全球地幔对流的数值模拟及其动力学意义
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摘要
对国内外关于地幔对流的研究进行了广泛而深入的调研，现有的研究结果表明，地幔对流
是地球内部热能传递并将之转化为板块运动所需动能的一种有效途径，是导致地表观测场异常
如大地水准面异常、重力异常、地表地形和岩石圈内部应力场异常以及长期海平面变化、大陆
造山带和大洋盆地的形成、世界范围内地震和火山活动等方面的最主要原因。作者发现仍有几
个问题需加强研究，如板块运动中的环型成分的激发机制，地幔粘度的处理，实际资料的引入
等。作者的学位论文针对这几个问题进行了研究，获得了许多新的结果。本论文的贡献主要表
现在以下几个方面：
1) 、 建立了常粘度的高级数模型。为了深化认识和理解常粘度下球层中非线性自由热对
流格局及其随热动力学参数--瑞利数和球谐级数m的演化特征，将前人在球谐级数m=0时
的零级数模型发展为高级数模型(m=0，1，2，…，l)。前者仅能获得2-D南北向剖面，而本论文
的模型可以获得一系列的南北向、东西向和深度上的3-D剖面。结果表明，瑞利数在非线性自
由热对流中具有重要的影响，随着瑞利数的增大，对流的速率加快，热对流会逐渐成为球层中
的主要传热方式，高温热柱区扩张，对流胞的数目增多。随着级数m的增加，温度剖面中的扰
动区域相应于零级数模型的增多，而导致对流环数目亦增加，且其纵横比变大；
2) 、 建立了一维粘度扰动下的变粘度模型。通过假定粘度为常粘度背景下存在仅随纬度
变化的小横向扰动，将常粘度模型发展为变粘度地幔对流模型。对比了不同边界模型、深度和
瑞利数时的环型场的变化特征。注意到环型场能量主要集中在球层的中、上部区域，其速度仅
占总速度的几个百分点，这个比例几乎不随瑞利数的变化而改变，但其对流图样受瑞利数的影
响较大。环型场的对流形态和速度的分布特征表现出了明显的纬向差异；
3) 、建立了三维粘度扰动下的变粘度模型，引入了三维地震波速异常来约束模型。将仅
随纬度变化的粘度发展为三维粘度变化形式，提供了相应的求解方法。然后将地震波速异常转
换为地幔内部的温度和粘度异常，获得了极型场和环型场分布特征。
4) 、探讨了地幔浅部对流场与地表构造的关系，获得了新的认识。在地幔浅部的极型场对
流剖面不但与板块边界对应很好，还显示出(1) 各主要板块的运动方向和相对速率大小；(2)
欧亚大陆南缘、西北缘和东缘分别受到印度洋板块的北向、大西洋板块的南东向以及太平洋板
块的北西-西向的碰撞和挤压，因而在其南缘和东缘分别形成了巨型造山带和俯冲带，但是由
于大西洋板快的运动速率和方向基本与欧亚板块的一致，这可能是在欧亚大陆西北缘不存在巨
型造山带和俯冲带的原因：(3) 在非洲大陆东北部存在一个明显的发散中心，这可能是形成东
非大裂谷的深部动力学原因。(4) 参与欧亚大陆南缘和美洲西缘造山活动的主体可能分别是
400km以浅的印度洋板块和美洲大陆；太平洋板块可能俯冲到了400km以下的深度。
首次提供了地幔浅部的环型场对流剖面，并探讨了其与浅部构造的联系：(1) 在赤道附近
的大致南东东-北西西的强对流条带可能与环赤道大型剪切系统的存在相关：(2) 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。
中国地震局地球物理所博士学位论文
5)初步探讨了固体地球的差异旋转。论文对固体地球的差异旋转现象、速率、证据以及
可能的产生机制进行了概述，并对岩石圈和地慢之间祸合的儿种可能力矩的量级进行了简单的
估算。地球差异旋转可能会对地慢对流的对流形态产生重要的影响，因此结合岩石圈、地慢以
及地核间差异旋转的地慢对流模型可能会对认识和理解地表全球构造的形成和演化起到积极
作用。但作者现在还无法找到如何合理地将地球的这种运动引入到地慢对流模型中，期望专家
们能为它们的结合提供建议，也愿意和感兴趣的研究者进行讨论。
当然，论文目前的模型还需改进，在未来开展的研究中，应考虑用更多的地表观测资料和
数据，如大水准面异常和地表重力位数据以及GPS资料等来约束模型，依此可以用来预测其它
地球物理场的状态和分布规律，通过对比分析预测结果和实际观测数据分布的差异，调节模型
尽量接近地球地慢的真实对流情况，从而找到浅部构造的深部动力学背景。
Widely reading the papers with respect to mantle convection throughout the world, we found that mantle convection is an effective way to transport quantity of heat and transform it into the kinetic energy of plate motion, and causes the anomalies of surface observed fields, e.g. geoid anomalies, gravity anomalies, surface topography and stress field anomalies within the lithosphere. It is also the main reason of the secular variations of sea level, the formation of continental erogenic zone and oceanic basin as well as the seismic and volcanic activity all over the world. However, a few aspects still deserve on study at present, e.g. the mechanism of toroidal component of plate motion, how to deal with mantle viscosity and use observations. These problems above are studied and some new results are obtained in my Ph.D. thesis. The main contributions are as follows.
1) Setting up a high-order model. In order to understand further the patterns of thermal free convection with thermodynamic parameter- Rayleigh number and spherical-harmonic order m in a spherical shell, Zero-order model is developed into high-order model expanded the scalar poloidal and fluctuating temperature fields into Legendre polynomials with degree / = 6 and order m - 0, 1, 2, ..., l but not m = 0 only. Compared with zero-order model (degree 1 = 6 and order m = 0), from which only 2-D southerly (r) profiles can be obtained, high-order model can provide a series of southerly (r), easterly (r and radial velocity profiles. With Rayleigh number increasing, the convective motion becomes stronger, thermal convection becomes the main way of heat transportation, the hotter plume zone becomes wider, and the convection cells increases. With the addition of order m, the number of the fluctuating zone in temperature profiles increases, which causes the convective cell increase and its aspect ratio larger.
2) Setting up a variable viscosity model with one-dimensional viscosity fluctuations. A constant viscosity mantle convection model is developed into a variable viscosity model assumed a latitude-dependent viscosity with small fluctuations on the basis of a constant background value. The features of toroidal field are studied for different boundary conditions, Rayleigh numbers and depths. It is found that the energy of toroidal field mainly concentrates in the middle and upper parts of the shell, and the ratio, hardly dependent on Rayleigh number, of toroidal to total velocities amounts to only a few percents. Rayleigh number has great effects on the convection patterns of toroidal field. The convection patterns and velocities of toroidal field have distinct differences in latitudinal direction.
3) Setting up a variable model with 3-D viscosity fluctuations and introducing 3-D seismic wave velocity into the model. One-dimensional variable viscosity is developed into 3-D viscosity variations and the corresponding solution is presented. The seismic wave velocity is transformed into fluctuating temperature field and viscosity variations within the mantle, then the poloidal and toroidal fields are solved.
4) Discussing the relationships of the velocity field and surface tectonics, and getting some new results. In the shallow part of the mantle, not only the convergent and divergent zones in poloidal velocity profile are well consistent with plate boundaries, but the profile shows (1) the moving
direction and velocity of each main plate; (2) that the southern, northwestern, and eastern margins of Eurasian continent are collided and compressed by the northward moving Indian plate, the southeastward moving Atlantic plate and the northwest-westward moving Pacific plate, respectively. Therefore, the large erogenic zone and subduction zone occur in its southern and eastern margins. However, there are no these tectonics in its northwestern margin since the rate and direction of Atlantic plate is consistent with that of Eurasian plate; (3) There is a divergent zone in northeast Africa, which probably causes the East African Rift Valley; (4) It is possible that
是地球内部热能传递并将之转化为板块运动所需动能的一种有效途径，是导致地表观测场异常
如大地水准面异常、重力异常、地表地形和岩石圈内部应力场异常以及长期海平面变化、大陆
造山带和大洋盆地的形成、世界范围内地震和火山活动等方面的最主要原因。作者发现仍有几
个问题需加强研究，如板块运动中的环型成分的激发机制，地幔粘度的处理，实际资料的引入
等。作者的学位论文针对这几个问题进行了研究，获得了许多新的结果。本论文的贡献主要表
现在以下几个方面：
1) 、 建立了常粘度的高级数模型。为了深化认识和理解常粘度下球层中非线性自由热对
流格局及其随热动力学参数--瑞利数和球谐级数m的演化特征，将前人在球谐级数m=0时
的零级数模型发展为高级数模型(m=0，1，2，…，l)。前者仅能获得2-D南北向剖面，而本论文
的模型可以获得一系列的南北向、东西向和深度上的3-D剖面。结果表明，瑞利数在非线性自
由热对流中具有重要的影响，随着瑞利数的增大，对流的速率加快，热对流会逐渐成为球层中
的主要传热方式，高温热柱区扩张，对流胞的数目增多。随着级数m的增加，温度剖面中的扰
动区域相应于零级数模型的增多，而导致对流环数目亦增加，且其纵横比变大；
2) 、 建立了一维粘度扰动下的变粘度模型。通过假定粘度为常粘度背景下存在仅随纬度
变化的小横向扰动，将常粘度模型发展为变粘度地幔对流模型。对比了不同边界模型、深度和
瑞利数时的环型场的变化特征。注意到环型场能量主要集中在球层的中、上部区域，其速度仅
占总速度的几个百分点，这个比例几乎不随瑞利数的变化而改变，但其对流图样受瑞利数的影
响较大。环型场的对流形态和速度的分布特征表现出了明显的纬向差异；
3) 、建立了三维粘度扰动下的变粘度模型，引入了三维地震波速异常来约束模型。将仅
随纬度变化的粘度发展为三维粘度变化形式，提供了相应的求解方法。然后将地震波速异常转
换为地幔内部的温度和粘度异常，获得了极型场和环型场分布特征。
4) 、探讨了地幔浅部对流场与地表构造的关系，获得了新的认识。在地幔浅部的极型场对
流剖面不但与板块边界对应很好，还显示出(1) 各主要板块的运动方向和相对速率大小；(2)
欧亚大陆南缘、西北缘和东缘分别受到印度洋板块的北向、大西洋板块的南东向以及太平洋板
块的北西-西向的碰撞和挤压，因而在其南缘和东缘分别形成了巨型造山带和俯冲带，但是由
于大西洋板快的运动速率和方向基本与欧亚板块的一致，这可能是在欧亚大陆西北缘不存在巨
型造山带和俯冲带的原因：(3) 在非洲大陆东北部存在一个明显的发散中心，这可能是形成东
非大裂谷的深部动力学原因。(4) 参与欧亚大陆南缘和美洲西缘造山活动的主体可能分别是
400km以浅的印度洋板块和美洲大陆；太平洋板块可能俯冲到了400km以下的深度。
首次提供了地幔浅部的环型场对流剖面，并探讨了其与浅部构造的联系：(1) 在赤道附近
的大致南东东-北西西的强对流条带可能与环赤道大型剪切系统的存在相关：(2) 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。
中国地震局地球物理所博士学位论文
5)初步探讨了固体地球的差异旋转。论文对固体地球的差异旋转现象、速率、证据以及
可能的产生机制进行了概述，并对岩石圈和地慢之间祸合的儿种可能力矩的量级进行了简单的
估算。地球差异旋转可能会对地慢对流的对流形态产生重要的影响，因此结合岩石圈、地慢以
及地核间差异旋转的地慢对流模型可能会对认识和理解地表全球构造的形成和演化起到积极
作用。但作者现在还无法找到如何合理地将地球的这种运动引入到地慢对流模型中，期望专家
们能为它们的结合提供建议，也愿意和感兴趣的研究者进行讨论。
当然，论文目前的模型还需改进，在未来开展的研究中，应考虑用更多的地表观测资料和
数据，如大水准面异常和地表重力位数据以及GPS资料等来约束模型，依此可以用来预测其它
地球物理场的状态和分布规律，通过对比分析预测结果和实际观测数据分布的差异，调节模型
尽量接近地球地慢的真实对流情况，从而找到浅部构造的深部动力学背景。
Widely reading the papers with respect to mantle convection throughout the world, we found that mantle convection is an effective way to transport quantity of heat and transform it into the kinetic energy of plate motion, and causes the anomalies of surface observed fields, e.g. geoid anomalies, gravity anomalies, surface topography and stress field anomalies within the lithosphere. It is also the main reason of the secular variations of sea level, the formation of continental erogenic zone and oceanic basin as well as the seismic and volcanic activity all over the world. However, a few aspects still deserve on study at present, e.g. the mechanism of toroidal component of plate motion, how to deal with mantle viscosity and use observations. These problems above are studied and some new results are obtained in my Ph.D. thesis. The main contributions are as follows.
1) Setting up a high-order model. In order to understand further the patterns of thermal free convection with thermodynamic parameter- Rayleigh number and spherical-harmonic order m in a spherical shell, Zero-order model is developed into high-order model expanded the scalar poloidal and fluctuating temperature fields into Legendre polynomials with degree / = 6 and order m - 0, 1, 2, ..., l but not m = 0 only. Compared with zero-order model (degree 1 = 6 and order m = 0), from which only 2-D southerly (r) profiles can be obtained, high-order model can provide a series of southerly (r), easterly (r and radial velocity profiles. With Rayleigh number increasing, the convective motion becomes stronger, thermal convection becomes the main way of heat transportation, the hotter plume zone becomes wider, and the convection cells increases. With the addition of order m, the number of the fluctuating zone in temperature profiles increases, which causes the convective cell increase and its aspect ratio larger.
2) Setting up a variable viscosity model with one-dimensional viscosity fluctuations. A constant viscosity mantle convection model is developed into a variable viscosity model assumed a latitude-dependent viscosity with small fluctuations on the basis of a constant background value. The features of toroidal field are studied for different boundary conditions, Rayleigh numbers and depths. It is found that the energy of toroidal field mainly concentrates in the middle and upper parts of the shell, and the ratio, hardly dependent on Rayleigh number, of toroidal to total velocities amounts to only a few percents. Rayleigh number has great effects on the convection patterns of toroidal field. The convection patterns and velocities of toroidal field have distinct differences in latitudinal direction.
3) Setting up a variable model with 3-D viscosity fluctuations and introducing 3-D seismic wave velocity into the model. One-dimensional variable viscosity is developed into 3-D viscosity variations and the corresponding solution is presented. The seismic wave velocity is transformed into fluctuating temperature field and viscosity variations within the mantle, then the poloidal and toroidal fields are solved.
4) Discussing the relationships of the velocity field and surface tectonics, and getting some new results. In the shallow part of the mantle, not only the convergent and divergent zones in poloidal velocity profile are well consistent with plate boundaries, but the profile shows (1) the moving
direction and velocity of each main plate; (2) that the southern, northwestern, and eastern margins of Eurasian continent are collided and compressed by the northward moving Indian plate, the southeastward moving Atlantic plate and the northwest-westward moving Pacific plate, respectively. Therefore, the large erogenic zone and subduction zone occur in its southern and eastern margins. However, there are no these tectonics in its northwestern margin since the rate and direction of Atlantic plate is consistent with that of Eurasian plate; (3) There is a divergent zone in northeast Africa, which probably causes the East African Rift Valley; (4) It is possible that
引文
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