## 3 Results  
### The Hayward Fault Case Study  
Ground motion polarization in the Hayward fault zone was recently investigated [17]. The Hayward Fault (HF) is located just east of San Francisco (CA), and shows a quite complex structure with a general trend of N340\({}^{\circ}\), a predominant strike-slip right- lateral movement, with 100 km offset during the past 12 Ma [52; 53]. Both geometric evidences and offsets of man-made structures adequately document the active surface trace of the HF, revealing that it has a significant creep [54; 55]. In spite of this, the fault has also shown moderate to large earthquakes (ex. the \(\sim\)6.8 magnitude earthquake in 1868) [54; 55; 56; 57]. The study area is located in the Fremont district near Niles Canyon, where the highest surface creep rate is observed and the HF is largely aseismic. In the eastern fault sector, several marine clastic sequences outcrop, while the western sector is characterized by the presence of Quaternary alluvium. The geological map (downloaded at [[https://ngmdb.usgs.gov/](https://ngmdb.usgs.gov/)]([https://ngmdb.usgs.gov/](https://ngmdb.usgs.gov/)), last accessed on 16 May 2021) is reported in Figure 2A. On the top-left, we also show a picture taken close to station ND6, showing the damage on a concrete sidewalk made by the fault creeping movement. Ground motion polarization was investigated in [17] by using earthquake waveforms recorded by a temporary accelerometric seismic array installed by the US Geological Survey across the fault. Their location is shown in Figure 2A. Stations were installed at small distances (hundreds of meters) across the fault, and operated between 2006 and 2013 (details about the data set can be found in Table 1 in [17]). In this work, we have extended the performed analysis, adding six additional stations (Table 1) installed in the same area and belonging to Northern California Seismic Network (NCSN). Since these stations were operating in different periods, we performed a further data selection using IRIS Wilber3 tool ([[http://ds.iris.edu](http://ds.iris.edu)]([http://ds.iris.edu](http://ds.iris.edu)), last accessed on 19 April 2021), selecting data with a magnitude higher than 3. The details can be found in Table S1, given as auxiliary material. We used the covariance matrix method applied to the three component records. The results obtained from the selected earthquake are combined, merging all the instantaneous polarization angles. In Figure 2A we show the horizontal polarization at each station through rose diagrams, merging the polarization angles of all of the events. The four on-fault stations have narrow rose diagrams, implying horizontally polarized motion: polarization at stations ND6 and ND7 is along the N80\({}^{\circ}\)-90\({}^{\circ}\) direction; at ND3 the pattern is more complex, with two effects at different frequencies (the N80\({}^{\circ}\)-90\({}^{\circ}\) direction only in the frequency band of 6-8 Hz, see also [7]); at NDR the polarization slightly rotates to N70\({}^{\circ}\) azimuth. Figure 2: Hayward fault near Niles Canyon, in the Fremont district (CA). (**A**) Geological map (downloaded at [[https://ngmdb.usgs.gov/](https://ngmdb.usgs.gov/)]([https://ngmdb.usgs.gov/](https://ngmdb.usgs.gov/)), last accessed on 16 May 2021), together with station location. Results by the covariance matrix analysis are shown as rose diagrams of the horizontal polarization (results from the selected earthquake are combined, merging all the instantaneous polarization angles). The picture on the top-left was taken (in 2009) close to station ND6, and shows the damage on a concrete sidewalk made by the fault creeping movement. (**B**) mean HVSRs averaged over the selected events for three selected stations as contour plots versus frequency and direction of motion. (**C**) Redrawn by [17]. Sketch (map view) of the right-lateral fault, moving along N160\({}^{\circ}\) direction (black arrows), with the regional stress field (red arrows) and the kinematic components of the local stress field (K1 and K3).