Non-singular expressions for the spherical harmonic synthesis of gravitational curvatures in a local north-oriented reference frame

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43927457" target="_blank" >RIV/49777513:23520/16:43927457 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cageo.2015.12.011" target="_blank" >http://dx.doi.org/10.1016/j.cageo.2015.12.011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cageo.2015.12.011" target="_blank" >10.1016/j.cageo.2015.12.011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Non-singular expressions for the spherical harmonic synthesis of gravitational curvatures in a local north-oriented reference frame

Popis výsledku v původním jazyce

Third-order gradients of the gravitational potential (gravitational curvatures) have already found some applications in geosciences. Observability of these parameters, describing the Earth's gravitational field in a more complex way than any other currently available gravitational parameter, such as gravitational acceleration (first-order gradient) or gravitational (second-order) gradient, is currently discussed by physicists. Moreover, first designs of observational devices (sensors) have already been proposed. The spherical harmonic analysis and synthesis are the common tools used by geoscientists to study spectral properties of various functionals of the Earth's gravitational potential. However, the conventional spherical harmonic expansions of the gravitational curvatures in the local north-oriented reference frame have rather complicated forms that depend on the first-, second- and third-order derivatives of the associated Legendre functions. Moreover, some of these expansions also contain singular terms at the poles. In this article, the conventional series are transformed to new simpler and non-singular forms based on relations between the associated Legendre functions and their derivatives. Numerical experiments demonstrate the applicability and correctness of the new expressions.

Název v anglickém jazyce

Non-singular expressions for the spherical harmonic synthesis of gravitational curvatures in a local north-oriented reference frame

Popis výsledku anglicky

Third-order gradients of the gravitational potential (gravitational curvatures) have already found some applications in geosciences. Observability of these parameters, describing the Earth's gravitational field in a more complex way than any other currently available gravitational parameter, such as gravitational acceleration (first-order gradient) or gravitational (second-order) gradient, is currently discussed by physicists. Moreover, first designs of observational devices (sensors) have already been proposed. The spherical harmonic analysis and synthesis are the common tools used by geoscientists to study spectral properties of various functionals of the Earth's gravitational potential. However, the conventional spherical harmonic expansions of the gravitational curvatures in the local north-oriented reference frame have rather complicated forms that depend on the first-, second- and third-order derivatives of the associated Legendre functions. Moreover, some of these expansions also contain singular terms at the poles. In this article, the conventional series are transformed to new simpler and non-singular forms based on relations between the associated Legendre functions and their derivatives. Numerical experiments demonstrate the applicability and correctness of the new expressions.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

DE - Zemský magnetismus, geodesie, geografie

OECD FORD obor

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Projekt

<a href="/cs/project/GA15-08045S" target="_blank" >GA15-08045S: Metody validace, zpracování a použití dat družicových misí v geodézii a geofyzice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

COMPUTERS &amp; GEOSCIENCES

ISSN

0098-3004

e-ISSN

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Svazek periodika

88

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

152-162

Kód UT WoS článku

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EID výsledku v databázi Scopus

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