Far-zone effects for spherical integral transformations I: Formulas for the radial boundary value problem and its derivatives
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F24%3A43969671" target="_blank" >RIV/49777513:23520/24:43969671 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10712-023-09818-4" target="_blank" >https://link.springer.com/article/10.1007/s10712-023-09818-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10712-023-09818-4" target="_blank" >10.1007/s10712-023-09818-4</a>
Alternative languages
Result language
angličtina
Original language name
Far-zone effects for spherical integral transformations I: Formulas for the radial boundary value problem and its derivatives
Original language description
Integral transformations represent an important mathematical tool for gravitational field modelling. A basic assumption of integral transformations is the global data coverage, but availability of high-resolution and accurate gravitational data may be restricted. Therefore, we decompose the global integration into two parts: 1) the effect of the near zone calculated by the numerical integration of data within a spherical cap, and 2) the effect of the far zone due to data beyond the spherical cap synthesised by harmonic expansions. Theoretical and numerical aspects of this decomposition have frequently been studied for isotropic integral transformations on the sphere, such as Hotine's, Poisson's, and Stokes's integral formulas. In this article, we systematically review the mathematical theory of the far-zone effects for the spherical integral formulas, which transform the disturbing gravitational potential or its purely radial derivatives into observable quantities of the gravitational field, i.e., the disturbing gravitational potential and its radial, horizontal, or mixed derivatives of the first, second, or third order. These formulas are implemented in a Matlab software and validated in a closed-loop simulation. Selected properties of the harmonic expansions are investigated by examining the behaviour of the truncation error coefficients. The mathematical formulations presented here are indispensable for practical solutions of direct or inverse problems in an accurate gravitational field modelling or when studying statistical properties of integral transformations.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10508 - Physical geography
Result continuities
Project
<a href="/en/project/GA23-07031S" target="_blank" >GA23-07031S: Ellipsoidal modelling of planetary gravitational fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Surveys in Geophysics
ISSN
0169-3298
e-ISSN
1573-0956
Volume of the periodical
45
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
33
Pages from-to
977-1009
UT code for WoS article
001217450100002
EID of the result in the Scopus database
2-s2.0-85192085895