Post-seismic velocity changes following the 2010 Mw 7.1 Darfield earthquake, New Zealand, revealed by ambient seismic field analysis

Post-seismic velocity changes following the 2010 Mw 7.1 Darfield earthquake, New Zealand,... Summary Quantifying seismic velocity changes following large earthquakes can provide insights into fault healing and reloading processes. This study presents temporal velocity changes detected following the 2010 September Mw 7.1 Darfield event in Canterbury, New Zealand. We use continuous waveform data from several temporary seismic networks lying on and surrounding the Greendale Fault, with a maximum interstation distance of 156 km. Nine-component, day-long Green’s functions were computed for frequencies between 0.1 and 1.0 Hz for continuous seismic records from immediately after the 2010 September 04 earthquake until 2011 January 10. Using the moving-window cross-spectral method, seismic velocity changes were calculated. Over the study period, an increase in seismic velocity of 0.14 ± 0.04  per  cent was determined near the Greendale Fault, providing a new constraint on post-seismic relaxation rates in the region. A depth analysis further showed that velocity changes were confined to the uppermost 5 km of the subsurface. We attribute the observed changes to post-seismic relaxation via crack healing of the Greendale Fault and throughout the surrounding region. New Zealand, Seismic interferometry, Seismic noise, Seismic tomography, Surface waves and free oscillations, Wave propagation 1 INTRODUCTION When considering hazards in earthquake-prone regions, knowledge of subsurface material properties is important. The monitoring of crustal properties, such as seismic surface wave velocities can elucidate valuable information about the regional stresses. Ambient seismic noise is increasingly being used to evaluate crustal seismic properties. Cross-correlations of long-duration seismic records yield information about the propagation velocities of scattered surface waves (Shapiro & Campillo 2004). For a pair of seismic stations, the cross-correlation functions contain positive and negative time lags, which are analogous to the causal and acausal Green’s functions (Bensen et al.2007; Yang et al.2008). That is, the positive time lags represent arrival times of waves traveling in one direction as if one station is a source and the other the receiver. Negative time lags represent waves traveling in opposite directions, with roles reversed. A method for detecting seismic velocity variations, known as moving-window cross-spectral (MWCS) analysis, using earthquake multiplets, was proposed by Ratdomopurbo & Poupinet (1995) and has been modified for ambient seismic noise (Clarke et al.2011; Lecocq et al.2014). Relative delay times between long-duration cross-correlation stacks and those of shorter duration are computed and can be used to calculate relative velocity changes. This technique has since been used to successfully detect seismic velocity variations following large earthquakes. Brenguier et al. (2008) first used the MWCS method to examine earthquake-induced seismic velocity changes with ambient noise cross-correlations. A 0.08  per  cent increase in velocity was recorded over three years following the Mw 6.0 Parkfield earthquake in California and velocities returned to pre-seismic levels at the same rate as Global Positioning System (GPS) displacements over several years. The use of ambient seismic noise in New Zealand is already well established. The first major study into the ambient seismic noise field in New Zealand produced Rayleigh wave group velocity maps, and highlighted the Canterbury basin as a low-velocity region (Lin et al.2007). Smaller scale studies considered several regions of New Zealand’s North Island. Behr et al. (2010) estimated a Moho depth of 28 km for the Northland Peninsula from surface wave dispersion curves, in agreement with active-source methods. Beamforming analyses of the ambient noise field in New Zealand highlighted the first higher mode Rayleigh waves (Brooks et al.2009) and suggested several possible sources concerning ocean-wave movements (Behr et al.2013). The Mw 7.1 Darfield earthquake of 2010 September 04 was the first and largest event in a damaging earthquake sequence that struck the Canterbury region in the South Island of New Zealand between 2010 and 2012. The earthquake occurred west of Christchurch on the previously unrecognized Greendale Fault (Bannister & Gledhill 2012). A surface rupture of nearly 30 km was observed, exhibiting predominantly right-lateral strike-slip motion (Quigley et al.2012). The aftershocks that followed revealed a broad pattern of eastwards hypocentral migration and included several earthquakes larger than ML 5 (Syracuse et al.2012, 2013). This sequence included the Mw 6.3 Christchurch earthquake of 2011 February 22, which struck at a depth of 3–4 km (Kaiser et al.2012), 6 km south of the central business district (Bannister & Gledhill 2012), causing widespread damage throughout the city, resulting in 185 deaths. Recorded ground accelerations of over 1.25 g during the Darfield earthquake were the largest recorded in New Zealand (Fry & Gerstenberger 2011) to that point and apparent stresses of almost 16 MPa are extremely high compared to global averages (Fry & Gerstenberger 2011). Fry et al. (2014) used ambient seismic noise on the permanent GeoNet network to measure anisotropy from surface wave dispersion of fundamental-mode Rayleigh waves throughout Canterbury. At upper crustal depths, east–west trending fast axes parallel to the Greendale Fault and Cretaceous faults were recorded. At lower crustal depths, fast axes were shown to be parallel to the present plate boundary strain direction (Fry et al.2014). Ambient noise cross-correlations within the region contain higher mode signals (Savage et al.2013) and comparisons of horizontal- and vertical-component correlation functions show strong first higher mode Rayleigh waves on paths parallel to nearby ocean-wave directions. A basement resonance frequency of approximately 0.4 Hz was obtained from H/V ratios of higher mode Rayleigh waves (Savage et al.2013). Several studies have focused on observing the co- and post-seismic responses of Canterbury. Beavan et al. (2012) observed post-seismic deformation following the Darfield earthquake using continuous GPS measurements and detected deformation to the east of the Darfield epicentre, close to the epicentre of the subsequent Christchurch earthquake. In addition, several distinct fault segments of the Greendale Fault were delineated. These findings were supported by Syracuse et al. (2012, 2013), who relocated aftershock hypocentres and computed focal mechanisms to highlight eight fault segments. Inversions of focal mechanisms and shear wave splitting analysis yields an average fast direction of 116 ± 18° (Holt et al.2013), similar to the azimuth of maximum horizontal compressive stress (Townend et al.2012). Some stations gave fast directions subparallel to the Greendale Fault, suggesting either structure dependent anisotropy, or stress changing near the fault (Holt et al.2013). Inversions of stress from focal mechanisms showed even clearer rotations of stress near the fault trace compared to those further from the trace. Assuming the rotations along the fault were caused by rotation due to the earthquake stress drop, Holt et al. (2013) inferred that 40  per  cent of pre-seismic differential stress on the Greendale Fault was released in the Darfield earthquake. A high coseismic stress drop was reported (Quigley et al.2012; Beavan et al.2012). Reyners et al. (2014) measured low seismic P- to S-wave ratios of 1.60 post-seismically, decreasing from 1.71 prior to the earthquake. They interpreted the cause to be weakened greywacke producing fault-zone cracking. Reyners et al. (2014) further suggested that the long delay between the Darfield earthquake and the later Christchurch event was a result of recovering rock strength through crack healing. Sustained hydrological effects in river discharge and groundwater levels were observed over an interval of a year after the earthquake, with the majority of recovery in the hours immediately following the event (Cox et al.2012). We report here on temporal velocity changes detected in the four months following the Darfield earthquake. Several temporary data sets were analysed in order to examine the short-term response of the seismic velocities in the Canterbury region. 2 DATA AND METHODS The data used in this study were acquired using two temporary, rapid-response networks deployed across the Canterbury region following the Darfield event to record the aftershock sequence (Fig. 1, top panel). The GeoNet rapid-response network consisting of nine short-period sensors was operational from 2010 September 05 to September 29 (Gledhill et al.2011). Thirteen seismometer stations were deployed by Victoria University of Wellington (VUW), the University of Wisconsin–Madison (UWM) and the University of Auckland (UA, Syracuse et al.2012; Savage et al.2013). These broad-band and short-period seismometers were in operation for four months from 2010 September 18 until 2011 January 13. The two temporary networks consisted of stations deployed on and surrounding the Greendale Fault. Interstation paths ranged from 6 to 156 km (Fig. 1, top panel). The two data sets were processed separately and augmented by data from several nearby permanent broad-band stations of the national GeoNet network (Peterson et al.2011). Figure 1. View largeDownload slide Top panel: map of Canterbury area showing the epicentre of the Darfield earthquake (yellow star). Mapped faults are shown by thin grey lines and the Greendale Fault (Quigley et al.2012) is highlighted in blue. Coloured symbols show locations of GeoNet permanent broad-band stations (brown diamonds), GeoNet rapid-response temporary stations (blue circles) and VUW–UWM–UA (red squares and purple triangles for on- and off-fault stations, respectively). Inset shows the location of the study area within New Zealand. Bottom panel: effect of stacking on cross-correlation functions. The example shown is for the vertical–vertical correlation function for on-fault station pair DAR04–DAR07 (path highlighted on top panel). The black trace is an individual daily correlation for 2010 November 19 and the red line is the corresponding average stack. Figure 1. View largeDownload slide Top panel: map of Canterbury area showing the epicentre of the Darfield earthquake (yellow star). Mapped faults are shown by thin grey lines and the Greendale Fault (Quigley et al.2012) is highlighted in blue. Coloured symbols show locations of GeoNet permanent broad-band stations (brown diamonds), GeoNet rapid-response temporary stations (blue circles) and VUW–UWM–UA (red squares and purple triangles for on- and off-fault stations, respectively). Inset shows the location of the study area within New Zealand. Bottom panel: effect of stacking on cross-correlation functions. The example shown is for the vertical–vertical correlation function for on-fault station pair DAR04–DAR07 (path highlighted on top panel). The black trace is an individual daily correlation for 2010 November 19 and the red line is the corresponding average stack. Daily cross-correlation functions were computed following the methodology of Bensen et al. (2007) using the MSNoise package (Lecocq et al.2014) for the duration of both temporary deployments. Several pre-processing steps enhanced the data for ambient noise analyses. Day-long vertical- and horizontal-component seismograms were resampled to 25 Hz and a 0.01–12 Hz bandpass filter was applied. The mean, trend and instrument responses were removed to allow cross-correlations across different networks, as several different instrument types were used. Spectral whitening between 0.05 and 10.0 Hz was applied to all daily traces, prior to one-bit normalization, suppressing higher amplitude signals from aftershocks and enhancing scattered waves. Although several methods of amplitude normalization exist (Bensen et al.2007), one-bit normalization is employed here as it is most robust in removing signals from aftershocks of all magnitudes, which dominate the records in this time period. For each pair of stations, the radial (R), transverse (T) and vertical (Z) seismograms from one station were cross-correlated with the other’s to yield nine cross-correlation functions (ZZ, ZR, ZT, RR, RT, RZ, TT, TR and TZ), approximating the nine-component Green’s function tensor. The two signals were cross-correlated in 15-min windows and stacked to produce daily cross-correlation functions (Fig. 1, bottom panel). For the resulting signals with positive time lags, the first letter represents the response of a force in that polarization at the first station, to be recorded by the corresponding component of the second station, denoted by the second letter. This is reversed for negative time lags (Shapiro & Campillo 2004). The daily functions are stacked for each station pair over the whole study period, of four months, to produce reference stacks in the 0.1–1.0 Hz frequency band. For every consecutive 10 d, shorter stacks were calculated for the same frequency band, herein referred to as moving stacks. Fig. 2 plots the cross-correlations of the ZZ components for the entire data set as a function of time and interstation distance. Peaks generally follow each other with moveouts suggesting velocities from between 1 and 3 km s−1, although some variation in peaks’ arrival times may be caused by lateral variations in velocity (Syracuse et al.2013). The coherence of the 10-d and 2-month stacks (Fig. 3) convinces us that the reference stacks are robust. Figure 2. View largeDownload slide Vertical-component cross-correlations as a function of interstation distance. Broad-band ZZ cross-correlation functions for all stations pairs are shown for positive lag times, to 100 s. Lines with moveout velocities of 1 km s−1 (red line), 2 km s−1 (blue) and 3 km s−1 (green) are shown as a guide to moveouts present across the study region. Figure 2. View largeDownload slide Vertical-component cross-correlations as a function of interstation distance. Broad-band ZZ cross-correlation functions for all stations pairs are shown for positive lag times, to 100 s. Lines with moveout velocities of 1 km s−1 (red line), 2 km s−1 (blue) and 3 km s−1 (green) are shown as a guide to moveouts present across the study region. Figure 3. View largeDownload slide Example of delay time versus lag time using the MWCS method for a representative 10-d stack for station pair DAR03–DAR08. Top panel shows the reference stack (red) and a representative 10-d stack for the 10 d prior to and including 2010 November 21 (black line). The inset shows an enlarged section of the cross-correlations highlighted by the black box. For the 10 s period, the delay time and corresponding coherence are calculated. This result contributes a point on the delay time versus lag time (lower panel) for the same day. The slope of a linear regression for lag times within the pink boxes, which are selected according to interstation distances, gives the relative delay time for that day. Figure 3. View largeDownload slide Example of delay time versus lag time using the MWCS method for a representative 10-d stack for station pair DAR03–DAR08. Top panel shows the reference stack (red) and a representative 10-d stack for the 10 d prior to and including 2010 November 21 (black line). The inset shows an enlarged section of the cross-correlations highlighted by the black box. For the 10 s period, the delay time and corresponding coherence are calculated. This result contributes a point on the delay time versus lag time (lower panel) for the same day. The slope of a linear regression for lag times within the pink boxes, which are selected according to interstation distances, gives the relative delay time for that day. The MWCS method (Clarke et al.2011) was used to examine velocity variations. The short-duration 10-d stacks of cross-correlations were compared to the reference stacks. The choice of moving stack length is determined by considering the length of the reference stack and the time scale on which velocity changes are expected to occur. The moving stack should be sufficiently short in comparison to the reference stack so that changes can be detected as we are considering the long-term recovery of the region. Taking this into account and to ensure that the moving stacks are stable through time, a 10-d stack was considered appropriate. A value of coherence and time delay between the reference stack and the moving stacks for each 10 s segment was computed (Fig. 3, inset). For coherence values below 0.7, the time delay measurement was discarded from subsequent processing. The slope of the time delays versus lag time for each moving stack gives an overall percentage time delay from the reference stack for each moving stack (Fig. 3). The inverse of the slope of the delay time versus lag time gives a 10-d value of relative velocity change, which is the percentage velocity deviation from the reference stack (Clarke et al.2011). The MWCS method is performed on each of the nine cross-correlation components for each station pair. For each component, results from all station pairs on a given day are combined to give a network-wide average weighted by delay time uncertainty. The two temporary deployments (both augmented by permanent stations) were processed separately as there was only a 10-d overlap when both stations were recording. The broad-band deployment was broken into two sets of measurements because there was a six week gap between the end of November and mid-December when data from several stations were missing or unsuitable for processing. As the MWCS measurements only give relative velocity measurements, we needed to correct for the likely absolute differences in velocities for the three sets of deployments. For the short-period and broad-band deployments there was an overlap of 10 d, so we assumed that the average velocities within the two sets of stations were the same, and corrected the broad-band station’s velocity changes by the average difference between the two sets of velocities over the common deployment time. Correcting for the last set of data was more difficult because there was no closely spaced network operating with which to compare. Therefore, we made an assumption that processes controlling the increase in velocity during the first two deployments continued at the same rate. We then fit the increase in velocity by a curve of the form y = a log(x/b) and extrapolated the curve to the time of the last set of velocity changes, fixing the zero for the last set to the extrapolated velocity change. We also extrapolated the curve backwards in time to determine an estimate of the possible total velocity change since the earthquake. These last extrapolation steps are considered the most tenuous, so we do not interpret the extrapolation except to compare the consistency of the assumption with the measured velocity changes to other studies. Several quality control measures were implemented through the processing procedure. Only station pairs with a minimum interstation distance of three wavelengths were considered, so that several full surface wave cycles were completed between stations (Lin et al.2007). In addition, when computing MWCS delay times, to examine only the direct surface wave coda, cross-correlation lag times that give surface wave velocities outside the range 0.7–4.0 km s−1 are discarded, dependent on interstation distance and assuming a simple speed = distance × time relationship. 3 RESULTS Fig. 1 (bottom panel) shows an example daily cross-correlation function for the on-fault station pair DAR04–DAR07 compared to its corresponding reference function for the two months with the longest continuous duration. Incoherent noise signals at longer lag times have been suppressed in the stacked trace and the surface wave arrivals are emergent and less contaminated with random noise. For this representative station pair (Fig. 1, bottom panel), signal amplitudes on the negative Green’s function, corresponding to waves traveling from east to west, are systematically larger than the positive response. The interstation path is orthogonal to the coastline, and so ocean waves traveling in from the coast towards the west dominate the noise field (Brooks et al.2009; Behr et al.2013). Cross-correlations as a function of interstation distance confirm average group velocities of 1–3 km s−1, consistent with earlier studies covering the region using subsets of this data (Savage et al.2013; Fry et al.2014). Relative velocity variations are shown in Fig. 4 for 0.1–1 Hz frequencies. The variations have been plotted relative to the beginning of the study period in mid-September 2010. The output of MWCS gives velocity differences from the average reference cross-correlation of all components for each station pair, shown in Fig. 4 as the dashed black and solid blue and green lines. The velocity variations for each component are plotted separately (thin grey lines). There is an overall increase of 0.13 ± 0.04  per  cent and variations between components can be seen. As explained in the previous methods section, in order to examine the overall regional velocity change following the earthquake, the results for the second data set are corrected by a constant to follow the trend of the GeoNet rapid response results, giving a pseudo-continuous velocity change curve. Although the stations sample the same overall region, the two temporary networks do not have the same lateral sensitivity. The correction assumes that the crustal seismic velocity recovery is laterally homogeneous over the entire region as sampled by the seismic networks. Spatial changes in velocity variations across the region are not strongly apparent. Fig. 5 shows velocity change curves for interstation paths including OXZ and DAR06. Station OXZ lies in the northwest corner of the study area, approximately 30 km to the north of the fault trace. DAR06 is situated in the centre of the fault trace. The stations do not have obvious differences in their trend, despite the differing locations. Using a longer stack does not provide enough measurements to confidently examine spatial variations. Once average velocity increases for each component (Fig. 4) are calculated, clearer trends are visible. This is due to each dt/t measurement being weighted according to time delay coherence and measurement uncertainty. Figure 4. View largeDownload slide Seismic velocity variations for the extended study period. Variations are shown relative to the beginning of the study period, immediately following the Darfield earthquake. Grey lines show the nine separate cross-correlation components. Blue and green lines are the means of all components for the separate data sets used in this study. The dashed line shows the VUW–AUCK–UWM results prior to shifting (see the text for explanation). Figure 4. View largeDownload slide Seismic velocity variations for the extended study period. Variations are shown relative to the beginning of the study period, immediately following the Darfield earthquake. Grey lines show the nine separate cross-correlation components. Blue and green lines are the means of all components for the separate data sets used in this study. The dashed line shows the VUW–AUCK–UWM results prior to shifting (see the text for explanation). Figure 5. View largeDownload slide Examples of individual relative velocity variation curves for individual station pairs. Ten-day stacks with a 1-d moving window are used to compute velocity variations. Each line represents the curve calculated for each interstation path from stations OXZ (top panel) and DAR06 (lower panel). Figure 5. View largeDownload slide Examples of individual relative velocity variation curves for individual station pairs. Ten-day stacks with a 1-d moving window are used to compute velocity variations. Each line represents the curve calculated for each interstation path from stations OXZ (top panel) and DAR06 (lower panel). 4 DISCUSSION The surface wave velocity change of 0.13 ± 0.04  per  cent over the two and a half month study period is comparable to that observed in other similar studies elsewhere. A 0.02  per  cent increase in velocity was recorded in the two months immediately following the lower magnitude Mw 6.0 Parkfield earthquake in California (Brenguier et al.2008). Pre-seismic levels were measured using continuous seismic waveforms from several years prior to the earthquake and velocities returned to pre-seismic levels at the same rate as GPS displacements over several years (Brenguier et al.2008). Using autocorrelations of seismic waveforms following the 2011 Tohoku-Oki Mw 9.0 event, Minato et al. (2012) observed a 1.5  per  cent velocity increase for the same two-month time period. Pre- and coseismic velocity levels cannot be determined in this study as the majority of the data are from rapid-response networks. Analysis was performed on several of the permanent continuous national stations, but these stations are too distant from the Greendale Fault to achieve a high enough signal-to-noise ratio to record any short-term velocity changes. Thus, we do not have enough data to determine pre- versus post-earthquake changes. If the Green’s function tensor components are examined separately (Fig. 6 and Table 1), cross-correlations with a transverse component (i.e. TT, ZT and TR) show slightly smaller increases in velocity (up to 0.03  per  cent) compared to those without (i.e. RR, ZZ, RZ and ZR), which predominately record Rayleigh waves. This could suggest that Rayleigh waves are perturbed by subsurface structures more than Love waves. However, these variations are all within the bounds of uncertainty for the delay time measurements (Table 1). There are some small, erratic, short-term velocity changes seen at all components that are not accounted for by measurement error and do not correlate with time across components. They are likely errors introduced by the recorded raw data, either by missing data or recording glitches that were not sufficiently suppressed during pre-processing. Figure 6. View largeDownload slide Seismic velocity variations for the nine cross-correlation components for the GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Figure 6. View largeDownload slide Seismic velocity variations for the nine cross-correlation components for the GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Table 1. Relative velocity increases by cross-correlation component. All measurements have 95  per  cent confidence intervals of ± 0.01  per  cent. Component  Velocity increase (per cent)  ZZ  0.13  RR  0.15  TT  0.13  ZR  0.15  RZ  0.14  ZT  0.12  RT  0.14  TR  0.12  TZ  0.14  Component  Velocity increase (per cent)  ZZ  0.13  RR  0.15  TT  0.13  ZR  0.15  RZ  0.14  ZT  0.12  RT  0.14  TR  0.12  TZ  0.14  View Large Fig. 7 shows the modeled fit to the data, with 95  per  cent confidence intervals. The data used for modeling were the GeoNet temporary network results and the VUW–UA–UWM results until the end of 2010 November (red closed and open circles). Results for the end of 2010 December and beginning of 2011 January follow a 6-week gap, where data from several stations were missing or unsuitable for processing. The results for this later time period were processed separately from the other data sets (Fig. 7, closed blue circles), and then shifted to fit the model, according to the average difference between the data points and the curve, as discussed in the methods section. The total seismic velocity increase for the 140 d following the earthquake is estimated to be 0.14  per  cent. The seismic velocity increase over the period for which we have most control is 0.1 ± 0.01  per  cent for the times between 10 and 85 d after the earthquake. The slope of the velocity changes between 110 and 130 d are consistent with extrapolation of the curve between 10 and 85 d, which would suggest a 0.14  per  cent change between 10 and 130 d after the earthquake. Figure 7. View largeDownload slide Modeled best fit to the velocity increase results, assuming a simple y=a*log(x/b) relationship, with 95  per  cent confidence intervals. The fitted data are shown in red (open and closed circles) with the later data (closed blue circles) shifted to confirm the validity of the model (open blue circles). The best-fit relationship is shown alongside the result. Figure 7. View largeDownload slide Modeled best fit to the velocity increase results, assuming a simple y=a*log(x/b) relationship, with 95  per  cent confidence intervals. The fitted data are shown in red (open and closed circles) with the later data (closed blue circles) shifted to confirm the validity of the model (open blue circles). The best-fit relationship is shown alongside the result. To assess possible mechanisms for the post-seismic velocity changes, the results for vertical-component cross-correlations have been divided into several narrow frequency bands (Fig. 8, left-hand panel). Velocities increase steadily for frequencies higher than 0.2 Hz, with the largest increases of up to 0.25  per  cent occurring within 0.5–1 Hz, with velocities increasing over the whole time period considered. The 0.2–0.5 Hz results show a steady increase to 0.12  per  cent until the end of October, then seismic velocities stabilize at these frequencies. Lower frequencies of 0.1–0.2 Hz do not show any increase in velocity over the study period. Fig. 8 (right-hand panel) gives fundamental mode Rayleigh wave sensitivity kernels for frequencies considered in this study, generated using an average regional velocity model (Eberhart-Phillips et al.2010) and the codes of Herrmann (2013). At shallow depths, the depth of maximum sensitivity in kilometres is approximately equal to the inverse of the surface wave frequency. Therefore, the highest velocity increases of 0.25  per  cent are occurring in the uppermost 2 km. The waves in the analysed frequency range have little sensitivity below 5 km depth. Comparable results have been seen for other large earthquakes. The 2003 San Simeon and 2004 Parkfield earthquakes in California showed that seismic velocity increases were largest for short periods less than 1 s, or 1 Hz frequency, up to 0.2  per  cent, with periods greater than 1.6 s (0.625 Hz) showing very little long-term increase (Wu et al.2016). Liu et al. (2014) and Hobiger et al. (2012) demonstrated similar results with negligible velocity increases at long periods for the 2008 Wenchuan and 2008 Iwate–Miyagi Nairiku events, respectively. Figure 8. View largeDownload slide Left-hand panel: vertical-component seismic velocity variations in the period band 0.1–1 Hz and three sub-bands of 0.5–1, 0.2–0.5 and 0.2–0.1 Hz, respectively. Changes are given for GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Right-hand panel: depth sensitivity kernels for the Canterbury basin. Presented are derivatives of the fundamental-mode Rayleigh wave group velocity with respect to shear wave velocity, at several periods. The derivatives are based on an average regional velocity model (Eberhart-Phillips et al.2010). Figure 8. View largeDownload slide Left-hand panel: vertical-component seismic velocity variations in the period band 0.1–1 Hz and three sub-bands of 0.5–1, 0.2–0.5 and 0.2–0.1 Hz, respectively. Changes are given for GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Right-hand panel: depth sensitivity kernels for the Canterbury basin. Presented are derivatives of the fundamental-mode Rayleigh wave group velocity with respect to shear wave velocity, at several periods. The derivatives are based on an average regional velocity model (Eberhart-Phillips et al.2010). Several possible mechanisms for velocity changes following earthquakes have been proposed, as summarized by Xu & Song (2009). First, seismic velocities could be affected by short-term groundwater responses and other fluid movements. Cox et al. (2012) and Gulley et al. (2013) observed groundwater responses following the Darfield earthquake throughout the region, on time scales of hours to days. Here, a moving-window length of 10 d was considered, so any short-term changes would not be recorded. A second possible mechanism is through damage of shallow crust from strong ground shaking. This is one likely mechanism present here, as the frequencies of 0.1–1 Hz analysed above equate to shallow crustal depths of the upper 2 km. One contributing mechanism likely is damage from the fault-zone rupture and subsequent healing of cracks. Velocity changes are seen across the region, not just for station pairs with paths crossing the Greendale Fault, indicating that the healing of microcracks in addition to crack healing of the Greendale Fault, was the dominant factor for change. The lack of difference between velocity changes in horizontal and vertical components suggests that if anisotropic velocity is present, crack healing has not changed it. This work has successfully shown an increase in surface wave velocities throughout the Canterbury region following the Darfield earthquake using the MWCS method. Average changes of up to 0.15  per  cent were seen down to 10 km depth across all nine components of the Green’s function tensor, with the largest velocity increases occurring in the uppermost 2 km. This method complements other studies following large earthquakes to examine the post-seismic stress relaxation and recovery of fault zones. Acknowledgements This work was funded by grant VUW1312 from the NZ Marsden fund and a Victoria University scholarship. The broad-band temporary station data were collected using funding from NSF grants EAR-1102767 and 10/CE618 from the New Zealand Earthquake Commission, and are available from the IRIS data management centre. Instrumentation for the temporary deployments was provided by PASSCAL, GNS Science Wairakei and the University of Auckland. GeoNet provided permanent and temporary seismic station data. Cross-correlations and velocity variations were computed using the MSNoise processing package. Comments on earlier versions of the manuscript were provided by F. Brenguier, A. Ferreira and two anonymous reviewers. REFERENCES Bannister S., Gledhill K., 2012. Evolution of the 2010–2012 Canterbury earthquake sequence, N. Z. J. Geol. Geophys. , 55( 3), 295– 304. https://doi.org/10.1080/00288306.2012.680475 Google Scholar CrossRef Search ADS   Beavan J., Motagh M., Fielding E.J., Donnelly N., Collett D., 2012. Fault slip models of the 2010–2011 Canterbury, New Zealand, earthquakes from geodetic data and observations of postseismic ground deformation, N. Z. J. Geol. 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Post-seismic velocity changes following the 2010 Mw 7.1 Darfield earthquake, New Zealand, revealed by ambient seismic field analysis

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Oxford University Press
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© The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.
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0956-540X
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1365-246X
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10.1093/gji/ggy021
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Abstract

Summary Quantifying seismic velocity changes following large earthquakes can provide insights into fault healing and reloading processes. This study presents temporal velocity changes detected following the 2010 September Mw 7.1 Darfield event in Canterbury, New Zealand. We use continuous waveform data from several temporary seismic networks lying on and surrounding the Greendale Fault, with a maximum interstation distance of 156 km. Nine-component, day-long Green’s functions were computed for frequencies between 0.1 and 1.0 Hz for continuous seismic records from immediately after the 2010 September 04 earthquake until 2011 January 10. Using the moving-window cross-spectral method, seismic velocity changes were calculated. Over the study period, an increase in seismic velocity of 0.14 ± 0.04  per  cent was determined near the Greendale Fault, providing a new constraint on post-seismic relaxation rates in the region. A depth analysis further showed that velocity changes were confined to the uppermost 5 km of the subsurface. We attribute the observed changes to post-seismic relaxation via crack healing of the Greendale Fault and throughout the surrounding region. New Zealand, Seismic interferometry, Seismic noise, Seismic tomography, Surface waves and free oscillations, Wave propagation 1 INTRODUCTION When considering hazards in earthquake-prone regions, knowledge of subsurface material properties is important. The monitoring of crustal properties, such as seismic surface wave velocities can elucidate valuable information about the regional stresses. Ambient seismic noise is increasingly being used to evaluate crustal seismic properties. Cross-correlations of long-duration seismic records yield information about the propagation velocities of scattered surface waves (Shapiro & Campillo 2004). For a pair of seismic stations, the cross-correlation functions contain positive and negative time lags, which are analogous to the causal and acausal Green’s functions (Bensen et al.2007; Yang et al.2008). That is, the positive time lags represent arrival times of waves traveling in one direction as if one station is a source and the other the receiver. Negative time lags represent waves traveling in opposite directions, with roles reversed. A method for detecting seismic velocity variations, known as moving-window cross-spectral (MWCS) analysis, using earthquake multiplets, was proposed by Ratdomopurbo & Poupinet (1995) and has been modified for ambient seismic noise (Clarke et al.2011; Lecocq et al.2014). Relative delay times between long-duration cross-correlation stacks and those of shorter duration are computed and can be used to calculate relative velocity changes. This technique has since been used to successfully detect seismic velocity variations following large earthquakes. Brenguier et al. (2008) first used the MWCS method to examine earthquake-induced seismic velocity changes with ambient noise cross-correlations. A 0.08  per  cent increase in velocity was recorded over three years following the Mw 6.0 Parkfield earthquake in California and velocities returned to pre-seismic levels at the same rate as Global Positioning System (GPS) displacements over several years. The use of ambient seismic noise in New Zealand is already well established. The first major study into the ambient seismic noise field in New Zealand produced Rayleigh wave group velocity maps, and highlighted the Canterbury basin as a low-velocity region (Lin et al.2007). Smaller scale studies considered several regions of New Zealand’s North Island. Behr et al. (2010) estimated a Moho depth of 28 km for the Northland Peninsula from surface wave dispersion curves, in agreement with active-source methods. Beamforming analyses of the ambient noise field in New Zealand highlighted the first higher mode Rayleigh waves (Brooks et al.2009) and suggested several possible sources concerning ocean-wave movements (Behr et al.2013). The Mw 7.1 Darfield earthquake of 2010 September 04 was the first and largest event in a damaging earthquake sequence that struck the Canterbury region in the South Island of New Zealand between 2010 and 2012. The earthquake occurred west of Christchurch on the previously unrecognized Greendale Fault (Bannister & Gledhill 2012). A surface rupture of nearly 30 km was observed, exhibiting predominantly right-lateral strike-slip motion (Quigley et al.2012). The aftershocks that followed revealed a broad pattern of eastwards hypocentral migration and included several earthquakes larger than ML 5 (Syracuse et al.2012, 2013). This sequence included the Mw 6.3 Christchurch earthquake of 2011 February 22, which struck at a depth of 3–4 km (Kaiser et al.2012), 6 km south of the central business district (Bannister & Gledhill 2012), causing widespread damage throughout the city, resulting in 185 deaths. Recorded ground accelerations of over 1.25 g during the Darfield earthquake were the largest recorded in New Zealand (Fry & Gerstenberger 2011) to that point and apparent stresses of almost 16 MPa are extremely high compared to global averages (Fry & Gerstenberger 2011). Fry et al. (2014) used ambient seismic noise on the permanent GeoNet network to measure anisotropy from surface wave dispersion of fundamental-mode Rayleigh waves throughout Canterbury. At upper crustal depths, east–west trending fast axes parallel to the Greendale Fault and Cretaceous faults were recorded. At lower crustal depths, fast axes were shown to be parallel to the present plate boundary strain direction (Fry et al.2014). Ambient noise cross-correlations within the region contain higher mode signals (Savage et al.2013) and comparisons of horizontal- and vertical-component correlation functions show strong first higher mode Rayleigh waves on paths parallel to nearby ocean-wave directions. A basement resonance frequency of approximately 0.4 Hz was obtained from H/V ratios of higher mode Rayleigh waves (Savage et al.2013). Several studies have focused on observing the co- and post-seismic responses of Canterbury. Beavan et al. (2012) observed post-seismic deformation following the Darfield earthquake using continuous GPS measurements and detected deformation to the east of the Darfield epicentre, close to the epicentre of the subsequent Christchurch earthquake. In addition, several distinct fault segments of the Greendale Fault were delineated. These findings were supported by Syracuse et al. (2012, 2013), who relocated aftershock hypocentres and computed focal mechanisms to highlight eight fault segments. Inversions of focal mechanisms and shear wave splitting analysis yields an average fast direction of 116 ± 18° (Holt et al.2013), similar to the azimuth of maximum horizontal compressive stress (Townend et al.2012). Some stations gave fast directions subparallel to the Greendale Fault, suggesting either structure dependent anisotropy, or stress changing near the fault (Holt et al.2013). Inversions of stress from focal mechanisms showed even clearer rotations of stress near the fault trace compared to those further from the trace. Assuming the rotations along the fault were caused by rotation due to the earthquake stress drop, Holt et al. (2013) inferred that 40  per  cent of pre-seismic differential stress on the Greendale Fault was released in the Darfield earthquake. A high coseismic stress drop was reported (Quigley et al.2012; Beavan et al.2012). Reyners et al. (2014) measured low seismic P- to S-wave ratios of 1.60 post-seismically, decreasing from 1.71 prior to the earthquake. They interpreted the cause to be weakened greywacke producing fault-zone cracking. Reyners et al. (2014) further suggested that the long delay between the Darfield earthquake and the later Christchurch event was a result of recovering rock strength through crack healing. Sustained hydrological effects in river discharge and groundwater levels were observed over an interval of a year after the earthquake, with the majority of recovery in the hours immediately following the event (Cox et al.2012). We report here on temporal velocity changes detected in the four months following the Darfield earthquake. Several temporary data sets were analysed in order to examine the short-term response of the seismic velocities in the Canterbury region. 2 DATA AND METHODS The data used in this study were acquired using two temporary, rapid-response networks deployed across the Canterbury region following the Darfield event to record the aftershock sequence (Fig. 1, top panel). The GeoNet rapid-response network consisting of nine short-period sensors was operational from 2010 September 05 to September 29 (Gledhill et al.2011). Thirteen seismometer stations were deployed by Victoria University of Wellington (VUW), the University of Wisconsin–Madison (UWM) and the University of Auckland (UA, Syracuse et al.2012; Savage et al.2013). These broad-band and short-period seismometers were in operation for four months from 2010 September 18 until 2011 January 13. The two temporary networks consisted of stations deployed on and surrounding the Greendale Fault. Interstation paths ranged from 6 to 156 km (Fig. 1, top panel). The two data sets were processed separately and augmented by data from several nearby permanent broad-band stations of the national GeoNet network (Peterson et al.2011). Figure 1. View largeDownload slide Top panel: map of Canterbury area showing the epicentre of the Darfield earthquake (yellow star). Mapped faults are shown by thin grey lines and the Greendale Fault (Quigley et al.2012) is highlighted in blue. Coloured symbols show locations of GeoNet permanent broad-band stations (brown diamonds), GeoNet rapid-response temporary stations (blue circles) and VUW–UWM–UA (red squares and purple triangles for on- and off-fault stations, respectively). Inset shows the location of the study area within New Zealand. Bottom panel: effect of stacking on cross-correlation functions. The example shown is for the vertical–vertical correlation function for on-fault station pair DAR04–DAR07 (path highlighted on top panel). The black trace is an individual daily correlation for 2010 November 19 and the red line is the corresponding average stack. Figure 1. View largeDownload slide Top panel: map of Canterbury area showing the epicentre of the Darfield earthquake (yellow star). Mapped faults are shown by thin grey lines and the Greendale Fault (Quigley et al.2012) is highlighted in blue. Coloured symbols show locations of GeoNet permanent broad-band stations (brown diamonds), GeoNet rapid-response temporary stations (blue circles) and VUW–UWM–UA (red squares and purple triangles for on- and off-fault stations, respectively). Inset shows the location of the study area within New Zealand. Bottom panel: effect of stacking on cross-correlation functions. The example shown is for the vertical–vertical correlation function for on-fault station pair DAR04–DAR07 (path highlighted on top panel). The black trace is an individual daily correlation for 2010 November 19 and the red line is the corresponding average stack. Daily cross-correlation functions were computed following the methodology of Bensen et al. (2007) using the MSNoise package (Lecocq et al.2014) for the duration of both temporary deployments. Several pre-processing steps enhanced the data for ambient noise analyses. Day-long vertical- and horizontal-component seismograms were resampled to 25 Hz and a 0.01–12 Hz bandpass filter was applied. The mean, trend and instrument responses were removed to allow cross-correlations across different networks, as several different instrument types were used. Spectral whitening between 0.05 and 10.0 Hz was applied to all daily traces, prior to one-bit normalization, suppressing higher amplitude signals from aftershocks and enhancing scattered waves. Although several methods of amplitude normalization exist (Bensen et al.2007), one-bit normalization is employed here as it is most robust in removing signals from aftershocks of all magnitudes, which dominate the records in this time period. For each pair of stations, the radial (R), transverse (T) and vertical (Z) seismograms from one station were cross-correlated with the other’s to yield nine cross-correlation functions (ZZ, ZR, ZT, RR, RT, RZ, TT, TR and TZ), approximating the nine-component Green’s function tensor. The two signals were cross-correlated in 15-min windows and stacked to produce daily cross-correlation functions (Fig. 1, bottom panel). For the resulting signals with positive time lags, the first letter represents the response of a force in that polarization at the first station, to be recorded by the corresponding component of the second station, denoted by the second letter. This is reversed for negative time lags (Shapiro & Campillo 2004). The daily functions are stacked for each station pair over the whole study period, of four months, to produce reference stacks in the 0.1–1.0 Hz frequency band. For every consecutive 10 d, shorter stacks were calculated for the same frequency band, herein referred to as moving stacks. Fig. 2 plots the cross-correlations of the ZZ components for the entire data set as a function of time and interstation distance. Peaks generally follow each other with moveouts suggesting velocities from between 1 and 3 km s−1, although some variation in peaks’ arrival times may be caused by lateral variations in velocity (Syracuse et al.2013). The coherence of the 10-d and 2-month stacks (Fig. 3) convinces us that the reference stacks are robust. Figure 2. View largeDownload slide Vertical-component cross-correlations as a function of interstation distance. Broad-band ZZ cross-correlation functions for all stations pairs are shown for positive lag times, to 100 s. Lines with moveout velocities of 1 km s−1 (red line), 2 km s−1 (blue) and 3 km s−1 (green) are shown as a guide to moveouts present across the study region. Figure 2. View largeDownload slide Vertical-component cross-correlations as a function of interstation distance. Broad-band ZZ cross-correlation functions for all stations pairs are shown for positive lag times, to 100 s. Lines with moveout velocities of 1 km s−1 (red line), 2 km s−1 (blue) and 3 km s−1 (green) are shown as a guide to moveouts present across the study region. Figure 3. View largeDownload slide Example of delay time versus lag time using the MWCS method for a representative 10-d stack for station pair DAR03–DAR08. Top panel shows the reference stack (red) and a representative 10-d stack for the 10 d prior to and including 2010 November 21 (black line). The inset shows an enlarged section of the cross-correlations highlighted by the black box. For the 10 s period, the delay time and corresponding coherence are calculated. This result contributes a point on the delay time versus lag time (lower panel) for the same day. The slope of a linear regression for lag times within the pink boxes, which are selected according to interstation distances, gives the relative delay time for that day. Figure 3. View largeDownload slide Example of delay time versus lag time using the MWCS method for a representative 10-d stack for station pair DAR03–DAR08. Top panel shows the reference stack (red) and a representative 10-d stack for the 10 d prior to and including 2010 November 21 (black line). The inset shows an enlarged section of the cross-correlations highlighted by the black box. For the 10 s period, the delay time and corresponding coherence are calculated. This result contributes a point on the delay time versus lag time (lower panel) for the same day. The slope of a linear regression for lag times within the pink boxes, which are selected according to interstation distances, gives the relative delay time for that day. The MWCS method (Clarke et al.2011) was used to examine velocity variations. The short-duration 10-d stacks of cross-correlations were compared to the reference stacks. The choice of moving stack length is determined by considering the length of the reference stack and the time scale on which velocity changes are expected to occur. The moving stack should be sufficiently short in comparison to the reference stack so that changes can be detected as we are considering the long-term recovery of the region. Taking this into account and to ensure that the moving stacks are stable through time, a 10-d stack was considered appropriate. A value of coherence and time delay between the reference stack and the moving stacks for each 10 s segment was computed (Fig. 3, inset). For coherence values below 0.7, the time delay measurement was discarded from subsequent processing. The slope of the time delays versus lag time for each moving stack gives an overall percentage time delay from the reference stack for each moving stack (Fig. 3). The inverse of the slope of the delay time versus lag time gives a 10-d value of relative velocity change, which is the percentage velocity deviation from the reference stack (Clarke et al.2011). The MWCS method is performed on each of the nine cross-correlation components for each station pair. For each component, results from all station pairs on a given day are combined to give a network-wide average weighted by delay time uncertainty. The two temporary deployments (both augmented by permanent stations) were processed separately as there was only a 10-d overlap when both stations were recording. The broad-band deployment was broken into two sets of measurements because there was a six week gap between the end of November and mid-December when data from several stations were missing or unsuitable for processing. As the MWCS measurements only give relative velocity measurements, we needed to correct for the likely absolute differences in velocities for the three sets of deployments. For the short-period and broad-band deployments there was an overlap of 10 d, so we assumed that the average velocities within the two sets of stations were the same, and corrected the broad-band station’s velocity changes by the average difference between the two sets of velocities over the common deployment time. Correcting for the last set of data was more difficult because there was no closely spaced network operating with which to compare. Therefore, we made an assumption that processes controlling the increase in velocity during the first two deployments continued at the same rate. We then fit the increase in velocity by a curve of the form y = a log(x/b) and extrapolated the curve to the time of the last set of velocity changes, fixing the zero for the last set to the extrapolated velocity change. We also extrapolated the curve backwards in time to determine an estimate of the possible total velocity change since the earthquake. These last extrapolation steps are considered the most tenuous, so we do not interpret the extrapolation except to compare the consistency of the assumption with the measured velocity changes to other studies. Several quality control measures were implemented through the processing procedure. Only station pairs with a minimum interstation distance of three wavelengths were considered, so that several full surface wave cycles were completed between stations (Lin et al.2007). In addition, when computing MWCS delay times, to examine only the direct surface wave coda, cross-correlation lag times that give surface wave velocities outside the range 0.7–4.0 km s−1 are discarded, dependent on interstation distance and assuming a simple speed = distance × time relationship. 3 RESULTS Fig. 1 (bottom panel) shows an example daily cross-correlation function for the on-fault station pair DAR04–DAR07 compared to its corresponding reference function for the two months with the longest continuous duration. Incoherent noise signals at longer lag times have been suppressed in the stacked trace and the surface wave arrivals are emergent and less contaminated with random noise. For this representative station pair (Fig. 1, bottom panel), signal amplitudes on the negative Green’s function, corresponding to waves traveling from east to west, are systematically larger than the positive response. The interstation path is orthogonal to the coastline, and so ocean waves traveling in from the coast towards the west dominate the noise field (Brooks et al.2009; Behr et al.2013). Cross-correlations as a function of interstation distance confirm average group velocities of 1–3 km s−1, consistent with earlier studies covering the region using subsets of this data (Savage et al.2013; Fry et al.2014). Relative velocity variations are shown in Fig. 4 for 0.1–1 Hz frequencies. The variations have been plotted relative to the beginning of the study period in mid-September 2010. The output of MWCS gives velocity differences from the average reference cross-correlation of all components for each station pair, shown in Fig. 4 as the dashed black and solid blue and green lines. The velocity variations for each component are plotted separately (thin grey lines). There is an overall increase of 0.13 ± 0.04  per  cent and variations between components can be seen. As explained in the previous methods section, in order to examine the overall regional velocity change following the earthquake, the results for the second data set are corrected by a constant to follow the trend of the GeoNet rapid response results, giving a pseudo-continuous velocity change curve. Although the stations sample the same overall region, the two temporary networks do not have the same lateral sensitivity. The correction assumes that the crustal seismic velocity recovery is laterally homogeneous over the entire region as sampled by the seismic networks. Spatial changes in velocity variations across the region are not strongly apparent. Fig. 5 shows velocity change curves for interstation paths including OXZ and DAR06. Station OXZ lies in the northwest corner of the study area, approximately 30 km to the north of the fault trace. DAR06 is situated in the centre of the fault trace. The stations do not have obvious differences in their trend, despite the differing locations. Using a longer stack does not provide enough measurements to confidently examine spatial variations. Once average velocity increases for each component (Fig. 4) are calculated, clearer trends are visible. This is due to each dt/t measurement being weighted according to time delay coherence and measurement uncertainty. Figure 4. View largeDownload slide Seismic velocity variations for the extended study period. Variations are shown relative to the beginning of the study period, immediately following the Darfield earthquake. Grey lines show the nine separate cross-correlation components. Blue and green lines are the means of all components for the separate data sets used in this study. The dashed line shows the VUW–AUCK–UWM results prior to shifting (see the text for explanation). Figure 4. View largeDownload slide Seismic velocity variations for the extended study period. Variations are shown relative to the beginning of the study period, immediately following the Darfield earthquake. Grey lines show the nine separate cross-correlation components. Blue and green lines are the means of all components for the separate data sets used in this study. The dashed line shows the VUW–AUCK–UWM results prior to shifting (see the text for explanation). Figure 5. View largeDownload slide Examples of individual relative velocity variation curves for individual station pairs. Ten-day stacks with a 1-d moving window are used to compute velocity variations. Each line represents the curve calculated for each interstation path from stations OXZ (top panel) and DAR06 (lower panel). Figure 5. View largeDownload slide Examples of individual relative velocity variation curves for individual station pairs. Ten-day stacks with a 1-d moving window are used to compute velocity variations. Each line represents the curve calculated for each interstation path from stations OXZ (top panel) and DAR06 (lower panel). 4 DISCUSSION The surface wave velocity change of 0.13 ± 0.04  per  cent over the two and a half month study period is comparable to that observed in other similar studies elsewhere. A 0.02  per  cent increase in velocity was recorded in the two months immediately following the lower magnitude Mw 6.0 Parkfield earthquake in California (Brenguier et al.2008). Pre-seismic levels were measured using continuous seismic waveforms from several years prior to the earthquake and velocities returned to pre-seismic levels at the same rate as GPS displacements over several years (Brenguier et al.2008). Using autocorrelations of seismic waveforms following the 2011 Tohoku-Oki Mw 9.0 event, Minato et al. (2012) observed a 1.5  per  cent velocity increase for the same two-month time period. Pre- and coseismic velocity levels cannot be determined in this study as the majority of the data are from rapid-response networks. Analysis was performed on several of the permanent continuous national stations, but these stations are too distant from the Greendale Fault to achieve a high enough signal-to-noise ratio to record any short-term velocity changes. Thus, we do not have enough data to determine pre- versus post-earthquake changes. If the Green’s function tensor components are examined separately (Fig. 6 and Table 1), cross-correlations with a transverse component (i.e. TT, ZT and TR) show slightly smaller increases in velocity (up to 0.03  per  cent) compared to those without (i.e. RR, ZZ, RZ and ZR), which predominately record Rayleigh waves. This could suggest that Rayleigh waves are perturbed by subsurface structures more than Love waves. However, these variations are all within the bounds of uncertainty for the delay time measurements (Table 1). There are some small, erratic, short-term velocity changes seen at all components that are not accounted for by measurement error and do not correlate with time across components. They are likely errors introduced by the recorded raw data, either by missing data or recording glitches that were not sufficiently suppressed during pre-processing. Figure 6. View largeDownload slide Seismic velocity variations for the nine cross-correlation components for the GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Figure 6. View largeDownload slide Seismic velocity variations for the nine cross-correlation components for the GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Table 1. Relative velocity increases by cross-correlation component. All measurements have 95  per  cent confidence intervals of ± 0.01  per  cent. Component  Velocity increase (per cent)  ZZ  0.13  RR  0.15  TT  0.13  ZR  0.15  RZ  0.14  ZT  0.12  RT  0.14  TR  0.12  TZ  0.14  Component  Velocity increase (per cent)  ZZ  0.13  RR  0.15  TT  0.13  ZR  0.15  RZ  0.14  ZT  0.12  RT  0.14  TR  0.12  TZ  0.14  View Large Fig. 7 shows the modeled fit to the data, with 95  per  cent confidence intervals. The data used for modeling were the GeoNet temporary network results and the VUW–UA–UWM results until the end of 2010 November (red closed and open circles). Results for the end of 2010 December and beginning of 2011 January follow a 6-week gap, where data from several stations were missing or unsuitable for processing. The results for this later time period were processed separately from the other data sets (Fig. 7, closed blue circles), and then shifted to fit the model, according to the average difference between the data points and the curve, as discussed in the methods section. The total seismic velocity increase for the 140 d following the earthquake is estimated to be 0.14  per  cent. The seismic velocity increase over the period for which we have most control is 0.1 ± 0.01  per  cent for the times between 10 and 85 d after the earthquake. The slope of the velocity changes between 110 and 130 d are consistent with extrapolation of the curve between 10 and 85 d, which would suggest a 0.14  per  cent change between 10 and 130 d after the earthquake. Figure 7. View largeDownload slide Modeled best fit to the velocity increase results, assuming a simple y=a*log(x/b) relationship, with 95  per  cent confidence intervals. The fitted data are shown in red (open and closed circles) with the later data (closed blue circles) shifted to confirm the validity of the model (open blue circles). The best-fit relationship is shown alongside the result. Figure 7. View largeDownload slide Modeled best fit to the velocity increase results, assuming a simple y=a*log(x/b) relationship, with 95  per  cent confidence intervals. The fitted data are shown in red (open and closed circles) with the later data (closed blue circles) shifted to confirm the validity of the model (open blue circles). The best-fit relationship is shown alongside the result. To assess possible mechanisms for the post-seismic velocity changes, the results for vertical-component cross-correlations have been divided into several narrow frequency bands (Fig. 8, left-hand panel). Velocities increase steadily for frequencies higher than 0.2 Hz, with the largest increases of up to 0.25  per  cent occurring within 0.5–1 Hz, with velocities increasing over the whole time period considered. The 0.2–0.5 Hz results show a steady increase to 0.12  per  cent until the end of October, then seismic velocities stabilize at these frequencies. Lower frequencies of 0.1–0.2 Hz do not show any increase in velocity over the study period. Fig. 8 (right-hand panel) gives fundamental mode Rayleigh wave sensitivity kernels for frequencies considered in this study, generated using an average regional velocity model (Eberhart-Phillips et al.2010) and the codes of Herrmann (2013). At shallow depths, the depth of maximum sensitivity in kilometres is approximately equal to the inverse of the surface wave frequency. Therefore, the highest velocity increases of 0.25  per  cent are occurring in the uppermost 2 km. The waves in the analysed frequency range have little sensitivity below 5 km depth. Comparable results have been seen for other large earthquakes. The 2003 San Simeon and 2004 Parkfield earthquakes in California showed that seismic velocity increases were largest for short periods less than 1 s, or 1 Hz frequency, up to 0.2  per  cent, with periods greater than 1.6 s (0.625 Hz) showing very little long-term increase (Wu et al.2016). Liu et al. (2014) and Hobiger et al. (2012) demonstrated similar results with negligible velocity increases at long periods for the 2008 Wenchuan and 2008 Iwate–Miyagi Nairiku events, respectively. Figure 8. View largeDownload slide Left-hand panel: vertical-component seismic velocity variations in the period band 0.1–1 Hz and three sub-bands of 0.5–1, 0.2–0.5 and 0.2–0.1 Hz, respectively. Changes are given for GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Right-hand panel: depth sensitivity kernels for the Canterbury basin. Presented are derivatives of the fundamental-mode Rayleigh wave group velocity with respect to shear wave velocity, at several periods. The derivatives are based on an average regional velocity model (Eberhart-Phillips et al.2010). Figure 8. View largeDownload slide Left-hand panel: vertical-component seismic velocity variations in the period band 0.1–1 Hz and three sub-bands of 0.5–1, 0.2–0.5 and 0.2–0.1 Hz, respectively. Changes are given for GeoNet (blue) and VUW–UA–UWM (green) data sets with associated 95  per  cent confidence intervals. Right-hand panel: depth sensitivity kernels for the Canterbury basin. Presented are derivatives of the fundamental-mode Rayleigh wave group velocity with respect to shear wave velocity, at several periods. The derivatives are based on an average regional velocity model (Eberhart-Phillips et al.2010). Several possible mechanisms for velocity changes following earthquakes have been proposed, as summarized by Xu & Song (2009). First, seismic velocities could be affected by short-term groundwater responses and other fluid movements. Cox et al. (2012) and Gulley et al. (2013) observed groundwater responses following the Darfield earthquake throughout the region, on time scales of hours to days. Here, a moving-window length of 10 d was considered, so any short-term changes would not be recorded. A second possible mechanism is through damage of shallow crust from strong ground shaking. This is one likely mechanism present here, as the frequencies of 0.1–1 Hz analysed above equate to shallow crustal depths of the upper 2 km. One contributing mechanism likely is damage from the fault-zone rupture and subsequent healing of cracks. Velocity changes are seen across the region, not just for station pairs with paths crossing the Greendale Fault, indicating that the healing of microcracks in addition to crack healing of the Greendale Fault, was the dominant factor for change. The lack of difference between velocity changes in horizontal and vertical components suggests that if anisotropic velocity is present, crack healing has not changed it. This work has successfully shown an increase in surface wave velocities throughout the Canterbury region following the Darfield earthquake using the MWCS method. Average changes of up to 0.15  per  cent were seen down to 10 km depth across all nine components of the Green’s function tensor, with the largest velocity increases occurring in the uppermost 2 km. This method complements other studies following large earthquakes to examine the post-seismic stress relaxation and recovery of fault zones. Acknowledgements This work was funded by grant VUW1312 from the NZ Marsden fund and a Victoria University scholarship. The broad-band temporary station data were collected using funding from NSF grants EAR-1102767 and 10/CE618 from the New Zealand Earthquake Commission, and are available from the IRIS data management centre. 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Geophysical Journal InternationalOxford University Press

Published: May 1, 2018

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