gravity and convection in a two layer mantle abstract one of the current models of mantle convection assumes that the circulation takes place in two superimposed layers separated by the 700 km discontinuity the present study reports two dimensional numerical experiments carried out to investigate the structural features and gravitational consequences of layered convection the models have two constant viscosity layers heated from below the main variable is the viscosity ratio other free parameters are the layer depths and the over all rayleigh number as the viscosity of the lower layer is increased with respect to that of the upper layer the flow structure shifts gradually from the dominance of viscous coupling of the layers towards thermal coupling viscous coupling prevails when the viscosity ratio is near to one and produces pairs of cells which turn oppositely in the two layers thermal coupling becomes predominant if the viscosity ratio is several hundred or more in a series of models with a depth ratio 1 2 thermal coupling leads to pairs of cells which turn in the same sense in the two layers during the transition between the extremes two or more small rolls appear in the thinner upper layer over one cell of the lower fluid gravity profiles and boundary deformations have been calculated for each model the transfer function admittance of gravity over top surface topography shows a characteristic variation with the viscosity ratio in a series with the depth ratio 1 4 negative values of the admittance are obtained when the lower viscosity is 10 50 times higher than the upper one negative admittance is a typical feature of the subcontinental convection operating behind subduction zones two layer models of this type of convection are able to explain not only the sign of admittance but also the magnitude of observed gravity anomalies

on geoid heights and flexure of the lithosphere at seamounts the sea surface height has now been mapped to an accuracy of better than 1 m by using radar altimeters on board orbiting satellites the major influence on the mean sea surface height is the marine geoid which is an equipotential surface we have carried out preliminary studies of how oceanic volcanoes which rise above the ocean floor as isolated seamounts and oceanic islands or linear ridges contribute to the marine geoid simple one and two dimensional models have been constructed in which it is assumed that the oceanic lithosphere responds to volcanic loads as a thin elastic plate overlying a weak fluid substratum previous studies based on gravity and bathymetry data and uplift subsidence patterns show that the effective flexural rigidity of oceanic lithosphere and the equivalent elastic thickness te increase with the age of the lithosphere at the time of loading the models predict that isolated seamounts emplaced on relatively young lithosphere on or near a mid ocean ridge crest will be associated with relatively low amplitude geoid anomalies about 0 4 0 5 m km of height while seamounts formed on relatively old lithosphere on ridge flanks will be associated with much higher amplitude anomalies 1 4 1 5 m km studies of the seasat altimetric geoid prepared by nasa s jet propulsion laboratory support these model predictions geoid amplitudes are relatively low over the mid pacific mountains and line islands which formed on or near a mid ocean ridge crest and relatively high over the magellan seamounts and wake guyots which formed off ridge direct modeling of the altimetric geoid over these features is complicated however by the wide spacing of the satellite tracks which can exceed 100 km and poor bathymetric control beneath individual satellite tracks in regions where multibeam bathymetric surveys are available models can be constructed that fit the altimetric geoid to better than 1 m studies of geoid anomalies over the emperor seamount chain for example suggest that these seamounts formed on 20 30 ma old oceanic lithosphere while anomalies over the louisville ridge and the hawaiian ridge suggest that these seamounts formed on lithosphere older than about 80 ma this indicates that geoid anomalies over bathymetrie features depend not only on the crustal structure prior to loading and the overall shape and density of the features but also on their tectonic setting we examine the implications of these results to studies which attempt 1 to separate temporal variations of the sea surface due to oceanographic effects 2 to predict seamounts directly from satellite derived gravity and geoid data and 3 to isolate the geoid effects of deep processes occurring beneath the lithosphere such as those due to mantle convection

long wavelength gravity and topography anomalies it is shown that gravity and topography anomalies on the earth s surface may provide new information about deep processes occurring in the earth such as those associated with mantle convection two main reasons are cited for this the first is the steady improvement that has occurred in the resolution of the long wavelength gravity field particularly in the wavelength range of a few hundred to a few thousand km mainly due to increased coverage of terrestrial gravity measurements and the development of radar altimeters in orbiting satellites the second reason is the large number of numerical and laboratory experiments of convection in the earth including some with deformable upper and lower boundaries and temperature dependent viscosity the oceans are thought to hold the most promise for determining long wavelength gravity and topography anomalies since their evolution has been relatively simple in comparison with that of the continents it is also shown that good correlation between long wavelength gravity and topography anomalies exists over some portions of the ocean floor

the dynamical equations of polar wander and the global characteristics of the lithosphere as extracted from rotational data abstract the initial value problem describing the linear responses of the spin axis of a layered viscoelastic planet from surface loading is studied by means of laplace transform techniques a complete solution of polar motion requires the usage of two classes of eigenspectra one arising from viscoelastic relaxation of the mantle due to surface forcing the other involving the gradual readjustment of the spin axis as a consequence of mantle viscoelasticity our analytical 4 layer model comprising an elastic lithosphere a two layer adiabatically stratified viscoelastic mantle and an inviscid core has been incorporated into this formalism in which rotational deformation and isostatic relaxation are taken into account for all times from employing both sets of rotational data polar variations from the 70 years of data from the international latitude service i l s and the non tidal deceleration of the length of the day l o d an estimate of the globally averaged lithosphere of between 130 and 200 km is obtained from the long wavelength flexural mode due to the degree two harmonic this range of values may have strong implications on the mode of continental evolution

steady state secondary convection beneath lithospheric plates with temperature and pressure dependent viscosity we have constructed a thermomechanical model for upper mantle convection such that the thickness and structure of the lithosphere are determined self consistently by the heat transported by convection in this study of the interaction between the lithosphere and upper mantle strongly temperature and pressure dependent rheologies for both newtonian and non newtonian creep mechanisms are employed for a strictly temperature dependent rheology an insignificant amount of heat less than 12 5 mw m2 can be transported convectively for an interior viscosity 0 1021 pas compatible with postglacial rebound on the other hand for similar values of the interior viscosity steady heat fluxes between 20 and 40 mw m2 are produced by introducing pressure dependence into the rheology for the temperature and pressure dependent flow law the horizontally averaged interior temperature displays very little variation with the amount of heat evacuated once all of the rheological parameters are fixed this finding may have important ramifications for parameterized convection we employ both the single mode mean field approximation and the complete two dimensional equations using finite elements to obtain solutions for the various types of rheologies from evaluating the geophysically relevant observables such as topography free air gravity anomalies surface heat flow and stress fields in the lithosphere we find that the lateral variations of these quantities predicted by a non newtonian rheology are much smaller than those derived from a linear rheology these results suggest that surface variations of geophysical observables are more compatible with a non newtonian rheology in the upper mantle

statistical analysis of the mean heat flow reduced heat flow relationship for continents and its tectonothermal implications previous analysis of the relationship between mean heat flow q and reduced heat flow qr indicated that qr 0 6q suggesting that the upper crustal radiogenic contribution to heat flow was coupled to changes in qr statistical reexamination of this relationship reveals that this empirical relationship results for several reasons and that other interpretations may apply in stable tectonic areas importantly the slope of the q qr line changes significantly when certain points are excluded from the regression with the strongest effect exerted by the basin and range and eastern australia because these areas were tectonically active during the cenozoic they may be outliers exhibiting disproportionate influence on the regression results because q and qr exhibit large errors and are correlated we used a computer simulation method to fit a straight line to correlated variables with errors we find that the slope of the line is reduced and that the fit is sensitive to outliers if we restrict the analysis to more stable tectonic regions we determine a q qr relationship with a small slope and large intercept inclusion of data from regions which have been tectonically active in the cenozoic gives results closer to the qr 0 6q relationship we suggest that this previous result reflects the presence of data from thermally perturbed regions in the q qr data set this in conjunction with the nearly horizontal line found for stable regimes indicates that coupling between the upper crust and mantle lower crust system is not implied furthermore q r for stable regions is about 27 mw m2 with a small standard deviation 4 mw m2 the average upper crustal radiogenic component is nearly equivalent but has a large standard deviation 14 mw m2 suggesting that variations in q for heat flow provinces in stable regions is largely controlled by upper crustal radiogenic variations

a numerical model of coupled subcontinental and oceanic convection abstract at least two different types of convection should exist in the earth s mantle a large scale flow which is revealed by the creation and subduction of oceanic crust and a circulation of unknown scale under the continents which does not approach the surface the effects of these coexisting and interacting modes on mantle dynamics and thermal regime are investigated by means of a finite element model system of two adjacent cells which are coupled thermally and mechanically at their interface an a priori viscosity distribution is applied in such a way that the surface layer of the longer cell can move with almost uniform velocity while it is immobile on the shorter cell the results suggest that the pattern of sub oceanic convection is stabilized to some extent by the frame of the highly viscous but moving lithosphere whereas convection under continents is more complex and less stable most of the sub continental heat is transferred into the oceanic cell this causes an imbalance of surface heat flow which is well in accordance with recent determinations of global heat loss distribution furthermore the model reflects at least semiquantitatively the continent ocean differences in lithospheric thickness mean topographic level and upper mantle temperatures while the average geotherms below ocean and continent diverge by up to 400 k at moderate depth they nearly coincide below 250 km depth thus giving no support for deep reaching continent ocean differences these results refer to convection penetrating the lower mantle if the circulation is confined to moderate depth the continental upper mantle is too hot compared with the oceanic however this may be due to the strict separation of the flow on either side the model results stimulate some speculations on the possible form of whole mantle convection

was the 2003 european summer heat wave unusual in a global context 1 we place the european summer heat wave of 2003 in the context of other extreme summer tropospheric temperature events from 22 n to 80 n since 1979 as well as globally using annual averages the analysis is performed in terms of standard deviations sd exceeded and correlations between regional extremes and temperatures at larger spatial scales as has been pointed out previously the heat wave was statistically unusual and was a deep tropospheric phenomenon in this analysis we also find the following 1 extreme warm anomalies equally or more unusual than the 2003 heat wave occur regularly 2 extreme cold anomalies also occur regularly and occasionally exceed the magnitude of the 2003 warm anomaly in terms of the value of sd 3 there is a correlation between global and hemispheric average temperature and the presence of warm or cold regional anomalies of the same sign i e warmer than average years have more regional heat waves and colder than average years have more cold waves 4 natural variability in the form of el nino and volcanic eruptions appear to be of much greater importance in causing extreme regional temperature anomalies than a simple upward trend in time extreme temperature anomalies in the wake of the 1997 98 el nino were larger than the anomalies seen in summer 2003 both in area affected and sd extremes exceeded 5 regression analyses do not provide strong support for the idea that regional heat waves are increasing with time

topography and geoid undulations caused by small scale convection beneath continental lithosphere of variable elastic thickness summary the effect of subcontinental upper mantle convection on topography gravity and geoid undulation is studied with special regard to the effective elastic thickness of the continental lithosphere hel we designed a numerical model of the upper mantle lithosphere system consisting of a constant viscosity fluid overlayed by a partly elastic plate the boundary tractions stresses at the top of the convecting mantle model were applied to the lithosphere model for which we used the thin plate approximation the total thickness of the lithosphere was kept constant to 150 km while the elastic thickness was varied between 0 and 150 km the aspect ratio of the convecting mantle was varied between 0 7 and 3 and the rayleigh number between 104 and 106 our calculations demonstrate the effect of a thick elastic lithosphere on the surface observables peak to peak averaged amplitude of topography geoid undulation and gravity are strongly reduced and their spectra are low pass filtered for an aspect ratio less than 1 and a very thick elastic lithosphere topography tends to zero and while geoid undulation and gravity may even become negative above the up welling plume the spectral relation of geoid or gravity to topography admittance is nearly unaffected for hie 70km for aie 70km admittance values for all wavelengths generally decrease with increasing elastic thickness of the plate and may become negative geoid admittance for the basic mode increases with larger aspect ratio while gravity admittance for hie 100 km slightly decreases associating higher rayleigh numbers of the convecting fluid with lower viscosity an increase in rayleigh number leads to considerable decrease of the surface observables however admittance values are only slightly affected and decrease approximately linearly with increasing rayleigh number comparison of our results with observations of the topography spectrum and the free air gravity admittance for north america suggests that large aspect ratio cells beneath continents are unlikely however convection cells of aspect ratio 1 or less underlying an elastic lithosphere of at least 100 km thickness is in agreement with data the rayleigh number should be as high as 106

surface deformation and geoid anomalies over single and double layered convective systems using a primitive variable formulation of the finite element method we have compared the differences in the surface observables such as topography and geoid produced by single and double layered thermal convection both constant and depth dependent viscosities have been considered for the same rayleigh number larger surface perturbations are produced by single cell convection for the same nusselt number the magnitudes of the surface observables are greater for double layered convection for the same surface heat flux surface topographies have similar magnitudes but the relative amplitudes of geoid anomalies depend greatly on the style of viscosity stratification this difference in the geoid between the two systems increases with greater surface heat flow regardless of viscosity structure

global relationship between oceanic geoid and seafloor depth new results a new global transfer function admittance between oceanic geoid and seafloor depth has been derived for the wavelength band 1000 4000 km after removal of lithospheric cooling effects using the most recently published crustal ages of the oceans in this wavelength band the admittance is positive reaches a maximum of 5m km around 2750 km wavelength then decreases to 2 5 m km on the average at shorter wavelengths between 2500 km and 1000 km these values are systematically higher by 30 40 than those we derived in a previous study using crustal ages of poorer quality in view of these new results we cannot exclude that part of the signal at the 2750 km wavelength is of convective origin unlike the conclusions of the previous study on the other hand at shorter wavelengths the observed admittance can still be interpreted in terms of crustal thickening and sediment loading

global relationship between oceanic geoid and topography in order to compare model predictions of upper mantle convection with surface observations we have computed global residual depth and geoid anomalies on a 5 5 grid over all oceans after removal of lithospheric cooling effects and long wavelength geoid components 4000 km related to lower mantle sources we have derived the transfer function admittance of geoid over topography as a function of wavelength in the range 1000 4000 km the observed admittance is positive at all and presents a maximum of 2 5 3 5 m km at 2750 km comparing this result with the theoretical admittance computed for the lithospheric cooling plate model we ascribe most of the admittance peak at 2750 km to errors in the depth age and geoid age correction this suggests that a standard age correction applied to all seafloor is not valid at shorter wavelengths the admittance remains roughly constant on the order of 1 5 m km and can be explained in terms of sediment loading and crustal thickening effects comparing spatially the residual geoid and depth anomaly maps we note a positive correlation over a few areas coinciding with hot spot swells volcanic plateaus or seafloor deeps the geoid versus depth ratio amounts then to 6 8 m km in agreement with the values predicted above upwellings and downwellings by models of constant viscosity convection however the global admittance analysis leads to much lower values at all wavelengths suggesting that these areas are too limited in number and in extent to produce any significant signal

evidence for small scale mantle convection from seasat altimeter data evidence for the early development of convective instability in the thermal boundary layer associated with cooling plates has been found from gravity anomalies and residual sea surface heights derived from seasat altimeter data subtle lineated patterns trending in the direction of plate motion in the hot spot reference frame are observed over the younger portions of the fast moving pacific and indo australian plates in particular for the east central pacific ocean the seasat derived data sets reveal lineations with 1 wavelengths in the range 150 500 km perhaps increasing with plate age and 2 peak to trough amplitudes of 5 20 mgal for gravity anomalies the lineated pattern over the pacific plate which first becomes discernable over seafloor 5 to 10 m y old west of the east pacific rise is clearly oblique to the trends of the prominent pacific farallon fracture zones onset of convective instability at such early ages can be understood if young oceanic lithosphere is underlain by a layer having a viscosity of about 1018 pa s 1019 p which is about 3 orders of magnitude less than mantle viscosity inferred from postglacial rebound studies recent numerical studies of convection in fluids with a temperature and pressuredependent viscosity support an early onset time for convective instability and low viscosity zones in the upper mantle beneath young lithosphere such low viscosity zones may correspond to similarly located regions of low shear wave velocities resolved through studies of surface waves

subducted slabs and the geoid constraints on mantle rheology and flow geoid anomalies are primarily the result of the density contrasts driving mantle convection and plate motion the total geoid anomaly resulting from a given density contrast in a convecting earth is affected by the mass anomalies associated with the flow induced deformation of the upper surface and internal compositional boundaries as well as by the density contrast itself these boundary deformations and hence the total gravity field depend on the radial distribution of effective viscosity if the internal density contrasts can be estimated as is the case for subducted slabs useful constraints can be placed on the depth and on the variation of viscosity with depth of the convecting system the degree 4 9 components of the observed long wavelength geoid are highly correlated with those predicted by a density model for seismically active subducted slabs the positive sign of the correlation requires that the effective viscosity increases with depth by a factor of 30 or more the amplitude of the correlation cannot be explained by the density contrasts associated with just the seismically active parts of subducted slabs however the amplitude can be explained if the density contrasts associated with subduction extend into the lower mantle or if old lithosphere is piled up at the base of the upper mantle beneath subduction zones to a thickness in excess of 350 km over horizontal distances of thousands of kilometers mantlewide convection in a mantle that has a viscosity increasing with depth provides a simple explanation of the long wavelength geoid anomalies over subduction zones

the effect of a shallow low viscosity zone on the apparent compensation of mid plate swells abstract a simple model for mid plate swells is that of convection in a fluid which has a low viscosity layer lying between a rigid bed and a constant viscosity region finite element calculations have been used to determine the effects of the viscosity contrast the layer thickness and the rayleigh number on the flow and on the perceived compensation mechanism for the resulting topographic swell as the viscosity decreases in the low viscosity zone the effective local rayleigh number for the top boundary layer of the convecting cell increases also because the lower viscosity facilitates greater velocities in the low viscosity zone the low viscosity layer produces proportionally greater horizontal flow near the conducting lid causing the base of the conducting lid to appear like a free boundary the change in the local rayleigh number and in the effective boundary condition both cause the top boundary layer to thin through a green s function analysis we have found that the low viscosity zone damps the response of the surface topography to the temperature anomalies at depth whereas it causes the gravity and geoid response functions to change sign at depth counteracting the positive contributions from the shallower temperature variations by increasing the viscosity contrast the conbined effects of the thinning of the boundary layer and the behaviour of the response functions allow the apparent depth of compensation to become arbitrarily small therefore shallow depths of compensation cannot be used to argue against dynamic support of mid plate swells furthermore we compared the distribution of the effective compensating densities which is used to obtain the geoid to that of pratt compensation which is often used to calculate the depth of compensation from geoid and topography data for mid plate swells for all of our calculations including those with no low viscosity layer the effective gravitational mass distribution is more complex than assumed in simple pratt models so that the pratt models are not an appropriate gauge of the compensation mechanism

a possible dependence of tectonic strength on the age of the crust in asia in asia the intensity and style of active tectonics appears to depend on the age of the last orogenic activity the shields have remained essentially undeformed during the india eurasian collision but paleozoic and mesozoic orogenic belts apparently have been reactivated by this collision with a suggestion of greater reactivation and more diffuse deformation of the younger belts if the greater observed heat flow in regions of more recent orogenic activity reflects at least in part a greater heat flow from the mantle beneath the younger belts then the temperatures in the mantle beneath the younger belts should be higher than beneath older belts and shields because of the strong dependence on temperature of the creep strength of minerals particularly of olivine the crust and mantle beneath the hotter younger belts should be much weaker than those beneath older belts this difference in temperature and consequent difference in strength may be the cause of the greater reactivation of younger belts

on the interaction between small and large scale convection and postglacial rebound flow in a power law mantle abstract some consequences arising from the superposition of flows of two different kinds or scales in a non newtonian mantle are discussed and applied to the cases mantle convection plus postglacial rebound flow as well as small plus large scale mantle convection if the two flow types have similar magnitude the apparent rheology of both flows becomes anisotropic and the apparent viscosity for one flow depends on the geometry of the other if one flow has a magnitude significantly larger than the other the apparent viscosity for the weak flow is linear but develops direction dependent variations about a factorn n being the power exponent of the rheology for the rebound flow lateral variations of the apparent viscosity about at least 3 are predicted and changes in the flow geometry and relaxation time are possible on the other hand rebound flow may weaken the apparent viscosity for convection secondary convection under moving plates may be influenced by the apparent anisotropic rheology other mechanisms leading to viscous anisotropy during shearing may increase this effect a linear stability analysis for the onset of convection with anisotropic linear rheology shows that the critical rayleigh number decreases and the aspect ratio of the movement cells increases for decreasing horizontal shear viscosity normal viscosity held constant applied to the mantle this model weakens the preference of convection rolls along the direction of plate motion under slowly moving plates rolls perpendicular to the plate motion seem to have a slight preference these results could be useful for resolving the question of newtonian versus non newtonian or isotropic versus anisotropic mantle rheology

old continental geotherms constraints on heat production and thickness of continental plates summary absolute and mutual constraints on radioactive heat productivity plate thickness and steady state continental geotherms are demonstrated for a model in which heat productivity comprises a near surface exponentially decreasing component and a component independent of depth for a given surface heat flux there are separate upper limits on each component and a limiting trade off curve between them below these limits there are linear trade offs imposed if either the plate thickness or the temperature at a given depth are known and in principle tighter bounds are imposed on each component preliminary application of the model shows that a kimberlite pyroxene geotherm requires a plate at least 200km thick and that lower plate upper continental mantle heat productivities may be but are not required to be as great as about 0 1 yw m3 which is about ten times the heat productivity of chrondrites the estimation of continental geotherms depends strongly on assumptions about the vertical distribution of radioactive heat sources in the continental plates and on whether or not a steady state is assumed to have been achieved the thickness of the plate is also directly involved since the base of the plate can be defined as the depth at which a characteristic temperature is reached it is the purpose of this paper to demonstrate using a simple but plausible model the relationships between temperature heat production and plate thickness including some absolute limits on heat production the relationships can be used to evaluate the implications of various independent estimates of these quantities and some examples are discussed here an obvious limit on heat production is that in the steady state no more heat can be generated in the plate than emerges at the surface a constraint with less obvious implications is that the geotherm must reach the mantle temperature at a reasonable depth these constraints will be demonstrated here using a simple model of heat source distribution which is nevertheless plausible enough to give quantitatively useful results attention will be confined here to steady state models although the possibility of indefinitely continued cooling and thickening of the continental plates has been discussed pollack chapman 1977 a severe problem with this hypothesis is that the associated thermal subsidence should be accompanied by lokm or more of crustal thickening a

the accommodation of arabia eurasia plate convergence in iran continental convergence between arabia and eurasia is taken up by distributed deformation in iran at wavelengths large compared with the thickness of the lithosphere this deformation is best described by a continuous velocity field the only quantitative source of information on the spatial distribution of strain rates within iran is the record of earthquakes we find that we can reproduce the style of deformation observed in the seismicity by simply minimizing the rate of work in a continuous viscous medium that has to accommodate the arabia eurasia plate motion between the defined shapes of iran s rigid borders when in addition we specify central iran azerbaijan and the southern caspian basin to be relatively rigid blocks within the deforming zone then the fit to the style of the observed strain rate distribution is even better we conclude that much of the pattern of deformation in iran is predetermined by the shape of its rigid borders and by the disposition of relatively rigid blocks within it this is likely also to have been a common occurrence in older orogenic belts we confirm earlier suggestions that earthquakes between 1909 and 1992 can account for only a small part 10 20 of the total deformation required by the convergence between the arabia and eurasia plates we then show that the whole plate motion can be accommodated by a velocity field with the same orientations and relative magnitudes of principal strain rates seen in the earthquakes but with larger absolute magnitudes there is therefore no requirement that the large proportion of aseismic deformation in iran is substantially different in style orientation or distribution from that released seismically in the earthquakes

geoid anomalies in a dynamic earth in order to obtain a dynamically consistent relationship between the geoid and the earth s response to internal buoyancy forces we have calculated potential and surface deformation love numbers for internal loading these quantities depend on the depth and harmonic degree of loading they can be integrated as green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts spherically symmetric self gravitating flow models are constructed for a variety of radial newtonian viscosity variations and flow configurations including both whole mantle and layered convection we demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound much less than the time scale for significant change in the convective flow pattern by calculating relaxation times for a series of spherically symmetric viscous earth models for uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads resulting in net negative geoid anomalies for positive density contrasts geoid anomalies from intermediate wavelength density contrasts are amplified by up to an order of magnitude geoid anomalies are primarily the result of density contrasts in the interior of convecting layers density contrasts near layer boundaries are almost completely compensated layered mantle convection results in smaller geoid anomalies than mantle wide flow for a given density contrast viscosity stratification leads to more complicated spectral signatures because of the sensitivity of the dynamic response functions to model parameters forward models for the geoid can be used to combine several sources of geophysical data e g subducted slab locations seismic velocity anomalies surface topography to constrain better the structure and viscosity of the mantle