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Supporting Information for
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An empirical study of the distribution of earthquakes with respect to
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rock type and depth
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Yuval Tal1 and Bradford H. Hager1
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1
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Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
Earth Resources Laboratory, Department of Earth, Atmospheric and Planetary
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Contents of this file
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Text 1
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Figures S1 to S8
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Text S1.
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The following faults have experienced offsets larger than 10 km. In the San
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Francisco Bay region, the San Andreas, San Gregorio, Rodgers Creek, Hayward,
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Calaveras, Concord-Green Valley, and Greenville faults [Graham and Dickinson, 1978;
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Graymer et al., 2002]. In Southern California, the San Andreas, San Jacinto, Garlock,
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Whittier-Elsinore, Pisgah, and Ludlow faults have experienced offsets larger than 10 km
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[Jachens et al, 2002; Stirling et al 1996].
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Text S2
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We calculate the depth and rock type distribution of b-value using the maximum
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likelihood estimate of Aki [1965] and Utsu [1965]. The standard errors are estimated
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using the formula of Shi and Bolt [1982]. Based on the global frequency-magnitude
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distributions between magnitudes 2 and 5 (Figure S2), we set the magnitude of
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completeness to 2 and 2.5 for southern California and the San Francisco Bay region,
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respectively.
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To account for variations in b-value with respect to rock type and depth, we
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calculate the b-values from the complete catalog ranges without consideration of time
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dependent variations, such as the California-wide change in the definition of ML in 2008
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– 2009 [Hutton et al., 2010; Tormann et al., 2010]. This change affects the statistics of
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the magnitude distribution mostly for events with magnitude smaller than 2.3 [Tormann
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et al., 2010], so it has a minor effect on the NCEDC catalog. We examine the temporal
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variations in b-values for basement rocks in southern California by dividing the
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earthquakes that occurred in basement rocks into 10 intervals (Figure S3), each with 8338
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earthquakes. We observe large temporal variations, but with no clear general trend of
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change in b-value with time. For sedimentary rocks, the uncertainties were too large to
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examine temporal variations.
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Figure S1. A histogram of earthquake number vs. depth distribution in southern
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California and the San Francisco Bay region.
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4.5
4.5
4
4
3.5
3.5
3
2.5
2
2
1.5
2
2.5
3
3.5
M
4
4.5
5
San Francisco
3
2.5
1.5
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logN(N)
logN(N)
Southern California
5
1
2
2.5
3
3.5
M
4
4.5
5
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Figure S2. Frequency-magnitude distributions between magnitudes of 2 and 5 for
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southern California and the San Francisco Bay region.
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San Francisco
0
2
2
4
4
6
6
Depth (km)
Depth (km)
Southern California
0
8
8
10
10
12
12
14
14
0.8
0.9
1
b value
1.1
1.2
0.7
0.8
0.9
1
b value
1.1
1.2
1.3
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Figure S3. Depth distribution of b-values for sedimentary (green) and basement (red)
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rocks in southern California and the San Francisco Bay region. The error bars half width
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is one standard error of Shi and Bolt [1982]. To reduce errors, the b-values for the San
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Francisco Bay region are for depth ranges of 2 km.
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Figure S4. Temporal variations of b-values of basement rocks in Southern California.
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Each time interval includes 8338 events (cumulative for all depths). Vertical bars
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represent the standard errors of the b-values, and horizontal bars represent the time
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interval.
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4.5
4
Earthquake density
3.5
3
x 10
−3
depth: 0−2
depth: 2−4
depth: 4−6
depth: 6−8
depth: 8−10
depth: 10−12
depth: 12−14
2.5
2
1.5
1
0.5
0
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Sedimentary
Granodiorite
Franciscan
Rock unit
Gabbro
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Figure S5. Earthquake density as a function of rock unit and depth in the San Francisco
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Bay region for earthquakes restricted to magnitude greater than 3. The four main rock
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units at depths of 0-14 km are included. The error bars were derived from 5000
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bootstraps and represent one standard error.
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Figure S6. A histogram of earthquake density vs. depth distribution in sedimentary and
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basement rocks in the San Francisco Bay region for earthquakes with magnitude greater
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than 2 and 3, where the basement rock does not include the Franciscan. The curves are
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running averages of the data with a window of 3 km. The curves (dashed) for earthquakes
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with magnitude greater than 3 were magnified by a factor of 10, so that they would plot
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on approximately the same scale. The error bars derived from 5000 bootstraps and
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represent one standard error.
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Figure S7. A histogram of earthquake density vs. depth distribution in sedimentary and
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basement rocks in southern California and the San Francisco Bay region for earthquakes
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with magnitude greater than 2 and 3 that occurred at distance greater than 0.5 km from
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large offset strike slip faults. The curves are running averages of the data with a window
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of 3 km. The curves (dashed) for earthquakes with magnitude greater than 3 were
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magnified by a factor of 10, so that they would plot on approximately the same scale. The
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error bars were derived from 5000 bootstraps and represent one standard error.
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5
Earthquake density
3.75
x 10
−3
depth: 0−2
depth: 2−4
depth: 4−6
depth: 6−8
depth: 8−10
depth: 10−12
depth: 12−14
2.5
1.25
0
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Sedimentary
Granodiorite
Franciscan
Rock unit
Gabbro
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Figure S8. Earthquake density as a function of rock unit and depth in the San Francisco
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Bay region for earthquakes that occurred at distance greater than 0.5 km from large offset
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strike slip faults. The four main rock units at depths of 0-14 km are included. The error
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bars derived from 5000 bootstraps and represent one standard error.
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References
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Graham, S. A., and W. R. Dickinson (1978), Evidence for 115 kilometers of right slip on
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the San Gregorio-Hosgri fault trend, Science, 199, 179-181.
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Graymer, R. W., A. M. Sarna‐Wojcicki, J. P. Walker, R. J. McLaughlin, and R. J. Fleck
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(2002), Controls on timing and amount of right‐lateral offset on the East Bay fault
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system, San Francisco Bay region, California, Geol. Soc. Am. Bull., 114(12), 1471–
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1479, doi:10.1130/0016-7606(2002)114<1471:COTAAO>2.0.CO;2.
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Hutton, K., J. Woessner, and E. Hauksson (2010), Earthquake monitoring in Southern
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California for seventy‐seven years (1932–2008), Bull. Seismol. Soc. Am., 100, 423–
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446.
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Jachens, R. C., V. E. Langenheim, and J. C. Matti (2002), Relationship of the 1999
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Hector Mine and 1992 Landers fault rupture to offsets on Neogene faults and
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distribution of late Cenozoic basins in the Eastern California shear zone, Bull.
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Seismol. Soc. Am., 92(4), 1592–1605, doi:10.1785/0120000915.
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Stirling, M. W., S. G. Wesnousky, and K. Shimazaki (1996), Fault trace complexity,
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faults: A global survey, Geophys. J. Int., 124, 833–868, doi:10.1111/j.1365-
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246X.1996.tb05641.x.
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Tormann, T., S. Wiemer, and E. Hauksson (2010), Changes of reporting rates in the
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Bull. Seismol. Soc. Am., 100(4), 1733–1742, doi:10.1785/0120090124.
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