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Depth (km)Coulomb Stress Change(bars)event, we obtain a distributed slip model with 182 triangulardislocations (Figure 4B), with Laplacian smoothing constraintsto regularize the inversion. We fix the slip rake direction to 64degrees, as reported by the Global Centroid Moment Tensor(GCMT) solution (http://www.globalcmt.org; Dziewonski etal. 1981). Inversions in which we allow rake to vary reveal similarsolutions. Our best-fit model strikes N57E and dips 70S beneaththe Banks Peninsula. This fault geometry agrees well with theGCMT south-dipping focal solution (N59E, 64S) and distributionsof aftershocks analyzed through the double-differencemethod (Bannister et al. 2011, page 839 of this issue). The slipmodel suggests peak slip of 2.1 m with the main rupture areaoccurring between 2 and 11 km and has a moment magnitudeMw 6.4 (Figure 4B). Some very shallow slip is observed in themodel, although this region corresponds to areas offshore whereno geodetic data is available and is probably an artifact of theinversion. Our slip model supports the ground and pixel-offsetobservations of no surface rupture during the Christchurchearthquake; however, data gaps in the InSAR observationswithin the city of Christchurch may inhibit our inversions frominferring any slip at the surface. Because only one pair of imagesis available to constrain slip during the 13-June event (Table 1,Figure S2), we do not present a distributed slip model. We showthe location of our best-fit single patch model in Figure 4C.Coulomb Stress ChangeIn order to model the potential effects of static Coulomb stresschange of the Darfield earthquake on the 22-Feb Christchurchearthquake, we use the Darfield earthquake slip distributiondescribed above (Figure 4A), which predicts a static Coulombstress change on a fault with the orientation and rake inferredfor the Christchurch earthquake as shown in Figure 5A. In ourcalculation, all slip inverted for the Christchurch earthquakeoccurs within the region of positive Coulomb stress change(Figure 5A, black curve). This suggests that static Coulombstress change from the Darfield earthquake indeed encouragedthe Christchurch earthquake. Peak calculated static Coulombstress change is 3.1 bars while the minimum is –4.5 bars.To obtain statistics describing the significance of theseinferred static Coulomb stress changes, we apply a MonteCarlo error propagation technique similar to that describedin Lohman and Barnhart (2010). We begin by simulating 500noisy data sets by adding spatially correlated noise with a spatialscale of 100 km to the predicted LOS surface displacementsfrom our best-fit slip distribution, using the same covariance aswe infer from the original Darfield data. We then invert for slipon the same four-fault geometry used above for each syntheticdata set. Lastly, we calculate the static Coulomb stress changeon the fault geometry and slip orientation inferred for theChristchurch earthquake for each realization of the syntheticdata. This method allows us to quantify errors in predictedCoulomb stress change (Figure 5B) induced by data noise, suchas correlated atmospheric water vapor. As can be seen in Figure5B, the expected variation due to these sources is far less thanthe inferred increase in stress resolved on the target fault planethat ruptured during the Christchurch earthquake. OtherDepth (km)0 West Along-StrikeLength (km) East030a9180918errors due to variations in fault plane geometry, crustal elasticstructure, or to the contribution from the rest of the aftershocksequence likely also contribute.DISCUSSION6-4Certain attributes of this earthquake sequence suggest reactivationof poorly developed faults. A particularly interestingattribute of seismicity during the 2010–2011 Canterbury earthquakesequence is the activity of steeply dipping (>50 degrees)reverse faults. First motion focal solutions for the Darfieldearthquake reveal reverse-motion rupture on a steep, eastdippingplane (Gledhill et al. 2011) before slip propagated toE-W-striking strike-slip faults. In addition, aftershock locationsand focal mechanisms located in NE-SW-trending zones at theends and center of the Darfield rupture reveal steeply dippingreverse-motion planes, and steep reverse faults are necessary tomodel geodetic observations of both the Darfield (Beavan et al.2010) and Christchurch earthquakes. Traditional Andersonianstylefaulting predicts that faults should form at angles of ~30degrees to the principal shortening direction (Anderson 1951),which results in reverse faults dipping 30 degrees with a horizontalshortening direction and normal faults dipping 60degrees with a vertical shortening direction. While Anderson’stheory predicts the angles at which faults form relative to thelocal stress field, preexisting faults can reactivate and new faults300.4StDev (bars)0.05▲ ▲ Figure 5. A) Static Coulomb stress change on the Christchurchearthquake fault plane predicted by the slip distribution inferredfor the Darfield earthquake (Figure 4A). Positive Coulomb stresschange encourages rupture, negative discourages rupture.Black outline shows extent of Christchurch earthquake slip withmagnitude > 0.7 m. B) 1σ standard deviation of static Coulombstress change, calculated using 500 realizations of the Darfieldearthquake slip distribution.bSeismological Research Letters Volume 82, Number 6 November/December 2011 821