjacent shear failure in the surrounding rock under the influence of an ambient stress for which the maximum principal stress is oriented vertically

subduction history reveals cretaceous slab superflux as a possible cause for the mid cretaceous plume pulse and superswell events abstract subduction is a fundamental mechanism of material exchange between the planetary interior and the surface despite its significance our current understanding of fluctuating subducting plate area and slab volume flux has been limited to a range of proxy estimates here we present a new detailed quantification of subduction zone parameters from the late triassic to present day 230 0 ma we use a community plate motion model with evolving plate topologies to extract trench normal convergence rates through time to compute subducting plate areas and we use seafloor paleo age grids to estimate the thickness of subducting lithosphere to derive the slab flux through time our results imply that slab flux doubled to values greater than 500 km3 yr from 180 ma in the jurassic to 130 ma in the mid cretaceous subsequently halving again towards the cretaceous paleogene boundary largely driven by subduction zones rimming the pacific ocean basin the 130 ma spike can be attributed to a two fold increase in mid ocean ridge lengths following the break up of pangea and a coincident increase in convergence rates with average speeds exceeding 10 cm yr with one third of the total 230 0 ma subducted volume entering the mantle during this short 50 myr period we suggest this slab superflux drove a surge in slab penetration into the lower mantle and an associated increase in the vigour of mantle return flow this mid cretaceous event may have triggered or at least contributed to the formation of the darwin rise mantle superswell dynamic uplift of the south african plateau and the plume pulse that produced the ontong java hikurangi manihiki and kerguelen plateaus among others the models presented here contribute to an improved understanding of the time evolving flux of material consumed by subduction and suggest that slab superflux may be a general feature of continental dispersal following supercontinent breakup these insights may be useful for better understanding how supercontinent cycles are related to transient episodes of large igneous province and superswell formation and the associated deep cycling of minerals and volatiles as well as leading to a better understanding of tectonic drivers of long term climate and icehouse to greenhouse transitions

anisotropy and shear velocity heterogeneities in the upper mantle long period surface waves are used to map lateral heterogeneities of velocity and anisotropy in the upper mantle the dispersion curves are expanded in spherical harmonics up to degree 6 and inverted to find the depth structure the data are corrected for the effect of surface layers and both love and rayleigh waves are used shear wave velocity and shear polarization anisotropy can be resolved down to a depth of about 450 km the shear wave velocity distribution to 200 km depth correlates with surface tectonics except in a few anomalous regions below that depth the correlation vanishes cold subducted material shows up weakly at 350 km as fast s wave anomalies in the transition region a large scale pattern appears with fast mantle in the south atlantic s anisotropy at 200 km can resolve uprising or downwelling currents under some ridges and subduction zones the pacific shows a nw se fabric

measurement of mantle wave velocities and inversion for lateral heterogeneity and anisotropy 1 analysis of great circle phase velocities long period 100 330 s fundamental mode love and rayleigh waves have been processed to measure the great circle phase velocities for about 200 and 250 paths respectively the observations are inverted for regionalized phase velocities and for an even order harmonic expansion of the lateral velocity heterogeneity the regionalized inversions achieve a maximum variance reduction of about 65 and 85 for the love and the rayleigh wave data respectively the l max 2 inversions give a maximum variance reduction of about 60 and 90 for love and rayleigh waves respectively the l max 8 inversion does not make a large improvement in the fit the love wave phase velocities have more power in l 4 and 6 relative to l 2 than the rayleigh waves for both love and rayleigh wave data the sectoral component dominates the l 2 harmonics and this component is stable if we increase l max from 2 to 6 heat flow also has strong sectoral components lm 22 which are approximately in phase with those of the phase velocities the l 2 harmonics of the nonhydrostatic geoid are dominated by large zonal lm 20 and moderate sectoral components the sectoral components are in phase with those of the phase velocities the sectoral pattern of heat flow and phase velocity is controlled by high heat flow low velocity of the east pacific rise and western north america which is reinforced by low velocities in the antipodal region red sea gulf of aden east african rift by contrast the geoid l 2 pattern is dominated by geoid highs over the western pacific subduction zones a spherical harmonic expansion of regionalized phase velocities shows that they have l 2 variations similar to those of the l max 2 nonregionalized inversions this means that the regionalization approach is appropriate as a first step for studying lateral heterogeneity of the earth however the great circle phase velocities are not sufficient by themselves to uniquely locate the lateral heterogeneity the same is true for free oscillation data regions of convergence have the interesting property of being slow for short period waves and fast faster than shields for long period waves

whole mantle p wave travel time tomography abstract a method of tomographic inversion to obtain three dimensional velocity perturbations in the earth s whole mantle has been developed and applied to more than two million p wave arrival time data reported by international seismology center isc the model is parameterized with 32 768 blocks the divisions in latitude longitude and radius are 32 64 and 16 respectively horizontal cell size is 5 6 5 6 the layer thicknesses vary with depth 29 km just below the surface and 334 km just above the core mantle boundary starting from a spherically symmetric earth model we obtained a three dimensional model using the following iterative procedures first we relocated all the events second we backprojected the residual into the whole mantle third we refined the spherically symmetric earth model the solutions have been converged in five iterations we adopted the following techniques in the backprojection procedure the first order smoothness was introduced as a damping which makes the solution independent of the starting model and its apparent fluctuation minimal the basic equations for delay times and smoothness are solved using the conjugate gradient method an iterative method which guarantees the convergence of solution into the exact least squares solution the weight on the smoothness i e the damping factor was objectively determined by a simplified cross validation technique the final solution was obtained as an average of the ten solutions each of which was derived from one tenth of the total data set the reliability of the solution is examined in two ways 1 mapping the resolution given by the reconstruction of checkerboard patterns and 2 mapping the variance given from the gaussian noise input this is the first result which delineates the whole mantle structure with its reliability mapping the longest wavelength anomalies of the lower mantle are similar to those of previous studies by dziewonski 1984 and hager and clayton 1989 however the shorter wavelength patterns have many discrepancies the fast anomalies of the uppermost mantle beneath the shield and the slow anomalies beneath the active tectonic regions are clearly seen we also revealed the l 2 pattern at the transition zone reported by the previous surface wave and free oscillation studies the most striking feature is that of the fast anomalies lying along the extension of the large subducting plate up to depths of about 1000 km or more the resolving powers in these regions are generally good

a theory of the earth hutton and humpty dumpty and holmes paradoxes can be viewed as a bother or as a rich source of information paradoxes fallacies and logical inconsistencies along with the unstated assumptions behind old worldviews often form the foundation for a new worldview this is where science differs from myth and just so stories mantle dynamicists and geochemists have developed a worldview that in many respects is incompatible with modem theories of planetary accretion geodynamics and geophysics and with the geological context of volcanoes a primordial undegassed mantle as both the furnace and the fuel of midplate volcanoes occupies a central role in the geochemical models although modem data alone are sufficient to overturn this view it is interesting to address it in terms of its own assumptions fallacies and inconsistencies and the history of ideas this is a vast field so in honour of james hutton i focus on volcanoes their products their causes and their sources

the 3 d shear wave structure in the mantle by overtone waveform inversion ii inversion of x waves r waves and g waves summary the 3 d upper mantle structure from the surface of the earth to a depth of about 1000 km is obtained by inverting waveforms of fundamental and higher mode surface waves minor and major arc waves of r waves g waves and x waves higher mode wave packets are used as basic data two features of the solution seem fairly robust one is the shallow structure in the upper few hundred kilometres which is strongly correlated with the age of the crust the second feature is the deep fast velocity anomaly near the western pacific indonesia philippines and mariana region and its antipodal region of south america both of which are subduction zones which forms a strong l 2 pattern simple slab models with 100 km thicknesses of 10 per cent faster velocity material do not explain such large scale fast velocity anomalies this may indicate large scale deformation of the 670 km discontinuity piling up of slabs in the upper mantle or thickening lithosphere in the lower mantle or large horizontal motions of subducted material these results are stable whether an earth model 1066a or prem is used as a starting model

predominance of long wavelength heterogeneity in the mantle analysis of travel time anomalies of long period shear waves recorded by the global digital seismographic network indicates that mantle heterogeneities which probably reflect patterns of mantle convection occur most prominently on length scales greater than about 6 000 km when projected onto a two dimensional map at the earth s surface models of mantle convection will need to be able to produce a similar power spectrum

effects of multiple phase transitions in a three dimensional spherical model of convection in earth s mantle numerical models of mantle convection that incorporate the major mantle phase changes of the transition zone reveal an inherently three dimensional flow pattern with cylindrical features and linear features that behave differently in their ability to penetrate the 670 km discontinuity the dynamics are dominated by accumulation of cold linear downwellings into rounded pools above the endothermic phase change at 670 km depth resulting in frequent avalanches of upper mantle material into the lower mantle the effect of the exothermic phase transition at 400 km depth is to reduce the overall degree of layering by pushing material through the 670 km phase change resulting in smaller and more frequent avalanches and a wider range of morphologies large quantities of avalanched cold material accumulate above the coremantle boundary cmb resulting in a region of strongly depressed mean temperature at the base of the mantle the 670 km phase change has a strong effect on the temperature field with three distinct regions being visible 1 the upper mantle containing linear downwellings and pools of cold material in the transition zone and characterized by a high amplitude long wavelength spectrum 2 the midmantle containing quasi cylindrical avalanche conduits and characterized by a low amplitude broad spectrum and 3 the deep mantle containing large pools of cold avalanched material and characterized by a high amplitude ultra red i e long wavelength spectrum the effect on the velocity field is very different flow penetration across the 670 km phase change is strongly wavelength dependent with easy penetration at long wavelengths but strong inhibition at short wavelengths thus when comparing numerical models with long wavelength seismic tomography diagnostics based on the density field such as the radial correlation function are much more sensitive to the effects of phase transitions than those based on the velocity field the amplitude of the geoid is not significantly affected by the partial layering because the contribution from the strong heterogeneity in the transition zone is almost perfectly balanced by the contribution from deflection of the 670 km discontinuity avalanches are associated with geoid lows however a more complex viscosity structure is required to correctly match the sign of the geoid over slabs in earth

the scales of mantle convection seismic topographic and gravity data show that there are two important scales of mantle convection these are associated with spherical harmonic degrees l 2 and 6 the l 2 pattern corresponds to the pattern of subduction cooling since the breakup of pangea most hotspots and ridges occur in the half of the globe unaffected by this cooling and all large igneous provinces were generated over this part of the mantle the l 2 distribution of upwellings and downwellings is likely to be a long lived feature of the earth cold regions of the mantle repeatedly attract continents and subduction reinforces the coldness an l 1 pattern of convection is probably related to supercontinents and their breakup degree 6 convection shows up in the spectrum of hotspots and upper mantle tomography and in the correlation of tomography and topography with the geoid cratons with their deep cold keels control the l 6 pattern and may even cause it by their role in establishing lateral temperature gradients and relief at the top of the convecting mantle subduction zones reinforce the craton pattern downwellings preferentially occur under cratons upwellings and hotspots occur at complementary locations supercontinents and their associated subduction zones l 1 constantly assemble and reassemble in the african atlantic hemisphere and the continental fragments in the dispersed state periodically settle into the polar band of geoid lows l 2 and 6 that now includes the americas antarctica australia and india if cratons control the l 6 pattern of convection and many patterns of l 6 are possible e g sectoral zonal checker board then upper mantle convection may reorganize roughly every 30 ma as cratons move about the hotspot spectrum is probably related to lithospheric extension as well as to broad upwellings a third and smaller scale of convection order 400 1000 km in dimension is just below the resolution of global tomography but shows up in the gravity field geoid and topography this scale is controlled by the depth of an endothermic phase change which tends to stratify mantle convection and the thickness of the upper mantle low viscosity zone convective domains of this dimension are also implied by the scales of chemical homogeneity lengths of rifts ridges and seamount chains fracture zone spacing and mid ocean ridge segmentation the temperature geochemistry and fertility of these upper mantle scale domains is controlled by their previous history of subduction continental insulation or refrigeration and processing by ridges fertile or volatile rich or hot cells can be mistaken for plumes hotspot swells are typically of the dimension that we argue is a characteristic upper mantle scale rather than a deep mantle plume scale geochemical domains of various sizes exist in the upper mantle they are broad scale features rather than point sources as in plume theories lithospheric dynamics and geometric focusing not mantle dynamics control the dimensions of so called hotspot eruptives

worldwide distribution of group velocity of mantle rayleigh waves as determined by spherical harmonic inversion we have determined the worldwide distribution of group velocity of mantle rayleigh waves for periods between 100 and 300 sec without assuming any regionalization group slowness 1 u is expressed by spherical harmonics and the coefficients up to angular order 7 have been determined from travel times of rayleigh waves by a least squares method from these u has been synthesized since we cannot obtain information about the odd terms of the expansion from one circuit measurements around the world we have used group velocities of mainly r 2 and r 3 the overall pattern of u for periods between 100 and 200 sec is consistent with results of previous pure path and regional studies group velocities for tectonically active regions are low and those of the shields and the northwestern pacific are high

komatiites and picrites evidence that the plume source is depleted high temperature magmas such as picrites and komatiites are candidates for the material in the hot axial region of mantle plumes in current plume theories these magmas should have an enriched ocean island basalt oib type chemistry high mgo magmas however are often more like depleted mid ocean ridge basalts morb in trace element and isotopic chemistry this is a paradox for deep mantle plume or primitive mantle theories but is expected if hotspots and morb share a common depleted source and the transition to oib chemistry involves shallow level cooling crystal fractionation and contamination ancient komatiites appear to have come from the same deep depleted reservoir as modern picrites and morb

relationship of el nino southern oscillation and pacific sea surface temperature with rainfall in various regions of the globe after characterizing every year in the 120 yr interval 1871 1990 as having an el nino en or southern oscillation minimum so or equatorial sea surface temperature maximum warm events w or minimum cold events c or any combination of these or none nonevents the rainfalls in various regions of the globe were examined for each category of year using the data of ropelewski and halpert who had identified some regions as having a negative response deficit rains and some as having a positive response excess rains to enso events the author finds that this response is best with ensow type events especially the unambiguous ones el nino in the early part of the year and so and w in the middle of the year though in some cases even ambiguous ensow gave good results also the response is reverse for c type events out of the 46 years having el nino all types and 36 years having cold c events the response for some regions is good but for some other regions only about half could be associated with the expected response making predictions uncertain in those regions factors other than enso may have considerable influence on rainfalls in different regions at different times thus distorting the enso effects

dynamically supported geoid highs over hotspots observation and theory hotspots are associated with long wavelength geoid highs an association that is even stronger when the geoid highs associated with subduction zones are removed we quantify these associations by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree the hotspot distribution spectrum is nearly white except for peaks at degrees 2 and 6 it is correlated positively with the slab residual geoid for degrees 2 6 with low seismic velocity in the lower mantle at degree 2 and with low seismic velocity in the upper mantle at degree 6 we test fluid mechanical models for hotspots including lithospheric delamination and hot plumes by calculating their predicted dynamic geoid responses and comparing them to the observations these models include the effects of temperature dependent rheology our preferred hotspot model based on observations of the geoid and seismic tomography has plumes preferentially occurring in regions of large scale background temperature highs in a mantle which has a substantial viscosity increase with depth although other models are possible alternatively strong plumes in the lower mantle may neck down and attenuate in the upper mantle due to changes in plume viscosity the major low density anomalies causing the geoid highs associated with plumes appear to be in the lower mantle we hypothesize that cold lower mantle underlying the complementary geoid lows is due to deeply subducted oceanic lithosphere and that hotspot plumes tend to be excluded from these cold regions of the mantle

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

partial melting in a thermo chemical boundary layer at the base of the mantle abstract seismological detections of complex structures in the lowermost mantle boundary layer the d region motivate a conceptual model of a compositionally stratified thermo chemical boundary layer tcbl within which lateral temperature variations sustained by large scale mid mantle flow cause variations of partial melt fraction partial melt fractions of from 0 to 30 in the tcbl occur due to the eutectic of the boundary layer material lying below the high temperature at the core mantle boundary cmb coupled with the presence of steep thermal gradients across the boundary layer regions of the tcbl with the highest temperatures have extensive partial melting producing lateral chemical variations and strong effects on seismic velocities and boundary layer dynamics this tcbl concept provides a relatively simple framework that can plausibly account for diverse seismological observations such as predominance of large scale volumetric elastic wave velocity heterogeneity in the boundary layer laterally extensive but intermittent abrupt shear and compressional velocity increases and decreases at the top of the d region small scale topography of d velocity discontinuities thin ultra low velocity zones at the cmb widespread shear wave anisotropy in d bulk sound velocity anomalies detected in low shear velocity regions of d and large scale upwellings from the most extensively melted regions of the boundary layer neutral or negative buoyancy of the partial melt in the tcbl is required along with an increase in bulk modulus and some density increase of the boundary layer material relative to the overlying mantle more complex models in which the partially melted chemical boundary layer is laterally displaced by mid mantle downwellings are also viable but these appear to require additional special circumstances such as a phase change efficient segregation of slab crustal material or abrupt onset of anisotropy in order to account for rapid velocity increases at the top of d the precise nature of the compositional anomaly or anomalies in d and the eutectic composition of this zone are yet to be determined but it appears likely that partial melting within the lowermost mantle plays a paramount role in the observed seismic velocity heterogeneity increased resolution geodynamic calculations of dense boundary layer structures with partial melting and attendant viscosity reductions and chemical heterogeneity are needed to quantify this tcbl concept