Some statistical aspects of the geomagnetic field

Some statistical aspects of the secular variation of the internal and external parts of the geomagnetic field are discussed. Studies of the long-term geomagnetic secular variation originating in the core, have conventionally used virtual geomagnetic pole positions and their associated dispersion as a function of latitude. Here, a new model is developed, using the statistical distributions of the Gauss coefficients in the spherical-harmonic representation of the field. Their distributions are based on the observation that the non-dipole part of the present-day geomagnetic spectrum is consistent with a white spectrum near the surface of the core. Using this information and a general form for the dipole's statistical distribution, the expected statistical distribution functions for declination and inclination at any latitude were derived. The second part of the thesis develops a new technique for obtaining maximum-likelihood estimates for the magnitude and phase of some periodic variations in the external part of the geomagnetic field. The method is an extension of the M-type estimation procedure widely used in robust regression analysis