Seismic source and wave propagation theories allow seismologists to compute long period synthetic seismograms that commonly match event subtle details of observed waveshapes, but the overal trace amplitudes must be scaled by arbitrary factors to emphasize the excellent waveshape correspondence. This unexplained amplitude scatter causes considerable difficulties when formally inverting observed waveforms for seismic source parameters. Omnilinear inversion simultaneously determines the linear model parameters and trace scaling factors to minimize the mismatch between observed and synthetic seismograms. Omnilinear inversion is applied to source time function deconvolution from long period P and SH waves. A simulation with synthetic data shows that omnilinear inversion finds the proper scaling factors, and the source time function and focal depth are better determined than for ''standard'' linear inversion. Omnilinear inversion is then applied to a data set of seven P waves and one SH wave from the underthrusting earthquake of July 5, 1968 (MS 6.6) in northern Honshu, Japan. Omnilinear inversion produces a best-fit focal depth of 36 km with a single pulse time function of 6 s duration and seismic moment of 4¿1018 N m (MW 6.4). This focal depth supports the notion that the seismically coupled plate interface extends no deeper than 40 km in northern Honshu. ¿ American Geophysical Union 1989