Global satellite data is useful for the approximation of the lower degree spherical harmonic contributions of the crustal magnetic or the gravity field. If one is interested in higher degree contributions, i.e., contributions that describe local variations, then ground data at the Earth's surface is required. Such ground data, however, is typically only available locally/regionally, e.g., over Australia.
With a multiscale approach it is possible to incorporate these two types of data. An initial scaling transform is used for the downward continuation of the satellite data while the subsequent wavelet transform deals with the ground data. The latter requires a good localization of the wavelet kernels. The downward continuation, on the other hand, needs to be regularized adequately to yield a stable approximation. In this talk we indicate how scaling and wavelet kernels can be constructed that meet both of these requirements.