Short-period and high-frequency NORESS observations from two after-shock sequences offshore western Norway, with epicentral distances of 424 and 405 km, respectively, have been used in testing a new hedgehog inversion procedure for determination of source spectral scaling characteristics, based on a previously developed spectral ratio method. This inversion procedure provides insight into resolution properties, uncertainties, and trade-off considerations between source parameters.
The two main events analyzed have ML magnitudes of about 5 while the smallest aftershocks are about 1.5, with seismic moments in the range 1017 to 1012 Nm. The observed spectral ratios support ω2 source models for both of the earthquake sequences, but only if certain constraints are imposed on the scaling parameter (δ) that determines the stress drop sensitivity with respect to seismic moment. In that case, stress drop is found to be almost independent of seismic moment (δ of 3.24) for one of the sequences and increasing with moment (δ of 3.80) for the other. Without such constraints, which may not be justifiable in the case of earthquake sequences, equally good solutions are found for ω3 models, in which case δ attains values around 5 to 6, indicating strongly increasing stress drop. External constraints on the source spectral slope and/or corner frequency will similarly help in resolving δ.
The method, which also simultaneously determines corner frequencies (or stress drop if adopting some model relating this to corner frequency) for all of the events, albeit with a poorer resolution, can either use independently determined seismic moments or it can determine these as part of the inversion. Quite similar results are obtained in those two cases, reflecting essentially the quality of the initial moment determinations. The observed variations in stress drop sensitivity between two earthquake sequences, only 84 km apart and occurring in similar tectonic environments, are consistent with the considerable variations that have been observed on a larger scale. Caution is therefore needed if the scaling relations derived in this study are applied to other events (larger ones and/or series of main events), or to different seismic regions.