Abstract Synthetic calibration functions for body-wave magnitudes are presented. They have been obtained from computations made under the assumption that the variation of amplitude spectra along the earth's surface is due to radial velocity heterogeneity and radial changes of the dissipation factor Q inside the earth only. The new calibration functions depend on the epicentral distance and the focal depth of the earthquake, as well as on the period of the body-wave under consideration. No single calibration function exists which would produce magnitude figures identical for all Fourier components of a body-wave. Observations on several hundreds of strong earthquakes in recent years show that the P-wave magnitudes vary systematically with the period of the wave. With the application of the synthetic calibration function a general increase of the teleseismically determined P-wave magnitudes with frequency is observed. This fact reconciles acceleration response spectra from narrowband strong-motion analyzers in the near-field of an earthquake and spectral magnitudes determined from far-field observations by sensitive narrow-band seismographs. The strength of high-frequent spectral components generally exceeds the strength of low-frequent components determined in both cases.