A method is presented for the determination of earthquake source parameters from Fourier spectra. This approach provides an objective and efficient way of processing large amounts of digital data. The method assumes that the Brune model (an omega-squared fall-off of the high frequency spectrum above a single corner frequency) is an adequate description of the earthquake source. The model is parameterized in terms of the seismic moment, corner frequency, and kappa, the high frequency decay constant due to attenuation. This model is fit to the observed spectrum using a least squares minimization technique. The parameters which give the smallest misfit between the observed spectrum and the model spectrum are assumed to be those corresponding to the source.
This technique is tested using a suite of synthetically derived acceleration time histories to obtain statistical characteristics of the derived parameters. The seismic moment, the corner frequency, and the stress drop obey a log-normal distribution; the kappa value obeys a normal distribution in these experiments. The performance of the method is also examined using time series that have been rounded to the nearest 1 cm/sec2 to simulate the effect of analog to digital conversion that occurs in actual recording on one particular type of instrument, a non-gain ranged strong motion accelerograph.
The results show that for records with sufficient signal to noise ratio, all of the spectral parameters can be resolved for events with moment magnitudes in the range MW = 3 - MW = 6. For smaller events (MW = 1 - MW = 2), moment and spectral decay parameter are still well determined from low frequencies in the data. The average corner frequency is stil reasonable in this case, but the uncertainties are much larger than for the larger magnitude earthquakes because the corner frequency occurs at a frequency where attenuation has a strong effect on the spectrum. Strong motion data recorded on the fixed gain instruments at a distance of 25 kilometers have adequate resolution of source parameters in the range MW = 4 - MW = 6. The useful range is somewhat smaller for data recorded at 50 kilometers.