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Modelisation regionale du champ magnetique terrestre

Abstract : The geomagnetic field above the Earth's surface in current free region may be expressed as the gradient of a scalar potential solving Laplace equation. For regions with a fairly dense coverage of data at different altitudes, a regional model ought to offer a better spatial resolution of the regional field over the volume under study than a global field expanded in Spherical Harmonics. The Spherical Cap Harmonics Analysis is an attractive regional modelling tool having close relationship with global Spherical Harmonics. With the Spherical Cap Harmonic Analysis (SCHA) adopted so far, difficulties arise in upward continuation of the field. It is also uneasy to establish a relationship between global and local Gauss coefficients. Indeed, such relationship would be useful for introducing prior constraint on inverse problems dealing with the estimation of local Gauss coefficients based upon a local dataset. In the present work, we show that these difficulties are overcome if the SCHA modelling is formulated as a boundary value problem in a cone bounded radially by the Earth's surface and an upper surface suitable for satellite data, and bounded laterally in order to encompass a specific region of study. In particular, this new formalism can be related to Spherical Harmonics and gives sensible relationship among both sets of Gauss coefficients. The reliability of these relations is demonstrated by reconstructing the three components of a global field with a pretty good accuracy. In order to foresee the inverse problem, we also establish useful analytical relationships based on spectrum concept and magnetic energy inside a cone. This provide powerful tools for regularizing inverse problems based on real data sparsely distributed. We finally tackle the inverse problem by examining several synthetic simulations for different data distributions ; from even to sparse distributions. All results suggest that the new proposal for regional modelling is efficient. Synthetic data are well resolved and models obey to basic properties of Newtonian potentials.
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Contributor : Erwan Thebault <>
Submitted on : Tuesday, March 8, 2005 - 3:29:40 PM
Last modification on : Friday, February 5, 2021 - 2:08:03 PM
Long-term archiving on: : Friday, November 25, 2016 - 8:59:29 AM


  • HAL Id : tel-00008725, version 1



Erwan Thebault. Modelisation regionale du champ magnetique terrestre. Géophysique [physics.geo-ph]. Université Louis Pasteur - Strasbourg I, 2003. Français. ⟨tel-00008725⟩



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