## 3 Results
### The Greendale Fault Case Study  
The Greendale Fault (GF) is located near the dextral-transressional deformation zone associated with the oblique collision of the Pacific plate with the Australian plate in New Zealand (Figure 3). It was unknown before the 2010-2011 Canterbury earthquake sequence, beginning in September 2010 with the Darfield Mw 7.1 earthquake (the epicenter identified by a red star in Figure 3A), and the following Mw 6.2 in February of 2011. This latter occurred beneath the city of Christchurch and caused high damage throughout the city due to extensive soil liquefaction (its epicenter is identified by a yellow star in Figure 3A). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **Network** & **Latitude** & **Longitude** & **Operating Period** & \\ \hline ND1 & GS & 37,57,333 & \(-\)121,992,523 & 27/04/06 & 13/06/13 \\ ND2 & GS & 37,573,181 & \(-\)121,989,609 & 24/04/06 & 12/06/13 \\ ND3 & GS & 37,57,309 & \(-\)121,985,939 & 24/04/06 &  
This complex right-lateral strike-slip fault system was described as \"immature\", according to the aftershock distribution [60; 61; 62; 63]. Field and geomorphic evidences are hidden by the Holocene river gravels composing many overlapping fans of glacier rivers descending from the Southern Alps (Figure 3A) that fill the 160 km-long and 50 km-wide Canterbury Plains ([64; 65; 66] and references therein), reaching a thickness of 1.5 km. The wavefield polarization was recently determined across the GF using earthquake data recorded by an array of 14 stations installed by the Victoria University of Wellington, together with the University of Auckland and the University of Wisconsin-Madison [34]. The majority of these stations were installed on the flat Canterbury Plains [67; 68]. In Figure 3 we show the geological map, modified after [65]. This array recorded thousands of aftershocks following the Darfield earthquake, and occurred from 8 September 2010 to 13 January 2011 [69]. In order to check the result stability independently of the seismic source and path, [34] selected four clusters (Cl-2, Cl-4, Cl41, Cl-54) among the data set prepared by [70] and comprising 163 earthquake magnitudes between 1.8 and 4.8. They assessed the polarization both in the frequency and time domains through the individual-station using HVSRs and covariance matrix analysis (see Section 2), respectively. In addition to earthquake records, they also used ambient noise continuously recorded for 72-days from 19 September 2010. [PERSON] [34] found that stations installed in the Canterbury Plains have an amplification peak between 0.1 and 0.3 Hz for both earthquakes and ambient noise. The HVSRs reported in Figure 3B were calculated using earthquake signals at stations Dar6 and Dar7. They clearly show the existence of such a low-frequency peak, with amplitudes up to a factor of three, that is related to the resonance of a considerable thickness (c. 1 km) of soft sediments lying over the metamorphic bedrock. The analysis performed using seismic events revealed the existence of another peak in amplification between 2 and 5 Hz at two on-fault stations, which was not visible in the noise analysis. In contrast to the lower  
Figure 3: The Greendale fault near Darfield, in the Canterbury Plains (NZ), redrawn after [34]. (**A**) A geological map modified after [65], together with station location. Results by the covariance matrix analysis in the time domain are reported as rose diagrams representing the horizontal polarization (the results from the selected earthquake are combined together). (**B**) mean HVSRs averaged over the selected events for on-fault stations Dar6 and Dar7, as contour plots versus frequency and direction of motion. (**C**) Redrawn by [67]. A sketch representing the right-lateral fault movement in the N90\({}^{\circ}\) direction (black arrows), with the regional stress field (red arrows), and the kinematic components of the local stress field (K1 and K3).