Potential Field Inversion using Harmonic Gradual Surface Blending.
Jean-Jacques Royer. ( 2010 )
in: Proc. 30th Gocad Meeting, Nancy
Abstract
Harmonic Gradual Surface Blending (referred as HGSB in the text) is a theoretical framework which relates the Harmonic components of a series of blended close surfaces Sλ to the Harmonic components of an initial S0 and target S1 surfaces used to define the blending.
As shown by Royer and Foudil-Bey [2009], the surface gravitational potential field produced by a constant dense solid B defined by a close surface S can be approximated by a Manifold harmonic basis (MHB) decomposition technique using the mth -first eigenfunctions of the Laplace-Beltrami operator. The gravitational potential U (P ) produced by the body B at a location P , is then a weighted sum of the elementary potential U k (P ) created by each uniform harmonic S k .
In this work, we coupled the Harmonic Gradual Surface Reshaping blending to the Manifold harmonic basis (MHB) decomposition technique to derive the potential field of any constant dense solid Bλ defined by a blended surface Sλ . It is shown that the resulting gravitational potential Uλ (P ) produced by Bλ at a location P depends only on a complex function in λ.
Given an experimental surface gravitational potential field Uobs , and two a priori possible shapes, the blended parameter λ is then optimized to guess the best fit of the unknown shape Bλ using a linearized least squares algorithm which minimizes the objective function [Tarantola, 1987] between the observed Uobs and blended gravitational potential field Uλ .
The initial and target shapes can be found from a neural network approach [Foudil-Bey et al., 2008] or using classical inversion stochastic inversion methods [Foudil-Bey et al., 2009]. These results are used in inverse problems to guess the body shape from two a priori solutions and a given gravitational surface anomaly.
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BibTeX Reference
@inproceedings{Royer3GM2010,
abstract = { Harmonic Gradual Surface Blending (referred as HGSB in the text) is a theoretical framework which relates the Harmonic components of a series of blended close surfaces Sλ to the Harmonic components of an initial S0 and target S1 surfaces used to define the blending.
As shown by Royer and Foudil-Bey [2009], the surface gravitational potential field produced by a constant dense solid B defined by a close surface S can be approximated by a Manifold harmonic basis (MHB) decomposition technique using the mth -first eigenfunctions of the Laplace-Beltrami operator. The gravitational potential U (P ) produced by the body B at a location P , is then a weighted sum of the elementary potential U k (P ) created by each uniform harmonic S k .
In this work, we coupled the Harmonic Gradual Surface Reshaping blending to the Manifold harmonic basis (MHB) decomposition technique to derive the potential field of any constant dense solid Bλ defined by a blended surface Sλ . It is shown that the resulting gravitational potential Uλ (P ) produced by Bλ at a location P depends only on a complex function in λ.
Given an experimental surface gravitational potential field Uobs , and two a priori possible shapes, the blended parameter λ is then optimized to guess the best fit of the unknown shape Bλ using a linearized least squares algorithm which minimizes the objective function [Tarantola, 1987] between the observed Uobs and blended gravitational potential field Uλ .
The initial and target shapes can be found from a neural network approach [Foudil-Bey et al., 2008] or using classical inversion stochastic inversion methods [Foudil-Bey et al., 2009]. These results are used in inverse problems to guess the body shape from two a priori solutions and a given gravitational surface anomaly. },
author = { Royer, Jean-Jacques },
booktitle = { Proc. 30th Gocad Meeting, Nancy },
title = { Potential Field Inversion using Harmonic Gradual Surface Blending. },
year = { 2010 }
}