Effects of plate and slab viscosities on the geoid

The effects of plate rheology (strong plate interiors and weak plate margins) and stiff subducted lithosphere (slabs) on the geoid and plate motions, considered jointly, are examined with three-dimensional spherical models of mantle flow. Buoyancy forces are based on the internal distribution of subducted lithosphere estimated from the last 160 Ma of subduction history. While the ratio of the lower mantle/upper mantle viscosity has a strong effect on the long-wavelength geoid, as has been shown before, we find that plate rheology is also significant and that its inclusion yields a better geoid model while simultaneously reproducing basic features of observed plate motion. Slab viscosity can strongly affect the geoid, depending on whether a slab is coupled to the surface. In particular, deep, high-viscosity slabs beneath the northern Pacific that are disconnected from the surface as a result of subduction history produce significant long-wavelength geoid highs that differ from the observation. This suggests that slabs in the lower mantle may be not as stiff as predicted from a simple thermally activated rheology, if the slab model is accurate.     

Numerical simulations of mantle flow around slab edges

A simple kinematic-dynamic model of mantle flow around the slab-edge is constructed in order to understand the flow complexity there. The flow velocity on the top and the small boundary region around the shallow plate boundary is kinematically imposed in order to achieve a subduction-like feature and the flow in other part is dynamically calculated. The geometry of the plate mimics the region around the junction of Aleutian Islands and Kamchatka, that are examples of the convergent-transform fault plate boundaries. In a simple model in which the overlying plate is almost stationary, the lateral flow from the mantle under the subducting slab to the mantle under the neighboring plate is of minor importance, once the slab penetrates into the high viscosity layer where the downward flow encounters the resistance. Similar situation was found when the trench is advancing, that is, the trench moves toward the overlying plate. For the case with retreating trench, that is, the trench moves toward the subducting plate, a lateral flow exists even after the slab penetrates into the high viscosity layer, although its magnitude is significantly smaller than that of the plate velocity. The presence of a low viscosity layer just beneath the subducting plate may promote the emergence of lateral flow. A significant lateral flow is observed when the high temperature anomaly, that is, buoyant and low viscosity block carried by the movement of subducting plate, approaches the slab. These results may have important implications for the possible existence of trench parallel flow in the sub-slab mantle.     

SEASAT geoid anomalies and the Macquarie Ridge complex

The seismically active Macquarie Ridge complex forms the Pacific-India plate boundary between New Zealand and the Pacific-Antarctic spreading center. The Late Cenozoic deformation of New Zealand and focal mechanisms of recent large earthquakes in the Macquarie Ridge complex appear consistent with the current plate tectonic models. These models predict a combination of strike-slip and convergent motion in the northern Macquarie Ridge, and strike-slip motion in the southern part. The Hjort trench is the southernmost expression of the Macquarie Ridge complex. Regional considerations of the magnetic lineations imply that some oceanic crust may have been consumed at the Hjort trench. Although this arcuate trench seems inconsistent with the predicted strike-slip setting, a deep trough also occurs in the Romanche fracture zone.Geoid anomalies observed over spreading ridges, subduction zones, and fracture zones are different. Therefore, geoid anomalies may be diagnostic of plate boundary type. We use SEASAT data to examine the Macquarie Ridge complex and find that the geoid anomalies for the northern Hjort trench region are different from the geoid anomalies for the Romanche trough. The Hjort trench region is characterized by an oblique subduction zone geoid anomaly, e.g., the Aleutian-Komandorski region. Also, limited first-motion data for the large 1924 earthquake that occurred in the northern Hjort trench suggest a thrust focal mechanism. We conclude that subduction is occurring at the Hjort trench. The existence of active subduction in this area implies that young oceanic lithosphere can subduct beneath older oceanic lithosphere.     

Landward flow in the upper mantle: effects of the heat sink and viscous coupling of the sinking slab

Regional studies landward of the trench show that gravity anomalies are low compared with those expected from the cold sinking slab and that residual depth anomalies are strongly negative at distances up to 1200 km from the trench. It is shown that flow models taking simultaneously account of the viscous coupling and of the cooling effect of the sinking slab are able to explain these facts: the viscous coupling being related only to observed data down to 400 km from the trench, while the cooling effect mainly explains data at larger distances from the subduction zone.     

The influence of trench migration on slab penetration into the lower mantle

A two-dimensional numerical convection model in cartesian geometry is used to study the influence of trench migration on the ability of subducted slabs to penetrate an endothermic phase boundary at 660 km depth. The transient subduction history of an oceanic plate is modelled by imposing plate and trench motion at the surface. The viscosity depends on temperature and depth. A variety of styles of slab behaviour is found, depending predominantly on the trench velocity. When trench retreat is faster than 2–4 cm/a, the descending slab flattens above the phase boundary. At slower rates it penetrates straight into the lower mantle, although flattening in the transition zone may occur later, leading to a complex slab morphology. The slab can buckle, independent of whether it penetrates or not, especially when there is a localised increase in viscosity at the phase boundary. Flattened slabs are only temporarily arrested in the transition zone and sink ultimately into the lower mantle. The results offer a framework for understanding the variety in slab geometry revealed by seismic tomography.     

西北太平洋俯冲带大地幔楔及地幔过渡带各向异性证据和特征

地震层析成像研究清晰给出了地球深部俯冲板片的大尺度形态,但与俯冲过程相关的地幔流动特征仍不明确.在俯冲地幔楔系统中,前人观测到了与海沟平行和垂直的快波偏振方向.本文研究了西北太平洋俯冲板片在地幔过渡带中停滞形成的"大地幔楔"中的各向异性特征.对具有长期稳定观测数据的MDJ台站SKS震相和区域深源地震的直达S波震相进行了...     

Effect of lateral viscosity variations in the core-mantle boundary region on predictions of the long-wavelength geoid

Seismic studies of the lowermost mantle suggest that the core-mantle boundary (CMB) region is strongly laterally heterogeneous over both local and global scales. These heterogeneities are likely to be associated with significant lateral viscosity variations that may influence the shape of the long-wavelength non-hydrostatic geoid. In the present paper we investigate the effect of these lateral viscosity variations on the solution of the inverse problem known as the inferences of viscosity from the geoid. We find that the presence of lateral viscosity variations in the CMB region can significantly improve the percentage fit of the predicted data with observations (from 42 to 70% in case of free-air gravity) while the basic characterisics of the mantle viscosity model, namely the viscosity increase with depth and the rate of layering, remain more or less the same as in the case of the best-fitting radially symmetric viscosity models. Assuming that viscosity is laterally dependent in the CMB region, and radially dependent elsewhere, we determine the largescale features of the viscosity structure in the lowermost mantle. The viscosity pattern found for the CMB region shows a high density of hotspots above the regions of higher-than-average viscosity. This result suggests an important role for petrological heterogeneities in the lowermost mantle, potentially associated with a post-perovskite phase transition. Another potential interpretation is that the lateral viscosity variations derived for the CMB region correspond in reality to lateral variations in the mechanical conditions at the CMB boundary or to large-scale undulations of a chemically distinct layer at the lowermost mantle.     

大地水准面高对InSAR大范围地壳形变监测的影响分析

由于InSAR数据处理所用的WGS84参考椭球系统与通用的DEM高程系统(EGM96大地水准参考面)不一致,在InSAR形变监测分析中会引入大地水准面高导致的误差.本文利用覆盖青藏高原北部阿尔金断裂带西段的27景Envisat ASAR宽幅模式数据和44景条带模式数据,研究了大地水准面高与InSAR大范围形变测量不确定性的关系:(1)模拟分析表明对于100 m的垂直基线,8.8 m的DEM测量误差,若研究区域存在20 m的大地水准面高的变化,对宽幅或条带模式InSAR形变测量造成的影响将由3 mm增至10 mm左右;(2)实例验证表明对于不同的研究区域,大地水准面高与该地区地形变化存在较大相关性,对于同一研究区域,垂直基线的大小决定了大地水准面高对InSAR不确定性的影响程度;(3)对于大地水准面高有较大梯度变化的研究区域,组合短基线方法与去除轨道平面的方法难以消除大地水准面高的影响.使用基于WGS84高程系统的DEM,可以为InSAR形变测量分析提供统一的高程基准,有效避免大地水准面高误差的影响.     

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.     

Transformation between gravimetric and GPS/levelling-derived geoids using additional gravity information

The transformation from the gravimetric to the GPS/levelling-derived geoid using additional gravity information for the covariance function of geoid height differences has been investigated in a test area in south-western Canada. A “corrector surface” model, which accounts for datum inconsistencies, long-wavelength geoid errors, vertical network distortions and GPS errors, has been constructed using least-squares collocation. The local covariance function of geoid height differences is usually obtained from residual values between the GPS/levelling and gravimetric geoid heights after the elimination of all known systematic distortions. If additional gravity data (in the form of gravity anomalies) are available, the covariance function of geoid height differences can be determined by the following steps: (1) transforming the GPS/levelling-derived geoid heights into gravity anomalies; (2) forming differences between the computed in step 1 and given gravity anomalies; (3) determining the parameters of the local covariance function of the gravity anomaly differences; (4) constructing an analytical covariance model for the geoid height differences from the covariance function of the gravity anomaly differences using the parameters derived in step 3. The advantage of the proposed method stems from the great number of gravity data used to derive the empirical covariance function. A comparison with the least-squares adjustment shows that the standard deviation of the residuals of the predicted geoid height differences with respect to the control point values decreases by 2.4 cm.     

Influence of variable uncertainties in seismic tomography models on constraining mantle viscosity from geoid observations

The radial viscosity structure of the Earth is explored on the basis of the geoid observations. The variations of uncertainty in seismic tomography models are accounted for when finding the radial viscosity structure. The new methodology we propose attempts to fit more closely those features of the geoid that are better constrained by tomography models and avoids to fit those features that are poorly constrained. This approach is particularly important because the error of geoid predictions caused by uncertainties in seismic tomography models is overwhelmingly larger than the noise in the geoid measurements. The synthetic tests indicate that the viscosity structures obtained by disregarding the uncertainty variations in seismic tomography models can be biased depending on the geoid spectral band and on the ‘input’ seismic tomography model. When the uncertainty variations in seismic models are considered in the inversion process, results do not indicate a viscosity in the transition zone lower than in the upper mantle. A robust feature found with the new method is a viscosity in the upper mantle two orders of magnitude smaller than in the lower mantle. The error covariance of seismic tomography models is critical for the method we suggest. A covariance matrix rigorously derived by seismologists should help to even more reliably infer the viscosity structure and relation between anomalies in density and seismic velocities from surface observations such as the geoid, and thus lead to a better knowledge of the Earth interior.     

Assessing “Urban Karst” Effects from Groundwater–Storm Sewer System Interaction in a Till Aquitard

Storm sewer systems and their associated utility trenches may strongly influence the effects of urbanization on a groundwater system. This study was undertaken to identify the causes of district-wide basement infiltration in an aquitard system. It comprised widespread continuous monitoring of utility trench wells and dye tracing from storm sewer system exfiltration tests. The results indicate that a major effect of urbanization on shallow groundwater is related to storm sewer system exfiltration, which is marked by a characteristic pattern of head variations in the aquitard unrelated to distributed surface infiltration. The aquitard constrains flow from storm sewer system exfiltration to the utility trench, creating an urban flow path for groundwater discharge. Temporary buildup of water levels in the utility trench drives relatively high-velocity flow through the permeable sewer bedding material of the utility trench to a separate foundation drainage collector system, ultimately causing a severe “urban karst” effect that produces system surcharging and widespread basement water infiltration. The main conditions causing the “urban karst” are the large hydraulic conductivity ratio between the utility trench material and the aquitard, and the shallow depth and low gradient of the storm sewer system imposed by a very flat drainage basin.     

上地幔俯冲板块的动力学过程:数值模拟

大洋板块俯冲到地幔转换带,进而可形成不同的形态:板块可以停滞在660km不连续面,抑或穿过地幔转换带进入下地幔.这些不同的俯冲模式可进一步影响到海沟的运动.为更好地理解上地幔中俯冲板片的变形行为以及俯冲过程与海沟运动之间的关系,本文通过建立一系列高精度二维热-力学自由俯冲的数值模型,揭示了俯冲板块在上地幔中的变形方式及其与地幔转换带之间的相互作用过程.模拟结果显示,在俯冲板块与地幔转换带的相互作用过程中,其动力学过程可以分为以海沟后撤主导、海沟前进主导以及稳定型海沟等三种主要动力学类型.对于年龄较老,厚度较大的俯冲板块容易形成海沟后撤型俯冲,俯冲板块停滞在660km不连续面.相反,年龄较小,塑性强度较小的板块容易形成海沟前进型俯冲,俯冲板块穿越660km不连续面.     

Density modeling of the Escollos Alijos Seamount from inversion of its geoid undulation anomaly

Escollos Alijos is a large seamount located in the NE Pacific Ocean about 300 km off the Baja California Peninsula. Geochronology and geochemical analysis of volcanic rocks capping the seamount indicate recent magmatism that resulted from extensive differentiation of a mildly alkalic basalt parent magma.Escollos Alijos is located towards the eastern edge of a long-wavelength geoid undulation minimum, of up to -47 m with respect of the WGS84 ellipsoid, which extends over the northeastern Pacific Ocean. Subtracting from the geoid undulation its long-wavelength component and the undulation due to the seamount topography itself, a negative undulation anomaly persists that indicates a mass deficit at depth. Linear inversion of the undulation anomaly yields a region characterized by a negative density contrast, localized under the seamount at a depth between 9 and 13 km.The age and chemical composition of Escollos Alijos, and the inferred mass deficit suggest magma trapped between the oceanic crust and the uppermost mantle, which explains the magmatic activity in recent times.     

On the combination of global and local data in collocation theory

Due to the successful operation of dedicated satellite gravity missions, nowadays high-accuracy global gravity field models have become available. This triggers the challenge to optimally combine this long to medium wavelength gravity field information derived from space-borne data with high-resolution terrestrial gravity data. In this paper, the least squares collocation concept is revised with the attempt to consistently unify the combination procedure in such a way that the full information contained in both data sets is merged. For example, in local or regional geoid determination the remove-restore method is usually applied only partially taking into account the accuracy of the global model coefficients used for the long-wavelength reduction. The key advantage of the extended formulation is the fact that it automatically accounts for the error covariance of all data types involved. The applicability, feasibility and performance of the proposed method is investigated in the frame of numerical closed-loop simulations. The two main fields of application, i.e., the improvement of a global gravity field model by terrestrial gravity field data, and, vice versa, the support to a regional geoid solution by the incorporation of a global gravity field model, have been analyzed and assessed. Although applied under simplified conditions, it could be shown that the method works and is practically applicable.     

Possible effects of lateral viscosity variations induced by plate-tectonic mechanism on geoid inferred from numerical models of mantle convection

In a traditional analytical method, the convective features of Earth’s mantle have been inferred from surface signatures obtained by the geodynamic model only with depth-dependent viscosity structure. The moving and subducting plates, however, bring lateral viscosity variations in the mantle. To clarify the effects of lateral viscosity variations caused by the plate-tectonic mechanism, I have first studied systematically instantaneous dynamic flow calculations using new density-viscosity models only with vertical viscosity variations in a three-dimensional spherical shell. I find that the geoid high arises over subduction zones only when the vertical viscosity contrast between the upper mantle and the lower mantle is O(10³) to O(10⁴), which seems to be much larger than the viscosity contrast suggested by other studies. I next show that this discrepancy may be removed when I consider the lateral viscosity variation caused by the plate-tectonic mechanism using two-dimensional numerical models of mantle convection with self-consistently moving and subducting plates, and suggest that the observed geoid anomaly on the Earth’s surface is significantly affected by plate-tectonic mechanism as a first-order effect.     

The gravity field and GGOS

The gravity field of the earth is a natural element of the Global Geodetic Observing System (GGOS). Gravity field quantities are like spatial geodetic observations of potential very high accuracy, with measurements, currently at part-per-billion (ppb) accuracy, but gravity field quantities are also unique as they can be globally represented by harmonic functions (long-wavelength geopotential model primarily from satellite gravity field missions), or based on point sampling (airborne and in situ absolute and superconducting gravimetry). From a GGOS global perspective, one of the main challenges is to ensure the consistency of the global and regional geopotential and geoid models, and the temporal changes of the gravity field at large spatial scales. The International Gravity Field Service, an umbrella “level-2” IAG service (incorporating the International Gravity Bureau, International Geoid Service, International Center for Earth Tides, International Center for Global Earth models, and other future new services for, e.g., digital terrain models), would be a natural key element contributing to GGOS. Major parts of the work of the services would, however, remain complementary to the GGOS contributions, which focus on the long-wavelength components of the geopotential and its temporal variations, the consistent procedures for regional data processing in a unified vertical datum and Terrestrial Reference Frame, and the ensuring validations of long-wavelength gravity field data products.     

The geoid and single-cell mantle convection

The geoid shows an antisymmetric departure from the spheroid of best fit. A single zero-elevation contour divides its surface into nearly equal strips in one of which the elevation is everywhere positive and in the other everywhere negative. These two areas are interleaved roughly like the strips covering a tennis ball. This pattern may indicate global single-cell convection in the mantle. It is argued that on this convection hypothesis, the upcurrents underlie the low-geoid strip, although the opposite view could be supported. No simple relation is to be expected between the proposed whole-mantle convection and plate motions, because other constraints act on plates and because the asthenosphere will partially decouple the whole-mantle motions from the lithosphere. However, the proposed whole-mantle convective system is consistent with rapid northwestward motion of the Pacific plate, with fast spreading of the East Pacific Rise and with slow spreading of the North Atlantic Ridge. Seismological velocity anomalies in the mantle, while highly relevant to whole-mantle convection, do not at present decide for or against the hypothesis here advanced.     

The modern geoid and ancient plate boundaries

The non-hydrostatic geoid is dominated by three large anomalies: an area of high gravity potential in the equatorial Pacific; another stretching from Greenland through Africa to the southwest Indian Ocean; and a semi-continuous low region passing from Hudson's Bay through Siberia to India and on to Antarctica. None of these three high-amplitude (greater than 60 m) and long-wavelength anomalies corresponds to present-day plate boundaries. However, if the modern geoid is plotted over the positions of continents and plate boundaries at 125 Ma B.P. (reconstructed relative to hotspots) a strong correlation emerges. The modern geoidal low corresponds in position to the areas of subduction surrounding the Pacific 125 Ma ago. The geoidal high now centered on Africa is entirely contained within ancient Pangaea, and the equatorial Pacific high overlies the location of the spreading centers preserved in the magnetic anomalies of the central Pacific. The most plausible cause of the large geoidal undulations is lower mantle convection only weakly coupled to plate motions. The correspondence between modern geoid and ancient plate boundaries implies either that the coupling was much more intimate in the past, or that there is a lag of at least 100 Ma in response of the lower mantle to upper mantle conditions.     

Slab pull,mantle convection,and Pangaean assembly and dispersal

Two global-scale mantle convection cells presently exist on Earth, centred on upwelling zones in the South Pacific Ocean and northeast Africa: one cell (Panthalassan) contains only oceanic plates, the other (Pangaean) contains all the continental plates. They have remained fixed relative to one another for >400 Ma. A transverse (Rheic–Tethyian) subduction system splits the Pangaean cell. Poloidal plate motion in the oceanic cell reflects circumferential pull of Panthalassan slabs, but toroidal flow in the Pangaean cell, reflected by vortex-type motion of continents toward the Altaids of central-east Asia throughout the Phanerozoic, has resulted from the competing slab-pull forces of both cells. The combined slab-pull effects from both cells also controlled Pangaean assembly and dispersal. Assembly occurred during Palaeozoic clockwise toroidal motion in the Pangaean cell, when Gondwana was pulled into Pangaea by the NE-trending Rheic subduction zone, forming the Appalachian–Variscide–Altaid chain. Pangaean dispersal occurred when the Rheic trench re-aligned in the Jurassic to form the NW-trending Tethyside subduction system, which pulled east Gondwanan fragments in the opposite direction to form the Cimmerian–Himalayan–Alpine chain. This re-alignment also generated a new set of (Indian) mid-ocean ridge systems which dissected east Gondwana and facilitated breakup. 100–200-Myr-long Phanerozoic Wilson cycles reflect rifting and northerly migration of Gondwanan fragments across the Pangaean cell into the Rheic–Tethyian trench. Pangaean dispersal was amplified by retreat of the Panthalassan slab away from Europe and Africa, which generated mantle counterflow currents capable of pulling the Americas westward to create the Atlantic Ocean. Thermal blanketing beneath Pangaea and related hotspot activity were part of a complex feedback mechanism that established the breakup pattern, but slab retreat is considered to have been the main driving force. The size and longevity of the two cells, organised and maintained by long-lived slab-pull forces, favours deep mantle convection as the dominant circulation process during the Phanerozoic.