Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43929058" target="_blank" >RIV/49777513:23520/17:43929058 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00190-016-0951-4" target="_blank" >http://dx.doi.org/10.1007/s00190-016-0951-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-016-0951-4" target="_blank" >10.1007/s00190-016-0951-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

Popis výsledku v původním jazyce

New spherical integral formulas among components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second and third-order gravitational tensors and initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (i) vertical-vertical, (ii) vertical-horizontal and (iii) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the correctness of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy

Název v anglickém jazyce

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

Popis výsledku anglicky

New spherical integral formulas among components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second and third-order gravitational tensors and initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (i) vertical-vertical, (ii) vertical-horizontal and (iii) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the correctness of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10508 - Physical geography

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

2017

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF GEODESY

ISSN

0949-7714

e-ISSN

—

Svazek periodika

91

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

27

Strana od-do

167-194

Kód UT WoS článku

000394264400004

EID výsledku v databázi Scopus

2-s2.0-84990854042