Geomagnetic field modelling using wavelet analysis

Abstract

The component of the earth's magnetic field attributed to internal processes can be obtained from its potential. Geomagnetic field modelling involves the derivation of a set of coefficients which are then used in a mathematical representation of the field to find the field's components at any location. Spherical harmonic analysis has been the principal modelling approach for a number of years. It represents the potential field as a finite series in spherical harmonics with the coefficients being calculated from field observations at various locations around the globe. Spherical harmonics have a global support and the method becomes unsustainable at representing regional features or analysis on a regional scale. Besides, the technique becomes very demanding for high resolution models. One alternative approach is wavelet analysis. The analysis is carried on a discrete number of points and the field's potential is then expressed as a series in a set of wavelets. The coefficients constitute the model used to regenerate the potential at any point. The wavelets used are the Poisson wavelets on a sphere and each set of wavelets can be related to multipole sources inside the earth. These functions also have the advantage of being localized on the sphere and both the value of the function itself and its harmonic prolongation are easily computable. This dissertation compares the two forms of modelling the internal field. It gives an account of the problems associated with spherical harmonic analysis and how wavelet analysis has been effectively used to address them. Applications of wavelet analysis on both regional and global scales are reviewed. An application to outline the computational aspects and practical implementation of wavelet analysis has been developed and tested on a region in Europe. The results show that modelling using wavelet analysis can be effectively used at both global and regional scales making it an efficient complimentary tool to spherical harmonic analysis in geomagnetic field modelling.