The radial integral of the geopotential

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43975725" target="_blank" >RIV/49777513:23520/25:43975725 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10712-025-09893-9" target="_blank" >https://link.springer.com/article/10.1007/s10712-025-09893-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10712-025-09893-9" target="_blank" >10.1007/s10712-025-09893-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The radial integral of the geopotential

Popis výsledku v původním jazyce

In Newtonian theory of gravitation, used in Earth’s and planetary sciences, gravitational acceleration is standardly regarded as the most fundamental parameter that describes any vectorial gravitational field. Considering only conservative gravitational field, the vectorial field can be described by a scalar function of 3D position called the gravitational potential from which other parameters (particularly the gravitational attraction and the gravitational gradient) are derived by applying the gradient operators. Gradients of the Earth’s gravity potential are nowadays measured with high accuracy and applied in various geodetic and geophysical applications. In geodesy, the gravity and gravity gradient measurements are used to determine the Earth’s gravity potential (i.e., the geopotential) that is related to geometry of equipotential surfaces, most notably the geoid approximating globally the mean sea surface. Reversely to the application of gradient operator, the application of radial integral to gravity yields the gravity potential differences and the same application to gravity gradient yields the gravity differences. This procedure was implemented in definitions of rigorous orthometric heights and differences between normal and orthometric heights (i.e., the geoid-to-quasigeoid separation). Following this concept, we introduce the radially integrated gravity potential (i.e., the geopotential), and provide mathematical definitions of this functional in spatial and spectral domains. We also define its relationship with other parameters of the Earth’s gravity field via Poisson, Hotine, and Stokes integrals. We then discuss prospects of using this functional in gravimetric geophysics in the context of interpreting the Earth’s inner structure. In numerical examples, we demonstrate that the indefinite radial integral of the disturbing potential (i.e., difference between actual and normal gravity potentials) has a spatial pattern that better exhibits a long-wavelength signature of deep mantle than the global geoidal geometry. This finding is explained by the fact that a more detailed spatial pattern attributed mainly to a lithospheric structure is filtered out proportionally with increasing degree of spherical harmonics in this functional. The global geoidal geometry, on the other hand, comprises not only a deep mantle signature but eventually also a gravitational signature of lithosphere, most notably across large orogens, even after applying spectral decompensation or filtering.

Název v anglickém jazyce

The radial integral of the geopotential

Popis výsledku anglicky

In Newtonian theory of gravitation, used in Earth’s and planetary sciences, gravitational acceleration is standardly regarded as the most fundamental parameter that describes any vectorial gravitational field. Considering only conservative gravitational field, the vectorial field can be described by a scalar function of 3D position called the gravitational potential from which other parameters (particularly the gravitational attraction and the gravitational gradient) are derived by applying the gradient operators. Gradients of the Earth’s gravity potential are nowadays measured with high accuracy and applied in various geodetic and geophysical applications. In geodesy, the gravity and gravity gradient measurements are used to determine the Earth’s gravity potential (i.e., the geopotential) that is related to geometry of equipotential surfaces, most notably the geoid approximating globally the mean sea surface. Reversely to the application of gradient operator, the application of radial integral to gravity yields the gravity potential differences and the same application to gravity gradient yields the gravity differences. This procedure was implemented in definitions of rigorous orthometric heights and differences between normal and orthometric heights (i.e., the geoid-to-quasigeoid separation). Following this concept, we introduce the radially integrated gravity potential (i.e., the geopotential), and provide mathematical definitions of this functional in spatial and spectral domains. We also define its relationship with other parameters of the Earth’s gravity field via Poisson, Hotine, and Stokes integrals. We then discuss prospects of using this functional in gravimetric geophysics in the context of interpreting the Earth’s inner structure. In numerical examples, we demonstrate that the indefinite radial integral of the disturbing potential (i.e., difference between actual and normal gravity potentials) has a spatial pattern that better exhibits a long-wavelength signature of deep mantle than the global geoidal geometry. This finding is explained by the fact that a more detailed spatial pattern attributed mainly to a lithospheric structure is filtered out proportionally with increasing degree of spherical harmonics in this functional. The global geoidal geometry, on the other hand, comprises not only a deep mantle signature but eventually also a gravitational signature of lithosphere, most notably across large orogens, even after applying spectral decompensation or filtering.

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

2025

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

46

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

33

Strana od-do

873-905

Kód UT WoS článku

001520038300001

EID výsledku v databázi Scopus

2-s2.0-105009525094