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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

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/GA21-13713S" target="_blank" >GA21-13713S: Uncertainty estimates for integral transformations in geodesy</a><br>

Continuities

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

Publication year

2024

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

1432-1394

Volume of the periodical

98

Issue of the periodical within the volume

6

Country of publishing house

DE - GERMANY

Number of pages

27

Pages from-to

—

UT code for WoS article

001259769400001

EID of the result in the Scopus database

2-s2.0-85195610144