Spectra of mantle Rayleigh waves recorded on the IDA network are inverted to determine the seismic moment tensor of the 9 June 1980 California-Mexico Border earthquake, the 29 July 1980 Vanuatu Islands earthquake, and the 9 July 1980 Santa Cruz Islands earthquake. Examinations are made to correct for phase velocity lateral heterogeneity and source process time. A simple regionalization (stable continent, tectonic region, young ocean, and old ocean) improves results of the linear inversion, but the phase correction is not large enough, and the discontinuous change of phase velocity across the boundary between regions causes an artificial rapid change in apparent phase velocity as a function of azimuth. Therefore, a more detailed but gradual representation of the lateral heterogeneity is desirable to correct for the propagation effect in the linear inversion. A source process time which consists of the nondirectional part of the apparent duration of main faulting and the delay time of the faulting from initial break is estimated by a phase analysis of Rayleigh waves. The source process time is generally proportional to the seismic moment on the log-log scale, but some earthquakes deviate considerably from the general relation. Therefore, the measurement of the source process time should be made before the moment tensor inversion. The phase errors introduced by the lateral heterogeneity and source process time may cause a bias to low scalar moment.