Application of the one-step integration method for determination of the regional gravimetric geoid

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43955551" target="_blank" >RIV/49777513:23520/19:43955551 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00190-019-01272-8" target="_blank" >https://doi.org/10.1007/s00190-019-01272-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-019-01272-8" target="_blank" >10.1007/s00190-019-01272-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Application of the one-step integration method for determination of the regional gravimetric geoid

Popis výsledku v původním jazyce

The regional gravimetric geoid solved using boundary-value problems of the potential theory is usually determined in two computational steps: (1) downward continuing ground gravity data onto the geoid using inverse Poisson’s integral equation in a mass-free space and (2) evaluating geoidal heights by applying Stokes integral to downward continued gravity. In this contribution, the two integration steps are combined in one step and the so-called one-step integration method in spherical approximation is implemented to compute the regional gravimetric geoid model. Advantages of using the one-step integration method instead of the two integration steps include less computational cost, more stable numerical computation and better utilization of input ground gravity data (reduced in each integration step to avoid edge effects). A discrete form of the one-step integral equation is used to convert mean values of ground gravity anomalies into mean values of geoidal heights. To evaluate mean values of the integral kernel in the vicinity of the computation point, a fast and numerically accurate analytical formula is proposed using planar approximation. The proposed formula is tested to determine the regional gravimetric geoid of the Auvergne test area, France. Results show a good agreement of the estimated geoid with geoidal heights estimated at GNSS-levelling reference points, with the standard deviation for the difference of 3.3 cm. Considering the uncertainty of geoidal heights derived at the GNSS/levelling reference points, one can conclude the geoid models computed by the one-step and two-step integration methods have negligible differences. Thus, the one-step method can be recommended for regional geoid modelling with its methodological and numerical advantages.

Název v anglickém jazyce

Application of the one-step integration method for determination of the regional gravimetric geoid

Popis výsledku anglicky

The regional gravimetric geoid solved using boundary-value problems of the potential theory is usually determined in two computational steps: (1) downward continuing ground gravity data onto the geoid using inverse Poisson’s integral equation in a mass-free space and (2) evaluating geoidal heights by applying Stokes integral to downward continued gravity. In this contribution, the two integration steps are combined in one step and the so-called one-step integration method in spherical approximation is implemented to compute the regional gravimetric geoid model. Advantages of using the one-step integration method instead of the two integration steps include less computational cost, more stable numerical computation and better utilization of input ground gravity data (reduced in each integration step to avoid edge effects). A discrete form of the one-step integral equation is used to convert mean values of ground gravity anomalies into mean values of geoidal heights. To evaluate mean values of the integral kernel in the vicinity of the computation point, a fast and numerically accurate analytical formula is proposed using planar approximation. The proposed formula is tested to determine the regional gravimetric geoid of the Auvergne test area, France. Results show a good agreement of the estimated geoid with geoidal heights estimated at GNSS-levelling reference points, with the standard deviation for the difference of 3.3 cm. Considering the uncertainty of geoidal heights derived at the GNSS/levelling reference points, one can conclude the geoid models computed by the one-step and two-step integration methods have negligible differences. Thus, the one-step method can be recommended for regional geoid modelling with its methodological and numerical advantages.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10508 - Physical geography

Projekt

<a href="/cs/project/GA18-06943S" target="_blank" >GA18-06943S: Teorie zpracování gradientů geopotenciálu vyšších řádů a jejich použití v geodézii</a><br>

Návaznosti

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

Rok uplatnění

2019

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

—

Svazek periodika

93

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

14

Strana od-do

1631-1644

Kód UT WoS článku

000500186800025

EID výsledku v databázi Scopus

2-s2.0-85068236113