The gravity field and crustal thickness of Venus

The gravity and topography of Venus obtained from observations of the Magellan mission, as well as the gravity and topography from our numerical mantle convection model, are discussed in this paper. We used the hypothesis that the geoid of degrees 2–40 is produced by sublithospheric mantle density anomalies that are associated with dynamical process within the mantle. We obtained the model dynamical admittance(the geoid topography ratio based on a convection model) by a numerical simulation of the Venusian mantle convection, and used it to correct the dynamical effect in the calculation of crustal thickness. After deducting the dynamical effect, the thickness of the Venusian crust is presented. The results show that the gravity and topography are strongly correlated with the Venusian mantle convection and the Venusian crust has a significant influence on the topography. The Venusian crustal thickness varies from 28 to 70 km. Ishtar Terra, and Ovda Regio and Thetis Regio in western Aphrodite Terra have the highest crustal thickness(larger than 50 km). The high topography of these areas is thought to be supported by crustal compensation and our results are consistent with the hypothesis that these areas are remnants of ancient continents. The crustal thickness in the Beta, Themis, Dione, Eistla, Bell, and Lada regiones is thin and shows less correlation with the topography, especially in the Atla and Imdr regiones in the eastern part of Aphrodite Terra. This is consistent with the hypothesis that these highlands are mainly supported by mantle plumes. Compared with the crustal thickness calculated with the dynamical effect, our results are more consistent with the crust evolution and internal dynamical process of Venus.     

On the effect of a low viscosity asthenosphere on the temporal change of the geoid—A challenge for future gravity missions

New satellite technology to measure changes in the Earth’s gravity field gives new possibilities to detect layers of low viscosity inside the Earth. We used density models for the Earth mantle based on slab history as well as on tomography and fitted the viscosity by comparison of predicted gravity to the new CHAMP gravity model. We first confirm that the fit to the observed geoid is insensitive to the presence of a low viscosity anomaly in the upper mantle as long as the layer is thin ( 200 km) and the viscosity reduction is less than two orders of magnitude. Then we investigated the temporal change in geoid by comparing two stages of slablet sinking based on subduction history or by advection of tomography derived densities and compared the spectra of the geoid change for cases with and without a low viscosity layer, but about equal fit to the observed geoid. The presence of a low viscosity layer causes relaxation at smaller wavelength and thus leads to a spectrum with relatively stronger power in higher modes and a peak around degrees 5 and 6. Comparing the spectra to the expected degree resolution for GRACE data for a 5 years mission duration shows a weak possibility to detect changes in the Earth’s gravity field due to large scale mantle circulation, provided that other causes of geoid changes can be taken into account with sufficient accuracy. A discrimination between the two viscosity cases, however, demands a new generation of gravity field observing satellites.     

Geoid and topography of Venus in various thermal convection models

Important though indirect information about the internal structure of Venus is provided by its topography and geoid. In the last decades this information has been used to constrain the Venus mantle viscosity structure and its dynamic regime. Recently, the geodynamic inversion of the Venus?? geoid and topography resulted in a group of best fitting viscosity profiles. We use these viscosity models here as an input to our mantle convection code. We carry out simulations of the Venus?? mantle evolution in a 3D spherical shell with depth dependent viscosity and check whether the character of the dynamic topography and the geoid represented by their power spectra fits the observed quantities. We compare the results with several other models obtained for different viscosity stratifications (constant, constant with highly viscous lithosphere, linear increase of viscosity). Further, we estimate the effect of other factors such as internal heating and varying Rayleigh number. We use a 2D spherical axisymmetric convection code to study the effect of lateral viscosity variations. In these 2D models we monitor the topography and the geoid developing above the axisymmetric plume and compare them with the observed elevations of Venus?? geoid and topography in several Regia. Though none of the models fits observed data perfectly, we can generally conclude, that the best fit between the observed and predicted quantities is reached for viscosity profiles with 200 km thick lithosphere followed by a gradual increase of viscosity with depth and with the upper mantle viscosity of 2 × 10 ²¹ Pa s. For all viscosity profiles the predicted geoid and topography spectra match the observed ones only up to the degree 40, thus indicating other than dynamic origin of these quantities for higher degrees.     

基于地形精化的金星重力场模型VGM2013

高精度金星重力场的获取,是金星探测的重要内容.本文利用最新的金星地形和重力模型,通过高通滤波后的残差地形（RTM）并在考虑均衡改正的情况下改进了重力的短波成分,最终提出了一个新的金星重力模型VGM2013,该模型赤道分辨率达10 km量级,大大高于现有的金星重力场模型,最终结果是金星表面重力加速度和重力扰动.研究中同时发现金星在Airy-Heiskanen均衡模型下的全球最优补偿深度为30 km,金星地壳的密度可能小于当前认为的2700~2900 kg·m^-3.VGM2013模型的结果可为将来的金星探测器定轨和着陆导航提供参考,作为重力计算的先验模型.但由于该模型没有包含短波重力观测信息,不建议直接用于更小尺度的地质和地球物理解释.     

The geoid in southeastern Brazil and adjacent regions: new constraints on density distribution and thermal state of the lithosphere

Least-squares collocation technique was used to process regional gravity data of the SE South American lithospheric plate in order to map intermediate (10–2000 km) wavelength geoid anomalies. The area between 35–10° S and 60–25° W includes the Paraná CFB Province, the Southern São Francisco Craton and its marginal fold/thrust belts, the Brazilian continental margin and oceanic basins. The main features in the geoid anomaly map are: (a) Paraná CFB Province is characterized by a 1000 km long and 500 km wide, NE-trending, 9 m-amplitude negative anomaly which correlates with the distribution of sediments and basalts within the Paraná basin. (b) A circular (600–800 km in diameter) positive, 8 m-amplitude geoid anomaly is located in the southern S. Francisco craton and extends into the northeastern border of the Paraná CFB Province. This anomaly partially correlates with Alto Paranaíba Igneous Province (APIP), where alkalic volcanism and tholeiitic dikes of ages younger than 80 Ma are found and where a low-velocity zone in the mantle has been mapped using seismic tomography. This positive geoid anomaly extends towards the continental margin at latitude 21° S and joins a linear sequence of short wavelength positive geoid anomalies associated with Vitoria–Trindade seamounts. (c) A NE-trending, 1000 km long and 800 km wide, 4 m-amplitude, positive geoid anomaly, which is located along the southeastern coast of Brazil, from latitude 24 to 35° S. The northern part of this anomaly correlates with the Ponta Grossa Arch and Florianopolis dyke swarm provinces. The age of this intrusive volcanism is 130–120 Ma. (d) A circular positive anomaly with 9 m of amplitude, located over the Rio Grande and Uruguay shields and offshore Pelotas basin. Few alkaline intrusives with ages between 65 and 80 Ma are found in the region and apatite fission track ages in basement rocks indicates cooling at around 30 Ma. A semi-quantitative analysis of the observed geoid anomalies using isostatic considerations suggests that the mechanism which generated Paraná CFB Province did not change, in a significant manner, the lithospheric thermal structure, since the same geoid pattern observed within this province continues northward over the Neoproterozoic fold/thrust belts systems separating the São Francisco and Amazon cratons. Therefore, this observation favours Anderson’s idea of rapid basaltic outpouring through a pull-apart mechanism along a major suture zone. A thermal component may still be present in the Southern São Francisco Craton and in the Rio Grande Shield and contiguous continental margins, sites of Tertiary thermal and magmatic reactivations.     

The effect of a shallow low viscosity zone on the apparent compensation of mid-plate swells

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.     

Plume-induced geoid anomalies from 2D axi-symmetric temperature- and pressure-dependent mantle convection models

A collection of numerical simulations of 2D axi-symmetric thermal convection is presented here. The aim is to investigate the shape of geoid anomalies and dynamic topography above a plume. The simulation is based on the Boussinesq approximation and infinite Prandtl number and is carried out in the spherical shell with strongly temperature- and depth-dependent Arrhenius-type viscosity. According to the Arrhenius law, plume models with purely depth-dependent rheology are unphysical and should be taken with care. The strongly coupled temperature- and depth-dependent viscosity enables us to better understand the plume's behavior inside the Earth.The topography and geoid anomalies produced from plumes are sensitive to rheology of the mantle and rheology of the plume; both have effects on shape and amplitude of the geoid anomalies. We determined different categories of the geoid which are related to various rheology. Depth-dependent viscosity models show a geoid with a negative sign above the plume, and temperature-dependent viscosity models depict a bell-shaped geoid. We identified different behaviors in the combined model with temperature- and pressure-dependent viscosity.     

Constraints on the dynamics of mantle plumes from uplift of the Hawaiian Islands

The ∼0.2 mm/yr uplift of Hawaiian islands Lanai and Molokai and Hawaiian swell topography pose important constraints on the structure and dynamics of mantle plumes. We have formulated 3-D models of mantle convection to investigate the effects of plume-plate interactions on surface vertical motions and swell topography. In our models, the controlling parameters are plume radius, excess plume temperature, and upper mantle viscosity. We have found that swell height and swell width constraints limit the radius of the Hawaiian plume to be smaller than 70 km. The additional constraint from the uplift at Lanai requires excess plume temperature to be greater than 400 K. If excess plume temperature is 400 K, models with plume radius between 50 and 70 km and upper mantle viscosity between 10²⁰ and 3×10²⁰ Pa s satisfy all the constraints. Our results indicate that mantle plume in the upper mantle may be significantly hotter than previously suggested. This has important implications for mantle convection and mantle melting. In addition to constraining plume dynamics, our models also provide a mechanism to produce the observed uplift at Lanai and Molokai that has never been satisfactorily explained before.     

地幔对流的数值模拟及其与表面观测的关系

本文从基本的热对流方程出发,并结合地幔对流特点,特别考虑到自重及非线性影响,探讨地幔对流及其与表面观测的关系,发展了相应的数值方法.结果表明,计算得到的长波大地水准面、地表地形、板块速度场水平散度与观测值符合程度较好.上、下地幔的非绝热温度异常与由地震层析得到的地震波速异常显示一定的相关性.地幔内部的流动呈现复杂形态,反映了高瑞利数对流的特征.     

The existence of a thin low-viscosity layer beneath the lithosphere

The horizontal temperature gradient at the base of the lithosphere at an oceanic fracture zone, where plate of different ages is juxtaposed, is expected to drive a local circulation, the characteristics of which can be constrained by the amplitude, wavelength and age-dependence of the geoid. Two-dimensional numerical models of convection in a fluid layer overlain by a solid conducting lid have been used to generate theoretical geoid profiles at right angles to the fracture zone. Only a thin, low-viscosity layer provides a reasonable fit to the data. The best model so far obtained has a fluid layer 150 km thick with viscosity 1.5 × 10¹⁹ Pa s under a 75 km lid. Such a layer, which is incapable of transmitting strong horizontal shear stresses, could provide the decoupling mechanism between plate and deep mantle flow required to balance the forces on the plates.     

Geoid anomalies over Gorringe Ridge,North Atlantic Ocean

Gorringe Ridge is a strong uplifted block of oceanic crust and upper mantle lying at the eastern end of the Azores-Gibraltar plate boundary. The geoid over this structure derived from Seasat altimeter data exhibits a 9-m height anomaly with a north-south lateral extension smaller than 200 km. An attempt is made to interpret this geoid together with the gravity anomalies and with the seismicity, which has been compiled as a function of depth.It is first shown that the flexure of the oceanic lithosphere due to the ridge loading does not provide a good fit of the geoid anomalies and probably should be discarded, as it assumes a continuous unfractured elastic plate.Models involving local heterogeneities are then tested. The comparison of the observed geoid anomalies with the anomalies due to the uncompensated relief indicates that the topographic high has no shallow compensation.Uncompensated models, previously proposed to explain the gravity anomalies, are tested using the geoid. One model (Purdy and Bonnin, in Bonnin [11]), which involves an uplift of upper mantle material at depth, generates too strong geoid anomalies and must be discarded. Another model, which represents a nascent subduction zone (Le Pichon et al. [25]), fits both the gravity and geoid anomalies, but leads to difficulties in explaining the deep seismicity north of Gorringe Ridge.A model in isostatic equilibrium is also able to fit both gravity and geoid anomalies. This model involves a deep root of density 3.0 g cm^?3, as has been previously proposed for many oceanic ridges and plateaus. This model is compatible with the deep seismicity, but the origin of this low-density material at great depth is up to now an unresolved question.More likely, dynamical models taking into account the forces induced by the convection related to the slow plate convergence in this area will have to be considered.     

Geoid anomalies over two South Atlantic fracture zones

Seasat altimetry profiles across the Falkland-Agulhas fracture zone (FZ) and the Ascension FZ in the South Atlantic were examined for evidence of step-like geoid offsets predicted from thermal modeling of the lithosphere. The geoid profiles exhibit much short-wavelength power and the step-like offsets are often small, making reliable estimation of the heights of the observed geoid offsets difficult. The offsets were estimated by the least-squares fitting of quadratic curves incorporating a step function to the altimetry profiles. A preferred offset value was determined for each profile by taking the average of step heights computed with various distances around the fracture zone excluded from the fit. The age of the crust surrounding the fracture zones, necessary for computing a theoretical geoid offset, was determined from surface ship magnetic anomaly data and from existing ocean floor age maps.Observed variations in geoid step height with age of the lithosphere are not consistent with those predicted from standard thermal plate models. For ages less than 30 Ma, the step offsets across both fracture zones decrease in a manner appropriate for an unusually thin plate with a thickness of 50–75 km. At greater ages, the offsets show complex behavior that may be due to bathymetric features adjacent to the fracture zones. Similar geoid patterns on opposite branches of the Falkland-Agulhas FZ are indicative of processes that act symmetrically on both sides of the Mid-Atlantic Ridge. This behavior of the geoid is consistent both with small-scale convection occurring beneath the lithosphere and with bathymetric features originally produced along the ridge crest and now located symmetrically on opposite sides of the ridge. The west flank of the Ascension FZ displays a regrowth in step height at about 40 Ma consistent with small-scale convection and in agreement with other studies of Pacific and South Atlantic fracture zones.     

罗斯海海域大地水准面异常的成因研究

本文利用数值法求解瞬时地幔对流问题以模拟大地水准面异常.利用两个较新的S波速度异常层析模型SEMUCB_WM1和TX2019slab,将其转换为密度异常作为控制方程的浮力驱动项;采取的黏度结构模型中,上下地幔的黏度比为1∶50.为了研究地幔不同结构对罗斯海海域大地水准面异常的影响,分别提取上、下地幔的密度异常正/负值,作为对流控制方程的输入项,计算相应的模拟大地水准面异常.将模拟大地水准面异常与观测值进行对比,发现罗斯海海域的大地水准面异常主要来自下地幔及上地幔的负密度(波速)异常,下地幔正密度异常对该区域大地水准面负异常也有一定的贡献.本文认为,地幔密度负异常在罗斯海海域大地水准面异常的形成中占据主导作用,地幔对流的动力学效应对该区域大地水准面异常的形成影响较弱.     

Time-dependent density anomalies in a stratified,viscoelastic mantle: Implications for the geoid,Earth's rotation and sea-level fluctuations

The effects on the = 2 geoid component and Earth's rotation due to internal mass anomalies are analyzed for a stratified viscoelastic mantle described by a Maxwell rheology. Our approach is appropriate for a simplified modeling of subduction. Sea-level fluctuations induced by long-term rotational instabilities are also considered. The displacement of the Earth's axis of rotation, called true polar wander (TPW) and the induced eustatic sea-level fluctuations, are extremely sensitive to viscosity and density stratification at the 670 km seismic discontinuity. Phase-change models for the transition zone generally allow for huge amount of TPW, except for large viscosity increases; the dominant contribution in Liouville equations comes from a secular term that reflects the viscous behaviour of the mantle. In chemically stratified models, TPW is drastically reduced due to dynamic compensation of the mass anomalies at the upper-lower mantle interface. When the source is embedded in the upper mantle close to the chemical density jump, transient rotational modes are the leading terms in the linear Liouville equations. Long-term rotation instabilities are valuable contributors to the third order cycles in the eustatic sea-level curves. Rates of sea-level fluctuations of the order of 0.05–0.1 mm/yr are induced by displacements of the Earth's axis of rotation compatible with paleomagnetic data.     

Contributions of terrestrial and GRACE data to the study of the secular geoid changes in North America

This paper tests and discusses different statistical methods for modelling secular rates of change of the geoid in North America. In particular, we use the method of principal component/empirical orthogonal functions (PC/EOF) analysis to model the geoid rates from Gravity Recovery and Climate Experiment (GRACE) satellite data. As demonstrated, the PC/EOF analysis is useful for studying the contributions from different signals (mainly residual hydrology signals and leakage effects) to the GRACE-derived geoid rates. The PC/EOF analysis leads to smaller geoid rates compared to the conventional least-squares fitting of a trend and annual and semi-annual cycles to the time series of the spherical harmonic coefficients. This is because we filter out particular spatiotemporal modes of the regional geoid changes.We apply the method of least-squares collocation with parameters to combine terrestrial data (GPS vertical velocities from the Canadian Base Network and terrestrial gravity rates from the Canadian Gravity Standardization Net) with the GRACE-derived vertical motion to obtain again the geoid rates. The combined model has a peak geoid rate of 1.4 mm/year in the southeastern area of Hudson Bay contrary to the GRACE-derived geoid rates that show a large peak of 1.6–1.7 mm/year west of Hudson Bay. We demonstrate that the terrestrial data, which have a longer time span than the GRACE data, are important for constraining the GRACE-derived secular signal in the areas that are well sampled by the data.     

Geophysical evidence on the structure of the Taupo Volcanic Zone and its hydrothermal circulation

The Taupo Volcanic Zone (TVZ) of New Zealand is characterised by extensive volcanism and by high rates of magma production. Associated with this volcanism are numerous high-temperature (> 250 °C) geothermal systems through which the natural heat output of 4200 ± 500 MW is channelled. Outside the geothermal fields the heat flow is negligible. The average heat flux from the central 6000 km² of the TVZ, which contains most of the geothermal fields, is 700 mW/m³. This heat flux appears to be more concentrated along the eastern margin of the TVZ.Schlumberger resistivity measurements (AB/2 of 500 m and 1000 m) have identified 17 distinct geothermal fields with natural heat outputs greater than 20 MW. An additional six, low-heat-output geothermal fields also occur, and may represent formerly more active systems now in decline. Two extinct fields have also been identified. The average spacing between fields is 10–15 km. The distribution of geothermal fields does not appear to be directly associated with individual volcanic features except for the geothermal system that occurs within Lake Taupo and which occupies the vent of the 1800 yr.B.P. Taupo eruption. The positions of the geothermal fields do not appear to have varied for at least the last 200,000 years. These data are consistent with a model of large-scale convection occurring throughout the TVZ, in which the geothermal fields represent the upper portion of the rising, high-temperature, convective plumes. The majority of the recharge to the convection system is provided by the downward movement of cold meteoric water between the fields which suppresses the heat flow in these regions.Gravity measurements indicate that to a depth of about 2.5 km the upper layers of the TVZ consist of low-density pyroclastic infill. A seismic refraction interface with velocity change from 3.2 km/s to 5.5 km/s occurs at a similar depth. The cross-sectional area of the convection plumes (identified electrically) appears to increase at depths of 1–2 km, consistent with a decrease in permeability at the depth at which the velocity and density increase.The seismicity is dominated by swarm activity which accounts for about half of all earthquakes and is highly variable in both space and time. The small number of seismic events (and swarms) that have well determined depths show a cut off of seismicity at depths of 7–9 km. The depth of the transition from brittle to ductile behaviour of the rocks is identified with the transition from a regime where heat is transported by (hydrothermal) convection and pore pressures are near-hydrostatic to a regime where heat transport is dominantly conductive and pore pressures are lithostatic. Within the convective region, temperatures are moderated by the circulation of water so that the depth of the transition from convective to conductive heat transfer can be linked to the bottom of the seismogenic zone. Rocks must become ductile within about 1 km of the bottom of the overlying convective zone.Seismic refraction studies suggest that the crust beneath the TVZ is highly thinned with a seismic velocity of about 7.5 km/ s, typical of the upper mantle, occurring at depth of 15 km. Seismological studies indicate the upper mantle is highly attenuating beneath the TVZ. Conductive heat transfer between the bottom of the convective system, at about 8 km, and the base of the material with crustal velocities, at 15 km, is not able to provide all the heat that is discharged at the surface. Repeated intrusion from the mantle may provide the additional heat transport required.     

New Perspectives on Mantle Dynamics from High-resolution Seismic Tomographic Model P1200

—Recently a high-resolution tomographic model, the P1200, based on P-wave travel times was developed, which allowed for detailed imaging of the top 1200 km of the mantle. This model was used in diverse ways to study mantle viscosity structure and geodynamical processes. In the spatial domain there are lateral variations in the transition zone, suggesting interaction between the lower-mantle plumes and the region from 600 km to 1000 km. Some examples shown here include the continental region underneath Manchuria, Ukraine and South Africa, where horizontal structures lie above or below the 660 km discontinuity. The blockage of upwelling is observed under central Africa and the interaction between the upwelling and the transition zone under the slow Icelandic region appears to be complex. An expansion of the aspherical seismic velocities has been taken out to spherical harmonics of degree 60. For degrees exceeding around 10, the spectra at various depths decay with a power-law like dependence on the degree, with the logarithmic slopes in the asymptotic portion of the spectra containing values between 2 and 2.6. These spectral results may suggest the time-dependent nature of mantle convection. Details of the viscosity structure in the top 1200 km of the mantle have been inferred both from global and regional geoid data and from the high-resolution tomographic model. We have considered only the intermediate degrees (l = 12–25) in the nonlinear inversion with a genetic algorithm approach. Several families of acceptable viscosity profiles are found for both oceanic and global data. The families of solutions for the two data sets have different characteristics. Most of the solutions asociated with the global geoid data show the presence of asthenosphere below the lithosphere. In other families a low viscosity zone between 400 and 600 km depth is found to lie atop a viscosity jump. Other families evidence a viscosity decrease across the 660 km discontinuity. Solutions from oceanic geoid show basically two low viscosity zones one lying right below the lithosphere; the other right under 660-km depth. All of these results bespeak clearly the plausible existence of strong vertical viscosity stratification in the top 1000 km of the mantle. The presence of the second asthenosphere may have important dynamical ramifications on issues pertaining to layered mantle convection. Numerical modelling of mantle convection with two phase transitions and a realistic temperature- and pressure-dependent viscosity demonstrates that a low viscosity region under the endothermic phase transition can indeed be generated self-consistently in time-dependent situations involving a partially layered configuration in an axisymmetric spherical-shell model.     

Pacific Plate motion and undulations in geoid and bathymetry

Previous studies have shown that the Pacific geoid and gravity fields exhibit lineated anomalies, trending approximately in the direction of absolute plate motion over the underlying mantle. Because the undulations obliquely cross fracture zones they have often been attributed a convective origin. Recently, lithospheric boudinage caused by diffuse extension has been proposed as a possible mechanism. We have examined the undulations in the free-air anomalies, geoid and bathymetry over a portion of the Pacific Plate to determine quantitatively how the undulations are related to plate motion. We compare the observed data to an axisymmetric, sinusoidal undulation defined in an arbitrary frame of reference; in particular, we seek the north pole of this reference frame that maximizes the correlation between data and model. Poles that are close to the Pacific hotspot pole represent copolar undulations possibly related to plate motion. The distance between the best-fitting poles and the hotspot pole is determined as a function of undulation wavelength and reveals several minima (with distance < 10°) for discrete geoid wavebands centered on wavelengths of 160 km, 225 km, 287 km, 400 km, 660 km, 850 km, 1000 km and 1400 km. Bathymetry data have copolar bathymetric expressions as well, giving an implied admittance of 2–3 m/km. The most co-polar geoid/bathymetry undulations (with poles within 2–3° of the average Pacific Euler pole) have wavelengths of 280 km and 1050 km, respectively. The latter could have a convective origin or be related to the spacing of hotspot swells. The former may reflect lithospheric boudinage formed in response to diffuse extension, but could also have a dynamic origin since flexural dampening may only have attenuated the bathymetric amplitude by 50% or less. Radiometric dating of volcanic ridges found in the troughs of prominent gravity lineations gives ages that correlate well with documented changes in Pacific and Indo/Australian Plate motion, suggesting the ridges formed in response to intermittent plate boundary stresses and not as a direct consequence of small-scale convection or diffuse extension.     

The mechanical state of the lithosphere in the Altiplano-Puna segment of the Andes

Information about topography, the shape of the geoid, seismicity, Neogene deformation and volcanism in the region of Altiplano-Puna of western South America is used to analyse the state of stress across the convergent plate margin in terms of the effects of topography and simple models of its compensation. An average elevation near 4 km is consistent with compensation by a yet unresolved combination of crustal root and hot uppermost mantle producing a geoid high of 22–27 meters, average horizontal compressive stress (in excess of a reference sea level lithostatic value) of 390 bars in a 150 km thick lithosphere, and an average shear stress of 170 bars along a 30° dipping interplate boundary. The basis for these estimates is evidence for a neutral to extensional stress regime within the high plateau contrasted with a compressional regime on the eastern slopes and along the interplate boundary itself. Comparison with other plateaus in a convergent plate tectonic setting suggests an evolutionary sequence from compressional to extensional tectonics as elevation of the plateau increases.     

Geoid anomalies across fracture zones and the thickness of the lithosphere

Recent advances in the measurement and interpretation of geoid height anomalies provide a new way to estimate the thickness of the oceanic lithosphere as a function of crustal age. GEOS-III satellite altimetry measurements show abrupt changes in sea level across fracture zones which separate areas of lithosphere with different ages. These changes have the correct location, amplitude, and wavelength to be caused by the combined gravitational attraction of the relief across the fracture zone and the isostatic support of this relief. Eight profiles of geoid height and bathymetry across the Mendocino fracture zone are inverted to determine the depth of the isostatic compensation, assuming that the compensation occurs in a single layer. These depths are then interpreted with a thermal boundary layer model of lithospheric growth. To explain satisfactorily the geoid measurements, the thermal diffusivity of the upper mantle must be 3.3 × 10^?3 cm² s^?1 and the thickness of the lithosphere, defined as the depth at which the geotherm reaches 95% of its maximum value, must be9.1km m.y.^?1/2 × t^1/2, where t is lithospheric age.