Seismic moment and the corresponding moment magnitude Mw are classically obtained from the spectrum of far-field body waves. Near-field seismograms are generally not used for that purpose, exclusively in the case of large earthquakes because different types of waves arrive concurrently, averting the definition of a simple relation between the seismic moment and the spectrum. here presented a method to determine Mw from the displacement spectra of near-field records. The spectral amplitude at low frequency obtained from the real seismograms is compared to that of synthetic seismograms computed using kinematic rupture models scaled with Mw. Synthetic records are computed and averaged for various fault orientations and for epicentral distances ranging from 10 to 100 km. The synthetic spectral values as a function of moment magnitude, epicentral distance, and filtering are computed only once and stored. The spectral amplitudes of the real records are simply interpolated in the tables of synthetic data, providing that fast determination of Mw