Local Multiscale Modelling of Geoid Undulations from Deflections of the Vertical

Freeden, Willi; Schreiner, Michael

doi:10.1007/s00190-005-0017-5

Cited by 39 publications

(14 citation statements)

References 12 publications

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“…Such regularizations of Green's function for the Beltrami operator have first been introduced in Freeden and Schreiner (2006) and Fehlinger et al (2007Fehlinger et al ( , 2008. In geomagnetic applications they have been used in Freeden and Gerhards (2010) and Gerhards (2011aGerhards ( , 2012.…”

Section: Green's Function For the Beltrami Operatormentioning

confidence: 98%

Multiscale Modeling of the Geomagnetic Field and Ionospheric Currents

Gerhards¹

2014

Handbook of Geomathematics

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This chapter gives a brief overview on the application of multiscale techniques to the modeling of geomagnetic problems. Two approaches are presented: one focusing on the construction of scaling and wavelet kernels in frequency domain and the other one focusing on a spatially oriented construction resulting in locally supported wavelets. Both approaches are applied exemplarily to the modeling of the crustal field, the reconstruction of radial current systems, and the definition of a multiscale power spectrum.

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Section: Green's Function For the Beltrami Operatormentioning

confidence: 98%

Multiscale Modeling of the Geomagnetic Field and Ionospheric Currents

Gerhards¹

2014

Handbook of Geomathematics

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“…Z odklonom navpičnice in geoidno višino je podana lega geoida glede na elipsoid v točki. Odklon navpičnice v obravnavani točki podaja informacijo o horizontalnem gradientu (naklonu) ploskve geoida (Freeden, Schreiner, 2006). Postopek izračuna ploskve geoida iz odklonov navpičnice je znan kot astronomonski nivelman (Hofmann-Wellenhof, Moritz, 2005).…”

Section: Uvodunclassified

Determination of deflection of the vertical from geoid heights

Kuhar¹,

Okorn²,

Stopar³

2010

geod. vestn.

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“…This second version is of special interest when working on spherical geometries, as is the case in geomagnetic modeling from satellite data (see, e.g., Backus et al 1996;Maier 2005;Sabaka et al 2010), but also in physical geodesy (e.g., Fehlinger et al 2008;Freeden and Schreiner 2006;Heiskanen and Moritz 1967) or ocean circulation (e.g., Fehlinger et al 2007;Freeden et al 2005;Pedlosky 1979;Stewart 2005). Representation (1.2) can be regarded as a decomposition of functions f : → R 3 that are only defined on the unit sphere = {x ∈ R 3 | r = |x| = 1}.…”

Section: Introductionmentioning

confidence: 98%

Spherical decompositions in a global and local framework: theory and an application to geomagnetic modeling

Gerhards

2011

Int J Geomath

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This paper gives an overview on decompositions of vector fields on the sphere that are of importance in geoscientific modeling. Various versions of the Mie and Helmholtz decomposition are presented. A special emphasis is set to integral representations for the different contributions, which is of interest, e.g., in numerical applications. Furthermore, the decompositions are treated in a global framework on the entire sphere and in a local framework on regular subsurfaces. In the end, an application to the modeling of ionospheric currents is indicated.

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Local Multiscale Modelling of Geoid Undulations from Deflections of the Vertical

Cited by 39 publications

References 12 publications

Multiscale Modeling of the Geomagnetic Field and Ionospheric Currents

Multiscale Modeling of the Geomagnetic Field and Ionospheric Currents

Determination of deflection of the vertical from geoid heights

Spherical decompositions in a global and local framework: theory and an application to geomagnetic modeling

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