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BERNARD PRICE INSTITUTE OF GEOPHYSICAL RESEARCH, UNIVERSITY OF THE WITWATERSRAND,, JOHANNESBURG, South Africa
Abstract
Spectra of ground displacement of P and S waves were measured for 24 tremors using records from a seismograph station on the surface of the East Rand Proprietary Mines near Johannesburg, South Africa. The tremors occurred in close proximity to mining at depths of the order of 3.2 km below the station and had magnitudes ranging from about 0 to 3. Ground displacement due to P and S waves is, to a first approximation, a unidirectional pulse of the order of 0.1 to 0.2 sec in width, although considerable complexity is often present in the wave forms. The corresponding spectra of displacement amplitude appear to be flat at low frequencies and generally diminish according to 
–3 at high frequencies, where is frequency. Analysis of the spectra using the model of Brune and its extension by Trifunac suggests source dimensions ranging from about 50 to 500 m and stress drops ranging from about 5 to 50 bars. Moments estimated from the low-frequency limits of the spectra vary from 1018 to 1021 dyne-cm. Seismic energies calculated from the records of ground velocity are in good agreement with the Gutenberg-Richter relationship between energy and magnitude, log E = 11.8 + 1.5 M.
The mine tremors appear to be highly similar to natural crustal earthquakes with regard to stress drops, the relationship between moment and magnitude, and the relationship between size and magnitude. Underground observations of damage caused by the larger tremors indicate that the actual rupture process is highly complex, consisting of many discrete failures; these observations cannot be fitted by a simple dislocation model.
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