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.     

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.     

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.     

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.     

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/...     

欧亚地区均衡残差大地水准面和上地幔强度

首先计算了欧亚地区均衡残差大地水准面．基于地幔热对流的内负荷理论和最新全球层析成像结果，探讨了欧亚地区中波长均衡残差大地水准面的地球动力学意义．研究结果表明，中波长均衡残差大地水准面主要受上地幔粘滞度和岩石层强度的影响，进而得出欧亚地区一些古老地盾和构造稳定地区的上地幔与年轻山脉及构造活动地区的上地幔结构存在着差异．这个差异主要是占老地盾和构造稳定地区，如波罗的海地盾、中西伯利亚地台、东欧等区域，冷却的上地幔已穿透地幔较深，上地幔与岩石层之间耦合较好;而年轻山脉和构造活动区，如帕米尔、天山、贝加尔活动带、青藏高原、日本海周围地区，在上地幔可能存在着热物质即粘滞度很低的软流层，上地幔与岩石层耦合程度较差，甚至有可能解耦．从欧亚地区上地幔属性的差异，可以解释该地区的一些地球动力学问题．     

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.     

青藏高原-天山地区岩石层构造运动的地幔动力学机制

利用全球重力大地水准面异常、板块绝对运动及全球地震层析成像数据,计算了青藏高原-天山地区岩石层下部地幔大尺度对流格局以及此种尺度对流驱动下岩石层内应力场分布;同时,利用区域均衡重力异常数据反演青藏高原中、北部到天山地区上地幔小尺度对流模型．结果表明,大尺度的地幔物质运移过程可能驱动着中国大陆岩石层整体从西部以南北方向为主的运动转向东部地区以北东和南东方向的运动;而该区域上地幔小尺度上升流动支持了现代青藏高原和天山地区的抬升运动．提出和讨论了青藏高原隆升的“断离隆升-挤压隆升-对流隆升”三阶段模式,并探讨了大陆岩石层构造运动的地幔深部动力学背景．     

中国及邻区大地水准面异常的场源深度探讨

利用中国及邻区地形、地震层析成像、沉积层底面、Moho面及岩石层底面资料,正演计算出中国及邻区岩石圈大地水准面异常;再从全阶大地水准面异常中扣除正演模拟得到的岩石圈大地水准面异常与不同阶次波段的大地水准面进行比较,寻求表示中国及邻区地幔物质不均匀的大地水准面异常的最佳阶次为2-60阶. 结果表明,对应于岩石圈的大地水准面异常的重力位球谐函数阶数为61-20阶;下地幔重力位球谐函数阶数为2-6阶;而-60阶重力位球谐函数则表示中国及邻近区域上地幔大地水准面异常.     

中国及邻区大地水准面异常的场源深度探讨

利用中国及邻区地形、地震层析成像、沉积层底面、Moho面及岩石层底面资料,正演计算出中国及邻区岩石圈大地水准面异常;再从全阶大地水准面异常中扣除正演模拟得到的岩石圈大地水准面异常与不同阶次波段的大地水准面进行比较,寻求表示中国及邻区地幔物质不均匀的大地水准面异常的最佳阶次为2-60阶. 结果表明,对应于岩石圈的大地水准面异常的重力位球谐函数阶数为61-20阶;下地幔重力位球谐函数阶数为2-6阶;而-60阶重力位球谐函数则表示中国及邻近区域上地幔大地水准面异常.     

动力地球表面形变

地幔对流使得地球表面及核幔边界发生形变，这种由地球深部的动力学过程所引起的形变对大地水准面异常的贡献与地球内部密度异常的贡献具有相当的量级，但符号相反，而由于地表的短周期地质作用所引起的地球表面形变的屏蔽作用，这种长波长、长周期的动力地球表面形变在目前还无法直接观测出来。本文首先从观测大地水准面异常中将地球内部密度异常的贡献去掉，并根据地震层析所得出的核幔边界形变，求得了动力地球表面形变。其结果将对地球内部的动力学过程尤其是粘滞度分布提供十分有用的信息。     

地幔粘度结构的研究

地幔的流变性质已成为认识地球内部结构及动力学过程的核心问题之一。本文总结了近年来地幔粘度结构研究的方法,其中包括利用地球物理观测资料进行反演计算和实验室试验研究,重点讨论了利用冰期后回跳,板块运动速度和大地水准面异常资料反演地幔粘度结构２的方法和结果以及地幔矿物的实验结果,并对不同方法进行了比较总结。最后简单讨论了地幔粘度结构研究存在的问题和未来的研究方向。     

大尺度地幔动力学研究的现状和展望

这篇综述讨论大空间、大时间尺度的地幔动力学近几十年的发展和现状,着重讨论了相关的观测及其动力学意义.这些观测包括现在地球的板块运动的基本特性,中、长波重力异常及大地水准面异常,地震层析成像得到的地幔结构,以及过去10亿年超级大陆Pangea和Rodinia的形成、裂解和演化,及火山岩浆活动.关于地球动力学模型的讨论是围绕着这些相关的观测而进行的.涉及到的一些主要问题包括以下.第一,地幔动力学研究显示,地震层析成像得到的下地幔的二阶结构（比如核幔边界附近的LLSVP结构）,和俯冲带的快速异常体,可以解释为过去1亿年左右的板块运动和地幔对流的结果;第二,地幔三维结构作为地幔对流的驱动力,是导致中、长波重力及大地水准面异常的直接原因;结合地幔动力学模拟,观测的大地水准面异常对地幔黏性结构提供了强有力的约束,很可靠的结果之一是下地幔的黏性比上地幔要高至少一个量级,并且最近的研究确定软流圈的存在;第三,过去10亿年大陆块体经历过的Rodinia和Pangea两期超级大陆的形成和破裂是地幔动力学在地表的反映.地幔结构在Pangea形成过程中是一阶结构（即一个半球是冷的下降流,而另一个半球是热的上涌流）主导的,而现在的二阶为主导的地幔结构是Pangea形成后,破裂前或破裂过程中才形成的;地幔动力学和其他研究支持地幔结构在一阶和二阶间转换的1-2-1模型;第四,板块构造在地球上的起源和动力机制依然是充满争议和不确定的课题,但是这些问题同时也是重要的地球动力学基本问题.

     

Using postglacial sea level,crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.     

Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.     

GIA-induced secular variations in the Earth's long wavelength gravity field: Influence of 3-D viscosity variations

Predictions of present day secular variations in the Earth's long wavelength geopotential driven by glacial isostatic adjustment (GIA) have previously been analyzed to infer the radial profile of mantle viscosity and to constrain ongoing cryospheric mass balance. These predictions have been based on spherically symmetric Earth models. We explore the impact of lateral variations in mantle viscosity using a new finite-volume formulation for computing the response of 3-D Maxwell viscoelastic Earth models. The geometry of the viscosity field is constrained from seismic-to-mographic images of mantle structure, while the amplitude of the lateral viscosity variations is tuned by a free parameter in the modeling. We focus on the zonal J˙_? harmonics for degrees ? = 2,…,8 and demonstrate that large-scale lateral viscosity variations of two to three orders of magnitude have a modest, 5-10%, impact on predictions of J˙₂. In contrast, predictions of higher degree harmonics show a much greater sensitivity to lateral variation in viscosity structure. We conclude that future analyses of secular trends (for degree ? > 2) estimated from ongoing (GRACE, CHAMP) satellite missions must incorporate GIA predictions based on 3-D viscoelastic Earth models.     

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.     

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.     

非洲南部地壳与上地幔地震波速度与径向各向异性特征及其对克拉通岩石圈中部不连续面的启示

克拉通地区发育的岩石圈中部不连续面(Mid-Lithosphere Discontinuity, MLD)对于理解克拉通的形成与演化有着重要的意义.非洲南部的卡普瓦尔克拉通(Kaavpvaal craton)较为稳定, 是研究MLD地震学特征及其成因机制的一个重点区域.本研究基于多个地震台网105个台站记录的700多个地震事件的面波波形, 通过Rayleigh波和Love波成像, 构建了非洲南部地壳与上地幔的三维剪切波速度与径向各向异性模型.研究结果表明, 卡普瓦尔克拉通的地壳与上地幔呈现相对高速异常, 其岩石圈与软流圈界面(LAB)出现在约220 km深.另外, 我们在卡普瓦尔克拉通岩石圈内部约100 km深观测到一个速度突变面, 可解释为MLD, 并在MLD下方观测到低速层.而各向异性在上地幔的垂直方向上并未显示明显的区域性突变, 似乎暗示MLD的地震各向异性特征更为复杂.结合前人的研究成果, 我们推测卡普瓦尔克拉通MLD与上地幔低速层的成因可能与温度密切相关.而镁值成分异常或岩浆侵入则会局部的改变该克拉通(尤其是其北部)上地幔速度.针对MLD与上地幔低速成因的研究还需结合更多的地球物理数据和岩石实验结果.本研究为理解克拉通的演化提供重要的基础.

     

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.