Does Poisson's downward continuation give physically meaningful results?

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43929709" target="_blank" >RIV/49777513:23520/17:43929709 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11200-016-1167-z" target="_blank" >http://dx.doi.org/10.1007/s11200-016-1167-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11200-016-1167-z" target="_blank" >10.1007/s11200-016-1167-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Does Poisson's downward continuation give physically meaningful results?

Popis výsledku v původním jazyce

The downward continuation (DWC) of the gravity anomalies from the Earth surface to the geoid is still probably the most problematic step in the precise geoid determination. It is this step that motivates the quasi-geoid users to opt for Molodenskij’s rather than Stokes’s theory. The reason for this is that the DWC is perceived as suffering from two major flaws: first, a physically meaningful DWC technique requires the knowledge of the irregular topographical density; second, the Poisson DWC which is the only physically meaningful technique we know, presents itself mathematically in the form of Fredholm integral equation of 1st kind. As Fredholm integral equations are often numerically ill-conditioned this makes some people believe that the DWC problem is physically ill-posed. According to a revered French mathematician Hadamard, the DWC problem is physically well-posed and as such gives always a finite and unique solution. The necessity of knowing the topographical density is, of course, a real problem but one that is being solved with an ever increasing accuracy; so sooner or later it will allow us to determine the geoid with the centimetre accuracy.

Název v anglickém jazyce

Does Poisson's downward continuation give physically meaningful results?

Popis výsledku anglicky

The downward continuation (DWC) of the gravity anomalies from the Earth surface to the geoid is still probably the most problematic step in the precise geoid determination. It is this step that motivates the quasi-geoid users to opt for Molodenskij’s rather than Stokes’s theory. The reason for this is that the DWC is perceived as suffering from two major flaws: first, a physically meaningful DWC technique requires the knowledge of the irregular topographical density; second, the Poisson DWC which is the only physically meaningful technique we know, presents itself mathematically in the form of Fredholm integral equation of 1st kind. As Fredholm integral equations are often numerically ill-conditioned this makes some people believe that the DWC problem is physically ill-posed. According to a revered French mathematician Hadamard, the DWC problem is physically well-posed and as such gives always a finite and unique solution. The necessity of knowing the topographical density is, of course, a real problem but one that is being solved with an ever increasing accuracy; so sooner or later it will allow us to determine the geoid with the centimetre accuracy.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10508 - Physical geography

Projekt

<a href="/cs/project/GA15-08045S" target="_blank" >GA15-08045S: Metody validace, zpracování a použití dat družicových misí v geodézii a geofyzice</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Studia Geophysica et Geodaetica

ISSN

0039-3169

e-ISSN

—

Svazek periodika

61

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

17

Strana od-do

412-428

Kód UT WoS článku

000406827400002

EID výsledku v databázi Scopus

2-s2.0-85009469091