IF 1 Q3 GEOCHEMISTRY & GEOPHYSICS Geodynamics Pub Date : 2019-07-01 DOI:10.23939/jgd2019.01.017
M. Fys, A. Brydun, M. Yurkiv, А. R. Sohor
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引用次数: 0

摘要

目的。在考虑任意阶斯托克斯常数的情况下,建立行星及其导数的三维质量分布函数的算法。基于这种方法,任务是对地球内部结构进行研究。方法。用双正交多项式的线性组合来表示非均匀质量分布的导数,其系数由方程组获得。这些方程是由Stokes常数的积分变换得出的,计算过程是通过顺序近似进行的,对于初始近似,我们采用一维密度模型,该模型与Stokes常数一致,直到第二次包含阶。然后,确定高阶势的展开系数,直至预定阶。在这种情况下,曲面积分密度的幂矩信息使得分析和控制迭代过程成为可能。结果。根据所描述的算法,利用该软件进行了计算。实现了三维质量分布函数的相当高的近似度(六阶)。卡托图是根据三维平均分布的偏差值(“等差”)创建的,它提供了地球内部结构的相当详细的图像。所呈现的特征深度(2891公里的地核-地幔,5150公里的内-外地核)的“非均匀性”图使我们能够得出关于全球物质运动的初步结论。同时,衍生品信息对解释具有重要意义。首先,需要注意的是,“非均匀性”的梯度是指向质心的。该梯度在垂直于旋转轴(水平面)的平面上的投影显示了空间位移的趋势。科学的新奇。梯度的矢量图与图相结合,给出了行星内部质量运动的动力学和可能机制的广泛图景。这些研究在一定程度上证实了质量的引力对流现象。现实意义。该算法可用于建立地球区域模型,数值结果可用于解释地球内部和表面的全球和局部地球动力学过程。
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GEODYNAMICS
Purpose. To create an algorithm for constructing a three-dimensional masses distribution function of the planet and its derivatives taking into account the Stokes constants of arbitrary orders. Being based on this method, the task is to perform the research on the internal structure of the Earth. Methodology. The derivatives of the inhomogeneous mass distribution are presented by linear combinations of biorthogonal polynomials which coefficients are obtained from the system of equations. These equations follow from integral transformations of the Stokes constants, the calculation process is carried out by a sequential approximation and for the initial approximation we take a one-dimensional density model that is consistent with Stokes constants up to the second inclusive order. Next, the coefficients of expansion of the potential of higher orders are determined up to a predetermined order. In this case, the information on the power moments of the density of surface integrals makes it possible to analyze and control the iterative process. Results. The results of calculations using the software according to the described algorithm are obtained. A fairly high degree of approximation (sixth order) of three-dimensional mass distributions function is achieved. Carto diagrams were created being based on the values of deviations of the three-dimensional average distributions (“isodens”), which give a fairly detailed picture of the Earth’s internal structure. The presented maps of “inhomogeneity’s” at characteristic depths (2891 km core – mantle, 5150 km internal – external core) allow us to draw preliminary conclusions about global mass movements. At the same time, the information on derivatives is significant for interpretation. First of all, it should be noted that the gradient of “inhomogeneity’s” is directed toward the center of mass. The presented projections of this gradient on a plane perpendicular to the rotation axis (horizontal plane) show the tendency of spatial displacements. Scientific novelty. Vector diagrams of the gradient, in combination with carto diagrams, give a broad picture of the dynamics and possible mechanisms of mass movement within the planet. To a certain extent, these studies confirm the phenomenon of gravitational convection of masses. Practical significance. The proposed algorithm can be used in order to build regional models of the planet, and numerical results can be used to interpret global and local geodynamic processes inside and on the Earth’s surface.
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Geodynamics
Geodynamics GEOCHEMISTRY & GEOPHYSICS-
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33.30%
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GEODYNAMICS GEODYNAMICS GEODYNAMICS GEODYNAMICS GEODYNAMICS
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