Uncertainties associated with integral-based solutions to geodetic boundary-value problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F24%3A43971832" target="_blank" >RIV/49777513:23520/24:43971832 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00190-024-01858-x" target="_blank" >https://link.springer.com/article/10.1007/s00190-024-01858-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-024-01858-x" target="_blank" >10.1007/s00190-024-01858-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Uncertainties associated with integral-based solutions to geodetic boundary-value problems

Popis výsledku v původním jazyce

Physical geodesy applies potential theory to study the Earth&apos;s gravitational field in space outside and up to a few km inside the Earth&apos;s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the 19th century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable, the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

Název v anglickém jazyce

Uncertainties associated with integral-based solutions to geodetic boundary-value problems

Popis výsledku anglicky

Physical geodesy applies potential theory to study the Earth&apos;s gravitational field in space outside and up to a few km inside the Earth&apos;s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the 19th century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable, the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10508 - Physical geography

Projekt

<a href="/cs/project/GA21-13713S" target="_blank" >GA21-13713S: Odhady nejistot pro integrální transformace v geodézii</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

Journal of Geodesy

ISSN

0949-7714

e-ISSN

1432-1394

Svazek periodika

98

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

27

Strana od-do

—

Kód UT WoS článku

001259769400001

EID výsledku v databázi Scopus

2-s2.0-85195610144