EXPLICIT CONSTRUCTION OF THE MODIFIED SPHERICAL HARMONIC SERIES FOR THE GRAVITY GRADIENTS AND ANALYSIS OF THEIR CHARACTERISTICS

被引:0
|
作者
Petrovskaya, M. S. [1 ]
Vershkov, A. N. [1 ]
机构
[1] Russian Acad Sci, Cent Pulkovo Astron Observ, Pulkovskoe Shosse 65-1, St Petersburg 196140, Russia
来源
ARTIFICIAL SATELLITES-JOURNAL OF PLANETARY GEODESY | 2007年 / 42卷 / 04期
关键词
Gravity gradients; Modified spherical harmonic expansions; Spectral coefficients; Degree variances; Digital maps for the gravity gradients in Fennoscandia region;
D O I
10.2478/v10018-009-0001-z
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
The present paper complements the research carried out in PV2008 (Petrovskaya and Vershkov, 2008), concerning the expansion of the gravity gradients in the local north-oriented reference frame in orthogonal series of modified spherical harmonics. In PV2008 procedures are developed for recovering the orthogonal bases of these series. Then an idea is briefly described how the spectral relations can be obtained between the gravity gradients and the geopotential. However no explicit procedures are demonstrated for their derivation. In the present paper successive transformations are described for each derivative which convert the initial non-orthogonal expansion into the orthogonal series. The resulting spectral relations are applied for evaluating the harmonic coefficients of these series at different altitudes, on the basis of the geopotential model EGM2008. The corresponding degree variances are estimated. The new simple expressions for the gravity gradients are convenient for various applications. In the present paper they are implemented for constructing digital colored maps for Fennoscandia region which attracts much attention of geophysicists. These maps visually demonstrate an anomalous behavior of the gravity gradients in this area.
引用
收藏
页码:185 / 214
页数:30
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