Abstract:
The far-field acceleration spectra of small earthquakes contain information about the earthquake source and the propagation medium. Modelling the acceleration spectra requires modelling the source function and the travel-path attenuation as neither can be individually measured. The instrument corrected acceleration spectra of 273 small earthquakes were chosen for analysis. The earthquakes were recorded digitally by a temporary seismograph network deployed in the Wellington Region between February 1989 and July 1989.
The study region was found to be one of low attenuation. The variation of attenuation with distance indicates that most of the attenuation is occurring in the crust. The results are consistent with a high attenuation surface layer 25-35 km thick, with an S-wave Q value of 568±70, overlying a low attenuation region with an S-wave Q value of 1316±150. Overall the attenuation observed for P-waves was found to be greater than for the S-waves. This may reflect greater attenuation due to scattering than to anelasticity in the crust.
For the earthquakes studied a Brune source model was used to estimate the seismic moment, source radius, and stress drop. The source parameters were found using a stable integral technique which uses Parseval's theorem to relate the source displacement function to the observed acceleration spectra. The integral method provides an analytical measurement of the observed earthquake corner frequency. The observed stress drops were found to increase with moment, in contrast to the near constant stress drops widely observed for large earthquakes. This may reflect a difference between earthquakes occurring within pre-existing zones of weakness and the higher stress drop earthquakes occurring in uniformly strong rock.
The average source parameters estimated from five stations were used to model the acceleration spectra at each station. By examining the difference between the observed and the predicted spectra, a site specific shape of the residuals was determined. The expected acceleration spectra at a site for a chosen source function can be estimated using the measured attenuation and site response functions. Hence the shape of the observed spectra of small earthquakes can be used to model the likely effect of a large earthquake, but the moment and stress drop must be independently assigned.
