Hi Abdel,

Spherical harmonics are used to describe global variables because they provide a set of orthogonal basis functions to decompose whatever variable you study (in this case, gravity) on a spherical surface. Using this method, you can express a spherical "surface" using a sum of different harmonics (or "frequencies"). You can probably understand spherical harmonics if you think of them as a Fourier series decomposition on a spherical surface.

Here is a nice article on SH that compares them to Fourier analysis, which is usually a more familiar method:

http://www.geo.arizona.edu/geo5xx/geo519.071/lectures/Harmonics.pdf

I recommend this appendix:

http://www.cs.dartmouth.edu/~wjarosz/publications/dissertation/appendixB.pdf

I also recommend you to read some basic Internet literature (i.e. Wiki)

http://en.wikipedia.org/wiki/Spherical_harmonics

There are plenty of articles and discussions on this topic. I hope this helps. Cheers,

Demián

Hi Abdel,

Spherical Harmonics are used not only because they are a set of orthogonal basis functions.

In the case of the gravitational field it is possible to prove that spherical harmonic are a solution (in spherical coordinates) of the equation Laplacian(V)=0. Therefore Spherical Harmonic assure the fundamental property of harmonicity (outside the masses) of the gravitational field. Note also that GGM allows to predict your a functional of the gravitational field everywhere.

The foundamental book for this kind of topic is: 

Hofmann-Wellenhof, B., & Moritz, H. (2006). Physical geodesy. Springer Science & Business Media.

I remember that a very clear and easy description can be found in:

Blakely, R. J. (1996). Potential theory in gravity and magnetic applications. Cambridge University Press.

While if you want an advanced book you can have a look at:

Sansò, F., & Sideris, M. G. (2013). Geoid Determination: Theory and Methods (Vol. 110). Springer Science & Business Media.

Dr..Gomez

Thank you very much for your answer

Thank you for this comparison (Fourier analysis, Spherical Harmonics)

Very Thank

Abdel Rahim

Dr.Sampietro

Thanks for adding your answer

Is it possible to send me soft copy of :-

- Blakely, R. J. (1996). Potential theory in gravity and magnetic applications. Cambridge University Press.

- Heiskanen W. A. and Moritz H., 1967. Physical geodesy

Please send me some link to download  this books for free

E-mail: [email protected]

Very Thank

Abdel Rahim