Far-zone effects for spherical integral transformations I: Formulas for the radial boundary value problem and its derivatives

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Far-zone effects for spherical integral transformations I: Formulas for the radial boundary value problem and its derivatives

Popis výsledku v původním jazyce

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&apos;s, Poisson&apos;s, and Stokes&apos;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.

Název v anglickém jazyce

Far-zone effects for spherical integral transformations I: Formulas for the radial boundary value problem and its derivatives

Popis výsledku anglicky

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&apos;s, Poisson&apos;s, and Stokes&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10508 - Physical geography

Projekt

<a href="/cs/project/GA23-07031S" target="_blank" >GA23-07031S: Elipsoidické modelování planetárních gravitačních polí</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Surveys in Geophysics

ISSN

0169-3298

e-ISSN

1573-0956

Svazek periodika

45

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

33

Strana od-do

977-1009

Kód UT WoS článku

001217450100002

EID výsledku v databázi Scopus

2-s2.0-85192085895