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The comment by Paolucci and colleagues (Paolucci et al., 2011) states that a probabilistic seismic hazard analysis (PSHA) can provide “reliable prediction of long-period spectral ordinates.” The result of such an analysis would be in contrast to the more uncertain prediction suggested by our empirical, and proposed theoretical, distribution of nearsource ground displacements in past, large magnitude earthquakes (Yamada et al., 2009). After addressing two specific concerns of Paolucci and colleagues, we use the balance of this reply to discuss the apparent differences between a PSHA and our observations. These two approaches to understanding the seismic hazard of long-period ground motions should be consistent even though they view the problem from different perspectives. Paolucci and colleagues prefer to use elastic spectral displacement as the intensity measure of long-period ground motions rather than peak ground displacement (PGD). Spectral displacement and PGD, however, are highly correlated. We calculate the elastic spectral displacements (Sd) of our original set of recorded ground motions. We first find Sd for each horizontal component over a range of periods from 3 to 9 s at a 0.02 s interval, with damping at 5% of critical. At each period, we take the square root of the sum of the maximum squared Sd of each component. Then we find the geometric mean over three ranges of periods: 3–5, 5–7, and 7–9 s. We average the spectral displacements in each range to find a more stable measure of the long-period spectrum. We also calculate pseudo-Sd from the spectral accelerations (Sa) reported in the current Next Generation Attenuation (NGA) database (see the Data and Resources section). Figure 1 shows that the logarithms of PGD and Sd are highly correlated, with correlation coefficients of 0.9405 (3–5 s), 0.9707 (5–7 s), and 0.9750 (7–9 s) for the records collected in Yamada et al. (2009). Also, we find similar correlations of PGD and pseudo-Sd from the NGA database. We prefer to use PGD because it is period independent, physically intuitive, and more concise than a family of spectral curves. Although the value of PGD is certainly sensitive to the processing of a recorded ground motion, our conclusions do not depend on particular values of PGD. In our original paper, we showed the distributions of peak ground acceleration (PGA) and PGD from near-source sites (that is, within 10 km of the surface projection of the rupture, also known as a Joyner–Boore distance less than 10 km) of large magnitude (between 6.5 and 8) earthquakes recorded in the years 1979 through 2004. We now add nearsource records from similar sites since 2004 (Table 1); Figures 2 and 3 update the PGA and PGD distributions, respectively, with these records. Our updated PGA and PGD distributions are consistent with the distributions presented in Yamada et al. (2009). In the years 2005 through 2009, there was no well-recorded large earthquake. Thus, we would not expect our observed distribution of PGD to change significantly. Figures 2 and 3 also overlay PGAs and PGDs from the near source of past events with magnitudes ≥ 6:5 as reported in the current NGA database (see the Data and Resources section). The NGA distributions are consistent with our empirical distributions. Furthermore, we perform statistical tests on the empirical distributions of PGA and PGD to determine whether they are consistent with log-normal or log-uniform distributions. We apply Lilliefors tests of the null hypothesis that each observed PGA dataset is drawn from a log-normal population distribution (Lilliefors, 1967). The null hypothesis cannot be rejected for the three PGA datasets: (1) YOH2009, p-value 0:4617; (2) YOH2009 updated, p-value 0:8070; (3) Pacific Earthquake Engineering Research Center (PEER) NGA, p-value 0:3236; these observed PGAs could have been drawn from a log-normal population distribution. We apply Chi-square tests of the null hypothesis that each

bulletin of the seismological society of america

Reply to "Comment on 'Statistical Features of Short-Period and Long-Period Near-Source Ground Motions' by Masumi Yamada, Anna H. Olsen, and Thomas H. Heaton" by Roberto Paolucci, Carlo Cauzzi, Ezio Faccioli, Marco Stupazzini, and Manuela Villani