Translated origin spherical cap harmonic analysis

The method of spherical cap harmonic analysis (SCHA), due to Haines (1985) is appropriate for regional geomagnetic field modelling as it includes the required potential field constraints and, for a given number of model parameters, describes shorter wavelength features than a global spherical harmonic model. If the origin of the coordinate system is moved from the centre of the Earth towards the surface then the Earth's surface is no longer equidistant from the origin. At the Earth's surface the minimum wavelength described by a SCH model in the new coordinate system is smaller at the centre of the region than at the edge. This method of
translated origin spherical cap harmonic analysis (TOSCA) has been applied to regional field modelling for Italy. The method is able to take advantage of the dense distribution of data at the centre of region and the model effectively smooths towards the periphery. The performance of the TOSCA model is discussed in relation to a model derived using conventional SCHA.

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