三维地震波速结构约束下的变黏度地幔对流及其动力学意义

建立了三维黏度扰动下的变黏度地幔对流模型，并提供了在引入地幔的三维地震波速度结构下相应的求解方法. 依此反演了瑞利数Ra = 106时，两种不同边界条件下的极、环型场对流图像，这有助于深化对地幔物质流动和大地构造运动的深部动力学过程的认识和理解. 研究结果表明，不但地幔浅部的极型场对流图像显示出了与大地构造运动的相关性并揭示了其深部动力学过程，更重要的是，地幔浅部的环型场对流图像首次为我们认识和理解板块构造的水平与旋转运动提供了重要的信息：环型场速度剖面中在赤道附近存在一条大致南东东—北西西向的强对流条带，可能与环赤道附近大型剪切带的形成相关，进而表明可能是该带强震发生的深部动力学背景；在南北半球存在的旋转方向相反的对流环表明它们整体上可能存在差异旋转.     

地幔对流与岩石层板块的相互耦合及影响──（Ⅰ）球腔中的自由热对流

板块运动是地幔对流的主要证据之一．同时，作为地球动力系统中一个相对独立部分，板块自身的存在和运动对地幔内部物质的流动形态有巨大影响．地幔内部的流动由两部分组成：一是由内部非绝热温度差异造成的自由对流解；另一部分是由在地表运动的板块所激发．作为系列工作的第一部分，本文研究球腔中的自由热对流问题．得到了对地幔对流研究有实际意义的下边界为自由、上边界为刚性情况下的临界瑞利数值，不同的瑞利数时球腔内流场和温度场的分布形态等．     

Convection model of post-glacial uplift

A new approach to analytical and numerical study of the process of the post-glacial uplifting of the Earth’s surface was proposed within the framework of a viscous model. Displacement of the Earth’s surface is considered as the motion of the density boundary due to chemico-density convection. It is shown that the incorporation of the non-Newtonian rheology at observed velocities of post-glacial uplifts requires an obligatory presence of faults in the lithosphere and gives rise to quasi-uniform motion of the mantle material, whose viscosity under the lithosphere is, on the average, sufficiently small and amounts to ～10¹⁹ Pa. The study of the stability of the constructed model of the post-glacial uplift considered as the chemico-density convection relative to the thermal convection shows that the velocity of thermal convection developing in the presence of a quasiuniform mantle flow related to the post-glacial recovery is ～1 m/yr.     

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.     

Mantle flow with existence of plates and generation of the toroidal field

The observed plate velocities contain two types of motions. The poloidal component is related to the formation of ridges and subduction zones and the toroidal field expresses the shearing of surface plates. One very important consideration in modeling flow in the earth's mantle is the existence and motion of the lithospheric plates. The motion of plates represents a large-scale circulation with strong viscous coupling to the mantle underneath. The mantle flow probably is neither a purely free convection driven by buoyancy forces due to nonadiabatic temperature gradients in the mantle nor a forced convection generated by boundary forces, but a mixed convection that combines the effects of boundary and buoyancy forces. We present, in this paper, the mixed convection model resulting in a surface velocity field that contains both the observed poloidal and toroidal components.     

利用地震层析成像数据计算地幔对流新模型的探讨

假设地幔地震层析成像数据对应的地幔横向不均匀结构是地幔热对流的结果. 将地震层析成像数据转化为地幔温度(或密度)不均匀分布，考虑热流体动力学的三个基本方程，顾及热输运方程中的非线性项，直接将地震层析成像转化的地幔温度不均匀分布作为内部荷载引入基本方程, 反演计算地幔对流. 本文在利用地震层析成像数据计算地幔对流模型的新理论和方法的基础上，用SH12WM13地震层析成像模型数据，计算了全球地幔对流格局. 结果表明，对流格局不仅依赖地震层析成像数据，而且在很大程度上受地幔动力学框架、热动力参数和边界条件的所确定的系统响应函数的影响. 显示了地幔中复杂的对流格局，特别是区域性层状对流以及多层对流环可能在地幔中存在的现象.     

Nonlinear free thermal convection in a spherical shell:A variable viscosity model

Introduction The velocity field of surface plate motion can be split into a poloidal and a toroidal parts.At the Earth′s surface,the toroidal component is manifested by the existence of transform faults,and the poloidal component by the presence of convergence and divergence,i.e.spreading and subduc-tion zones.They have coupled each other and completely depicted the characteristics of plate tec-tonic motions.The mechanism of poloidal field has been studied fairly clearly which is related to …     

板块绝对运动及地幔热对流

本文以板块绝对运动AM1-2模型为边界条件探讨了不同的瑞利数下地幔热对流模型.结果表明,瑞利数小于10000（529.41）时,地幔对流呈现以板块驱动图式,运动的极型场和环型场由板块运动激发,两种场占有差不多相同的功率.当瑞利数增加到接近或略超过最低临界值时（约1.5倍）,对流呈现出复杂状态:1.板块运动速率小于下伏地幔对流速率;2.区域性的双层对流环出现;3.对流谱成分发生变化;4.环型场仅在地幔很浅的区域中起作用,而在地幔深部对流图式中影响很小.     

黏滞分层地幔中密度异常驱动对流模型的研究

在地震层析成像计算的地幔密度异常直接驱动地幔对流的新方法的基础上,发展了在上、下地幔不同黏性结构框架下,密度异常驱动地幔对流的物理模型.利用 Grands和S12 WM13等地震层析成像模型推得的地幔密度异常分布,设置板块绝对运动极型场为运动上边界,考虑深度660km地震波不连续面为界的上、下地幔之间存在黏滞性的差异,直接反演了不同黏滞系数的双层地幔结构下地幔对流的模式.研究中选取地幔平均密度为ρ=5500kg/m3, 上层地幔平均黏滞系数为μ=1021Pa·s,计算了上、下地幔黏滞系数之比为1∶1, 1∶10, 1∶100和1∶1000时地幔大圆剖面、以及区域剖面上的流场.结果表明,两种模型在球谐展开1～13阶的范围内其对流的基本格局相似.当下地幔黏滞性超过上地幔的100倍时,下地幔流场速度与上地幔的流场速度相比显著减小,但是对流仍然表现出单层对流环的基本格局.论文还用 240km深度球面上的对流格局讨论了对流和全球构造之间的关系.     

利用多种地球物理观测资料直接反演地幔对流模型

假定地幔为一个均匀的、粘滞系数为常数、同时均匀分布放射性热源的流体球层,其内部存在的对流则由流体力学3个基本方程:运动方程、能量方程和连续性方程确定.如果假定地幔处于低瑞利数的状态（临界瑞利数1.5倍左右）,那么上述方程中的非线性项可以忽略不计.作为一类可能的模型,本文计算一组用6个边界条件确定6个未知数的线性方程组.这些条件包括板块绝对运动极型场、地球大地水准面异常和地震层析结果提供的地幔密度分布横向不均匀相应的“刚性地球”水准面异常等.模型计算表明:1.地幔中流体运动格局不仅受地幔热动力学参数（瑞利数）控制,而且强烈地受边界条件的影响.2.若不限定下边界为等温边界,则上、下地幔之间并不呈现出活动性明显差异;但是在模型瑞利数加大到一定值时,核-幔边界附近将出现一些局部的小尺度对流环.3.当模型瑞利数从很小增加时,对流格局将发生变化,这些格局可能反应由地幔热动力学参数决定的地幔固有特性.4.当瑞利数为50000和80000时,核-幔边界形变与PcP波得到的结果吻合较好.     

Hotspots,mantle convection and plate tectonics: A synthetic calculation

A model is developed that unifies vigorous hotspots with global-scale mantle convection and plate tectonics. The convection dynamics are assumed to generate flow patterns that emerge as closely packed polygonal cells in approaching the asthenosphere, and whose geometry is completely determined by a defining set of vigorous hotspots. Overlying viscously coupled rigid plates are driven with unique velocities (Euler vectors) at which the area integral of the shear forces is zero; these velocities are dynamically stable. The computed plate velocities, resulting from convection based on 15 hotspots, are compared with the velocities of plate motion models AM1-2 (Minster andJordan, 1978) and HS-NUVEL1 (Gripp andGordon, 1990), which combine transform fault geometries, magnetic anomalies and seismic data. The comparison shows a striking agreement for a majority of the plates. Geophysical implications of this numerical exercise are discussed.     

地震波速度约束的大横向黏度变化的地幔对流研究

本文将横向黏度变化提高到3个量级,获得了地震波速度结构约束下的大横向黏度变化的地幔浅部的极型场和环型场对流图像.与小横向黏度变化下的结果相比,本文的结果具有显著的改善.对极型场对流图像,主要体现在本文结果能更清楚地解释太平洋板块、大洋洲和南美洲以及东太平洋洋中脊处的现今运动状态;对环型场对流图像,能更合理地解释北太平洋...     

三维球壳地幔流动形式探讨

建立三维球壳模型，将地壳和地幔作为不可压缩牛顿粘性流体处理，考虑了大陆、大洋、洋脊及俯冲带的不同物性参数，利用有限元法求解流体运动的基本方程组，研究地幔流动、板块运动与大地构造之间的关系。计算表明，速度边界条件、粘度分布等是影响地幔流动形式的主要因素。若地表径向取应力边界条件，且径向速度自由，则没有封闭的对流环存在。计算得到的地表径向速度分布与全球的构造分区具有显著的对应关系：在岛弧区、造山区速度向上运动，在大洋区、边缘海及裂谷区速度向下运动。     

横向黏度变化对球层中热对流的影响

本文在常黏度的基础上,加上横向黏度变化,纯粹研究了横向黏度变化对球层中热对流的影响.结果表明,横向黏度变化可以加速或阻碍球层中的热对流,并对球层中热传输方式有调节作用,但是横向黏度变化对球层中热对流的影响会限制在一定的强度范围内,并且难以改变球层中热对流的格局.横向黏度变化所产生的环型场速度占总速度场的比例最多为十几个百分点,难以解释观测到的地表板块运动中的环型场能量大小.     

Two-dimensional mantle flow beneath a rigid accreting lithosphere

This study considers two-dimensional mantle flow beneath a rigid lithosphere. The lithosphere which forms the upper boundary of a convecting region moves with a prescribed uniform horizontal velocity, and thickens with distance from the accreting plate boundary as it cools. Beneath the lithosphere, the mantle deforms viscously by diffusion creep and is heated radiogenically from within. Solutions for thermal convection beneath the lithosphere are obtained by finite-difference methods. Two important conclusions have resulted from this study: (1) convective patterns of large aspect ratio are stable beneath a rigid moving lithosphere; (2) even for a lithosphere velocity as small as 3 cm/yr. and a Rayleigh number as large as 10⁶, mantle circulation with large aspect ratio is driven dominantly by the motion of the lithosphere rather than by temperature gradients within the flow. Gravity, topography and heat flow are determined and implications for convection in the upper mantle are discussed.     

Long wavelength thermal convection between non-conducting boundaries

Non-linear Rayleigh-Bénard convection in a fluid layer is considered as a model of convection in the Earth's upper mantle. Previous studies have shown that when the temperature is held fixed at one of the boundaries of the layer, convection takes place in cells of width of the order of the layer depth or less. We investigate the effects of a different thermal boundary condition, in which the flux of heat is held fixed on both layer boundaries; then if this flux is just greater than that required for the onset of convection, motion takes place on horizontal scales much greater than the layer depth. An analytical treatment of the equations, based on an expansion in the depth-to-width ratio of the cells, shows that cells of a definite horizontal scale are the fastest growing according to linearised theory, but that these cells are unstable to ones of larger wavelength than themselves. Thus the dominant wavelength lengthens with time. The results hold whether the heat flux is generated internally of comes from beneath the layer. These results produce flow patterns similar to those found when the heat flux is much greater than the critical value. The results have important consequences for the understanding of mantle convection.     

环渤海地区的地震层析成像与地壳上地幔结构

利用环渤海地区的天然地震P波到时资料，采用纬度和经度方向分别为05°×06°的网格划分，反演了该地区地壳上地幔的三维P波速度结构.初步结果表明，环渤海地区地壳上地幔的速度结构具有明显的横向不均匀性：京津唐地区地壳中上部的速度异常反映了浅表层的地质构造特征，造山带和隆起区对应于高速异常，坳陷区和沉积盆地对应于低速异常；地壳下部出现大规模的低速异常与华北地区广泛存在的高导层相对应，估计与壳内的滑脱层和局部熔融、岩浆活动有关；莫霍面附近的速度异常反映了地壳厚度的变化及壳幔边界附近热状态的差异；上地幔顶部大范围的低速异常可能是上地幔软流层热物质大规模上涌所致.     

地幔对流与岩石层板块的相互耦合及影响──（Ⅱ）地幔混合对流理论及其应用

观测到的板块运动包含两种能量分布几乎相等的运动形态：极型场和环型场．纯粹的由热驱动的地幔自由对流不能预期和解释环型运动的产生．本文提出地幔混合对流理论，既考虑了热驱动的自由对流，也考虑了由板块自身激发的强迫对流．根据板块处于动力学平衡状态的观测事实，建立了相应的模型．数值结果表明，根据混合对流模型所预期的板块速度场，既能产生极型场，也能产生环型场，而且在空间分布特征及功率谱分布上与观测资料符合相当好．地幔物质的上升流动基本和洋脊对应，而下降流动和俯冲带对应．     

地幔对流与岩石层板块的相互耦合及影响──（Ⅱ）地幔混合对流理论及其应用

观测到的板块运动包含两种能量分布几乎相等的运动形态：极型场和环型场．纯粹的由热驱动的地幔自由对流不能预期和解释环型运动的产生．本文提出地幔混合对流理论，既考虑了热驱动的自由对流，也考虑了由板块自身激发的强迫对流．根据板块处于动力学平衡状态的观测事实，建立了相应的模型．数值结果表明，根据混合对流模型所预期的板块速度场，既能产生极型场，也能产生环型场，而且在空间分布特征及功率谱分布上与观测资料符合相当好．地幔物质的上升流动基本和洋脊对应，而下降流动和俯冲带对应．     

A note on convection in the earth's mantle

In the present note a boundary-layer model of thermal convection throughout the mantle is outlined. It is shown that recent criticisms of mantle-wide convection by A.E. Ringwood do not apply to this model. The phase transitions discussed by Ringwood are consistent with the model, and in fact provide an additional driving force for the convective motion. It is further noted that the model offers explanations of the core-mantle coupling hypothesized by R. Hide from consideration of correlations between the earth's magnetic and gravity fields, and of the appearance in several parts of the world of pairs of trenches separated by distances of the order of 2000 km.