The amplitude ratioPcP/P and the core-mantle boundary

Summary Using the Haskell matrix formulation, theoretical reflection coefficient curves have been calculated for a multi-layered core-mantle boundary for comparison with observational data. Two cases are considered, first when the shear velocity in the core is equal to zero and second when the core has a finite rigidity. If the velocity contrast is large between the imbedded layer and the mantle, the reflection coefficient curves for the multi-layered medium are irregular in shape as compared to those for two half-spaces, representing the core and the mantle, respectively. The reflection coefficient curves show an oscillatory character if the imbedded layer is thick and has a high velocity contrast.The observational data consist of short-period vertical-component seismograph records ofP andPcP from nuclear explosions in the Aleutian chain, Nevada, Novaya Zemlya, Kazakh and Sahara. Attenuation and geometrical spreading are taken into consideration. Four different models for the quality factorQ are applied to the observational data. The data are found to be much affected by theQ-model used for the corrections.Based on proposedQ-values, a model for the core-mantle boundary is found, characterized by two low-velocity layers at the bottom of the mantle. The thicknesses are 16.10 km (outer layer) and 19.96 km (inner layer), the compressional wave velocities 12.17 km/sec and 10.94 km/sec and the shear wave velocities are 6.29 km/sec and 5.33 km/sec, respectively. A better fit to this model is found when in addition the shear velocity in the outer core is 2.20 km/sec and the density ratio at the core-mantle boundary is 1.07. In other words, the observations favour a layer of finite rigidity in the outer core rather than a fluid one.     

Hydromagnetic spin-up under conditions of the earth's core-mantle boundary

Summary The disturbances of the velocity and magnetic fields close to the Earth's core-mantle boundary, caused by sudden irregular changes in the Earth's rotation, are investigated. The problem leads to the investigation of the structure of the Ekman-Hartman hydromagnetic boundary layer, the magnetic diffusive region and the currentless region. Precise Laplacean inversions of the images of all disturbances in the Earth's core-mantle system are obtained for the limiting case of a zero magnetic Prandtl number, =0. The disturbance of the velocity in the direction of the axis of rotation (Ekman suction) in the currentless region has the nature of inertial oscillations with a frequency of 2. Additional disturbances (with respect to the case of =0) of the velocity in the azimuthal and radial directions, particularly for the EHL and MDR region, are determined for the case when 0< « 1. The disturbance in the velocity again has the character of inertial oscillations with the frequency 2, being exponentially damped in EHL asexp (–2²t) and in MDR asexp (–²t).     

On the formation of a stably stratified layer near the core-mantle boundary

Within the framework of a model of liquid immiscibility in the outer core, we calculate a stably stratified layer about 11 km thick near the core-mantle boundary and discuss its reflection and scattering properties for seismic waves.     

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.     

Three-dimensional modelling convection in the earth's mantle: Influence of the core-mantle boundary

Summary Mass heterogeneities in the Earth's mantle are derived from the spherical expansions of the core-mantle boundary topography, the surface topography and the external gravity field. The obtained density distribution provides the body forces driving the convection in the mantle. Assuming Newtonian rheology, the convection is modelled by solving the Stokes problem in the region extending from the top of the D"-layer to the base of the lithosphere. The derived model of mantle motions favours the concept of whole-mantle convection; its pattern connects the shape of the core-mantle boundary with surface tectonics.

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Effect of the irregularities of shape of the Earth's core-mantle boundary on pole wandering

Summary Using a simple model, the motion of the Earth's axis of rotation due to local, axially asymmetric irregularities in the distribution of masses at the Earth's core-mantle boundary, is investigated. Under the assumption of linear displacement of the pole of inertia with time, expressions have been derived for the motion of the pole of the axis of rotation. A numerical estimate of the extent of this motion is made for the characteristic dimensions of the irregularities.     

Inhomogeneities near the core-mantle boundary evidenced from scattered waves: A review

Statistical properties of small-scale inhomogeneities (wavelengths between 20 and 70 km) near the core-mantle boundary are inferred from scattered core waves. Observations of scattered core waves at large seismic arrays and worldwide networks indicate that the inhomogeneities have a global nature with similar characteristics. However, there may exist a few regions having markedly stronger or weaker strengths. Scattering by volumetric inhomogeneities of about 1% inP-wave velocity in the lower mantle or by about 300 m of topographic relief of the core-mantle boundary can explain the observations. At present it is not possible to rule out either of these two alternatives, or a combination of both.     

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).     

Effects of a rigid core on the reflection and transmission coefficients from a multi-layered core-mantle boundary

Summary The aim of this paper is to present the formulations which can be used in calculating reflection and transmission coefficients when the rigidity in the core is taken into consideration. The theoretical curves presented can be used as a guide for studies of the physical parameters of the core-mantle boundary. It is hoped that these curves may lead to a clarification of the great differences between observed data and theoretical calculations, when the geometrical spreading and attenuation are taken into account.The Thomson-Haskell matrix formulations are used to calculate the reflection and transmission coefficients for a multi-layered medium imbedded between two half-spaces representing the solid mantle and a rigid core. A rigid core is defined here as having a rigidity in the range 10¹⁰<<10¹¹ cgs units. For five proposed models of the core-mantle boundary the rigidity in the core is varied and the results are compared with those for a liquid core.     

超导重力技术在探讨核幔边界黏性特征中的初步应用

旋转椭球型地球的固体地幔与液态地核间相互作用而产生的逆向本征模通常称之为地球自由核章动,自由核章动的品质因子（Q值）能有效反映核幔边界层能量耗散特征,与核幔边界的黏滞度密切相关.本文首次利用全球地球动力学计划网络23个台站27组高密度采样的高精度超导重力仪器观测数据,采用迭积技术,确定了自由核章动参数Q值,进而计算了核幔边界的黏滞系数.数值结果说明获得的核幔边界动力学黏滞系数达到103 Pa·s量级,与加拿大科学家Smylie等利用VLBI观测资料获得的最新结果一致,这说明重力技术是有效应用于研究地球深内部结构的重要手段之一.     

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.     

东南亚下方核幔边界D″层地震各向异性

本文利用中国国家数字地震台网(CDSN)和国际数字地震台网(FDSN)的宽频带远震资料,采用S和ScS震相剪切波差异分裂方法对东南亚下方核幔边界D″层地震各向异性进行研究.共获得了来自7个深震(400km)的24对高质量的S和ScS剪切波分裂参数,其中S震相的分裂参数与前人上地幔各向异性研究结果十分吻合,表明S震相观测结果反映了观测台站下方的上地幔各向异性.通过对上地幔各向异性校正后的波形数据进行进一步的分裂参数分析,最后得到了24个可靠的ScS剩余各向异性分裂参数.结果显示,在经度107°~112°范围内分裂参数均为空值(Null);而在该经度范围东西两侧区域,主要表现为明显分裂特征.这种分裂参数的分布指示了核幔边界D″层的各向异性特征的区域变化,我们推测这种变化可能与停滞在核幔边界的古特提斯和/或古太平洋俯冲板块相关.     

Scattered PKKP: Further evidence for scattering at a rough core-mantle boundary

PKKP signals from Novaya Zemlya recorded at LASA at distances around 60° show consistent anomalies in both slowness and azimuth. The observed anomaly suggests that the signal is a BC branch arrival, although the arrival time corresponds to the DF branch. The BC branch, however, does not extend back to this distance. The azimuth of approach is in the range 229–245°, instead of the expected 186°. These anomalies are associated only with PKKP; analysis of the core phases PKiKP and P′P′ (BC) from the same events show that they arrived at LASA with the appropriate slownesses and azimuths.The PKKP signals can be interpreted as “scattered” PKKP; the scattering occurs on underside reflection at the core-mantle boundary and is probably caused by topographic irregularities on the boundary itself. The calculated scattering region has a surface projection at about 60°S, 134°E, which is outside the diametral plane through source and receiver, and about 21° from the expected PKKP reflection point at 76°S, 95°E.Both the “direct” and “scattered” arms of the PKKP signal have a PK path close to that of the “C” end of the BC branch. The unexpectedly large amplitude of the arrival suggests that there may be a focusing of energy at C, which would indicate a change in velocity gradient just above the inner core boundary. The observations nevertheless require, on the scattering interpretation, lateral variations in the topography of the core-mantle boundary and a region of relatively large topography responsible for the anomalous PKKP observations.     

Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction

Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y ₂² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core.     

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.     

The interaction of elastic waves with a solid-liquid interface,with applications to the core-mantle boundary

The paper discusses basic ideas and principles underlying methods, which have proved useful in the interpretation of diffraction and scattering phenomena by a smooth or slightly rough solid-liquid interface. Generally, the wave interaction may be formulated as an excitation problem; it involves (1) finding an equivalent dislocation or source distribution on the interface, and (2) evaluating the excited wave field. These steps are taken through perturbation theory and/or adopting the appropriate generalization of ray theory. In this context an explicit form of Green's function is also given. The methods have been applied to the core-mantle boundary, with a view toward the interpretation of recent data: (a) diffracted P and S waves around the core (in particular, their attenuation); (b) scattered short-period core phases (in particular, precursors to PKP and PKKP). Other types of wave interaction, and implications for models of the core-mantle boundary structure, are briefly mentioned.Paper presented at the EGS/ESC workshop on Generation and propagation of seismic waves in Neustadt, Federal Republic of Germany, August 1978.     

The radius of the core-mantle boundary inferred from travel time and free oscillation data; A critical review

A review is given of the present status of the information on the core radius, indicating its most likely value, but with the understanding that it must be made compatible with the remaining features of the Standard Earth Model, which are not known to us at the present time.