2D Fourier series representation of gravity quantities on the sphere
20/09/2016 | 11:30 | Session 2: Computational Methods
Author(s): Khosro Ghobadi-Far, Mohammad Sharifi and Nico Sneeuw
Khosro Ghobadi-Far, Mohammad Sharifi and Nico Sneeuw
2D Fourier series representation of geopotential is conventionally derived by making use of the Fourier series of the Legendre functions in the spherical harmonic representation. This representation has been confined so far to a scalar field like geopotential. It is shown that the 2D Fourier series representation can be generalized to represent any functionals of geopotential if it is seen from a different point of view as an expansion of transformed spherical harmonics in a rotated frame. Transformation of spherical harmonics under rotation is known from representation theory. In the obtained 2D Fourier series representation, each functional, either isotropic or anisotropic, is linked to the geopotential using a spectral transfer. As a consequence, the problem of global spherical harmonic analysis of anisotropic functionals given on a spherical grid, which cannot be done using spherical harmonic representation, is solved similarly to the case of isotropic functionals in this formulation. This important characteristic makes it a general and unified formalism, as opposed to the spherical harmonic representation. Furthermore, it can serve as a tool for a variety of analyses concerning the gravity field on the sphere, such as error analysis of different functionals and contribution analysis in a combined gravity field modeling. Finally, since the spectral transfers provide the spectral characteristics of the gravitational functionals, this formalism is in close relationship with the so-called Meissl scheme. In addition, due to establishing a link between the individual anisotropic functionals and geopotential in the spectral domain, in a way, it extends the Meissl scheme. Power and applicability of the introduced formulation is demonstrated by presenting some numerical examples.