Source of the 6 February 2013 M w = 8 . 0 Santa Cruz Islands Tsunami

On 6 February 2013 an Mw = 8.0 subduction earthquake occurred close to Santa Cruz Islands at the transition between the Solomon and the New Hebrides Trench. The ensuing tsunami caused significant inundation on the closest Nendo Island. The seismic source was studied with teleseismic broadband P-wave inversion optimized with tsunami forward modelling at DART buoys (Lay et al., 2013) and with inversion of teleseismic body and surface waves (Hayes et al., 2014a). The two studies also use different hypocentres and different planar fault models and found quite different slip models. In particular, Hayes et al. (2014a) argued for an aseismic slip patch SE from the hypocentre. We here develop a 3-D model of the fault surface from seismicity analysis and retrieve the tsunami source by inverting DART and tide-gauge data. Our tsunami source model features a main slip patch (peak value of ∼ 11 m) SE of the hypocentre and reaching the trench. The rake direction is consistent with the progressively more oblique plate convergence towards the Solomon trench. The tsunami source partially overlaps the hypothesized aseismic slip area, which then might have slipped coseismically.


Introduction 34
On 6 February 2013 an M w 8.0 earthquake occurred in the Pacific Ocean nearby the 35 archipelago of Santa Cruz Islands.The hypocenter (165.138°E10.738°S, depth ~29 km, 36 USGS, http://earthquake.usgs.gov/earthquakes/eqarchives/poster/2013/20130205.php) is 37 located at the subduction interface between the Australia and the Pacific plates, 76 km West 38 from Lata, the main city of Nendo Island (Fig. 1 and Fig. 2).39 This earthquake, the largest in 2013, occurred on a complex section of the Australia-Pacific 40 plate boundary at the northern end of the New Hebrides trench (Hayes et al., 2012), nearby a 41 short segment of dominantly strike-slip plate motion that marks the transition between 42 Vanuatu and the Solomon Islands subduction zones.This segment is characterized by a 43 complex tectonic regime that becomes progressively more oblique westward as revealed by 44 the focal mechanisms of the local seismicity (Fig. 1).In this region the relative convergence 45 velocity between Australia and Pacific plates is ~9.4 cm/yr (DeMets et al., 2010).46 The Santa Cruz Islands earthquake generated a tsunami that struck the Nendo Island, in 47 particular the city of Lata with waves higher than 1 m.Several runup and flowdepth 48 measurements have been collected during a field survey conducted on some islands of the 49 archipelago a few days after the earthquake (Fritz et al., 2014), reporting maximum tsunami 50 wave heights of about 11 m in the western part of the Nendo Island.In addition, the tsunami 51 propagated in the Pacific Ocean, also reaching the coasts of Hawaii (Lay et al., 2013).52 Seismic and tsunami source of this earthquake have been previously studied with different 53 methodologies (Lay et al., 2013;Hayes et al., 2014a), highlighting some differences 54 between the resulting models in terms of both slip patch positions and slip amplitude.In addition, the LA13 source model is more efficient in terms of tsunami wave excitation 69 than that of HA14 and quite well predicts the tsunami observations recorded at the DART 70

buoys. 71
The usual pattern of the aftershocks distribution following a great subduction earthquake 72 should show a large number of events occurring along the unbroken portion of the 73 subduction interface , eventually also bordering the broken asperities (Aki, 1979).On the 74 other hand, as already extensively discussed (Hayes et al., 2014a;Lay et al., 2013), after the 75 6 February 2013 event, very few events were located along the subduction interface.76 Furthermore, most of early aftershocks in the epicentral area (~200 events within 48 hours 77 from the mainshock, http://earthquake.usgs.gov/earthquakes/?source=sitenav) showed 78 strike-slip and normal mechanism, including two earthquakes with M w > 7 occurred in the 79 upper crust portion of the Pacific plate and in the outer-rise trench region.HA14 proposed a 80 block-like motion behaviour of the Pacific upper plate to explain these observations.In 81 particular, they argued that a large number of anomalous right-lateral strike-slip events 82 located southeast of Nendo Island were triggered by significant aseismic slip along a portion 83 of the megathrust south-eastward from the epicentral area.However, LA13 model features 84 significant coseismic slip on this portion of the fault; these differences may be due to the 85 different data used and/or to the different fault models adopted in the inversions.86 Here we study the coseismic tsunami source of the Santa Cruz Islands earthquake by 87 inverting the available tsunami waveforms.We compute the Green's functions at the DART 88 buoys and tide gauges using a 3D fault model that honours the complex geometry of the 89 subduction interface.After retrieving the tsunami source model, we discuss it in comparison 90 with LA13 and HA14 source models.91 http://www.ndbc.noaa.gov/dart.shtml)and 3 tide gauges (Lata Wharf, Honiara, and Lautoka, 99 http://www.ioc-sealevelmonitoring.org) that distinctly recorded a tsunami signal and that 100 allow a good azimuthal coverage (Fig. 2, further details in Supplementary Material).Before 5 using the tsunami data in the inversion, we remove the tide from the original signals by 102 using a robust LOWESS procedure (Barbosa et al., 2004).103 The fault model geometry can greatly influence the results of source inversion.Adopting a 104 fault geometry that honours the complexities of the subduction interface then may help to 105 reduce the epistemic uncertainties associated to forward modelling (Romano et al., 2014).106 This is particularly true for earthquakes of this size occurring in subduction zones 107 characterized by strong variations of strike and/or dip (e.g.Hayes et al., 2014b), even more 108 so in complex tectonic environments like the Santa Cruz Islands region.109 Thus, analysing the aftershocks distribution occurred after the 6 February mainshock, the 110 local seismicity, and considering the rupture area expected for a M8 event, we built a 3D 111 non-planar fault model with variable strike and dip angles in order to account for such 112 geometrical complexities of the subduction interface on both the New Hebrides and 113 Solomon trenches (Bird, 2003).In particular, we selected from the EHB global relocation 114 earthquake catalogue (http://www.isc.ac.uk/ehbbulletin/;Engdahl et al., 1998) the events 115 occurred in the area covered by the aftershocks of the Santa Cruz Islands earthquake and 116 having M > 4.5.After removing those ones relatively distant from the trench (distance > 200 117 km), we drew sections perpendicular to the trench at a distance of ~20 km each (measured 118 along the trench) projecting on them all the events in a neighbourhood of 30 km.We 119 obtained several 2D profiles by fitting the data of each section.The resulting suite of 2D 120 profiles was then further interpolated using CUBIT software (http://cubit.sandia.

Satake, 1996). 136
For tsunami modelling at the DART buoys we use a bathymetric grid with a spatial 137 resolution of 1 arc-min, whereas the Green's functions at the tide gauges are computed on a 138 grid of 30 arc-sec in order to better model the nearshore tsunami propagation.The 139 bathymetric data set used for tsunami simulations is SRTM30+ 140 (http://topex.ucsd.edu/WWW_html/srtm30_plus.html), which is resampled for the grid of 1 141 arc-min.142 We solve the inverse problem by using the Heat Bath algorithm, which is a particular 143 implementation of the Simulated Annealing technique (Rothman, 1986).For tsunami 144 waveforms we use a cost function that is sensitive both to amplitude and phase matching 145 (Spudich and Miller, 1990).This approach and the a-posteriori analysis of the explored 146 ensemble of models have been extensively tested and used in previous works (detailed 147 description of the method can be found for example in Piatanesi  We make some a-priori assumptions on ranges for slip and rake: for each subfault the slip 150 can vary from 0 to 15 m at 0.5 m steps, whereas the rake can vary from 40° to 100° at 5° 151 steps on 3 large blocks (see Fig. S1).Furthermore, we assume a circular rupture front that 152 propagates with a rupture velocity of 1.5 km/s (Lay et al., 2013).153 In each inversion we retrieve the best fitting slip distribution model, the average model 154 obtained by the ensemble of models that fits the data fairly well, and the standard deviations 155 for each inferred model parameter (Table S3).156 157

Checkerboard resolution test 158
We evaluate the resolving power of the inversion setup (i.e., fault parameterization and 159 instrumental azimuthal coverage) by means of a synthetic test.In particular, we attempt to 160 reproduce a slip distribution assuming a target checkerboard pattern with slip values of 0 and 161 10 m on alternating subfaults (Fig. 3a).In addition, we set the target rake angle on the 162 easternmost, middle, and westernmost blocks equal to 90°, 70°, and 50°, respectively.We 163 invert the synthetic tsunami waveforms resulting from the target slip pattern by following 164 the same inversion procedure described above.Synthetic tsunami waveforms are corrupted 165 by adding Gaussian random noise with a variance that is the 10% of the clean waveform 166 amplitude variance.The average model for slip distribution (Fig. 3b) reproduces very well 167 the checkerboard target (Fig. 3a).We observe that the maximum differences between the 168 target and the retrieved slip models are smaller than 1 m on average (absolute value), with a 169 maximum discrepancy of ~2.5 m along the deepest subfaults.The chosen inversion setup is 170 also well calibrated to recover the target slip direction (i.e., the rake angle) on the fault 171 plane, and the comparison between the synthetic and predicted tsunami waveforms shows an 172 excellent agreement (Fig. S3).We point out that such a checkerboard test only allows the 173 analysis of the resolution that is granted in principle by the inversion setup (model geometry, 174 station distribution).Possible epistemic uncertainty that is inherent in the numeric tsunami 175 model and/or due to the inaccuracy of the bathymetric model cannot be quantified in this 176 way.Accordingly, the uncertainty associated to the average slip model (Table S3) is 177 addressed through the analysis of the model ensemble, as discussed in the previous section.Santa Cruz Islands earthquake.The coseismic rupture pattern (average model, Table S3) 184 shows a main patch of slip (Fig. 4), located SE from the hypocenter, centred around 185 hypocenter and centred at a depth of ~29 km around ~165°E ~10.5°S (Fig. 4).This patch 190 has a maximum slip of ~4 m.We found an average rake angle of ~85° in the easternmost 191 part of the fault that is consistent with the relative convergence of the Australia and Pacific 192 plates in this portion of the megathrust.On the other hand, the remaining part of the fault 193 plane to the west is characterized by a slip angle lower than 50°.Hence, the dislocation there 194 highlights a relevant strike-slip component, according with the change of the tectonic regime 195 in this region, from purely thrust to left-lateral, as also shown by the regional seismicity.196 Figure 5 shows an overall good agreement between observed and predicted tsunami 197 waveforms.During the inversion we applied a time shift (+2 min) to the Green's functions 198 of Lata Wharf tide gauge due to the systematic anticipation of the predicted tsunami 199 waveform with respect to the observed signal.This systematic difference between observed 200 and predicted data is likely due to the relatively low accuracy of the nearshore bathymetry 201 around this station.We also proved the validity of the linearity assumption at the coastal tide 202 gauges.The tsunami signals predicted with the time-shifted and linearly combined Green's 203 functions are compared to the tsunami signals produced with a single forward run forced by 204 the average slip model (Figure S4).This is in fair agreement with recent results of Yue et al. 205 (2015).206 The total seismic moment associated to the slip distribution resulting from the inversion, 207 using a shear modulus equal to 30 GPa, is M 0 = 1.033x10 21Nm, that is equivalent to a 208 moment magnitude M w = 8.0 and in agreement with the estimations obtained from previous 209 The slip model in this study, LA13, and HA14 models have been obtained using three 224 different fault geometries (Fig. 6).Indeed, both LA13 and HA14 use a planar fault, whereas 225 we adopt a 3D fault surface honouring the subduction zone interface.In addition, the fault in 226 LA13 is overall shallower with respect to that in HA14, and LA13 also assumes a shallower 227 hypocenter (~13 km, whereas it is ~29 km in HA14, compare Figs.6b,d explain tsunami data to a similar extent, then the main differences between the two may be 234 ascribed either to differences in the adopted fault geometry, or to poor resolving power of 9 our synthetic test, the latter does not seem to be the case, at least as regards the most 237 tsunamigenic part of the source, that is the one with a dominant dip slip component in LA13 238 model.Besides this, we also may argue that the HA14 source, which shows a deeper slip 239 centroid than LA13 (and lower peak slip of about 4 m, Fig. 6a), should result less 240 tsunamigenic with respect to LA13 (peak slip > 10 m, Fig. 6c), and then likely 241 underestimate tsunami observations.242 The centroid of the main asperity individuated in the present study is shifted SE with respect 243 to the main one of HA14 and it features quite larger slip (Fig. 6a).Conversely, it features 244 comparable peak slip values to the shallower patch in LA13 (Fig. 6c), but it is nearer to the 245 Nendo Island, as the two are only partially overlapped.246 We also observe that the rake angle associated to our model is pretty consistent with the 247 relative convergence direction between Australia and Pacific plates.In particular, the slip 248 direction has behaviour close to a thrust-like motion (rake ~85°) in the SE part of the fault 249 just nearby the northern-end of Vanuatu subduction zone; then the slip direction becomes 250 progressively more oblique highlighting a significant left-lateral component that is in 251 agreement with the kinematics (DeMets et al., 2010) and the seismicity of the NW segment 252 of the subduction (Fig. 1).On the other hand, we observe an opposite behaviour of the rake 253 angle in LA13; indeed, the southeastern shallower patch in LA13 has a slip direction with a 254 strong oblique component, whereas the northern deeper patch shows a thrust-like fault 255 motion.Thus, the main tsunamigenic patch in LA13 is located around the hypocenter, 256 whereas in the present study it is located in front of the Nendo Island, very close to the area 257 where the maximum tsunami wave heights have been observed (Fig. 1; Fritz et al., 2014; 258 NOAA/NGDC, http://www.ngdc.noaa.gov/hazard/tsu_db.shtml).Hence, as a likely less 259 tsunamigenic patch is involved, these differences may be due to a combination of the effects 260 of different resolving power of the data used and of different fault geometry.261 In a further analysis, we observe that ~97% of the total seismic moment in our model is 262 released within 75 s from the nucleation.In particular, ~60% of the moment release occurs 263 between 15 and 45 s, as this time window includes most of the main asperity and the peak 264 slip area (Fig. 4).Thus, at least qualitatively, the moment rate we derive by combining the 265 retrieved slip distribution and the imposed rupture velocity is in agreement with the moment 266 rate function resulting from teleseismic inversions.267 268

Seismic rupture propagation SE from the hypocenter 269
The distribution of the early aftershocks (in the first 48h after the mainshock, 270 http://earthquake.usgs.gov/earthquakes/?source=sitenav), shows a lack of significant 271 seismic events occurring at the subduction interface, a feature that might be indicative of a 272 complete stress drop associated to the main 6 February event.On the other hand, a large 273 number of seismic events have been observed mainly in the upper crust of the Pacific plate 274 and in the eastern edge of the Australia plate oceanic crust (Fig. 4).In particular, the largest 275 one in the Pacific plate (M w 7+) occurred North of Nendo Island with a strike-slip right-276 lateral mechanism (Fig. 1) that is consistent with the kinematics of the coseismic slip 277 (HA14).In addition, a cluster of shallow right-lateral aftershocks occurred SE from the 278 mainshock epicenter (magenta ellipse in Fig. 4).In their study, HA14 propose that 279 occurrence of these strike-slip earthquakes is caused by the block-like motion behaviour of 280 the Pacific upper plate.However, they also argue that the Coulomb stress change 281 distribution resulting from the HA14 coseismic model would promote events with left-282 lateral behaviour, whereas significant additional slip located SE from the hypocenter would 283 promote the observed right-lateral aftershocks.They conclude that such slip (see magenta 284 shaded ellipse in Fig. 6a), as not observed in HA14, then should be aseismic, should occur at 285 the megathrust interface, and, in agreement with the Coulomb stress transfer estimation, 286 should release a seismic moment of M 0 = 3.1x10 20 Nm.Thus, the total (coseismic + 287 aseismic) seismic moment released along the southeastern portion of the fault results to be 288 M 0 = 3.9x10 20 Nm.Noteworthy, our slip model is partially overlapped with the aseismic slip 289 area argued by HA14; in particular, we observe larger slip values, up to 9 m confined in a 290 smaller area, versus an average of 2 m of slip on a larger portion of the megathrust (Fig. 6a).291 The seismic moment associated to this portion of slip distribution in our model is M 0 = 292 4.08x10 20 Nm, that is quite compatible with the estimation by HA14.293 The location of the coseismic tsunami source that we found here is not in contradiction with 294 the images of the rupture propagation resulting from back-projection analyses (IRIS, 295 http://ds.iris.edu/spud/backprojection/1065729).Indeed, all of these analyses, while showing 296 different features depending on the seismic network employed, highlight a possible rupture 297 propagation south-eastward from the hypocenter, shown as well by the slip models obtained 298 using tsunami data (this study and LA13).Furthermore, on one hand in the back-projection 299 analyses the surface projection of the radiated energy shows coherent high-frequency 300 radiation along a portion of the megathrust corresponding to the seismogenic layer; on the 301 other hand, the coherence of seismic high-frequency radiation appears to degrade south-302 eastward at shallower depths.This feature, along with the slip propagation up to the trench 11 (a zone likely rich of sediments) and the relatively low rupture velocity (1.5 km/s, LA13) 304 suggests that part of the seismic rupture SE of Nendo Island may have been characterized by 305 slow slip, as indicated by LA13.Therefore, we cannot rule out that this portion of the 306 megathrust, at least partially, may have slipped coseismically triggering the right-lateral 307 strike-slip aftershocks.308 309 310

Conclusion 311
We retrieved the coseismic tsunami source of the 2013 Santa Cruz Islands earthquake by 312 inverting tsunami observations recorded in the Pacific Ocean by several DART buoys and 313 tide gauges.We also computed the Green's functions using a 3D fault model honouring the 314 geometrical complexities of the subduction interface.The retrieved coseismic tsunami 315 source is mainly located SE from the hypocenter, with maximum slip value of ~11 m and 316 with the coseismic rupture reaching the shallow part of the megathrust with slip amplitudes 317 up to 6 m.The seismic moment resulting from our coseismic slip model is equivalent to an 318 M w 8.0 moment magnitude, in agreement with previous studies.The spatial pattern of the 319 tsunami source is in agreement with the Australia and Pacific plates convergence direction 320 that becomes progressively more oblique in the NW segment, and the slip distribution well 321 reproduces the tsunami data.However, our model, compared with previously published 322 models, features some differences in terms of tsunamigenesis and pattern of coseismic slip, 323 that we have discussed in relation to the different resolving power of the data used and on 324 the different fault geometry adopted.A common feature to all the models is the presence of 325 slip SE from the hypocentre, which we argue to have occurred during the coseismic stage, 326 possibly with a slow slip component, rather than being aseismic as previously suggested.
Hayes 55 et al. (2014a) studied the Santa Cruz Islands earthquake by inverting teleseismic body and 56 surface waves; Lay et al. (2013) performed a teleseismic broadband P wave inversion 57 optimized with tsunami forward modelling at DART buoys.These studies used different 58 hypocenters and different planar fault models; in particular, Lay et al. (2013) adopted both 59 hypocenter and fault plane shallower than those used by Hayes et al. (2014a).The best-60 fitting source model in Hayes et al. (2014a, hereinafter HA14) has a main patch of slip 61 centred around the hypocenter with a maximum slip of about 4 m and a second smaller patch 62 located SE of the Nendo Island and characterized by relatively low slip (~0.5 m).On the 63 other hand, the source model in Lay et al. (2013, hereinafter LA13) features two patches 64 with slip larger than 10 m; the first patch is located around the hypocenter, whereas the 65 second one is shallower and located SE of the hypocenter.The surface projection of the slip 66 in LA13 is roughly consistent with the HA14 patches even though they are at different 4 depths (and featuring quite different slip values), because of the different fault planes used.68 by the Santa Cruz Islands earthquake propagated both in the North 95 and South Pacific Ocean and it has been observed in the open sea at several DART buoys 96and at some tide gauges located along the coasts of Solomon and Fiji Islands.We select 5 97 gov) in 121 order to obtain a 3D fault model, meshed into 45 quadrangular patches (9 along strike and 5 122 along dip, Figs. 2, S1, S2) with an average size of about 20 x 20 km.Our final fault model is 123 consistent with the northern interface of Vanuatu slab model in Slab1.0 (Hayes et al., 2012, 124 http://earthquake.usgs.gov/data/slab/)and extends both up to the trench and in the north-125 west direction for ~40-60 km.The dimensions of the resulting fault are ~180 km along strike 126 and ~90 km along dip (see Figs. 2, S1, S2).'s functions are computed by means of NEOWAVE, a nonlinear 131 dispersive model for tsunami waves propagation (Yamazaki et al., 2009; Yamazaki et al., 132 2011).The initial conditions for tsunami propagation are analytically computed (further 133 details in Meade, 2007; Romano et al., 2012) and they also include the contribution of the 6 coseismic horizontal deformation in the region of steep bathymetric slopes (Tanioka and 135

4
Source of the 2013 Santa Cruz Islands tsunami 181We use the same inversion scheme, fault parameterization, and set of DART buoys and tide 182 gauges data used for the checkerboard test to retrieve the coseismic tsunami source of the 183 ~165.5°E ~11°S, and featuring a maximum slip value of ~11 m at a depth of ~25 km.The 186 coseismic rupture reaches the shallowest portion of the subduction interface and it spreads 187 along strike in NW direction with maximum slip values of ~6 m.The dislocation model 188 resulting from the inversion shows a second smaller patch of slip located NW from the 189 with previous Santa Cruz Islands earthquake source 214 models 215 In principle, teleseismic data well constrain the earthquake seismic moment and the seismic 216 rupture history, and, compared to tsunami data, they are less sensitive to the spatial details of 217 the slip distribution (e.g.Yue, 2014; Gusman et al., 2015).Moreover, adopting different 218 fault geometries (and hypocenter) may result in different earthquake slip distributions (e.g.219 Baba et al., 2009; Hayes et al., 2014b).220 The comparison among the present model, LA13, and HA14 shows some differences in 221 terms of tsunami source that may be ascribed to the different data and fault model used in 222 the inversions.223

). 228
As shown in Lay et al. (2013), the slip distributions of the Santa Cruz Islands earthquake 229 obtained by using only teleseismic data, adopting a hypocenter deeper than 15 km, and an 230 overall deeper fault plane result in an under-prediction of tsunami observations at DART 231 buoys.For this reason, Lay et al. (2013) prefer, among teleseismic solutions, the one 232 obtained by imposing a shallower hypocenter.Since the model in this study and LA13 233

Figure 1 -Figure 2 -Figure 3 -Figure 4 -Figure 5 -Figure 6 -
Figure 1 -Location map of the 2013 Santa Cruz Islands earthquake.Red star and red 443 beach ball indicate epicenter and focal mechanism of the mainshock, respectively.Green 444 and blue beach balls indicate the focal mechanisms of the largest strike-slip (M w 7.0) and 445 normal (M w 7.1) aftershocks occurred few hours after the mainshock.Orange beach balls 446 indicate the regional historical seismicity (since 1976 to present, GCMT catalogue, 447 http://www.globalcmt.org/CMTsearch.html)and the corresponding focal mechanisms for 448 earthquake magnitude 6+.White arrows indicate the convergence direction of the Australia 449 Plate.450 and Lorito, 2007; Lorito et 148 al., 2011; Romano et al., 2014 and references therein).149