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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10508 - Physical geography

Project

<a href="/en/project/GA15-08045S" target="_blank" >GA15-08045S: Methods for validation, analysis and application of data from satellite missions in geodesy and geophysics</a><br>

Continuities

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

Publication year

2017

Confidentiality

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

Name of the periodical

JOURNAL OF GEODESY

ISSN

0949-7714

e-ISSN

—

Volume of the periodical

91

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

27

Pages from-to

167-194

UT code for WoS article

000394264400004

EID of the result in the Scopus database

2-s2.0-84990854042