We use classic expressions of the excitation and propagation of Rayleigh waves to develop a mantle magnitude Mm, measured at variable period between 40 and 300 s. We justify theoretically the use of distance and source excitation corrections, and obtain simplified expressions for them. We also explore the possible influence of the presence of a corner frequency in the spectrum. Finally, we relate frequency-domain measurements to the standard practice of measuring magnitudes in the time domain, and justify the latter for wavetrains with strong dispersion. ¿ American Geophysical Union 1987