On the distribution of anomalous mass within the Earth: forward models of the gravitational potential spectrum using ensembles of discrete mass elements

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We investigate forward models of the gravitational potential spectrum generated by ensembles of discrete sources of anomalous mass, having radial distributions with different statistical properties. Models with a random distribution of point source locations throughout the volume of the mantle produce spectra similar to that of the Earth only when the (absolute) source magnitudes increase strongly with depth, at least as d ^1.5. The effects of the geographic (latitude-longitude) distribution of source locations are generally unimportant in determining the general degree dependence of the potential spectrum. The dimensions of the sources are also of secondary importance, at least up to an angular diameter of about 40, i.e., continent-sized. Sources of this size confined to the upper mantle do not appear capable of producing the degree dependence of the observed geopotential spectrum; the low harmonics (2-4) in particular appear to require lower mantle sources of considerable strength. Further, at least some of these deep sources must be largely monopolar in nature, (i.e., uncompensated) due to the stronger depth attenuation of dipole (compensated) sources. Because topography on the core-mantle boundary must be either isostatically or dynamically compensated, it may contribute little strength to the observed potential spectrum.     

Spherical harmonic representation of the gravitational potential of discrete spherical mass elements

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We present expressions in a spherical harmonic framework for the gravitational potential of discrete point, surface, and volume mass elements located at any depth within a sphere. Through analysis of the spherical harmonic spectrum, insight is gained into the properties of the potentials arising from a variety of mass distributions. A point mass at the surface of a sphere displays the richest harmonic spectrum in all degrees; spectra become increasingly reddened as the source mass is distributed through larger elements of area or volume, or is located at greater depths below the surface of the reference sphere. The spectra of dipolar distributions, useful in representing compensated masses, are depressed, especially in the low harmonic degrees, relative to the spectra of monopole elements.     

Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.     

"数字地球"与对地观测

在２１世纪到来之际,人类向“数字地球”这一地球信息科学新领域发起了挑战。这是在信息社会、知识经济、可持续发展时代背景下,由空间科学、信息科学、地球科学和环境科学的相互交融,在全球及区域尺度上的一次大整合、大聚焦。是面向２１世纪地球系统科学思维模式的开拓大跳跃。对地观测技术系统的蓬勃发展,是“数字地球”的不可缺少的基础。数字地球的发展,离不开对地观测技术系统的支撑。     

The correspondence between gravitational attraction and surface displacement due to volume expansion

Summary. It is shown that the formulas for the calculation of surface displacement due to a volume source in a half-space may be derived from a potential of the same form as the gravitational potential. The similarity between these expressions allows the use of methods developed for gravity in the study of surface displacement. As an example of the applicability of the correspondence, an efficient algorithm is developed for the calculation of uplift due to volume expansion within a homogeneous half-space. The method may be generalized to three-dimensional volumes undergoing expansion in a half-space.     

海岸带与地球系统科学研究

从系统的定义出发, 本文简要回顾了提出地球系统科学的背景与过程。地球系统科学研究已经成为地学领域的研究焦点与热点,并带动和加速了地球信息机理、陆地地球系统科学和全球变化的研究。本文重点分析海岸带在地球系统中所处的特殊位置,海岸带研究在地球系统科学研究中起着重要作用。简要介绍海岸带科学前沿-海岸带海陆交互作用计划 （LOICZ）.