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The dynamics of external contributions to the geomagnetic field is investigated by applying time-frequency methods to magnetic observatory data. Fractal models and multiscale analysis enable obtaining maximum quantitative information related to the short-term dynamics of the geomagnetic field activity. The stochastic properties of the horizontal component of the transient external field are determined by searching for scaling laws in the power spectra. The spectrum fits a power law with a scaling exponent beta, a typical characteristic of self-affine time-series. Local variations in the power-law exponent are investigated by applying wavelet analysis to the same time-series. These analyses highlight the self-affine properties of geomagnetic perturbations and their persistence. Moreover, they show that the main phases of sudden storm disturbances are uniquely characterized by a scaling exponent varying between 1 and 3, possibly related to the energy contained in the external field. These new findings suggest the existence of a long-range dependence, the scaling exponent being an efficient indicator of geomagnetic activity and singularity detection. These results show that by using magnetogram regularity to reflect the magnetosphere activity, a theoretical analysis of the external geomagnetic field based on local power-law exponents is possible.
In this study we analyse the error distribution in regional models of the geomagnetic field. Our main focus is to investigate the distribution of errors when combining two regional patches to obtain a global field from regional ones. To simulate errors in overlapping patches we choose two different data region shapes that resemble that scenario. First, we investigate the errors in elliptical regions and secondly we choose a region obtained from two overlapping circular spherical caps. We conduct a Monte-Carlo simulation using synthetic data to obtain the expected mean errors. For the elliptical regions the results are similar to the ones obtained for circular spherical caps: the maximum error at the boundary decreases towards the centre of the region. A new result emerges as errors at the boundary vary with azimuth, being largest in the major axis direction and minimal in the minor axis direction. Inside the region there is an error decay towards a minimum at the centre at a rate similar to the one in circular regions. In the case of two combined circular regions there is also an error decay from the boundary towards the centre. The minimum error occurs at the centre of the combined regions. The maximum error at the boundary occurs on the line containing the two cap centres, the minimum in the perpendicular direction where the two circular cap boundaries meet. The large errors at the boundary are eliminated by combining regional patches. We propose an algorithm for finding the boundary region that is applicable to irregularly shaped model regions.