Analyses of peak amplitudes of strong earthquake ground motion have been carried out with the emphasis on their dependence on earthquake magnitude, epicentral distance, and geological conditions at the recording site. Approximate empirical scaling functions have been developed which, for a selected confidence level, yield an estimate of an upper bound of peak accelerations, velocities, and displacements. The parameters in these scaling functions have been computed by least-squares fitting of the recorded data on peak amplitudes which are now available for a range of epicentral distances between about 20 and 200 km and are representative for the period from 1933 to 1971 in the Western United States.

The possibility of extrapolating the derived scaling laws to small epicentral distances where no strong-motion data are currently available has been tested by comparing predicted peak amplitudes with related parameters at the earthquake source. These source parameters (average dislocation and stress drop) can be derived from other independent studies and do not contradict the inferences presented in this paper. It has been found that for an approximate 90 per cent confidence level the presently available data suggest that peak accelerations, velocities, and displacements at the fault and for the frequency band between 0.07 and 25 Hz probably do not exceed about 3 to 5 g, 400 to 700 cm/sec, and 200 to 400 cm, respectively.

The logarithms of the peaks of strong ground motion seem to depend in a linear manner on earthquake magnitude only for small shocks. For large magnitudes this dependence disappears gradually and maximum amplitudes may be achieved for M ≈ 7.5. The influence of geological conditions at the recording site appears to be insignificant for peak accelerations but becomes progressively more important for peaks of strong-motion velocity and displacement.

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