This chapter provides a theoretical overview of analytical methods for the spatial harmonic characterization of VLF and static electromagnetic sources. By breaking down complex sources into simpler components, the text establishes a framework for multipole imaging based on multidimensional harmonic analysis. This approach utilizes elementary sources to generate unique, orthogonal field patterns that efficiently encapsulate the source region. The analysis spans various geometries, beginning with spherical harmonic analysis of circular coils, three-phase cables, and permanent-magnet rotors. The methodology then extends to elongated sources, which are modeled within prolate spheroidal boundaries for applications such as the degaussing of marine vehicles, and to substantially flattened sources, approximated by oblate spheroids. By adjusting coefficient groupings for these specific coordinate systems, the chapter delivers efficient algorithms for fast magnetic multipole imaging across a diverse range of practical source structures.