GROUND MOTION MAPS BASED ON RECORDED MOTIONS FOR THE EARTHQUAKES IN THE CANTERBURY EARTHQUAKE SEQUENCE

GROUND MOTION MAPS BASED ON RECORDED MOTIONS FOR THE EARTHQUAKES IN THE CANTERBURY EARTHQUAKE SEQUENCE Robert Buxton 1, Graeme McVerry 2, Tatiana Goded 3 ABSTRACT: There has been a demand for maps of estimated ground motions in the Canterbury earthquake sequence, taking account of the recorded motions, to assist in the evaluation of the performance of structures and engineering systems. The Canterbury earthquake sequence comprises many thousands of earthquakes. The work here concentrates on four of the larger earthquakes, the Mw 7.1 September 2010, the Mw 6.3 February 2011, the Mw 6.3 June 2011 and the Mw 6.0 December 2011 earthquakes. Work at GNS Science has implemented a methodology previously applied to the Canterbury region by Bradley using his Ground Motion Prediction Equation (GMPE). GNS has applied the methodology to the McVerry et al. GMPE as an alternative to the Bradley GMPE, to assess the sensitivity of the maps to the selected GMPE. The ground-motion maps reproduce the recorded motions at their sites. Elsewhere, the estimated motions and their error bounds reflect the site conditions, the distances from the recording stations, and the overall level of the recorded motions in a particular event compared to median estimates of the GMPE. So far, maps have been produced for conditional Peak Ground Acceleration (PGA) and 0.5 second Spectral Acceleration (SA) values. Work presented includes an overview of the method and a comparison of the results with other work that has aimed to produce maps based on recorded station accelerations. KEYWORDS: Conditional PGA, GMPE, Canterbury earthquakes 1 R. Buxton, GNS Science, Lower Hutt, New Zealand r.buxton@gns.cri.nz 2 G..H. McVerry, GNS Science, Lower Hutt, New Zealand g.mcverry@gns.cri.nz 3T. Goded, GNS Science, Lower Hutt, New Zealand t.goded@gns.cri.nz

INTRODUCTION The Canterbury region of South Island, New Zealand has, since September 2010, been subjected to a number of large and damaging earthquakes. The events of note are listed in Table 1. Table 1: The earthquakes of note in the Canterbury sequence. Event Mag Depth Lat Lon Sep-10 7.1 9.9-43.539 172.156 Feb-11 6.3 6.3-43.571 172.683 Jun-11 6.3 7.1-43.561 172.74 Dec-11 6.0 5.8-43.617 172.822 The sequence, in particular, the September and February events, caused a substantial amount of damage to the Canterbury region. The damage to housing, commercial buildings and support infrastructure is measured in the NZ$10s of billions and the reconstruction project is likely to last several years and be one of the largest construction projects in New Zealand history. analysis beyond a simple consideration of the records. Ground Motion Prediction Equations (GMPEs) allow the prediction of acceleration values at sites of interest on ground of known composition, for a given magnitude of earthquake centred at some known position, with some known faulting mechanism. Often the GMPEs are created empirically by calibrating the forms of the equations against catalogues of past earthquake events. There are many well-known, recognised GMPEs, including those of McVerry [1] and Bradley [2] for New Zealand. Although the current GMPEs provide a general indication of the levels of shaking locations around an earthquake, suitable for purposes like developing improved fragility functions and liquefaction assessments from observed behaviour, more specific prediction of probable ground accelerations at the observation points may be required for other purposes. Examples include work by Bradley and Hughes [3],[4] and O Rourke [5]that required maps of calculated earthquake motions for the Christchurch region based on measurements. THE MAPS OF O ROURKE AND BRADLEY Figure 1: The Canterbury earthquakes and aftershocks to September 2012 (GeoNet). The Canterbury earthquake sequence was well recorded by the strong-motion accelerographs of the GeoNet network (www.geonet.org.nz) The GeoNet network of seismic recording devices was established in the 1990s and has steadily improved since its inception. The density of instruments in a relatively small country means that a large amount of high quality seismic data can be collected from the main shocks and their associated aftershock sequences. Although the network of instruments gives scientists and engineers access to a relatively large number of acceleration records for the Canterbury events, the need for assessment of probable acceleration levels at locations of varying distances from the instruments requires some THE WORK OF O ROURKE Work by O Rourke using a technique developed by O Rourke and Jeon [6] used ordinary kriging methods to produce PGA contours based on the GeoNet station records. The kriging approach can estimate acceleration values at points that are not coincident with recording station locations. The approach involves creating a grid of cells which is placed over the area covered by the recording sites. Each of the intersection points is defined as a node. The kriging method generates weights at surrounding nodal points and unknown nodal values are calculated according to a weighting scheme which gives higher weights to nearer recorded values according to a semivariogram that is developed by looking at the spatial nature of the data. A contour map can then be generated by mapping the calculated and recorded nodal values. O Rourke has used this approach to map Peak Ground Velocity (PGV) values for the Northridge earthquake and has applied it to producing PGA maps for some of the major Christchurch earthquakes. Figure 2 shows O Rourke s kriging approach applied to the September 2010, Darfield event. Although the approach is guided by the recorded motions it has no mechanism to independently

calculate the estimated accelerations in areas away from the station points. It also takes no account of ground conditions. Figure 3: The February PGA map produced by O Rourke [5]. Figure 2: The Darfield PGA map produced by O Rourke [5]. The kriging approach in Figure 2 correctly identifies the area close to Darfield as having the highest accelerations. The approach results in a regular pattern of contours in this western area resulting in a bullseye effect in the Darfield region and at some other station locations where they are isolated. O Rourke s map of the February 2011 event (Figure 3) indicates a pattern of very rapid attenuation with estimated acceleration values falling away extremely rapidly beyond the local Christchurch area. O Rourke s maps for the June and December 2011 events (Figure 4 and 5) show the effects of the epicentres moving more offshore. Both maps show 0.1g shaking affecting a large area. Figure 4: The June PGA map produced by O Rourke [5].

Bradley s map of the Darfield earthquake PGAs (Figure 6) has a pattern of estimated ground motions that is very different from that proposed by O Rourke. The Bradley map depicts a much smaller area. The complex lobe-like pattern at the south western extreme of the map appears to be caused by the interactions of recorded motions from Rolleston and Templeton stations and the GMPE since this is still some distance east of the Greendale and Darfield areas where the highest shaking was centred and which is shown in O Rourke s map. There are also very different interpretations of the information provided by the station at Kaiapoi, which is the northern-most station considered in the Bradley map. In the Bradley map, the record at the Kaiapoi station results in a bullseye pattern and without this record the estimated accelerations would be somewhere in the region of 0.16-0.17g. In the O Rourke map the bullseye caused by the Kaiapoi record results in disjointed and poorly constrained contours in the 0.22-0.2g range. Figure 5: The December PGA map produced by O Rourke [5]. THE WORK OF BRADLEY Work by Bradley and Hughes [3, 4] uses a different approach to that of O Rourke. Bradley develops an approach that combines the use of a GMPE, in this case his own, and also the input from some of the ground motion records. The maps show conditional ground-motions, where conditional indicates that the estimates are as given by the GMPE conditional on the recorded motions. This approach allows the conditional motions to be estimated at any percentile-level, with the 50- percentile (median) or 84-percentile levels usually selected. Figure 7: The conditional median estimates of the PGA accelerations using the Bradley model [4] for the February earthquake. More differences between the Bradley and O Rourke interpretations are evident in the February maps. Bradley s use of a fault source model and the GMPE results in a radial pattern of contours centred roughly on the Heathcote Valley station location. O Rourke s map has a similar radial pattern in the area of the densest concentration of stations but then becomes more disjointed as the distance from the CBD increases. Figure 6: The conditional median estimates of the PGA accelerations using the Bradley model [4] for the September, Darfield earthquake.

provide a better estimate of motions than given by a GMPE or the smoothing of recorded measurements alone. Figure 8: The conditional median estimates of the PGA accelerations using the Bradley model [4] for the June earthquake. The June and December maps (Figures 8 and 9) show very similar characteristics to those already discussed. Dissimilarities between the Bradley and O Rourke interpretations could stem from the O Rourke approach lacking guidance from any kind of GMPE in the areas between and away from instrumented sites. It should be noted that the work of O Rourke is based on the geometric mean of the horizontal accelerations and since Bradley s GMPE outputs the estimated geometric mean it is assumed the accelerations in the maps are consistent on this basis. Figure 9: The condition median estimates of the PGA accelerations using the Bradley model [4] for the December earthquake. The approach of Bradley was used as a basis in the work undertaken by GNS. THE APPROACH USED INTRODUCTION The basis of the approach is the use of the residuals resulting from the difference between the predicted accelerations and the recorded accelerations in combination with a spatial correlation function to THE SITES USED The larger horizontal component PGA and 0.5s spectral acceleration recordings for the seismic stations around the Canterbury region together with the station coordinates and a record of the ground characteristics at the site were used. The larger horizontal component is used for structural design in New Zealand. Slightly different numbers of stations were available for each event. For the Darfield (September 2010) earthquake the records from 62 stations have been used, for the February earthquake 45 records were used, 50 records from the June earthquake were used and 74 from the December event. The GeoNet station sites have a range of NZS1170 site classes, where NZS1170 Class B corresponds to Rock, Class C corresponds to Shallow Soil. Some of the records are Class E meaning Very Soft Soil, Class D corresponding to Deep/Soft soil and a small number are classified as D-E. For the purposes of the modelling all Class E are treated as Class D, Deep/Soft Soil. THE FAULT MODELS For each of the four earthquakes considered, the most up-to-date fault model was used. The fault models provide a 3D representation of the faulting plane or planes divided into 1km by 1km patches together with estimates of the amount of slippage per patch. The use of detailed fault models means that an accurate estimate of the path distance from the fault to each of the stations can be calculated. The fault model used for the M7.1 Darfield earthquake is the model of Beavan [7]. This is a geodetic fault model based on GPS and differential InSAR data. The model represents the fault as 887 patches and for the purposes of any calculation the centre of a patch is taken as being representative of the whole patch. For the other 3 earthquakes, similar fault models by Holden and Beavon are used. The February [8] and December [9] models use 400 1km by 1km patches, whereas the June model [9] has two fault planes each represented by 400 1km by 1km patches. THE RESIDUALS, INTRA- AND INTER- EVENT TERMS The standard equation representing the spectral acceleration (here represented as the Peak Ground Acceleration (PGA) at a site x is: lnpga x =lnpgap x (site, event) + + x (1)

where lnpga x is the logarithm of the PGA recorded by an instrument at location x; lnpgap x (site, event) is median of the logarithm of the PGA calculated using a GMPE; is the inter-event residual and x is the intra-event residual. The unconditional distribution of shaking is: lnpga x ~ N(lnPGAP x, 2 + 2 ) (2) where right hand side of the expression denotes a normal distribution with a mean of lnpgap x and a variance of 2 + 2.Recorded measurements from a single earthquake have the same inter-event residual, but the intra-event residual term is unique to each site. The McVerry GMPE was used to produce an unconditional estimate of the shaking at each station site considered for each earthquake and the residual is taken as the difference between the log transformed site record and the log transformed unconditional estimate arising from the GMPE. The standard deviations, σ ε, of the intra-event residuals by event is listed in Table 2. Table 2: The standard deviations of the intra-event residuals per event used in the modelling. Intra-event σ ε Event(mag) PGA 0.5sSA 7.1 0.408 0.526 6.3 0.488 0.629 6.3 0.581 0.793 6 0.457 0.645 The inter-event term is the standard deviation of the mean residual values of events. The inter-event values used in the modelling are listed in Table 3. Table 3: The standard deviations of the inter-event residuals for PGA and 0.5s used in the modelling. Inter-event SD σ η PGA 0.5sSA 0.209 0.157 The intra-event residuals at different locations are related through the covariance matrix, where elements Ʃ(i,j) for locations i and j are defined in terms of a spatial covariance function ρ ij. Ʃ(i,j) = ρ ij σ ε 2 (3) Work by Goda and Hong [10] is used as a basis for the calculation of the spatial correlation function. The form of the function used by Goda and Hong is shown in equation (4). ρ ij (Δ) = exp(-αδ ij β ) (4) Where Δ ij is the distance between two sites and α and β are empirically derived constants. Goda and Hong quote several α and β values for PGA, 0.3s, 1s and 3s spectral accelerations. Figure 10: The spatial correlation functions used PGA and 0.5s, from Goda & Hong (2008). For the purposes of this research, for PGA an α of 0.35 and a β of 0.34 has been used, which is the middle of the dotted lines on Figure 10. For the 0.5s values, an α of 0.48 and a β of 0.3 was taken which represent values partway between the 0.3s and 1s values from Goda and Hong. The maps produced in this study are based on conditional PGAs modelled from those given by the McVerry et al [1] GMPE, conditional on the recorded values. If the conditional PGA, for location a, for event x is ConPGA a,x then: LnConPGA a,x =N(LnPGAP a,x + η a +µ εsite εstation, σ 2 εsite εstation) (5) Where the inter-event residual η a for event a is: η = [σ ε 2 /η station σ ε 2 +σ η 2 ]Ʃ stations (lnpga a, station - lnpgap a,station ) (6) Where σ ε 2 is the variance of the station residuals and σ η 2 is the variance of the inter-event residuals calculated across 4 events rather than the value from the GMPE. The covariance matrix Ʃ(i,j) is partitioned into: [ σ ε 2 Σ 12 Σ 21 Σ 22 ] where subscript 1 indicates a site of interest and subscript 2 indicates the stations. It can be shown that: µ Ʃsite Ʃstation = Ʃ 12 Ʃ 22-1 ε station (7)

ε station = lnpga a, station (lnpgap a, station + η a ) (8) The conditional variance is: σ 2 Ʃsite Ʃstation=σ ε 2 -Ʃ 12 Ʃ 22-1 Ʃ 21 (9) Where Ʃ 12 is a 1 by s column vector where s is the number of recording sites and is the product of the spatial contribution of each site (calculated by Eq.(3)) and the square of the intra-event term from Table 2. Where Ʃ 22-1 is the inverse of a square matrix (Ʃ 22 ) of size s by s. Ʃ 22 is a spatial co-variance matrix where each cell is the product of the intra-event term squared (Table 2) and Eq. (4) between each site. deviations at 10,000 equidistant points spread over a one degree by one degree area. Additionally, for each event, the station locations used in the generation of the model are also plotted which gives a useful sanity check of the model run since the PGA values should exactly match the recorded GeoNet values for that particular earthquake event. These points contribute to the contouring of the maps but are not labelled on the maps themselves. RESULTS THE CONDITIONAL PGA MAPS For the purposes of direct comparison with previous work and in the interests of clarity only the PGA maps and their associated mapped standard deviation values are shown here. Figure 12: The conditional PGA map for the February M6.3 earthquake (a = 0.35, b = 0.34), NZS1170 ground classes). Figure 11: The conditional PGA map for the M7.1 earthquake (a = 0.35, b = 0.34), NZS1170 ground classes). All of the maps were created by calculating the conditional PGA and conditional standard

Figure 13: The conditional PGA map for the June M6.3 earthquake (a = 0.35, b = 0.34), NZS1170 ground classes). Figure 14: The conditional PGA map for the December M6 earthquake (a = 0.35, b = 0.34), NZS1170 ground classes). A COMPARISON OF PGA MAPS WITH BRADLEY AND O ROURKE For the purposes of a comparison the Bradley and O Rourke maps were viewed using the Canterbury Geotechnical Database [11], which allows the map layers to be superimposed on GoogleEarth. A visual comparison of the Bradley results for the Darfield (September) earthquake (Figure 6) with those obtained using the McVerry GMPE (Figure 11) show that, despite the use of different GMPEs and potentially different spatial decay parameters, the overall spatial patterns of conditional accelerations can be quite similar. Predictably, the two models are most similar in the areas where the GeoNet stations are most densely grouped, while farther away from the influence of the stations the estimates can differ in a more pronounced fashion. Some of the differences could be due to the fact that this study considers a greater area of coverage and uses an NZS1170 ground class map as opposed to smoothly changing VS30 and depth to bedrock values that are used in the Bradley model. The McVerry maps show a greater area affected by 0.2g shaking and above and also show some areas of 0.3g shaking which are not shown in the Bradley map. Some of these differences could simply be from the use of the larger horizontal component records in the McVerry GMPE. Predictably the maps using the McVerry GMPE are more similar to the Bradley maps than to the kriging derived O Rourke (Figure 2) interpretations. The differences in the patterns of contours are many -fold and are generally those already raised when comparing the Bradley and O Rourke maps. In the February M6.3 earthquake, the Bradley results (Figure 7) show that the model seems to attenuate more quickly than the McVerry model (Figure 12). The result of this is that the McVerry model generally estimates that a larger area is affected by 0.1g 0.6g shaking compared to the equivalent Bradley result. In the Bradley map the area affected by 0.6g shaking and above is displaced slightly to the east compared with the McVerry map. Overall, however, the pattern is quite similar, which could be largely due to the higher density of controlling stations in the vicinity of the earthquake origin. Again, the February McVerry map is more similar to the Bradley map than to the O Rourke map (Figure 3). For the June M6.3 earthquake, both models produce very similar patterns of estimated accelerations. But, similar to the previous cases, the McVerry model (Figure 13) estimates that a larger area is affected for the higher accelerations. This effect seems to reduce with the acceleration levels such that the Bradley model (Figure 8) estimates a

very similar area was affected by 0.1g accelerations. The Bradley map of the December (Figure 9) earthquake has some differences from the McVerry map (Figure 14) in that a small zone of 0.4g shaking is indicated on the coast. This doesn t appear in the McVerry map, which seems to indicate stronger shaking to the south west than is apparent in the Bradley map. The McVerry map also indicates a larger area was affected by 0.2g shaking. THE CONDITIONAL STANDARD DEVIATION MAPS Bradley has also produced conditional standard deviation maps for his modelled PGA estimations and although, in the interests of saving space none of those maps are shown here, a brief discussion of the comparison of the two models is warranted. Because of the approach adopted, the standard deviations for both models are, by definition, zero at the exact locations of the stations. This results in bullseye patterns of closely stacked contours radiating out from the station locations with larger standard deviation values situated at increasing distances away from the station locations. For the Darfield earthquake estimates, the Bradley model results in a maximum contoured standard deviation value of about 0.41, whereas the McVerry model standard deviation for roughly the same area reaches a maximum of about 0.37. The modelling of the February earthquake results in a maximum conditional standard deviation of about 0.47 for the Bradley model and a maximum value of about 0.37 for the McVerry model in the area shown by the Bradley report. For the June M6.3 event, the Bradley model has a reported maximum conditional standard deviation of about 0.5, whereas the McVerry model has a value of about 0.45 over the same area. The December earthquakes result in conditional standard deviations of about 0.49 for the Bradley model and about 0.35 for the McVerry model in the same area. The maximum standard deviation value reached by the McVerry model for this event is about 0.41. Since the standard deviation is consistently less, although admittedly by a small amount in most cases, it would be reasonable to assume that there is less uncertainty in the conditional estimates of PGA values using the McVerry GMPE coupled with this approach. CONCLUSIONS A comparison has been undertaken of the conditional PGA maps and their associated conditional standard deviations produced using the McVerry GMPE with other work aiming to produce similar maps. Some of the other work used a quite dissimilar approach based purely on the recorded accelerations with no GMPE to provide additional guidance. As a result the PGA contour patterns in these (O Rourke) maps are quite different from those produced in this work and the work of Bradley. A better comparison is between the maps produced in this work and those produced by Bradley using his own GMPE, where it is shown that the conditional estimates based on the McVerry GMPE have smaller conditional standard deviations and, hence, less uncertainty for all four events considered. ACKNOWLEDGEMENT The authors thank Anna Kaiser and Caroline Holden for providing seismic station data and fault model data. The authors also wish to thank Jim Cousins and Mostafa Nayyerloo for providing an independent review. REFERENCES [1] McVerry, G.H., Zhao, J.X., Abrahamson, N.A., Somerville, G.H.: New Zealand Acceleration Response Spectrum Attenuation Relations for Crustal and Subduction Zone Earthquakes. Bulletin of the New Zealand Society for Earthquake Engineering, 39(1): 1-58, 2006 [2] Bradley, B.A.: A New Zealand-Specific Pseudospectral Acceleration Ground-Motion Prediction Equation for Active Shallow Crustal Earthquakes Based on Foreign Models. Bulletin of the Seismological Society of America, 103(3):1801-1822, 2013, Doi:10.1785/0120120021 [3] Bradley, B.A., Hughes, M.: Conditional Peak Ground Accelerations in the Canterbury Earthquakes for Conventional Liquefaction Assessment. Technical report Prepared for the Department of Building and Housing, 2012 [4] Bradley, B.A., Hughes, M.: Conditional Peak Ground Accelerations in the Canterbury Earthquakes for Conventional Liquefaction Assessment: Part 2. Technical report Prepared for the Department of Building and Housing, 2012 [5] O Rourke, T.D., Jeon, S.-S.,Toprak, S., Cubrinovski, M. and Jung, J.K.: Underground Lifeline System performance during the Canterbury Earthquake Sequence, Proceedings of the 15th World Congress on Earthquake Engineering (15WCEE), Lisbon, Portugal, 24-28 th Sept. 2012 [6] Jeon, S.-S., O Rourke, T.D.: Northridge Earthquake effects on pipelines and residential buildings. Bulletin of the Seismological Society of America, 95(1):294-318, 2005, Doi:10.1785/0120040020

[7] Beavan, J., Motagh, M., Fielding, E.J., Donnelly, N. and Collett, D.: Fault slip models of the 2010-2011 canterbury, New Zealand, earthquakes from geodetic data and observations of postseismic ground deformation, New Zealand Journal of Geology and Geophysics, 55(3):207-221, 2012, Doi:10.1080/00288306.2012.697472 [8] Holden, C.: Kinematic source model of the 22 February Mw 6.2 Christchurch Earthquake using strong-motion data. Seismological research letters. 82(6):783-788, 2011, Doi:10.1785/gssrl.82.6.783 [9] Holden, C. and Beavon, J.: Source studies of the ongoing (2010-2011) sequence of large earthquakes in Canterbury, Proceedings of the 15th World Congress on Earthquake Engineering (15WCEE), Lisbon, Portugal, 24-28 th Sept. 2012 [10] Goda, K., Hong, H.P.: Spatial correlation of peak ground motions and response spectra. Bulletin of the Seismological Society of America, 98:354-365, 2008, Doi:10.1785/0120070078 [11] Canterbury Geotechnical Database (2013) "Ground Motion", Map Layer CGD5170-28 May 2013, retrieved [23/1/2014] from https://canterburygeotechnicaldatabase.pr ojectorbit.com/