The seismic moment and source area of an earthquake can be determined by fitting theoretical displacement amplitude spectra to observed ones. From these basic parameters the dislocation at the source and the stress-drop can be estimated. This method was tested in the case of four earthquakes for which the source parameters were known from observed surface ruptures. The uncertainty in the moment and area determinations was found to be approximately a factor of 2; for the displacement and stress-drop it was approximately a factor of 3 and 5 respectively. The application of spectral analysis of body waves to earthquakes in the deep seismic zone of Tonga-Kermadec indicate that stress-drop as well as apparent stress increase with depth and decrease again at great depth. This observation is interpreted as reflecting increasing material strength in the deep seismic zone near 450 km, with a reduction of strength at still greater depths. It is proposed that the temperature distribution in the downgoing slab of lithosphere causes this pattern.