Gravitational potential from surface harmonics transform.

@inproceedings{Royer4GM2009,
 abstract = { This paper generalizes the classical projection technique which decomposes the gravity potential on Spherical harmonic functions to surface harmonics. The gravitational potential field produced by a dense solid body B is calculated using a Manifold Harmonics Basis (MHB) decomposition technique. Manifold Harmonics Transform is a Fourier-like method proposed by Vallet and Lévy (2008) to decompose a surface S into a series of m surface components Sk using the m-first eigenfunctions of the Laplace-Beltrami operator. The envelop S of the constant density rho uniform solid body B buried at a depth h is decomposed into a series of surfaces Sk using the harmonic decomposition formula. By means of the Green's theorem, it is shown that the gravitational potential U(P) produced by the body B at a location P, is a weighted sum of the elementary gravitational potential Uk(P) created by each uniform harmonic Sk. The main advantages of the suggested method are: (i) to reduce the parameter number describing the unknown investigated shape, hence making resolution of inverse problem faster and more robust as only the shape of dense bodies is gradually deformed; (ii) to provide a flexible method for controlling the resolution scale during inversion, implying that low spatial frequencies related to noise should only impact the low frequencies of the response. These results are used in inverse problems to guess the body's shape from an a priori solution and a given gravitational surface anomaly. },
 author = { Royer, Jean-Jacques AND Foudil Bey, Nacim },
 booktitle = { Proc. 29th Gocad Meeting, Nancy },
 title = { Gravitational potential from surface harmonics transform. },
 year = { 2009 }
}