A theoretical relationship between seismic moment and local magnitude ML is derived from the relationship between magnitude ML and source dimension given by Randall (1973). For a circular fault of radius smaller than about 0.5 km, the magnitude ML is proportional to the logarithm of the seismic moment Mo, and these values alone cannot specify other source parameters. For greater radii the values of Mo and ML define Brune's (1970) far-field spectrum and in these cases other source characteristics can be readily obtained. The seismic moment can be estimated from the long-period amplitudes, and therefore the moment-magnitude relation provides a convenient method for determination of the source properties.
The relationship between the logarithm of the various source parameters and seismic moment is considered for a number of regions and earthquake sequences. It appears to be of linear form and, furthermore, it seems that the same slope coefficient can be used in different regions. Source properties show regional differences, and the most suitable parameter to describe these differences is the average displacement.
Besides the regional variations, there seems to be a time variation of source properties. This is the case for the Inangahua aftershock sequence, during which the variation of the displacement residuals correlates with the variation of the coefficient b, which defines the frequency-magnitude relation.