Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XL-1/W5, 689-694, 2015
https://doi.org/10.5194/isprsarchives-XL-1-W5-689-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
 
11 Dec 2015
REPRESENTATION OF GRADIENTS OF A SCALAR FIELD ON THE SPHERE USING A 2D FOURIER EXPRESSION
M. A. Sharifi1,2 and K. Ghobadi-Far1 1School of Surveying and Geospatial Engineering, University college of engineering, University of Tehran, Tehran, Iran
2Research Institue of Geoinformation Technology (RIGT), University college of engineering, University of Tehran, Tehran, Iran
Keywords: 2D Fourier series, gradients, representation coefficients, D-functions, spectral transfers Abstract. Representation of data on the sphere is conventionally done using spherical harmonics. Making use of the Fourier series of the Legendre function in the SH representation results in a 2D Fourier expression. So far the 2D Fourier series representation on the sphere has been confined to a scalar field like geopotential or relief data. We show that if one views the 2D Fourier formulation as a representation in a rotated frame, instead of the original Earth-fixed frame, one can easily generalize the representation to any gradient of the scalar field. Indeed, the gradient and the scalar field itself are simply linked in the spectral domain using spectral transfers. We provide the spectral transfers of the first-, second- and third-order gradients of a scalar field in a local frame. Using three numerical examples based on gravity and geometrical quantities, we show the applicability of the presented formulation.
Conference paper (PDF, 1690 KB)


Citation: Sharifi, M. A. and Ghobadi-Far, K.: REPRESENTATION OF GRADIENTS OF A SCALAR FIELD ON THE SPHERE USING A 2D FOURIER EXPRESSION, Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XL-1/W5, 689-694, https://doi.org/10.5194/isprsarchives-XL-1-W5-689-2015, 2015.

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