Solving for source parameters using nested array data: A case study from the Canterbury, New Zealand earthquake sequence
The seismic spectrum can be constructed by assuming a Brune spectral model and estimating the parameters of seismic moment ( M 0 ), corner frequency ( f c ), and high-frequency site attenuation ( κ ). Using seismic data collected during the 2010–2011 Canterbury, New Zealand, earthquake sequence, we apply the non-linear least-squares Gauss–Newton method, a deterministic downhill optimization technique, to simultaneously determine the M 0 , f c , and κ for each event-station pair. We fit the Brune spectral acceleration model to Fourier-transformed S-wave records following application of path and site corrections to the data. For each event, we solve for a single M 0 and f c , while any remaining residual kappa, κ r "> κ r κr , is allowed to differ per station record to reflect varying high-frequency falloff due to path and site attenuation. We use a parametric forward modeling method, calculating initial M 0 and f c values from the local GNS New Zealand catalog M w, GNS magnitudes and measuring an initial κ r "> κ r κr using an automated high-frequency linear regression method. Final solutions for M 0 , f c , and κ r "> κ r κr are iteratively computed through minimization of the residual function, and the Brune model stress drop is then calculated from the final, best-fit f c . We perform the spectral fitting routine on nested array seismic data that include the permanent GeoNet accelerometer network as well as a dense network of nearly 200 Quake Catcher Network (QCN) MEMs accelerometers, analyzing over 180 aftershocks M w,GNS ≥ 3.5 that occurred from 9 September 2010 to 31 July 2011. QCN stations were hosted by public volunteers and served to fill spatial gaps between existing GeoNet stations. Moment magnitudes determined using the spectral fitting procedure ( M w,SF ) range from 3.5 to 5.7 and agree well with M w,GNS , with a median difference of 0.09 and 0.17 for GeoNet and QCN records, respectively, and 0.11 when data from both networks are combined. The majority of events are calculated to have stress drops between 1.7 and 13 MPa (20th and 80th percentile, correspondingly) for the combined networks. The overall median stress drop for the combined networks is 3.2 MPa, which is similar to median stress drops previously reported for the Canterbury sequence. We do not observe a correlation between stress drop and depth for this region, nor a relationship between stress drop and magnitude over the catalog considered. Lateral spatial patterns in stress drop, such as a cluster of aftershocks near the eastern extent of the Greendale fault with higher stress drops and lower stress drops for aftershocks of the 2011 M w,GNS 6.2 Christchurch mainshock, are found to be in agreement with previous reports. As stress drop is arguably a method-dependent calculation and subject to high spatial variability, our results using the parametric Gauss–Newton algorithm strengthen conclusions that the Canterbury sequence has stress drops that are more similar to those found in intraplate regions, with overall higher stress drops that are typically observed in tectonically active areas.