Assessment of regional geomagnetic field modelling methods using a standard data set: spherical cap harmonic analysis

Various methods that take account of the potential nature of the field have been proposed for modelling geomagnetic data on a regional scale. Several of these have been applied to a standard data set based on annual mean values from observatories in Europe. Here, we examine some of the properties of spherical cap harmonic analysis when applied to this data set, and compare the quality of fit with that of the other models. It is found that, for this data set, rectangular polynomial analysis provides a compact fit to main field data, but that in most other cases, for both main field and anomaly data, spherical cap harmonic analysis provides the better fit. Although relatively insensitive to chosen cap size, spherical cap harmonic analysis deteriorates more rapidly than the other methods when the number of coefficients is reduced

Rectangular polynomial analysis of the regional geomagnetic field

The method of rectangular polynomial analysis (RPA) is developed and refined to represent a curl-free potential field of internal origin. It is applied to annual mean values of the geomagnetic field from 42 European observatories. RPA is found to be an efficient means of representing the regional held, though less suitable for modelling the anomaly held

Rectangular harmonic analysis revisited

Alldredge's method of rectangular harmonic analysis has been reexamined. After correction of errors, it is found to give improbable values between the data points and wild values outside them. A much more realistic model has been obtained by (1) determining only the most significant coefficients.(those that exceed their standard deviations, obtained by an iterative process), (2) introducing new parameters to allow for a linear trend across the region, and (3) increasing the scaling factors so that the sinusoids start and finish outside the region. Modification 1 is the most important for improving the interpolative qualities of the model. Modifications 2 and 3 reduce, but do not entirely eliminate, the wild values near the edges