We studied strong-motion spectra observed for three Mw 7.8 to 8.0 earthquakes (the 1985 Michoacán, Mexico; 1985 Valparaíso, Chile; and 1983 Akita-Oki, Japan earthquakes). We determined the decay of spectral amplitude with distance from the station, considering different measures of distance from a finite fault. We compared strong-motion spectra (Fourier acceleration spectra) observed for these three earthquakes with those estimated from the source spectrum determined from teleseismic P waves. We scaled the teleseismic source spectra to produce reference strong-motion spectra at periods from 1 to 10 sec using a simple physical model of far-field S body waves from a point source recorded at the surface of a homogeneous half-space. For all three earthquakes the reference spectral amplitudes at periods of 1 to 5 sec are about half the observed ones at distances of about 50 km. The difference increases as the distance increases. At distances of 200 to 300 km, the reference spectrum is about 1/10 of the observed one. The difference between the reference and the observed spectrum is attributed to the contribution of phases other than direct S waves and to site response. We applied corrections for the finiteness (spatial extent) of the source using a simple model of rupture propagation on a dipping two-dimensional fault. Including the source finiteness did not improve the estimate substantially at periods from 1 to 20 sec, but it modeled significant changes in the signal duration as a function of azimuth for the 1985 Michoacán earthquake. Our results can be used to establish empirical relations between the observed spectra and the half-space responses, depending on the distance and the site condition. If such empirical relations can be established, source spectra determined from teleseismic records may be used to estimate strong motions.