Waveform inversion of tsunami data provides independent and reliable information on earthquake source processes. The propagation effects of tsunamis are accounted for by computing Green's functions using a finite difference method and using the known bathymetry, which is much better constrained than the seismic velocity structure. The observed tsunami waveforms are corrected for the response of the tide gage system by using the results of in situ measurements. Using Green's functions computed from bathymetric data on a 2.5-km grid and the observed waveforms digitized at 1-min intervals, the spatial resolution of the faulting heterogeneity by the present method is as small as 30 km. This method is applied to the 1968 Tokachi oki and 1983 Japan Sea earthquakes. The slip is cencentrated at the northwestern part of the fault plane for the 1968 event. For the 1983 event the slip on the fault just north of the epicenter is twice that of the other parts. These asperity distributions are similar to those inferred from seismic wave analysis. However, the recovered total seismic moments are smaller. The present method is shown to be a useful technique for estimating heterogeneous fault motion, especially for historical events with no or poor seismic records, and tsunami earthquakes in which the excitations of seismic and tsunami waves are different. ¿ American Geophysical Union 1989