Various methods for the spherical harmonic analysis of the quiet daily variation of geomagnetic fields (Sq) measured at the Earth's surface have been used to represent the separation of the external (source) and internal (induced) currents. The results of such methods differ because the modeling techniques often reflect differing special objectives of the researcher. One method utilizes the observed field measurements at all world locations determined at a specific instant of time. A second method uses only observations in one primary hemisphere, appropriately mirroring field values for the analysis in the opposite hemisphere. The third method, a variation of the second, uses field values in the opposite hemisphere that are mirrored from a primary region that is shifted in time by 6 months. A variation of these three methods uitlizes only a longitude line of observatories and assumes that the 24 hours of Sq field variation represents a 360¿ rotation of the analysis sphere. For the comparison, power spectral representation, global current patterns in different seasons, and deviations of model-computed field values from the surface observations were all evaluated. The power spectral study showed that the spherical harmonic analysis of Sq should be extended to order m=6 and degree n=m+17. The northern hemisphere current system seemed to be consistently stronger than the southern hemisphere system. Exclusion of the mid-latitude vortex polynomials with (n-m)=0 and 1 was shown to be a useful technique for exposing the unique polar cap current pattern Sqp. The global method was generally best for modeling; however, the hemisphere mirroring methods with 6-month time shift were almost as good in their representation of the Sq fields. Different special regions of effective and poor modeling were identified for all three methods.