Topography on the D′′ region from analysis of a thin dense layer beneath a convecting cell

In this study, we examine the development of topography on a thin dense layer at the base of the lower mantle. The effect of the convecting mantle above is represented as a traction acting on the upper surface of the layer. Topography on the layer boundaries is predicted by a balance of dynamic flow stress and external traction. The nature of boundary topography depends on the magnitude of the driving tractions and the density variation within the layer. If we assume that the layer density is greatest beneath areas of mantle downwelling and decreases to a minimum beneath areas of mantle upwelling (the layer is thermally coupled to the convection in the overlying mantle) then its upper boundary develops a cusp-like peak beneath the upwelling mantle. The height of this peak is potentially much greater than the layer thickness. If, however, the layers are effectively coupled by viscous shear then internal density gradients of the opposite sign may be established. In this case, we observe solutions where the layer is completely swept away beneath areas of mantle downwelling leaving steep-sided ‘islands’ of dense material. This mechanism therefore provides a possible explanation for steep-sided anomalously slow regions at the base of the mantle observed by seismic methods (e.g. beneath south Africa) or for discrete ultralow velocity zones detected at the core-mantle boundary beneath locations of surface hotspots. The magnitude of the upper boundary driving tractions compared to the density gradient within the layer is the key parameter that determines the nature of flow in, and consequently boundary topography of, the layer. The deflection of the core-mantle boundary is small compared with that of the top of the dense layer, but a change in sign of the ratio of these deflections is observed as the magnitude of the driving tractions changes relative to the magnitude of the internal density gradient. We compare seismic measurements of core-mantle boundary topography and D′′ topography with the predictions of this model in an attempt to constrain model parameters, but no clear correlation seems to exist between D′′ thickness and CMB topography.     

Core mantle boundary topography from short period PcP, PKP, and PKKP data

We use a total of 839,369 PcP, PKPab, PKPbc, PKPdf, PKKPab, and PKKPbc residual travel times from [Bull. Seism. Soc. Am. 88 (1998) 722] grouped in 29,837 summary rays to constrain lateral variation in the depth to the core-mantle boundary (CMB). We assumed a homogeneous outer core, and the data were corrected for mantle structure and inner-core anisotropy. Inversions of separate data sets yield amplitude variations of up to 5 km for PcP, PKPab, PKPbc, and PKKP and 13 km for PKPdf. This is larger than the CMB undulations inferred in geodetic studies and, moreover, the PcP results are not readily consistent with the inferences from PKP and PKKP. Although the source-receiver ambiguity for the core-refracted phases can explain some of it, this discrepancy suggest that the travel-time residuals cannot be explained by topography alone. The wavespeed perturbations in the tomographic model used for the mantle corrections might be too small to fully account for the trade off between volumetric heterogeneity and CMB topography. In a second experiment we therefore re-applied corrections for mantle structure outside a basal 290 km-thick layer and inverted all data jointly for both CMB topography and volumetric heterogeneity within this layer. The resultant CMB model can explain PcP, PKP, and PKKP residuals and has approximately 0.2 km excess core ellipticity, which is in good agreement with inferences from free core nutation observations. Joint inversion yields a peak-to-peak amplitude of CMB topography of about 3 km, and the inversion yields velocity variations of ±5% in the basal layer. The latter suggests a strong trade-off between topography and volumetric heterogeneity, but uncertainty analyses suggest that the variation in core radius can be resolved. The spherical averages of all inverted topographic models suggest that the data are best fit if the actual CMB radius is 1.5 km less than in the Earth reference model used (i.e. the average outer core radius would be 3478 km).     

核－幔边界的动力学背景

根据传播矩阵方法，并把由联合反演得到的同时满足长波地形起伏、板块运动速度、重力位异常资料以及地震层析先验知识的全地幔三维异常密度作为载荷，以求取核－幔边界的动力学背景．计算结果显示：１．所求的核－幔边界起伏图像与Ｈａｇｅｒ等根据格林函数方法所求得的核－幔边界的起伏在全球范围内基本相符．２．核－幔边界处的环型场仅在数量上降为地表处的环型场的１／８左右，而极型场较地表处的极型场的流动图像有显著变化，数值也增为地表处极型场的３倍左右．     

核－幔边界的动力学背景

根据传播矩阵方法，并把由联合反演得到的同时满足长波地形起伏、板块运动速度、重力位异常资料以及地震层析先验知识的全地幔三维异常密度作为载荷，以求取核－幔边界的动力学背景．计算结果显示：１．所求的核－幔边界起伏图像与Ｈａｇｅｒ等根据格林函数方法所求得的核－幔边界的起伏在全球范围内基本相符．２．核－幔边界处的环型场仅在数量上降为地表处的环型场的１／８左右，而极型场较地表处的极型场的流动图像有显著变化，数值也增为地表处极型场的３倍左右．     

Core–mantle boundary topography as a possible constraint on lower mantle chemistry and dynamics

The origin of large low shear-wave velocity provinces (LLSVPs) in the lowermost mantle beneath the central Pacific and Africa is not well constrained. We explore numerical convection calculations for two proposed hypotheses for these anomalies, namely, thermal upwellings (e.g., plume clusters) and large intrinsically dense piles of mantle material (e.g., thermochemical piles), each of which uniquely affects the topography on Earth's core–mantle boundary (CMB). The thermochemical pile models predict a relatively flat but elevated CMB beneath piles (presumed LLSVPs), with strong upwarping along LLSVP margins. The plume cluster models predict CMB upwarping beneath upwellings that are less geographically organized. Both models display CMB depressions beneath subduction related downwelling. While each of the two models produces a unique, characteristic style of CMB topography, we find that seismic models will require shorter length scales than are currently being employed in order to distinguish between the end-member dynamic models presented here.     

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.     

Mass heterogeneities and convection in the earth's mantle inferred from gravity and core-mantle boundary irregularities

Mass heterogeneities in the earth's mantle are retrieved from the gravity data and the topography of the core-mantle boundary as well as the topography of the earth's surface. A mantle circulation induced by the heterogeneities is modelled by solving the Stokes problem for incompressible Newtonian fluid. The derived models of mantle motions correlate well with the plate tectonics and point at a close relation between the surface tectonic activity and the processes in the vicinity of the core-mantle boundary.     

Structural heterogeneity of an ultra-low-velocity zone beneath the Philippine Islands: Implications for core–mantle chemical interactions induced by massive partial melting at the bottom of the mantle

An ScP phase reflected and converted at the core–mantle boundary (CMB) beneath the region east of the Philippine Islands shows clear pre- and postcursors, recorded on short-period seismic networks in Japan. These waveform variations can be explained by interaction of the ScP wavefield with thin layers at the CMB. The results of forward modeling of double-array stacks reveal two different structural heterogeneities in the lowermost mantle beneath the region east of the Philippine Islands. One of the structures represents a decreased velocity, and increased density across the reflector at the lowermost ～10 km of the mantle, with P- and S-wave velocity reductions of 5–10% and ～30%, respectively, and an increase in density of 5–10%. Another structure consists of a pair of reflectors at ～10 km and ～5 km above the CMB, both of which are characterized by reduced P- and S-wave velocities. The upper reflector is the interface of a low-velocity zone in which P- and S-wave velocities decrease of 10% and 30%, respectively, accompanied by an extremely large increase in density (20–25%). The lower reflector is characterized by a 25% reduction in S-wave velocity relative to the above low-velocity layer, as well as a 5% decrease in P-wave velocity and no change in density. The nature of the low-velocity zone detected locally at the CMB is comparable with that of ultra-low-velocity zones (ULVZs) observed by various seismic probes in the South Pacific and Central America. Extensive observations of the ULVZ beneath the region east of the Philippine Islands indicate massive partial melting at the bottom of the mantle. Low-S-velocity basal layer partly detected within the ULVZ may be resulting from core–mantle chemical interactions, driven by massive partial melting.     

Theoretical study on the influence of CMB topography on the core reflection ScS

Computing synthetic seismograms for media with localized heterogeneous regions can be performed using hybrid methods. Here, a combination of a finite-difference (FD) technique and a frequency-wavenumber (ω − k) filtering is applied to model wave reflection at different kinds of core-mantle boundary (CMB) topography. The FD method is only applied in the neighbourhood of the CMB, while the ω − k filter is used to continue the reflected wavefield to the Earth's surface. Synthetic SH-seismograms for ScS with a dominant frequency of 0.5 Hz are computed at epicentral distances from 44° to 69°. The topography varies in amplitude (maximum amplitude of 1.0–2.7 km) and in its wavenumber spectrum; it is either monochromatic (wavelengths from 55 to 270 km) or statistical (coloured noise). The seismograms for a CMB with topography are compared with those for a plane CMB. We observe that monochromatic topography with short wavelengths (less than 100 km) results in amplitude reduction and shorter travel times than in the case of a plane CMB, but no variations with epicentral distance appear, whereas greater wavelengths exhibit amplitude variations with distance as well as travel time residuals, which both correlate with the CMB topography. Statistical models show amplitude variations with epicentral distance, while the travel time residuals are very small (less than 0.1 s). All synthetics illustrate that wavefront healing occurs along the ray path from the CMB to the Earth's surface. While the seismograms at the CMB exhibit strong fluctuations, the fluctuations at the surface are smoothed and reduced. This demonstrates that it is necessary to use wave theoretical methods for computing synthetic seismograms for complicated structures at greater depth. It also follows that travel times are less sensitive to the structure than the amplitudes.     

A new insight into the Hawaiian plume

Although many geochemical, geophysical and seismological studies have suggested that the Hawaiian mantle plume originates from the core–mantle boundary (CMB), so far no tomographic model shows a continuous image of the Hawaiian plume in the entire mantle because of the few seismic stations on the narrow Hawaiian island chain. Here we present a new tomographic image beneath Hawaii determined by using simultaneously 10 kinds of seismic phases, P, pP, PP, PcP, Pdiff, PKPab, PKPbc, PKiKP, PKKPab and PKKPbc, extracted from the data set compiled by the International Seismological Center. Of these phases, PKiKP, PKKPab and PKKPbc are, for the first time, attempted to use in the global seismic tomography. Our results show a slow anomaly beneath Hawaii ascending continuously from the CMB to the surface, implying that the Hawaiian plume indeed originates from the CMB. This image is improved notably over the previous results in the whole mantle, particularly in and below the middle mantle, suggesting that later phases, PP, Pdiff, PKP and particularly PKiKP, are of great importance for better imaging the Hawaiian plume. This slow anomaly is considered to be a plume conduit being tilted, which is likely caused by the mantle flow. This indicates that the position of the Hawaiian hotspot on the surface is not stationary, as evidenced by the recent paleomagnetic and numerical modeling studies.     

Global P-wave tomography: On the effect of various mantle and core phases

In this work, many global tomographic inversions and resolution tests are carried out to investigate the influence of various mantle and core phase data from the International Seismological Center (ISC) data set on the determination of 3D velocity structure of the Earth's interior. Our results show that, when only the direct P data are used, the resolution is good for most of the mantle except for the oceanic regions down to about 1000 km depth and for most of the D″ layer, and PP rays can provide a better constraint on the structure down to the middle mantle, in particular for the upper mantle under the oceans. PcP can enhance the ray sampling of the middle and lower mantle around the Pacific rim and Europe, while Pdiff can help improve the spatial resolution in the lowermost mantle. The outer core phases (PKP, PKiKP and PKKP) can improve the resolution in the lowermost mantle of the southern hemisphere and under oceanic regions. When finer blocks or grid nodes are adopted to determine a high-resolution model, pP data are very useful for improving the upper mantle structure. The resulting model inferred from all phases not only displays the general features contained in the previous global tomographic models, but also reveals some new features. For example, the image of the Hawaiian mantle plume is improved notably over the previous studies. It is imaged as a continuous low velocity anomaly beneath the Hawaiian hotspot from the core-mantle boundary (CMB) to the surface, implying that the Hawaiian mantle plume indeed originates from the CMB. Low-velocity anomalies along some mid-oceanic ridges extend down to about 600 km depth. Our results suggested that later seismic phases are of great importance in better understanding the structure and dynamics of the Earth's interior.     

Axial and equatorial rotations of the Earth's cores associated with the Quaternary ice age

The differential axial and equatorial rotations of both cores associated with the Quaternary glacial cycles were evaluated based on a realistic earth model in density and elastic structures. The rheological model is composed of compressible Maxwell viscoelastic mantle, inviscid outer core and incompressible Maxwell viscoelastic inner core. The present study is, however, preliminary because I assume a rigid rotation for the fluid outer core. In models with no frictional torques at the boundaries of the outer core, the maximum magnitude of the predicted axial rotations of the outer and inner cores amounts to ∼2° year⁻¹ and ∼1° year⁻¹, respectively, but that for the secular equatorial rotations of both cores is ∼0.0001° at most. However, oscillating parts with a period of ∼225 years are predicted in the equatorial rotations for both cores. Then, I evaluated the differential rotations by adopting a time-dependent electromagnetic (EM) torque as a possible coupling mechanism at the core-mantle boundary (CMB) and inner core boundary (ICB). In a realistic radial magnetic field at the CMB estimated from surface magnetic field, the axial and equatorial rotations couple through frictional torques at the CMB, although these rotations decouple for dipole magnetic field model. The differential rotations were evaluated for conductivity models with a conductance of 10⁸ S of the lowermost mantle inferred from studies of nutation and precession of the Earth and decadal variations of length of day (LOD). The secular parts of equatorial rotations are less sensitive to these parameters, but the magnitude for the axial rotations is much smaller than for frictionless model. These models, however, produce oscillating parts in the equatorial rotations of both cores and also in the axial rotations of the whole Earth and outer and inner cores. These oscillations are sensitive to both the magnitude of radial magnetic field at the CMB and the conductivity structure. No sharp isolated spectral peaks are predicted for models with a thin conductive layer (∼200 m) at the bottom of the mantle. In models with a conductive layer of ∼100 km thickness, however, sharp spectral peaks are predicted at periods of ∼225 and ∼25 years for equatorial and axial rotations, respectively, although these depend on the strength of radial magnetic field at the CMB. While the present study is preliminary in modelling the fluid outer core and coupling mechanism at the CMB, the predicted axial rotations of the whole Earth may be important in explaining the observed LOD through interaction between the equatorial and axial rotations.     

The effect of a rough core-mantle boundary on PKKP

Scattering by a slightly-rough core-mantle boundary (CMB) with small-scale radial variations of up to a few hundred metres, has been an attractive (though non-unique) interpretation of at least part of the precursors to PKIKP. Here it is shown that a slightly-rough CMB has an observable effect on PKKP as well, if the signal-to-noise ratio is sufficiently high. The effect may be observed as precursive arrivals and is due to back-scattering

at CMB. This work was prompted by observations by Chang and Cleary at LASA of “PKKP” and precursors from the Novaya Zemlya explosions. NORSAR data from several source regions are presented here; small-scale radial variations of 100–200 metres are inferred from these data, although in some regions the CMB appears to be much smoother. On the other hand, the LASA data are anomalous and suggest much larger topography in the sampled region of the CMB. Both large- and small-scale topography must be dynamically produced, if current estimates of the viscosity of the lower mantle (～10²² Poise) are correct.     

地幔对流环型场的激发(Ⅰ)

讨论了地幔内部的粘滞度及施加在地表和CMB 的边界条件对地幔对流环型场的激发分析表明,当粘滞度侧向均匀时,环型场与极型场自然解耦,且环型场不影响重力位,当粘滞度侧向不均时,环型场与极型场耦合在一起.两者共同影响重力位.当引入板块运动速度时,边界条件非零,也能激发环型场;对侧向均匀粘滞度地幔,零边界条件不能激发环型场     

On the effect of oceanic tides on the inertial coupling between the liquid core and the mantle

The amplitudes and phases of forced nutation and diurnal earth tides depend significantly on the moment of forces between the liquid core and mantle of the Earth, resulting from the differential rotation of the core. The solution to the dynamic problem of rotation of an imperfectly elastic mantle with an imperfectly liquid core and an ocean indicates that the predominant role is played by the so-called core-mantle inertial coupling (related to the effect of hydrodynamic pressure in the liquid core on the ellipsoidal core-mantle boundary). The magnitude of this coupling depends significantly not only on the dynamic flattening of the liquid core but also on the elastic and inelastic properties of the mantle, as well as on the amplitudes and phases of oceanic tides. In this paper, the effects of oceanic tides on the magnitude of inertial coupling between the liquid core and the mantle and on the period and damping decrement of free nearly diurnal nutation are estimated.     

深内部地球结构对内核平动振荡本征周期的影响

地球固态内核的平动振荡是地球的基本简正模之一,又称Slichter模,其本征周期大约为几个小时,与地球内部结构密切相关.为了研究影响内核平动振荡的本征周期与内部结构的依赖关系,本文利用球对称、非自转、弹性和各向同性地球模型（SNREI）,通过自由振荡运动方程的数值积分,以地球模型PREM为基础,理论上系统研究了地球内部介质（包括密度、地震波速等）分布异常对Slichter模本征周期的影响.数值结果表明,Slichter模周期随着内外核边界（ICB）密度差的增加以类似于双曲线的特征显著减小,当ICB密度差从597 kg·m^-3减小到200 kg·m^-3时,周期增大66.44%,当ICB密度差从597 kg·m^-3增大到1000 kg·m^-3时,周期减小21.48%;Slichter模周期随着核幔边界（CMB）密度差的增大而缓慢增大;相对于PREM,地球模型1066A在ICB和CMB的密度差分别相差45.321%和1.132%,内部地震波速度和密度梯度也存在差异,但是,当密度差减小到1066A模型提供的数值时,得到的Slichter模周期与基于1066A获得的结果（4.599 h）非常接近,差异分别只有3.762%和0.037%;表明Slichter模本征周期与地球内部介质的精细结构关系不大,而对ICB的密度差非常敏感.内、外核P波波速分布异常对Slichter模周期的影响基本相当,当内核和外核P波波速均增加5%时,Slichter周期分别减小1.02%和1.69%,P波波速分别减小5%时,Slichter模周期分别增加1.27%和1.847%,内核S波波速分布异常比P波波速分布异常对Slichter模周期的影响小1个量级;与地核相比,地幔中的地震波速异常对Slichter模本征周期的影响小1~2个量级;表明地核中地震波速异常对Slichter模周期的影响很小,目前有关Slichter模周期理论计算的差异主要来自于所采用的地球模型中内核边界的密度差的差异,本文结果可以为Slichter模的研究、探测及其对地球深内部结构的约束提供理论依据.     

Reversed polarity patches at the CMB and geomagnetic field reversal

The International Geomagnetic Reference Field models (IGRF) for 1900–2000 are used to calculate the geomagnetic field distribution in the Earth’ interior from the ground surface to the core-mantle boundary (CMB) under the assumption of insulated mantle. Four reversed polarity patches, as one of the most important features of the CMB field, are revealed. Two patches with +Z polarity (downward) at the southern African and the southern American regions stand out against the background of ™Z polarity (upward) in the southern hemisphere, and two patches of ™Z polarity at the North Polar and the northern Pacific regions stand out against the +Z background in the northern hemisphere. During the 1900–2000 period the southern African (SAF) patch has quickly drifted westward at a speed of 0.20–.3° /a; meanwhile its area has expanded 5 times, and the magnetic flux crossing the area has intensified 30 times. On the other hand, other three patches show little if any change during this 100-year period. Extending upward, each of the reversed polarity patches at the CMB forms a chimney-shaped “reversed polarity column” in the mantle with the bottom at the CMB. The height of the SAF column has grown rapidly from 200km in 1900 to 900km in 2000. If the column grows steadily at the same rate in the future, its top will reach to the ground surface in 600–700 years. And then a reversed polarity patch will be observed at the Earth’s surface, which will be an indicator of the beginning of a magnetic field reversal. On the basis of this study, one can describe the process of a geomagnetic polarity reversal, the polarity reversal may be observed firstly in one or several local regions; then the areas of these regions expand, and at the same time, other new reversed polarity regions may appear. Thus several poles may exist during a polarity reversal.     

全球地幔垂直流动速度研究

用高分辨率地震体波速度成像以及相关的地球物理资料,计算地幔垂直流动形式及流动速度,得到全球地幔流垂直运动模式.从全球尺度来看,地幔流基本可划分为以下几个区域：欧亚大陆—澳大利亚、北美洲—南美洲为两个大规模下降流区域,西印度洋—非洲及大西洋、中南太平洋及东太平洋为两个大规模地幔上升流区域.地幔上升流起源于核幔边界,主要表现在地幔中部和上地幔下部.地幔垂直流动速度约每年1～4cm.地幔流动对地表板块运动、海洋中脊和中隆、俯冲带和碰撞带的分布起着控制作用.地幔上升流与地表现代热点有密切关系.从东亚尺度看,地幔流大体分为三个区域：东亚边缘裂谷系和西太平洋边缘海为上升流、西伯利亚地幔深度表现为物质下降流、青藏高原—缅甸—印度尼西亚特提斯俯冲带地幔下降流,这三个区域地幔流动与地表的西太平洋构造域、亚洲构造域和特提斯构造域相吻合.勾勒出南海地区构造特征：从上到下的大体结构是上部呈“工"字型、中间为圆柱型、底部呈盾形的地幔上升流.     

现代板块运动驱动地幔块体置换度及地幔混合的研究

定义了描述地幔混合程度的新的统计学量度——地幔块体对流置换度和对流混合扩散度.地幔块体对流置换度等于至少被置换一次的块体数与地幔总块体数之比,对流混合扩散度等于示踪元初始体密度与示踪元终体密度之比.本研究假设地幔对流是稳定的,上地幔和下地幔的黏滞性存在差异,其驱动力为板块运动或地幔中密度异常分布.实验中地幔被划分为20736 个块体（5°×5°×300 km）,2376个示踪元被放置在地幔顶部100 km深度或底部100 km高度的5°×5°的网格点上.模型计算表明, 地幔块体对流置换度随运转时间变化.就全地幔而言,在系统运行四十亿年后,大多数模型对应的块体对流置换度均超过80%,而上地幔块体置换度则达到90%.这预示大多数的地幔块体将被来自其他位置的块体所取代.对于放置在地幔顶部或底部,浓缩于很小空间10°×10°(间距0.25°) 中的两组1681个示踪元而言,尽管其对流混合扩散度在开始有较大的差异,但是在运行一段时间之后,此两组对应的对流混合扩散度均趋于常数,示踪元比较均匀地分布于全地幔之中.由以上的结果可以推断,在经历了四十五亿年的演化过程后,由于对流的作用使地幔基本上已经均匀混合,地幔中不大可能存在尺度大于5°×5°×300 km的异常块体.     

Plume heat flow is much lower than CMB heat flow

Plumes rising from the core–mantle boundary (CMB) are often assumed to transport most, or all, of the heat conducted across the CMB. Here this assumption is explored using numerical convection models in idealized geometries that lead to a single plume under steady-state or near steady state conditions. Plume heat transport is calculated for different internal heating rates using two methods and compared to the CMB heat flux. For these conditions, it is found that the heat flux transported by plumes in the upper mantle is only a fraction of the core heat flux and, thus, core heat flow estimates derived from observed hotspots could be multiplied by a factor of several.