乌克兰国立理工大学的Mykhailo Fys和Mariana Yurkiv近日的研究，揭示了使用双正交级数表示地球内部的三维质量分布及其在研究行星内部结构中的应用。该研究于2023年12月21日发表于国际一流学术期刊《大地测量与地球动力学》杂志上。

研究人员为使用三维(双正交)多项式精确地确定这些系数，提出了几种可能的方法。通过将地球内部的质量分布函数及其内部势表示为级数，引入了一种计算引力能的算法。这种算法能够估计重力能量的波动。该算法的实现提供了确定地球作为天体偏离流体静力平衡状态的程度的手段。研究强调，由于上述方法已经进行了计算以验证其有效性和可靠性。因此，这个例子是用来说明研究行星内部结构的一种方法。

据研究人员介绍，利用从单个视点在椭球内近似的数学概念，来呈现地球内部的空间质量分布函数及其内部势。主要重点在于构建行星内部质量的体积分布，膨胀系数是斯托克斯常数的线性组合。

附：英文原文

Title: Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet

Author: Mykhailo Fys, Mariana Yurkiv, Andrii Brydun, Andrii Sohor

Issue&Volume: 2023/12/21

Abstract: This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential. The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional (biorthogonal) polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body. Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.

DOI: 10.1016/j.geog.2023.11.003

Source: https://www.sciencedirect.com/science/article/pii/S1674984723001003