About: Analytical Continuation in Physical Geodesy Constructed by Means of Tools and Formulas Related to an Ellipsoid of Revolution

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In physical geodesy mathematical tools applied for solving problems of potential theory are often essentially associated with the concept of the so-called spherical approximation (interpreted as a mapping). The same holds true for the method of analytical (harmonic) continuation which is frequently considered as a means suitable for converting the ground gravity anomalies or disturbances to corresponding values on the level surface that is close to the original boundary. In the development and implementation of this technique the key role has the representation of a harmonic function by means of the famous Poisson’s formula and the construction of a radial derivative operator on the basis of this formula. In this contribution an attempt is made to avoid spherical approximation mentioned above and to develop mathematical tools that allow implementation of the concept of analytical continuation also in a more general case, in particular for converting the ground gravity anomalies or disturbances to corresponding values on the surface of an oblate ellipsoid of revolution. The respective integral kernels are constructed with the aid of series of ellipsoidal harmonics and their summation, but also the mathematical nature of the boundary date is discussed in more details. In physical geodesy mathematical tools applied for solving problems of potential theory are often essentially associated with the concept of the so-called spherical approximation (interpreted as a mapping). The same holds true for the method of analytical (harmonic) continuation which is frequently considered as a means suitable for converting the ground gravity anomalies or disturbances to corresponding values on the level surface that is close to the original boundary. In the development and implementation of this technique the key role has the representation of a harmonic function by means of the famous Poisson’s formula and the construction of a radial derivative operator on the basis of this formula. In this contribution an attempt is made to avoid spherical approximation mentioned above and to develop mathematical tools that allow implementation of the concept of analytical continuation also in a more general case, in particular for converting the ground gravity anomalies or disturbances to corresponding values on the surface of an oblate ellipsoid of revolution. The respective integral kernels are constructed with the aid of series of ellipsoidal harmonics and their summation, but also the mathematical nature of the boundary date is discussed in more details. (en)
Title	Analytical Continuation in Physical Geodesy Constructed by Means of Tools and Formulas Related to an Ellipsoid of Revolution Analytical Continuation in Physical Geodesy Constructed by Means of Tools and Formulas Related to an Ellipsoid of Revolution (en)
skos:prefLabel	Analytical Continuation in Physical Geodesy Constructed by Means of Tools and Formulas Related to an Ellipsoid of Revolution Analytical Continuation in Physical Geodesy Constructed by Means of Tools and Formulas Related to an Ellipsoid of Revolution (en)
skos:notation	RIV/00025615:_____/14:#0002083!RIV15-GA0-00025615
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0090), P(GA14-34595S)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Nesvadba, Otakar Holota, Petr
http://linked.open.../riv/druhVysledku	A(V) - Audiovizuální tvorba se vzdáleným přístupem
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Výzkumný ústav geodetický, topografický a kartografický, v.v.i.
http://linked.open...dnocenehoVysledku	2885
http://linked.open...ai/riv/idVysledku	RIV/00025615:_____/14:#0002083
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Earth’s gravity field; linear gravimetric boundary value problem; integral representation of the solution; Neumann’s function; vertical derivative of the disturbing potential; vertical gradient of gravity (en)
http://linked.open.../riv/klicoveSlovo	Earth’s gravity field Neumann’s function integral representation of the solution linear gravimetric boundary value problem vertical derivative of the disturbing potential vertical gradient of gravity
http://linked.open...i/riv/kodPristupu	L
http://linked.open...ontrolniKodProRIV	[B87E4CE2A0D8]
http://linked.open...i/riv/mistoVydani	Vienna
http://linked.open...telVyzkumneZpravy	European Geosciences Union
http://linked.open...in/vavai/riv/obor	DE
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	NTIS - New Technologies for Information Society Mathematical methods for Earth’s gravity field studies
http://linked.open...UplatneniVysledku	2014
http://linked.open...iv/tvurceVysledku	Holota, Petr Nesvadba, Otakar

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