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▲ ▲ Figure 9. Comparison between recorded and simulated (GNS “smooth”) velocity time histories (in cm/s), on the EW, NS, and UDcomponent for the whole set of stations at R e < 40 km. The label on the left vertical axis reports the peak value of the correspondingtime history.tion of soil mechanical properties. To give a broad picture ofseismic wave propagation effects, Figure 10 depicts the spatialdistribution of PGV values obtained through GeoELSE alongwith the observed values (superimposed filled dots) for boththe INGV and GNS “smooth” models. Furthermore, Figure11 shows some representative snapshots of the simulated faultnormal velocity wavefield, in which the seismic wave propagationfield with the high contrast between rock and alluvial soiland the directivity toward the city of Christchurch is clearlydistinguishable. In particular, looking at Figure 10 it is possibleto notice that the GNS fault model better reproduces the variabilityof PGV values on the whole modeled area. From Figures10 and 11 it is apparent that the INGV source model producesstrong “up-dip” directivity effects in the central-eastern part ofChristchurch, in reasonable agreement with the spatial distributionof observed damage and liquefaction phenomena. Thewave propagation pattern obtained with the GNS fault modelproduces noticeable directivity off the sides of the fault due tothe relatively shallow hypocenter (around 6.5 km) and becausethe rake is oblique (145°). This leads to larger ground motionamplitudes in the southwestern portion of the city.Comparison with Observed Standard Spectral RatiosAs a concluding check of the quality of 3D numerical simulations,in this section we compare simulations with observationsin terms of standard spectral ratios (SSRs). Most of the 23 stationsincluded in the numerical model are located on alluvialsoil, while three of them lie on outcropping volcanic rock,namely HVSC, LPCC, and MQZ. For our purposes, we consideredthe four stations located in the Christchurch CBD, onsoft alluvial sediments, namely CCCC, REHS, CHHC, andCBGS. Station LPCC, located on rock around 15 km southeastfrom the CBD, is considered as reference rock station.The SSRs computed as the ratio of the Fourier spectrumof the recordings at CCCC, REHS, CHHC, and CBGS (geometricmean of the horizontal components), over that at LPCCreference station, are shown in Figure 12, for 4 September 2010Darfield earthquake, with the epicenter located around 40 kmwest of the considered set of stations. We refer to the Darfieldearthquake because we believe that this event is more reliablethan the Christchurch one in evaluating the SSR because ofthe strong nonlinear soil behavior verified in the latter and theshort distance (less than 10 km) between the epicenter and theconsidered stations. It is worth noting that stable resonancepeaks are found at around 0.3, 0.6, 1.3, and, more consistently,at around 1.7 Hz. The recorded SSRs are compared, on the onehand, with the 1D analytical transfer function obtained for asystem of four layers (layers 1, 2, 3, and 5 in Table 2) over a halfspace(layer 6 in Table 2), and, on the other hand, with the SSRsobtained through 3D numerical simulation (GNS “smooth”model). Compared with the 1D amplification function, the 3DSSRs show a better agreement with the records, pointing outresonance frequencies at about 0.4, 0.7, 1.3, and 1.7 Hz.CONCLUDING REMARKSThe main aim of this paper was to perform 3D numerical simulationsof the M W 6.2 Christchurch earthquake on 22 FebruarySeismological Research Letters Volume 82, Number 6 November/December 2011 777