# Bulletin of the Seismological Society of America

## Abstract

*Online Material: *Corrected figures and strain, rotation, and displacement gradient time series.

In Spudich and Fletcher (2008), henceforth SF, small start‐time variations at each UPSAR station were erroneously omitted from the analysis, causing phase errors in the seismograms and affecting the strains, rotations, and displacement gradients inferred from the mainshock and aftershocks. The rms error in broadband peak strains and rotations is about 6%, with a maximum error of 16%. Unfortunately, the effects of this error, although small, are pervasive, affecting nine published figures, three tables, and all time series, including those presented in the electronic supplement of SF. However, none of the errors is large enough to affect any of the conclusions of the original paper. In this article we show examples of the most important changes, and we present corrected tables. In the accompanying electronic supplement to this Erratum, we present corrected figures (exclusive of those included here) and time series.

## Summary of Changes

Table 1 presented here shows the correct time of the first sample (TFS) for each UPSAR station’s mainshock acceleration time series (all three components at each station have the same start time). In the original analysis, we mistakenly assumed that all time series started simultaneously. (This error was not made in Fletcher *et al.*, 2006.) The third column shows the difference of the TFS and its modal value, 26.425 s. This difference indicates the phase error. In SF we used subarrays 1–3, 8–11 (consisting of stations 8, 9, and 11), and 5–12 (consisting of stations 5, 6, 7, 8, 9, 11, and 12). (Station 13 was not used, but its TFS is reported here for completeness.) For the subarray 1–3, the maximum start time error is only 0.005 s, leading to only small corrections in general. For subarray 8–11, the maximum start time error is 0.020 s, which is small but has a sometimes significant (20%) effect on the corrected version because there is no redundancy in a three‐station array. For subarray 5–12, the maximum start time error is 0.12 s, but there is some redundancy in the subarray. Consequently, as we will show, this error has a moderate (≤12%) effect on the subarray 5–12 results. Although this discussion addresses the mainshock, a similar error was made in the analysis of the three aftershocks, and it is corrected here.

Of the time series published in SF, their figure 4 is the most visibly altered by correction of the error. (Henceforth, SFn means figure n of SF.) Figure 1 shows a magnified version of the published erroneous (black line) rotation and strain time series from SF4 for subarray 5–12, 1.4 Hz low‐pass filtered mainshock. The gray line in Figure 1 shows the corrected time series. In general, the corrected time series are phase‐shifted slightly earlier. Waveforms are somewhat altered in the total dilatation around 22 to 32 s and in the tilt and tilt rate around 28 s. Figure 2 shows the corrected version of SF4. Corrected versions of Figures 5, 6, 7, and 8 of SF are shown in the accompanying online materials. Corrected versions of SF5 and SF6 are nearly indistinguishable from the erroneous versions. Corrected versions of SF7 and SF8 differ from the erroneous versions only a little.

Table 2 presented here shows corrected bandlimited peak strains and rotations (this table is a corrected version of SF table 3). Table 2 also shows the percentage difference between the corrected and erroneous values. Largest errors are associated with dilatation and tilts, and errors are greatest for the 2721724 event, which is the smallest of the events studied, having the noisiest data. SF tables 1, 2, and 4 are not affected by the error.

Table 3 presented here is the corrected version of SF table 5, the most important table in the paper; it contains average broadband estimates of peak rotations and strains for all events considered. Table 4 presented here shows the percentage change of each element of Table 3 compared with SF table 5. The largest change in the mainshock results is 7% for tilt rate; all other mainshock strains and rotations change by 3% or less. The largest change for any rotation or strain for any event is 16%, for horizontal shear strain for the 2721724 event, the smallest, noisiest event.

Table 5 presented here is the corrected version of SF table 6, the ratio of three‐station to seven‐station subarray results. Table 6 presented here shows percentage changes in Table 5 compared with SF table 6. Row and column averages, which were used in SF, change by 10% or less.

The following is an exhaustive list of statements in the paper that have been modified, in the strike‐out underline format deletion insertion. A comment is appended if warranted.

p. 1901: . . . we infer that strains and rotations inferred from the small arrays 1–3 and 8–11 in the wider 0.1–3.6 Hz band . . . will be accurate to a factor of about two three or better.

p. 1901–1906: We infer little from it, although we assume, based on the previous discussion, that its peak values are in error by a factor of 2 3 or less.

p. 1908: Our mainshock horizontal shear strain, 88 89 microstrain,. . . .

p. 1908: The horizontal shear strains for all three of our events in table 5 fall between the scaling lines in Paolucci and Smerzini’s figure 7. The fourth falls slightly outside.

p. 1909: Considering the UPSAR Parkfield measurements, torsions and torsion rates are almost always greater than tilts and tilt rates.

p. 1912: Thus, the average peak torsion measured over all events on the 1–3 and 8–12 arrays is 1.18 1.21 times the average peak torsion of all events measured on the 5–12 array. Tilt in the small arrays is 19% 27% larger than in the 5–12 array.

p. 1912: For the four Ito events it ranges from about 50 to 375 m/s, whereas for the Parkfield events it ranges from about 700 750 to 1700 1650 m/s.

p. 1912: Estimates of *c* that we formed from translation/rotation ratios for this record are in the 50–150 m/s range, much less than the 700 750–1700 1650 m/s range of Parkfield events.

p. 1914: Our correction factor for the 0.1–3.6 Hz band for mainshock torsion, shear strain, and dilatation, 1.18 1.22, agrees reasonably well with the 1.09 and 1.16 ratios of unfiltered to filtered mainshock dilatations presented by Borcherdt…. (The correction factor could have been 2 or 3. Our number and Borcherdt’s show that not much is lost by filtering.)

## Effects on Interpretation

None of the conclusions of the original paper is changed. Figure 3 shows a corrected version of SF12, the summary figure. None of the Parkfield symbols in Figure 3 has shifted by more than half the height of a symbol. Our inferred scaling (SF equation 2a and 2b) of peak rotation and peak rotation rate with PGV and PGA, respectively, have not changed.

- Manuscript received 21 May 2010.