<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Explicit Construction of the Modified Spherical Harmonic Series for the Gravity Gradients and Analysis of their Characteristics

Central (Pulkovo) Astronomical Observatory, Russian Academy of Sciences, Pulkovskoe Shosse 65/1, St. Petersburg, 196140, Russia

Artificial Satellites

The present paper complements the research carried out in PV2008 (Petrovskaya and Vershkov, 2008), concerning the expansion of the gravity gradients in the...

Explicit Construction of the Modified Spherical Harmonic Series for the Gravity Gradients and Analysis of their Characteristics

Online veröffentlicht: 05. Feb. 2009

Seitenbereich: 185 - 214

DOI: https://doi.org/10.2478/v10018-009-0001-z

Schlüsselwörter
Gravity gradients, Modified spherical harmonic expansions, Spectral coefficients, Degree variances, Digital maps for the gravity gradients in Fennoscandia region

This content is open access.

Explicit Construction of the Modified Spherical Harmonic Series for the Gravity Gradients and Analysis of their Characteristics

Online veröffentlicht: 05. Feb. 2009

Seitenbereich: 185 - 214

DOI: https://doi.org/10.2478/v10018-009-0001-z

SchlüsselwörterGravity gradients, Modified spherical harmonic expansions, Spectral coefficients, Degree variances, Digital maps for the gravity gradients in Fennoscandia region

This content is open access.

Schlüsselwörter
Gravity gradients, Modified spherical harmonic expansions, Spectral coefficients, Degree variances, Digital maps for the gravity gradients in Fennoscandia region