An inversion that fits spectra of earthquake waveforms and gives robust estimates of corner frequency and low-frequency spectral amplitude has been used to determine source parameters of 223 microearthquakes induced by hydraulic fracturing in granodiorite. Assuming a ω−2 source model, the inversion fits the P-wave spectra of microearthquake waveforms to determine individual values of corner frequency and low-frequency spectral amplitude for each event and one average frequency-independent Q for all source-receiver paths. We also implemented a constraint that stress drops of all microearthquakes be similar but not equal and found that this constraint did not significantly degrade the quality of the fits to the spectra. The waveforms analyzed were recorded by a borehole seismometer. The P-wave Q was found to be 1070. For Q values as low as 600 and as high as 3000, the misfit between model and spectra increased by less than 5 per cent and the average corner frequency changed by less than 15 per cent from those obtained with a Q of 1070. Average stress drop was 3.7 bars. Seismic moments obtained from spectra ranged from 1013 to 1018 dyne-cm. The low stress drops are interpreted to result from underestimation of the actual stress drops because of a nonuniform distribution of stress drop and slip along the fault planes. Spatially varying stress drops and slips result from the strong rock heterogeneity due to the injection of fluid into the rock. Stress drops were found to be larger near the edges of the seismic zone, in regions that had not been seismically active during previous injections.
The seismic moments determined from spectra were used to obtain a coda length-to-moment relation. Then, moments were estimated for 1149 events from measurements of coda lengths from events whose moments could not be measured from spectra because of saturation or a low signal-to-noise ratio. The constant of proportionality between cumulative number of events and seismic moment is higher than that found for tectonic regions. The slope is so high that the seismic energy release is dominated by the large number of small events. In the absence of information about the number of events smaller than we studied, we cannot estimate the total seismic energy released by the hydraulic injection.