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1 Fault Scaling Relationships Depend on the

2 Average Fault Slip Rate

3 John G. Anderson, Glenn P. Biasi, Steven G. Wes-

4 nousky

5 Abstract

6 This study addresses whether knowing the slip rate on a fault improves es-

7 timates of magnitude (MW ) of shallow, continental surface-rupturing earth-

8 quakes. Based on 43 earthquakes from the database of Wells and Coppersmith

9 (1994), Anderson et al. (1996) previously suggested that estimates of MW from

10 rupture length (LE)areimprovedbyincorporatingthesliprateofthefault

11 (SF ). We re-evaluate this relationship with an expanded database of 80 events,

12 that includes 57 strike-slip, 12 reverse, and 11 normal faulting events. When the

13 data are subdivided by fault mechanism, magnitude predictions from rupture

14 length are improved for strike-slip faults when slip rate is included, but not for

15 reverse or normal faults. Whether or not the slip rate term is present, a linear

16 model with M log L over all rupture lengths implies that the stress drop W ⇠ E

17 depends on rupture length - an observation that is not supported by teleseismic

18 observations. We consider two other models, including one we prefer because it

19 has constant stress drop over the entire range of LE for any constant value of

20 SF and fits the data as well as the linear model. The dependence on slip rate for

21 strike-slip faults is a persistent feature of all considered models. The observed

22 dependence on SF supports the conclusion that for strike-slip faults of a given

23 length, the static stress drop, on average, tends to decrease as the fault slip rate

24 increases.

1 25 Introduction

26 Models for estimating the possible magnitude of an earthquake from geological

27 observations of the fault length are an essential component of any state-of-the-

28 art seismic hazard analysis. The input to either a probabilistic or deterministic

29 seismic hazard analysis requires geological constraints because the duration of

30 instrumental observations of seismicity are too short to observe the size and

31 estimate the occurrence rates of the largest earthquakes (e.g. Allen, 1975; Wes-

32 nousky et al., 1983 ). Thus, wherever evidence in the geological record suggests

33 earthquake activity, it is essential for the seismic hazard analysis to consider

34 the hazard from that fault, and an estimate of the magnitude of the earthquake

35 (MW ) that might occur on the fault is an essential part of the process. The

36 primary goal of this study is to determine if magnitude estimates that are com-

37 monly estimated from fault length (LE)canbeimprovedbyincorporatingthe

38 slip rate (SF )ofthefault.

39 Numerous models for estimating magnitude from rupture length have been

40 published. Early studies were by Tocher (1958) and Iida (1959). Wells and Cop-

41 persmith (1994) published an extensive scaling study based on 244 earthquakes.

42 Some of the more recent studies include Anderson et al., (1996), Hanks and

43 Bakun (2002, 2008), Shaw and Wesnousky (2008), Blaser et al. (2010), Strasser

44 et al. (2010), and Leonard (2010, 2012, 2014). For probabilistic studies, and

45 for earthquake source physics, it is valuable to try to reduce the uncertainty

46 in these relations. Motivated by Kanamori and Allen (1986) and Scholz et al.

47 (1986), Anderson et al. (1996) (hereafter abbreviated as AWS96) investigated

48 whether including the fault slip rate on a fault improves magnitude estimates

49 given rupture length. They found that it does, and proposed the relationship

50 M =5.12 + 1.16 log L 0.20 log S ,thusindicatingthatsliprateisafactor. W E F

51 Aphysicalinterpretationofasignificantdependenceonsliprateisthat,fora

2 52 common rupture length, faults with higher slip rates tend to have smaller static

53 stress drop. Since the publication of AWS96, the number of earthquakes with

54 available magnitude, rupture length, and slip rate estimates has approximately

55 doubled. This paper considers whether these new data improve or modify the

56 conclusions from the earlier study.

57 One consideration in developing a scaling model is that seismological obser-

58 vations have found stress drop in earthquakes to be practically independent of

59 magnitude. Kanamori and Anderson (1975) is one of the early papers to make

60 this observation. Recent studies that have supported this result include Allman

61 and Shearer (2009) and Baltay et al. (2011). Apparent exceptions have been

62 reported based on Fourier spectra of smaller earthquakes, but as magnitude

63 decreases, attenuation can cause spectral shapes to behave the same as they

64 would for decreasing stress drop (e.g. Anderson, 1986). Studies that have taken

65 considerable care to separate these effects have generally concluded that the

66 average stress drop remains independent of magnitude down to extremely small

67 magnitudes (e.g. Abercrombie, 1995; Ide et al., 2003; Baltay et al., 2010, 2011).

68 However all of these studies find that for any given fault dimension the range

69 of magnitudes can vary considerably (e.g. Kanamori and Allen, 1986). In spite

70 of this variability, it seems reasonable to evaluate a scaling relationship that is

71 based on a constant stress drop before considering the additional effect of the

72 fault slip rate. This vision guides the development of the considered scaling

73 relationships. Details of these models for the relationship of stress drop and the

74 fault dimensions are deferred to the Appendix. The following sections describe

75 the data, present the summary equations for three alternative models, fit the

76 alternative models to the data, and discuss the results.

3 77 Data

78 Tables 1 and 2 give the preferred estimates of MW , LE,andSF for the earth-

79 quakes used in this analysis. These values and their corresponding uncertainty

80 ranges are given in Table S1 (Electronic Supplement), along with references for

81 all estimates. Events considered for analysis come from AWS96 and Biasi and

82 Wesnousky (2016). Some AWS96 events were not used because uncertainties

83 in one or more of the magnitude, length, or slip rate parameters were consid-

84 ered too large or too poorly known to contribute to the parametric regressions.

85 Events in Biasi and Wesnousky (2016) were selected on the basis of having a

86 well mapped surface rupture and non-geologically estimated magnitude. Their

87 list builds on the list of fault ruptures of Wesnousky (2008) by adding more

88 recent events and by including surface ruptures newly documented by geologic

89 field work. Interested readers are referred to these previous papers for further

90 description of each event. Overall, the database is heavily weighted toward

91 surfacing rupturing earthquakes. Some events in Biasi and Wesnousky (2016)

92 were not included for lack of a resolved fault slip rate, or because their rupture

93 lengths were too short. Events with LE < 15 km were generally not included.

94 The smallest preferred estimate of MW is 5.7.

95 Earthquakes after 1900 were only included if some independent (non-geologic)

96 means was available to estimate magnitude. Moment estimates from waveform

97 modeling were preferred to body wave magnitudes where both were available.

98 The six earthquakes prior to 1900 are particularly well documented, as described

99 in the E-supplement. Since LE is known for these events and the uncertainty

100 in MW introduced by uncertain depth of faulting is less than 0.1, the measured

101 slip in these events controls MW . It follows that estimating MW from LE alone

102 for these events is not circular. The rupture length is normally taken as the

103 distance between the ends of primary coseismic surface rupture. The sum of

4 104 the lengths of overlapping traces may be used as the length in the analysis

105 (e.g. Event 53, Hegben Lake, 1959) where the overlapping portions were judged

106 to contribute materially to the moment release. Rupture lengths based on af-

107 tershock distributions have generally been avoided, with the exception of six

108 moderate strike-slip event, all in California. These were retained for continuity

109 with AWS96 and for support of the regressions at moderate magnitudes. None

110 control the results. Fault slip rates are taken from offsets of geologic features

111 10 ky to 100 ky in age where possible, to represent a stable recent slip rate

112 estimate. Fault slip rates from paleoseismic offsets of one or a few individual

113 earthquakes were avoided because it is not clear how that activity would relate

114 to the longer-term average slip rate. Similarly, fault slip rates from geodetic

115 estimates were avoided where possible because they measure the current-day

116 rate but may not represent the longer-term average. Fault creep effects were

117 considered, but no corrections were attempted in the database. First, creep is

118 believed to affect only a few percent or less of events, and at a fraction of the

119 full slip rate. Second, uncertainty in fault slip rate will be seen below to have

120 little effect on the regression.

121 Figure 1 shows the cumulative number of earthquakes used as a function of

122 time. From 1954-2013, the rate of usable events is relatively steady, about 0.9

123 events per year. The rate is lower prior to ~1954 suggesting that the earlier

124 historical record is less complete.

125 The earthquakes are separated into general categories of strike-slip, normal,

126 and reverse faulting. Figure 2 shows the exceedance rates of considered earth-

127 quakes in each of these categories as a function of magnitude, both combined

128 and separated by focal mechanism. To estimate the rates, the number of earth-

129 quakes for each of the curves was divided by 100 years. This is obviously an

130 approximation, but considering Figure 1, the events prior to ~1910 may roughly

5 131 compensate for the missing events since 1910. For instance, Figure 2 suggests

132 that continental events that cause surface rupture with M 7.0 have oc- W -1 133 curred at a rate of about 0.5 yr , or roughly once every two years. The rates of

-1 -1 134 strike-slip, reverse, and normal mechanisms are about 0.4 yr ,0.075yr ,and

-1 135 0.045 yr .Roundedtothenearest5%thisimpliesthatabout75%ofthose

136 events were strike slip, about 15% had reverse mechanisms, and about 10% had

137 normal mechanisms.

138 Figure 3 shows maps with locations of all events, using different symbols to

139 distinguish among mechanisms. The insets shows more details on locations of

140 events fom the western US, the eastern Mediterranean region, and Japan.

141 Figure 4 plots the preferred slip rates versus the preferred rupture lengths.

142 Figure 4a emphasizes the overall distribution of the data, while parts b), c) and

143 d) exphasize the data available to evaluate slip-rate dependency for the three

144 fault types. The points in Figure 4a are distinctly upper-triangular. The main

145 diagonal associates an increase in fault length with an increase in fault slip rate,

146 which in turn is likely function of cumulative slip (e.g. Wesnousky, 1988, 1999).

147 The data above the diagonal shows that (1) the entirety of long faults and fault

148 systems do not always break and that (2) small fast faults may exist. There are

149 two alternatives to explain the lack of long ruptures on faults with low slip rates.

150 The first could be purely statistical, since events in the lower-right corner of the

151 plot could be too rare to be represented in the historical record. Alternatively,

152 due to what Perrin et al. (2016) call “the competition between damage and

153 healing processes”, faults with slow slip rates might, during the interseismic

154 period, be sufficiently affected by differential healing, influences from adjacent

155 faults, or other processes that long ruptures on slow faults never occur.

156 Figures 4b, c, and d emphasize the data available to search for slip-rate

157 dependency for the three fault types. Figure 4b shows a distribution of points

6 158 spanning rupture lengths mostly between 20-400 km and slip rates between 0.3-

159 30 mm/yr. Rupture lengths for reverse faults (Figure 4c) range from 13-240 km

160 although most are between 20-100 km. Slip rates for reverse faults are mostly

161 between 0.4-4 mm/yr, with outliers at 0.005 and 12.9 mm/yr. Rupture lengths

162 and slip rates for normal faults (Figure 4d) range from 14-102 km and 0.08-2

163 mm/yr, but are unevenly distributed within these limits.

164 Modeling Approaches

165 The effect of slip rate is tested against three model shapes for the scaling re-

166 lationship to confirm that it is not an artifact of a particular assumption for

167 how magnitude depends on rupture length. The first, M1, explores a linear

168 regression of MW with the logs of length and slip rate:

SF MW = c0 + c1 log LE + c2 log (1) S0

169 where LE is the rupture length (measured along strike) of a specific earth-

170 quake, MW is the reported moment magnitude for the respective earthquake

171 (Kanamori, 1977), SF is the slip rate of the fault on which the earthquake oc-

172 curred determined from geological observation, S0 is the average of the logs of

173 all slip rates in the data set being considered (e.g. strike-slip faults, normal

174 faults, etc), and c0, c1,andc2 are coefficients of regression to be determined.

175 Mathematically, c trades offwith c log S , which allows the parameter S to 0 2 0 0

176 be rounded to two significant digits. In this model, setting SF = S0 is math-

177 ematically equivalent to setting c2 =0,andthusalsoequivalenttothemodel

178 approach used by Wells and Coppersmith (1994) and others who estimate a

179 linear dependence of MW on log LE without including the slip rate on the fault.

180 Two misfit parameters are considered. The first, 1L is the standard deviation

7 181 of the difference between observed and predicted magnitudes when c2 =0,so

182 only LE is used to estimate MW ,while1S is the corresponding standard de-

183 viation when the slip rate term in Equation 1 is incorporated. A consequence

184 of the assumed model M1 is that unless c1 fortuitiously equals 2/3, stress drop

185 increases for large earthquakes as a function of rupture length LE,regardlessof

186 whether slip rate is included or not (Table A.1, Appendix).

187 The second, M2, constrains the slope to give constant stress-drop for small

188 and large earthquakes with a slope change at the break point magnitude Mbp.

189 The stress drop for small and large earthquakes is allowed to differ:

LE SF Mbp + c1C log( L )+c2 log S LE LE SF <>Mbp + c1L log( )+c2 log LE Lbp Lbp S0 > ⇣ ⌘ :> 190 where c1C =2and c1L =2/3 for rupture lengths that are respectively less

191 than or greater than Lbp, the rupture length where slope changes from 2 to 2/3.

192 The three unknown parameters in model M2 are Lbp, the rupture length where

193 the slope changes from 2 to 2/3, Mbp,themagnitudeatthattransition,and

194 c2 which is again the sensitivity of magnitude to fault slip rate. Ruptures of

195 length less than Lbp are considered to be a small earthquake, and scale like a

196 circular rupture in Table A.1 of the Appendix, implying that constant stress

197 drop occurs when c1C =2. An earthquake with rupture of length greater than

198 Lbp is considered to be a large earthquake and corresponds to one of the models

199 for a long fault in Table A.1 (depending on fault mechanism), for which the value

200 c1L =2/3 results in constant stress drop. However Equation 2 does not require

201 the stress drop for the small earthquakes to be the same as the stress drop for

202 large earthquakes. Equation 2 has the same number of unknown parameters

203 to be determined from the data as Equation 1. The two standard deviations

204 of the misfit for Model M2 are 2L and 2S which correspond directly to the

8 205 parameters 1L and 1S of model M1.

206 The third model, M3, is derived from the model of Chinnery (1964) for a

207 vertical strike-slip fault that ruptures the surface. It is assumed that stress drop

208 for the top center of the fault in this model, ⌧C ,isconstantacrossallrupture

209 lengths and magnitudes:

2 2 2⇡ SF LE 2 log LE + log ⌧C + log 2 16.1 + c2 log 2 2 2 2⇡Wmax SF LE <> log LE + log ⌧C + log 16.1 + c2 log Wmax 3 3 3 C() S0 CLW > ⇣ ⌘ ⇣ ⌘ (3) :> 210 where

cos sin (3 + 4 sin ) C () = 2 cos + 3 tan (4) (1 + sin )2

211 Details on the development of the model M3 equations are provided in the

212 Appendix. The value is the angle from the top center of the fault to either of

213 the bottom corners, i.e. tan =2WE/LE where WE is the downdip width of

214 the earthquake rupture. The model variables include four parameters. These

215 are the aspect ratio of the fault for small ruptures, CLW = LE/WE,thestress

216 drop, ⌧C ,thecoefficientthatquantifiestheslipratedependence,c2,and

217 the maximum fault width Wmax.Equation3assumesthattheaspectratio

218 is constant for small earthquakes, and that when the selected aspect ratio in

219 combination with LE implies a width greater than Wmax the width is set to

220 Wmax.FormodelM3,thetwostandarddeviationsofthemisfitare3L and

221 3S,correspondingtotheparameters1L and 1S of model M1. As written,

222 the coefficients of the term in log LE appear to be the same as in model M2,

223 but for the long ruptures, depends on LE, so the term with C () modifies

224 the slope.

225 Model Equations 1, 2, and 3 require different strategies to obtain their un-

9 226 known coefficients. The simplest way to find the unknown coefficients for Equa-

227 tion 1 is by using a linear least-squares regression, which minimizes the misfit

228 of the prediction of MW ,butdoesnotaccountforuncertaintiesinLE or SF .

229 AWS96 approached this difficulty by carrying out multiple regressions for points

230 chosen at random within the range of allowed values of all three parameters,

231 and then looked at the distribution of derived values of the coefficients of the

232 regression. Alternative approaches to find the coefficients, described variously

233 as “total least squares” or “general orthogonal regression” (e.g. Castellaro et

234 al., 2006; Castellaro and Borman, 2007; Wikipedia article “Total Least Squares”

235 accessed Feb. 15, 2015) were also considered for this analysis. The approach

236 by AWS96 turned out to give the least biased results for a set of synthetic data

237 with an uncertainty model that we considered to be realistic and consistent

238 with the actual data, so their approach is also used in this study. The parame-

239 ters for Equation 1 were determined from 10,000 realizations of the randomized

240 earthquake parameters to find the distributions of coefficients..

241 In implementing the AWS96 approach, MW , LE,andSF are chosen at

242 random from the range of uncertainties given in the Online Supplement. The

243 probability distributions for the randomized parameters reflect that uncertainty

244 ranges are not symmetrical around the preferred value. The preferred value is

th 245 set to be the median. As an example, the probability distribution for the i

246 randomized value of LE is:

1 pref min (A) (LE LE ) p (LEi)=8 (5) > 1 (B) < Lmax Lpref ( E E ) > :> 247 In Equation 5, case A has probability of 0.5, case B has probability of 0.5,

min max 248 LE and LE are the minimum and maximum of the range on the rupture pref 249 length, and LE is the preferred value. The seismic moment and slip rate are

10 250 randomized using the same algorthm, and MW is found from the randomized

251 moment. The standard deviations of the misfit, 1L and 1S,aretheaverage

252 values from the multiple realizations.

253 Equation 2 has the additional complication of being non-linear in Lbp.We

254 approach the solution by reorganizing Equation 2 as

SF LE M + c log = M c log (6) bp 2 S W 1x L ✓ 0 ◆ ✓ bp ◆

255 where c1x is either c1C or c1L depending of LE .AssumingavalueforLbp,it

256 is straightforward to find the unknown coefficients Mbp and c2 .Weconsidered

257 asetofclosely-spacedvaluesofLbp from the smallest to the longest rupture

258 length in the data, and choose the value with the smallest total misfit. For

259 each trial value of Lbp, we solved for the unknown coefficients 10,000 times with

260 values of MW , LE,andSF randomized as in Equation 5, and our preferred

261 model is the mean of the coefficients from the multiple realizations.

262 Model M3 (Equation 3) has four unknown parameters, where the effects of

263 CLW and Wmax are nonlinear (Appendix, Figure A.1). For this reason, a grid

264 of values of CLW and Wmax was searched; there were 506 points on this grid.

265 For each grid point, ⌧C and c2 were determined by linear least squares for

266 10,000 randomly chosen realizations of MW , LE,andSF . The average value of

267 ⌧C and c2 was found from the distributions of these realizations, together with

268 average values of 3L and 3S. This permitted creating a contour plots of 3L

269 and 3S as a function of the trial values of CLW and Wmax. The minima in 3L

270 and 3S did not generally occur for the same combinations of CLW and Wmax.

271 Because the results of model M3 might potentially be used for faults where slip

272 rate is unknown, we minimized 3L. The minimum in 3L is broad compared to

273 the grid spacing of CLW and Wmax,sothevaluesthatareusedcomeasnearas

274 possible, within the minimum of 3L,tominimize3S as well. The grid limits

11 275 considered maximum fault widths from 10 to 20 km for strike-slip faults, while

276 for reverse and normal faulting the grid limits considered maximum fault widths

277 from 18 to 30 km. The larger widths were considered because of the suggestions

278 of King and Wesnousky (2007), Hillers and Wesnousky (2008) and Jiang and

279 Lapusta (2016) that a dynamic rupture in a large earthquake might reasonably

280 extend deeper than the brittle crustal depths associated with microearthquakes.

281 Analysis Results

282 Figures 5, 6, and 7 show results for models M1, M2, and M3 respectively,

283 for strike-slip, reverse, and normal faulting earthquakes. For each mechanism, ˆ 284 the curve in the upper frame shows predicted values of magnitude, MW ,for

285 SF = S0. The lower frame shows the residuals from this prediction, defined as

M = M Mˆ (7) Wi Wi Wi

286 for each considered earthquake, and the solid line is given by MW = c2 log (SF /S0).

287 Model coefficients and uncertainties in estimates of MW for models M1, M2, and

288 M3 are given in Tables 3, 4, and 5, respectively.

289 Model M1: The linear model

290 The parameters for the linear models are given in Table 3. Figure 8 shows

291 the distribution of coefficients found for 10,000 trials for strike-slip faults. The

292 widths of these distributions are used to estimate the uncertainty in each coef-

293 ficient. The coefficients c0, c1,andc2 are found simultaneously, as opposed to a

294 possible alternative approach in which c0 and c1 could be found first, and then

295 c2 determined by a second independent linear fit to the residuals.

296 For strike-slip events, which dominate the data, c = 0.198 0.023 (Figure 2 ±

12 297 5a) so MW is observed to be a decreasing function of slip rate, similar to

298 AWS96. The data with a reverse mechanism support MW increasing, rather

299 than decreasing, with increased slip rate (Figure 5b), while for the events with a

300 normal mechanism the slip-rate dependence of MW is not distinguishable from

301 zero (Figure 5c). Considering the distribution of slip rate data for reverse faults

302 in Figure 5b, it may be observed that the finding of slip rate dependence is the

303 result of mainly a single outlier, the Marryat earthquake (M5.8, #28 in Table

304 1) which is reported to have a slip rate of .005 mm/yr. Intracontinental events

305 are included considering, based on Byerlys Law, that the physics of rupture

306 of crystalline rocks within the range of typical crustal compositions is not, a-

307 priori, different merely because the fault is located far from a plate boundary

308 or that rock type might be different (e.g. Byerly, 1978; Scholz, 2002). Also, the

309 Marryat Creek event tends to decrease the slip rate dependence of MW ,asa

310 consideration of the remaining points would reveal. Nonetheless, the positive

311 slope of MW in Figure 5b for reverse faulting is not a robust result.

312 Considering Figure 5, the results for the linear model provide an indication

313 that it is not appropriate to combine different fault mechanisms in this type

314 of regressions. The AWS96 model from all rupture mechanisms was MW =

315 5.12 + 1.16 log L 0.20 log S , which is only slightly different from the strike- E F

316 slip case in Figure 5a. That result is consistent with the AWS96 model being

317 dominated by strike-slip earthquakes, and thus demonstrates continuity with

318 the previous study. However, results here separated by mechanism indicate

319 that the slip-rate dependence in AWS96 is controlled by the behavior of strike

320 slip earthquakes, and not much affected by the normal mechanisms that show

321 little or no slip-rate dependence, and the reverse mechanisms that potentially

322 show a different dependence. Suppose as a thought experiment that the dip-slip

323 cases have no slip rate dependence, or in other words that the variability with

13 324 slip rate is pure noise. A strong strike-slip case plus some noise will still resolve

325 to a decently significant trend even though we added only noise. In applying

326 the combined regression to dip-slip faults, we may be projecting back from the

327 strong case into the noise, and saying things about future dip-slip earthquake

328 expectations that aren’t likely based on the available data.

329 Model M2: The bilinear model

330 Table 4 gives estimated coefficients for Model M2 (Equation 2), and Figure 6

331 illustrates the fit to the data. Without the slip-rate adjustment, the bilinear

332 model fits the observed magnitudes as well or better than the linear model M1,

333 as shown by similar or smaller values of 2L than the corresponding values of

334 1L. The results again show a dependence of magnitude on slip rate for strike-

335 slip faults (Figure 6a) but not dip-slip faults (Figure 6b, c). The value of 2S is

336 comparable to 1S for the strike-slip case, but larger for the dip-slip faults. For

337 the strike-slip case, the fit to the data in Figure 6a is better at large rupture

338 lengths than in Figure 5a.

339 Model M3: The constant stress drop model

340 Parameters for model M3 are given in Table 5, and the fit to the data is illus-

341 trated in Figure 7. Some features of Figure 7 are noteworthy. For the strike-slip

342 case, the points for faults with low slip rates (solid points) are mostly above

343 the average model, while points with high slip rates (open circles) are mostly

344 below the average. This slip-rate dependence is reinforced in the lower frame

345 of Figure 7a, where the slope of the linear fit to the residuals is more than five

346 standard deviations of the slope different from zero. The variance reduction by

347 the addition of the slip rate term is statistically significant with 80% confidence,

348 based on the F-test. The same remarks apply for models M1 (Figure 5) and M2

14 349 (Figure 6).

350 The strike-slip case in Figure 7a uses Wmax = 15 km, while Table 5 gives

351 Model M3 parameters for Wmax = 20 km as well. The data do not prefer

352 either of these two models, as the curves and the misfits characterized by 3L

353 and 3S are barely distinguishable, so the plot for the Wmax=20 km model

354 is not shown. For these strike-slip cases, both 3L and 3S are smaller than

355 the equivalent uncertainties in models M1 or M2. While this improvement is

356 small and statistically insignificant, it is encouraging that a model with constant

357 stress drop achieves this result. Hanks and Bakun (2014) have discussed the

358 difficulties associated with several scaling models for long strike-slip faults, which

359 fit the longest earthquakes either by increasing the rupture width by penetrating

360 into the crust below the depths of microearthquakes or by increasing the stress

361 drop. While Hanks and Bakun consider the deep penetration of strike-slip faults

362 below the depth of microearthquakes to be unlikely, we provide both models.

363 Recent studies that favor deep penetration include Graves and Pitarka (2015),

364 based on experience in modeling ground motions near the fault and Jiang and

365 Lapusta (2016) based on the seismic quiesence of along the ruptures of past

366 large earthquake such as the 1857 earthquake on the San Andreas fault.

367 The ability to model the data using Equation 3 unfortunately does not re-

368 solve the “no high stress drop / no deep slip enigma” articulated by Hanks and

369 Bakun (2014), but rather pushes it into issues with the aspect ratio and the

370 absolute value of the constant stress drop. The Wmax = 15 km model uses a

371 large aspect ratio of CLW =3.8,comparedtoCLW =2.9 for the Wmax = 20 km

372 model, or 2.4 at the transition to fixed width of 15 km in the Hanks and Bakun

373 (2014) model. The higher aspect ratio for the Wmax = 15 km model would also

374 imply that earthquakes like the M6.6 Superstition Hills event (#25) or the M6.2

375 Parkfield 1966 event (#49) only penetrate from the surface to about 7 km depth.

15 376 Also, the stress drop for the W = 15 km model is rather high, ⌧ 25 max C ⇡

377 bars, considering that this corresponds to ⌧ 50 bars (See Appendix) in S ⇡

378 the more frequently used model of Kanamori and Anderson (1975). We suggest

379 that variability of the aspect ratio must contribute to the uncertainties in these

380 scaling relations at the lower magnitudes.

381 For the reverse faulting data we considered values of Wmax up to 30 km since

382 reverse faults can have low dips, and that upper limit is the preferred value. For

383 normal faulting, we only considered values of Wmax > 18 km, as constrained

384 observations of normal faults imply that the fault width can be that wide (e.g.

385 Richins et al., 1987). For M3 to fit the sparse normal-faulting data as well as

386 M2, we would need to use a much smaller value of Wmax.

387 Comparisons

388 Figure 9 compares the models for the three different types of mechanism. Models

389 M2 and M3 tend to resemble each other most closely, while model M1, being

390 linear, tends to give larger magnitudes for long and short faults, but smaller

391 magnitudes in the center of the length range.

392 Discussion

393 The larger data set modeled here compared to AWS96 expands our understand-

394 ing of slip rate dependence for the scaling of magnitude and rupture length.

395 Improvements in estimates of the magnitudes of earthquakes are realized with

396 slip rate dependence for strike-slip faults for all three models considered here.

397 Thus the slip-rate dependence in this case is not an artifact of the underlying

398 scaling model. The distribution of data in L S space (Figure 4b) gives E F

399 further reason for confidence in the strike-slip case. On the other hand, individ-

400 ual models for reverse and normal faulting have, at best, an equivocal place for

16 401 slip rate dependence. This again is consistent with the uneven distribution of

402 data on the plots of L S in Figures 4c and 4d. For models M1 and M2 of E F

403 the normal faulting events, but not model M3, the sign of slip rate dependence

404 agrees with the strike-slip case. Thus normal faulting could could have slip rate

405 dependence nudging estimates toward smaller magnitudes for higher slip rate

406 faults, but lack sufficient data to prove it. The reverse faulting events disagree

407 even at the sign of the effect. The disagreement is present whether we retain

408 either or both of the apparent outliers in Figures 5-7. Thus based on the current

409 data, we do not find support for the general reduction of magnitude with slip

410 rate implied by the combined set regression of ASW96. It appears that the

411 strength of the slip rate effect among strike slip events and their shear num-

412 bers relative to dip slip events overwhelm the ambiguous (normal) and contrary

413 (reverse) data, leading to an apparently general slip-rate relationship among

414 all data. Thus our new data set contributes the understanding that slip rate

415 dependence is dominantly a strike-slip fault effect that is not inconsistent with

416 normal faulting, and not apparently consistent with reverse mechanism fault

417 rupture. The data available to AWS96 did not permit this distinction.

418 If we are guided by studies of earthquake source physics, model M3 may

419 be preferable to M1 or M2. Specifically, the advantage would be the constant

420 stress drop of earthquakes over the full range of magnitudes, consistent with

421 e.g. Allmann and Shearer (2009). The slope of the linear model, M1, with rup-

422 ture length implies that stress drop increases significantly with rupture length

423 for large earthquakes. The slopes of the bilinear model, M2, are consistent

424 with simple models for scaling with constant stress drop in the small and large

425 earthquake domains, but the stress drops in the two domains are different. In

426 addition, since the buried circular rupture model by construction does not reach

427 the surface, its applicability to the short ruptures of M2 is not obvious.

17 428 Constant stress drop model M3 has the important advantage compared to

429 dislocation models in an unbounded space, in that it is explicitly designed for

430 surface-rupturing earthquakes. Stress differences due to the free surface effect

431 of rupture are recognized as having significant effects on ground motion. For

432 this reason we can expect that it will perform well where magnitude scaling is

433 required for application to strong ground motions. The Chinnery (1964) model

434 has a singularity of stress drop near its edges, which enables a closed form

435 solution. The approximation of uniform slip with a singularity at the edges

436 is probably no more significant than those already made to summarize spatial

437 variability across the fault in stress drop of actual individual earthquakes with

438 a single average value. The application of the same functional form for dip-slip

439 earthquakes is entirely ad-hoc, of course. Although it is more complicated, its

440 consistency with a physical model with a constant stress drop commends it as

441 a preferred regression. Compared with the better-known equations summarized

442 by Kanamori and Anderson (1975), the stress drop parameter in this model is

443 smaller, emphasizing that all average stress drop estimates are model dependent.

444 The adjustment that decreases magnitude for high-slip rate strike-slip faults

445 implies that the stress drop on those faults is lower than faults of the same length

446 with lower slip rate. The finding is consistent with the observations of Kanamori

447 and Allen (1986) and Scholz et al. (1986) that a longer healing time results in

448 alargerstressrequiredtoinitiaterupture,andthusahigherstressdrop.For

449 normal or reverse faulting, the slip-rate dependence is low, and the slip-rate

450 coefficient c2 is indistinguishable from zero. The findings suggest that, if c2

451 is not zero for these cases, then c2 is positive for reverse faulting earthquakes.

452 This is contrary to the hypothesis of Kanamori and Allen. We suggest that if

453 this positive slope is confirmed with added data, the physical mechanism may

454 be related to the dynamics of rupture. For a reverse fault, the dynamic stresses

18 455 on a rupture propagating updip are tensile as rupture approaches the surface,

456 so the coefficient of friction or cohesion on the fault is less relevant.

457 There are a number of future studies that should be performed to improve

458 upon the results presented here. The first is to examine the consistency of the

459 models, and especially M3, with observed fault displacement. If the results,

460 based on the definition of seismic moment (Equation A.2) agree with seismic

461 data, the scaling relationship presented here would be an alternative to the self-

462 consistent scaling model of Leonard (2010, 2014) for earthquakes in continental

463 crust.

464 Asecondissuethatdeservesattentionishandlingmulti-segmentfaults.We

465 consider, for instance, the 1905 Bulnay, Mongolia, earthquake, which is the

466 strike-slip point in Figures 5, 6, and 7 at 375 km and M8.5. The 375 km

467 length is the distance from one end of the rupture to the other, and does not

468 include a spur fault in between that is 100 km long. This event points out that

469 the standard deviations xL and xS for all three models include the potential

470 presence of spur or subparallel faults that do not increase the total end-to-end

471 length of the rupture. Several other faults in Table 1 and 2 have similar issues. A

472 better understanding of how seismic moment is distributed on multiple segments

473 and fault splays, as well as how best to measure the lengths of multiple segment

474 ruptures and how to recognize these features ahead of the earthquake would

475 help to reduce uncertainties in future studies of scaling relations. If the result

476 is different from the approach used by UCERF3, it could have a direct impact

477 on future seismic hazard analyses.

478 Conclusions

479 The primary question asked by this research is if the introduction of slip rate

480 on a fault helps to reduce the uncertainties in estimates of magnitude from

19 481 observations of rupture length. We find that such a slip rate dependence is

482 reasonably well established for strike-slip cases: as the slip rate increases for

483 any given fault length, the predicted magnitude tends to decrease. This result

484 is robust in the sense that the slope of the residuals with slip rate is significantly

485 different from zero and the variance reduction is modestly significant for all three

486 of the considered models relating rupture length and magntiude. For reverse and

487 normal faulting mechanisms, on the other hand, our data do not demonstrate

488 the presence of a significant slip rate effect in the relationship between rupture

489 length and magnitude. Compared to original results in AWS96, we now suggest

490 slip rate be included only for strike-slip faults.

491 The constant stress drop model presented here has potential for progress

492 on a standing difficulty in ground motion modeling of an internally consistent

493 scaling of magnitude, length, down-dip width, and fault displacement. Current

494 relations in which magnitude scales with length or area lead to unphysical stress

495 drops or unobserved down-dip widths, respectively. By working from the model

496 of Chinnery (1964) our constant stress drop model has the advantage of starting

497 with realistic physics including the stress effects of surface rupture. Work re-

498 mains in comparing displacements predicted from our model with observations,

499 but the fact that it fits the current magnitude-length-slip rate data as well or a

500 bit better than the linear and bilinear models suggests that the constant stress

501 drop model is preferable to models that do not have this feature.

502 Data and Resources

503 The Wikipedia article “Total Least Squares” (https://en.wikipedia.org/wiki/Total_least_squares)

504 was accessed Feb. 15, 2015.

20 505 Acknowledgements

506 Research supported by the U.S. Geological Survey (USGS), Department of the

507 Interior, under USGS award number G14AP00030. The views and conclusions

508 contained in this document are those of the authors and should not be in-

509 terpreted as necessarily representing the official policies, either expressed or

510 implied, of the U.S. Government.

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655 List of Figures

656 1 Cumulative number of events used in this analysis (Table 1 and

657 2),shownasafunctionoftime...... 32

658 2 Event rates, as a function of magnitude and event types. The

659 rates are estimated based on the approximation that the data

660 represent about 100 years of seismicity, as discussed in the text. 33

26 661 3Locationsofeventsconsideredinthisstudy.Opencirclesshow

662 locations of events with a strike-slip mechanism. Upward-pointed

663 triangles represent reverse events, and downward-pointed trian-

664 gles represent normal mechanisms...... 34

665 4Rupturelength-slipratedistributionofthedatainTables1and

666 2. All points are shown combined in each part of the figure. a)

667 Each fault type is given equal emphasis. b) Strike-slip faults are

668 emphasized. c) Reverse faults are emphasized. d) Normal faults

669 are emphasized...... 35

670 5ModelsM1(Equation1)for(a)strike-slip,(b)reverse,and(c)

671 normal faults. For each mechanism, the upper frame shows MW

672 plotted as a function of LE.Pointsareallthepreferredvalues,as

673 given in Tables 1 and 2. Solid points represent low slip-rate faults.

674 The solid line uses coefficients given in Table 3 for SF = S0. The

675 lower frame shows the residuals, MW ,ofthepointsintheupper

676 frame from the solid line. The line in the lower frame shows the

677 predicted effect of SF based on the coefficients in Table 3, i.e.

678 MW = c2 log (SF /S0).Forstrike-slipfaults,thesignificant

679 effect of fault slip rate is seen in the clear separation of low and

680 high slip-rate faults in the upper panel, and the negative slope

681 of the fit to the residuals in the lower panel. For reverse and

682 normal faults, the sparse data suggest a different trend in the

683 residuals, indicating that mixing the three mechanism types is

684 not appropriate...... 38

685 6ModelsM2(Equation2)for(a)strike-slip,(b)reverse,and(c)

686 normal faults. Coefficients for the lines are given in Table 4.

687 Other figure details are as in Figure 5...... 41

27 688 7ModelsM3(Equation3)for(a)strike-slip,(b)reverse,and(c)

689 normal faults. Coefficients for the lines are given in Table 5.

690 Other figure details are as in Figure 5...... 44

691 8 Coefficient distributions for the linear, strike-slip model (M1,

692 Equation 1). The bar chart shows number of occurrences of pa-

693 rameter values among 10,000 realizations for randomly selected

694 values of MW , LE,andSF within the uncertainty range of each.

695 Solid gray line shows the mean value of each parameter. The

696 dashed grey line shows the value found for the preferred value of

697 MW , LE,andSF for each earthquake. The clear negative value

698 of c2 corresponds to decreasing relative magnitude predictions

699 withincreasingsliprate...... 45

700 9 Comparisons of models M1, M2, and M3 for a) strike-slip, b)

701 reverse, and c) normal faults, using SF = S0 for each mechanism. 46

702 A.1 Model for MW based on Chinnery (1964) scaling as given in Equa-

703 tion A.18. Top: effect of changing the stress drop ⌧C .Center:

704 effect of changing the aspect ratio of the fault. Bottom: effect of

705 changing the limiting rupture width Wmax...... 56

706 Tables

28 Table 1: Earthquakes from 1968-2011 used in this study. Event Event Name Event Date Mw Rupture Slip Rate, Mech Num. Length, mm/yr km 2 Fukushima- 11-Apr-2011 6.7 15 0.02 N Hamadori, Japan 4 Yushu, China 14-Apr-2010 6.8 52 12 S 5 El Mayor Cucapah 4-Apr-2010 7.3 117 2.5 S 6 Wenchuan, China 12-May-2008 7.9 240 1.3 R 7 Kashmir, Pakistan 8-Oct-2005 7.6 70 3.1 R 8 Chuya,Russia 27-Sep-2003 7.2 70 0.5 S (Gorny Altay) 9 Denali, Alaska 3-Nov-2002 7.8 340 12.4 S 10 Kunlun, China 14-Nov-2001 7.7 450 10 S 11 Duzce, Turkey 12-Nov-1999 7.1 40 15 S 12 Hector Mine, 16-Oct-1999 7.1 48 0.6 S California 13 Chi-Chi, Taiwan 21-Sep-1999 7.7 72 12.9 R 14 Izmit, Turkey 17-Aug-1999 7.5 145 12 S 15 Fandoqa, Iran 14-Mar-1998 6.6 22 2 S 16 Manyi, China 8-Nov-1997 7.4 170 3 S 17 Sakhalen Island 27-May-1995 7.0 40 4 S (Neftegorsk) 18 Northridge 17-Jan-1994 6.7 21 0.4 R 19 Landers 28-Jun-1992 7.2 77 0.4 S 20 Luzon 16-Jul-1990 7.7 112 15 S 21 Rudbar 20-Jun-1990 7.4 80 1 S 22 Loma Prieta 17-Oct-1989 6.8 35 3.2 R 25 Superstition Hill 24-Nov-1987 6.6 25 3 S 26 Edgecumbe 2-Mar-1987 6.4 15.5 2 N 28 Marryat 3-Mar-1986 5.8 13 0.005 R 29 Morgan Hill 24-Apr-1984 6.1 20 5.2 S 30 Borah Peak 28-Oct-1983 6.9 36 0.15 N 31 Coalinga 2-May-1983 6.4 25 1.4 R 32 Sirch 29-Jul-1981 7.1 65 4.3 S 33 Corinth 25-Feb-1981 6.1 14 1.7 N 34 Corinth 4-Mar-1981 5.9 15 0.3 N 35 Daofu 24-Jan-1981 6.7 44 12 S 36 El Asnam (Ech 10-Oct-1980 6.9 36 0.8 R Cheliff) 37 Imperial Valley 15-Oct-1979 6.4 36 17 S 38 Coyote Lake 6-Aug-1979 5.8 14 11.9 S 40 Tabas 16-Sep-1978 7.4 90 1.3 R 41 Bob-Tangol 19-Dec-1977 5.8 19.5 4 S 42 Motagua 4-Feb-1976 7.5 230 12 S 29 43 Luhuo 6-Feb-1973 7.5 90 14 S 44 San Fernando 9-Feb-1971 6.8 19 1.8 R 45 Tonghai 4-Jan-1970 7.2 60 2 S 46 Dasht-e-Bayaz 31-Aug-1968 7.1 80 5 S 47 Borrego Mntn 9-Apr-1968 6.6 33 6.7 S Table 2: Earthquakes from 1848 - 1967 used in this study. Event Event Name Event Date Mw Rupture Slip Mech Num. Length, Rate, km mm/yr 48 Mudurnu Valley 22-Jul-1967 7.3 80 18 S 49 Parkfield 28-Jun-1966 6.2 28 30 S 51 Alake Lake - or - 19-Apr-1963 7.0 40 12 S Tuosuohu Lake or Dulan 52 Ipak or Buyin-Zara 1-Sep-1962 7.0 100 1 R 53 Hebgen Lake 18-Aug-1959 7.3 25 0.5 N 54 Gobi-Altai 4-Dec-1957 8.1 260 1 S 55 San Miguel 14-Feb-1956 6.6 20 0.3 S 56 Fairview Peak 16-Dec-1954 7.1 46 0.14 N 57 Dixie Valley 16-Dec-1954 6.6 47 0.5 N 58 Gonen-Yenice 18-Mar-1953 7.3 60 6.8 S 60 Gerede-Bolu 1-Feb-1944 7.3 155 18 S 61 Tosya 26-Nov-1943 7.6 275 19 S 62 Tottori 10-Sep-1943 6.9 33 0.3 S 63 Niksar-Erbaa 20-Dec-1942 6.8 50 19 S 64 Imperial Valley 19-May-1940 7.1 60 17 S 65 Erzincan 25-Dec-1939 7.8 330 19 S 66 Tuosuo Lake - 7-Jan-1937 7.6 150 11 S Huashixia 67 Parkfield 8-Jun-1934 6.2 25 30 S 68 Long Beach 10-Mar-1933 6.4 22 1.1 S 69 Changma 25-Dec-1932 7.6 149 5 S 70 Fuyun 10-Aug-1931 7.9 160 0.3 S 71 N. Izu 25-Nov-1930 6.9 28 2.4 S 72 Laikipia 6-Jan-1928 6.8 38 0.18 N 73 Tango 7-Mar-1927 7.0 35 0.3 S 74 Luoho-Qiajiao 24-Mar-1923 7.3 80 10 S (Daofu) 75 Haiyuan 16-Dec-1920 8.0 237 7 S 76 Pleasant Valley 3-Oct-1915 7.3 61 0.1 N 77 Chon-Kemin 3-Jan-1911 8.0 177 2 R (Kebin) 78 San Francisco 18-Apr-1906 7.9 497 21 S 79 Bulnay 23-Jul-1905 8.5 375 3 S 80 Laguna Salada 23-Feb-1892 7.2 42 2.5 S 81 Rikuu 31-Aug-1896 7.2 40 1 R 82 Nobi/ Mino-Owari 28-Jun-1908 7.4 80 1.6 S 83 Canterbury 01-Sep-1888 7.1 65 14 S 84 Sonora 13-May-1887 7.2 101.8 0.08 N 85 Owens Valley 26-Mar-1872 7.4 110 3.5 S 86 Hayward 1-Oct-1868 6.9 61 8 S 30 87 Fort Tejon 9-Jan-1857 7.8 339 25 S 88 Marlborough 16-Oct-1848 7.5 134 5.6 S Table 3: Coefficients for Model, M1, for use in Equation 1, for the different fault types considered separately, for earthquakes listed in Table 1 and 2. Strike-Slip Reverse Normal c 4.73 0.062 5.12 0.11 5.25 0.18 0 ± ± ± c 1.30 0.031 1.15 0.065 1.02 0.12 1 ± ± ± c -0.198 0.023 0.264 0.036 -0.115 0.109 2 ± ± ± S0,mm/yr 4.8 1.1 0.25 1L 0.241 0.322 0.318 1S 0.211 0.238 0.303

Table 4: Coefficients for Model M2, for use in Equation 2, for the different fault types considered separately, for earthquakes listed in Table 1 and 2. Strike-Slip Reverse Normal L 73.8 9.4 46.4 6.4 24.3 1.10 bp ± ± ± M 7.38 0.070 7.23 0.091 6.80 0.031 bp ± ± ± c -0.176 0.031 0.169 0.042 -0.107 0.091 2 ± ± ± S0,mm/yr 4.80 1.1 0.25 2L 0.238 0.281 0.289 2S 0.215 0.253 0.277

Table 5: Coefficients for Model M3, for use in Equation 3, for the different fault types considered separately, for earthquakes listed in Table 1 and 2. Strike Slip (15 km) Strike-Slip (20 km) Reverse Normal ⌧ ,bars 24.9 1.1 15.3 0.7 10.6 0.7 14.0 1.5 C ± ± ± ± CLW 3.8 2.9 1.4 1.2 Wmax,km 15 20 30 18 c -0.170 0.029 -0.174 0.029 0.144 0.027 -0.056 0.095 2 ± ± ± ± S0,mm/yr 4.8 4.8 1.1 0.25 3L 0.236 0.235 0.281 0.312 3S 0.214 0.210 0.255 0.305

31 707 Figures

Figure 1: Cumulative number of events used in this analysis (Table 1 and 2), shown as a function of time.

32 Figure 2: Event rates, as a function of magnitude and event types. The rates are estimated based on the approximation that the data represent about 100 years of seismicity, as discussed in the text.

33 Figure 3: Locations of events considered in this study. Open circles show loca- tions of events with a strike-slip mechanism. Upward-pointed triangles represent reverse events, and downward-pointed triangles represent normal mechanisms.

34 Figure 4: Rupture length - slip rate distribution of the data in Tables 1 and 2. All points are shown combined in each part of the figure. a) Each fault type is given equal emphasis. b) Strike-slip faults are emphasized. c) Reverse faults are emphasized. d) Normal faults are emphasized.

35 Strike Slip Surface Rupture Events a) 9

8

W 7 M

SF > 4.8 mm/yr

6 SF <= 4.8 mm/yr

MW= 4.73 + 1.3 log LE = 0.241 5 1L 101 102 103 L , km E

Residual from Top Plot

MW = -0.198 log ( SRF / 4.8 mm/yr )

1

0.5 W

M 0

-0.5 = 0.211 -1 1S 10-1 100 101 102 S , mm/yr F

708

36 Reverse Surface Rupture Events b) 9

8

W 7 M

SF > 1.1 mm/yr

6 SF <= 1.1 mm/yr

MW= 5.12 + 1.15 log LE = 0.322 5 1L 101 102 103 L , km E

Residual from Top Plot

MW = 0.264 log ( SRF / 1.1 mm/yr )

1

0.5 W

M 0

-0.5 = 0.238 -1 1S 10-3 10-2 10-1 100 101 102 S , mm/yr F

709

37 Normal Surface Rupture Events c) 9

8

W 7 M

SF > 0.25 mm/yr

6 SF <= 0.25 mm/yr

MW= 5.25 + 1.02 log LE = 0.318 5 1L 101 102 103 L , km E

Residual from Top Plot

MW = -0.115 log ( SRF / 0.25 mm/yr )

1

0.5 W

M 0

-0.5 = 0.303 -1 1S 10-2 10-1 100 101 S , mm/yr F

Figure 5: Models M1 (Equation 1) for (a) strike-slip, (b) reverse, and (c) normal faults. For each mechanism, the upper frame shows MW plotted as a function of LE.Pointsareallthepreferredvalues,asgiveninTables1and2.Solidpoints represent low slip-rate faults. The solid line uses coefficients given in Table 3 for SF = S0. The lower frame shows the residuals, MW ,ofthepointsinthe upper frame from the solid line. The line in the lower frame shows the predicted effect of SF based on the coefficients in Table 3, i.e. MW = c2 log (SF /S0). For strike-slip faults, the significant effect of fault slip rate is seen in the clear separation of low and high slip-rate faults in the upper panel, and the negative slope of the fit to the residuals in the lower panel. For reverse and normal faults, the sparse data suggest a different trend38 in the residuals, indicating that mixing the three mechanism types is not appropriate. Strike Slip Surface Rupture Events a) 9

8

W 7 M

SF > 4.8 mm/yr

6 SF <= 4.8 mm/yr

L bp = 73.8; M bp = 7.38 = 0.238 2L 5 101 102 103 L , km E

Residual from Top Plot

MW = -0.176 log ( SF / 4.8 mm/yr)

1

0.5 W

M 0

-0.5 = 0.215 -1 2S 10-1 100 101 102 S , mm/yr F

710

39 Reverse Surface Rupture Events b) 9

8

W 7 M

SF > 1.1 mm/yr

6 SF <= 1.1 mm/yr

L bp = 46.4; M bp = 7.23 = 0.281 2L 5 101 102 103 L , km E

Residual from Top Plot

MW = 0.169 log ( SF / 1.1 mm/yr)

1

0.5 W

M 0

-0.5 = 0.253 -1 2S 10-3 10-2 10-1 100 101 102 S , mm/yr F

711

40 Normal Surface Rupture Events c) 9

8

W 7 M

SF > 0.25 mm/yr

6 SF <= 0.25 mm/yr

L bp = 24.3; M bp = 6.8 = 0.289 2L 5 101 102 103 L , km E

Residual from Top Plot

MW = -0.107 log ( SF / 0.25 mm/yr)

1

0.5 W

M 0

-0.5 = 0.277 -1 2S 10-2 10-1 100 101 S , mm/yr F

Figure 6: Models M2 (Equation 2) for (a) strike-slip, (b) reverse, and (c) normal faults. Coefficients for the lines are given in Table 4. Other figure details are as in Figure 5.

41 Strike Slip Surface Rupture Events a) 9

8

W 7 M

SF > 4.8 mm/yr

6 SF <= 4.8 mm/yr

MC( =24.9 bars, CLD=3.8, Wmax=15) [SF=4.8 mm/yr] = 0.236 5 3L 101 102 103 L , km E

Residual from Top Plot

MW= -0.17 log( SF / 4.8 mm/yr )

1

0.5 W

M 0

-0.5 = 0.214 -1 3S 10-1 100 101 102 S , mm/yr F

712

42 Reverse Surface Rupture Events b) 9

8

W 7 M

SF > 1.1 mm/yr

6 SF <= 1.1 mm/yr

MC( =10.6 bars, CLD=1.4, Wmax=30) [SF=1.1 mm/yr] = 0.281 5 3L 101 102 103 L , km E

Residual from Top Plot

MW= 0.144 log( SF / 1.1 mm/yr )

1

0.5 W

M 0

-0.5 = 0.255 -1 3S 10-3 10-2 10-1 100 101 102 S , mm/yr F

713

43 Normal Surface Rupture Events c) 9

8

W 7 M

SF > 0.25 mm/yr

6 SF <= 0.25 mm/yr

MC( =14 bars, C LD=1.2, Wmax=18) [SF=0.25 mm/yr] = 0.312 5 3L 101 102 103 L , km E

Residual from Top Plot

MW= -0.056 log( SF / 0.25 mm/yr )

1

0.5 W

M 0

-0.5 = 0.305 -1 3S 10-2 10-1 100 101 S , mm/yr F

Figure 7: Models M3 (Equation 3) for (a) strike-slip, (b) reverse, and (c) normal faults. Coefficients for the lines are given in Table 5. Other figure details are as in Figure 5.

44 Strike Slip Surface Rupture Events 500

0 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.85 4.9 4.95 5 c 0 500

0 1.15 1.2 1.25 1.3 1.35 1.4 1.45 c 1

500

0 -0.3 -0.28 -0.26 -0.24 -0.22 -0.2 -0.18 -0.16 -0.14 -0.12 -0.1 c 2

500

0 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 σ 1L

500

0 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 σ 1S

Figure 8: Coefficient distributions for the linear, strike-slip model (M1, Equation 1). The bar chart shows number of occurrences of parameter values among 10,000 realizations for randomly selected values of MW , LE,andSF within the uncertainty range of each. Solid gray line shows the mean value of each parameter. The dashed grey line shows the value found for the preferred value of MW , LE,andSF for each earthquake. The clear negative value of c2 corresponds to decreasing relative magnitude predictions with increasing slip rate.

45 (a) 8.5 Strike Slip, S = S = 4.8 mm/yr 8 F 0 7.5

W 7 M 6.5 M1 M2 6 M3 5.5 101 102 103 (b) 8.5 Reverse, S = S = 1.1 mm/yr 8 F 0 7.5

W 7 M 6.5 M1 M2 6 M3 5.5 101 102 103 (c) 8.5 Normal, S = S = 0.25 mm/yr 8 F 0 7.5

W 7 M 6.5 M1 M2 6 M3 5.5 101 102 103 Rupture Length, km

Figure 9: Comparisons of models M1, M2, and M3 for a) strike-slip, b) reverse, and c) normal faults, using SF = S0 for each mechanism.

46 714 A Appendix: Fault scaling relations

715 Basics

716 This paper proposes models to estimate the moment magnitude of earthquakes

717 based on observed surface rupture lengths and slip rates. The moment magni-

718 tude definition that we use is, implicit in Kanamori (1977):

2 M = (log M 16.1) (A.1) W 3 0

719 The units of seismic moment, M0, are dyne-cm in Equation A.1 . This definition

720 differs slightly from the equation used by Hanks and Kanamori (1979), but is

721 the equation recommended for seismic network operations by the International

722 Association of Seismology and Physics of the Earths Interior (IASPEI, 2005,

723 2013; Borman et al, 2012), and thus is the relationship used by most seismic

724 networks throughout the world. The seismic moment is defined as:

M0 = µAED¯ E = µLEWED¯ E (A.2)

725 where µ is the shear modulus, AE is the fault area ruptured in the earthquake, ¯ 726 and DE is the average slip over that area. For a fault that is approximately

727 rectangular, AE = LEWE where LE is the rupture length measured along strike,

728 and WE is the downdip rupture width.

729 Substituting Equation A.2 into Equation A.1, one obtains (for cgs units)

2 2 2 2 M = log L + log W + log D¯ + (log µ 16.1) (A.3) W 3 E 3 E 3 E 3

730 This justifies models that relate magnitude to the log of fault length, width, and

731 mean slip. Slopes different from 2/3 result from correlations among the fault ¯ 732 parameters LE, WE,andDE. Wells and Coppersmith (1996) found that the

47 733 model

MW = c1 log LE + c0 (A.4)

734 predicts magnitude from rupture length with a standard deviation of the misfit,

735 1 =0.28.

736 The possible dependence of stress drop or magnitude on slip rate was recog-

737 nized by Kanamori and Allen (1986) and Scholz et al. (1986). With the addition

738 of the slip rate term, Equation A.4 becomes, used by AWS96:

MW = c0 + c1 log LE + c2 log SF (A.5)

739 Testing for a logarithmic dependence on the geological fault slip rate, SF ,can

740 be motivated by findings in Dieterich (1972). In this paper, Equation A.5 is

741 equivalent to Model 1, or more briefly M1.

742 Constant Stress Drop Scaling

743 The static stress drop, ⌧S,istheaveragedecreaseintheshearstressacting

744 on the fault as a result of the earthquake, and is proportional to the ratio

745 of average slip to a fault dimension. Seismic observations have found that the

746 average value of ⌧S is approximately constant (~4 MPa, ~40 bars) over a broad

747 range of earthquake magnitudes (e.g. Kanamori and Anderson, 1975; Allmann

748 and Shearer, 2009), although there is considerable scatter in these data. Seismic

749 moment, and thus MW through Equation A.1, can be expressed as a function

750 of fault dimension and stress drop, as recognized by Kanamori and Anderson

751 (1975). Selected models are summarized in Table A.1.

752 The equations in Table A.1 indicate that constant stress drop implies the

753 slope c1 =2.0 for small faults (Case 1) when LE is equated to the diameter of the

754 circular fault and c1 =2/3 for long faults (Cases 2 and 3). These observations

48 755 motivate a bilinear approach to fit the data, which is model M2 in the main

756 text of the paper. The bilinear approach is formulated as follows:

LE SF MW = Mbp + c1C log( L )+c2 log S LE

758 the scaling relationship changes from the small fault model with slope c1C =2

2 759 to the long fault model with slope c1L = 3 . The slip rate S0 is a reference slip

760 rate which can be chosen arbitrarily, but is conveniently chosen to be the log

761 average slip rate in the data, so that setting SF = S0 gives the best fit when slip

762 rate is unknown. The constant Mbp is the magnitude corresponding to a fault

763 with length LE = Lbp and slip rate SF = S0.NotethatEquationA.6hasthree

764 unknown coefficients (Mbp, Lbp,andc2), which is the same number as Equation

765 A.5.

766 However, there are issues with the applicability of the equations 1, 2, and 3

767 in Table A.1. The foremost, for the long faults, is the width of the seismogenic

768 zone. Table A.1 shows that WE is twice as influential as the fault length, so

769 it needs to be considered carefully. One approach to estimate this width is

770 to use the maximum depth of microearthquakes. By this approach, for strike-

771 slip earthquakes the maximum depth of microearthquakes equates directly to

772 an estimate of the fault width, while for a reverse or normal fault the dip is

773 incorporated. The problem is that the maximum depth of seismogenic rupture

774 in large earthquakes is difficult to observe. King and Wesnousky (2007) discuss

775 this difficulty, and present arguments for why the downdip width might be

776 larger in large earthquakes, at least up to some limit greater than that inferred

777 from the depth range of small earthquakes, because rocks below the depths of

778 mircoearthquakes might experience brittle failure under high strain rates. If

779 the width increases in general for long ruptures, stress drop is no longer as

49 780 high for these events because stress drop is inversely proportional to WE,and

781 furthermore the slope c1 can no longer be reliably constrained by the models

782 in Table A.1. King and Wesnousky propose that this explains the proposal

783 by Scholz (1982) that slip in large earthquakes is more nearly proportional to

784 rupture length than to rupture width.

785 Another issue is that Equation 1 of Table A.1 assumes that the circular

786 fault is confined within the Earth and thus neglects free surface effects, while

787 by definition all of the events considered in this study rupture the surface. This

788 motivates development of the model that is described in the next section.

789 Relations based on Chinnery (1964)

790 Chinnery (1963, 1964) calculated a stress drop for a rectangular, strike-slip

791 fault that ruptures the surface. Unlike the circular slip model, the free surface

792 in the Chinnery model is present for small earthquakes. His equations assume

793 a uniform slip on the fault. Thus the stress drop is variable over the fault,

794 and becomes singular at the edge of the fault. His equations give the stress

795 drop on the surface at the midpoint of the rupture. Numerical solutions in

796 Chinnery (1963) show relatively uniform stress drop over large portions of the

797 fault. Chinnery (1963) thus suggests that the results are valid to represent the

798 fault stress drop so long as the zone of slip fall-offis much smaller than the area

799 of the fault. The key advantage provided by this approach is to provide a useful

800 analytical solution.

801 For the rectangular fault with length LE, width WE,andaspectratioCLW =

802 LE/WE, the stress drop in the Chinnery model, ⌧C ,atthemidpointatthe

803 surface is

µD¯ E ⌧ = C (L ,W ) (A.7) C 2⇡ 1 h E

50 804 where 2Lh 3 Lh (3a +4WE) C1 (Lh,WE)= + 2 (A.8) (aWE Lh a (a + WE) )

1 2 2 2 805 Note that Lh = LE/2,anda = Lh + WE .ObservethatC1 has dimensions 1 806 of 1/length,andthusC1 is effectively the fault dimension that is used for

807 calculating the strain. In other words, the strain change in the earthquake is ¯ 808 D C .Anequationfortheseismicmomentcanbeobtainedbysolving ⇠ E 1 ¯ 809 Equation A.7 for DE and substituting in Equation A.2. The result is

LEWE M0 =2⇡⌧C (A.9) C1 (Lh,WE)

810 and thus

2 2 2 2⇡WE 2 MW = log LE + log ⌧C + log 16.1 (A.10) 3 3 3 C1 (Lh,WE) 3 ·

811 Additional insight into the geometrical term can be obtained by observing

812 that a is the length of the diagonal from the midpoint of the fault at the surface

813 to either of the bottom corners. If the dip of this line is ,thentan =

814 WE/Lh =2/CLW , Lh = a cos , WE = a sin , and one can rewrite

1 C1 (Lh,WE)= C () (A.11) WE

815 where cos sin (3 + 4 sin ) C () = 2 cos + 3 tan (A.12) (1 + sin )2

816 Thus one can rewrite Equation A.7 as

C () D¯ E ⌧C = µ (A.13) 2⇡ WE

¯ 817 Solving Equation A.13 for DE and substituting into Equation A.2 gives the

51 818 moment of a vertical strike-slip fault that ruptures the surface as:

2⇡ M = ⌧ L W 2 (A.14) 0 C () C E E

819 Because ,andthusC (),dependsonthefaultaspectratio,EquationsA.9,or

820 A.14, can be used to model a transition from small-earthquake behavior (e.g.

821 the circular fault in Table A.1) to a long-fault behavior. This paper, similar to

822 Hanks and Bakun (2002) , maintains a constant aspect ratio as the fault length

823 increases, until that aspect ratio implies that the fault width would exceed some

824 maximum. For longer faults, the width is set to that maximum. Before reaching

825 that maximum, and C () are constant, and

3 2⇡ LE LE M0 = ⌧C 2

826 For longer faults, for which the width is limited, Equation A.14 becomes

2⇡ 2 LE M0 = ⌧C LEW Wmax (A.16) C() max CLW

827 In this case, as the fault length increases while width is held constant, will be

o 828 decreasing. For the limit of small (roughly . 25 ) , Equation A.12 shows

829 that C () 2,soEquationA.9approaches !

2 M0 = ⇡⌧C LEWmax (A.17)

830 Equation A.17 differs from Case 2 in Table A.1 for the long strike-slip fault by a

831 factor of 2 (⌧S = 2⌧C ), where the difference is due to the different boundary

832 conditions used for the two solutions at depth.

833 From Equations A.15 and A.16, converting to magnitude, the implied scaling

52 834 relationship based on the Chinnery model is

2 2 2⇡ LE 2 log LE + log ⌧C + log 2 16.1 2 2 2 2⇡Wmax LE <> log LE + log ⌧C + log 16.1 Wmax 3 3 3 C() CLW > ⇣ ⌘ (A.18) :> 835 Equation A.18 will be the third model, M3, considered in this study, with

SF 836 +c log the addition of a slip rate contribution, 2 S0 ,tothetwobranchesof ⇣ ⌘ 837 the equation . The unknown parameters in M3 are ⌧C , CLW , Wmax,and

838 c2. Thus this model has four parameters to be determined, compared to three

839 parameters in M1 and M2. Figure A.1 shows the effect of the three prameters

840 ⌧C , CLW , Wmax on magnitude predictions. The stress drop scales the entire

841 curve upwards. The aspect ratio CLD adjusts the level of the magnitude for

842 short rupture lengths. The maximum width affects the curvature and how

2 843 rapidly the curve approaches the asymptotic slope of 3 log LE for long rupture

844 lengths.

845 Other models and considerations

846 Sato (1972) overcomes the singularity introduced by Chinnery (1963, 1964)

847 by assuming a smooth ad-hoc slip function on a finite, rectangular/elliptical -

848 shaped fault, and for that function, calculating the average stress drop resulting

849 from that slip function. While the results are informative for source physics

850 studies, the major disadvantages of this approach for our application are that

851 the fault is embedded in a whole space, and there is no analytical solution

852 comparable to Equation A.7. Rather, the geometrical factor equivalent to C ()

853 can be computed numerically using equations in Sato (1972) or read from a

854 figure in the paper. Considering these limitations, this model was not considered

855 further.

856 Shaw and Scholz (2001) and Shaw and Wesnousky (2008) implement a nu-

53 857 merical model for fault slip in a half space with depth-dependent friction. They

858 examine the statistics of events that rupture the surface. These papers are in-

859 teresting for the finding that large surface rupturing events also slip below the

860 brittle crustal depths. The scaling found in the model has properties similar

861 to the scaling in the Chinnery model. However the scaling relationship that

862 they determine has an ad-hoc shape, and thus we preferred the analytical func-

863 tional form of Equation A.18, as discussed above. The physics-based solution

864 of Chinnery was also preferred to a related constant stress drop model by Shaw

865 (2009). This model proposes three regimes of magnitude scaling from length

866 based on intermediate length-width-displacement scaling relations and heuristic

867 arguments for transitions between them.

868 Rolandone et al (2004) found some empirical evidence that might be inter-

869 preted to support the penetration of rupture below the brittle seismogenic layer

870 in large earthquakes. They found that the maximum depth of aftershocks of

871 the Landers earthquake were deeper immediately after the main shock, and then

872 the maximum depth returned to pre-earthquake levels over the next few years.

873 This might be explained by high strain rates in the uppermost part of the duc-

874 tile crust, as high strain rates favor brittle failure. However, post-seismic strain

875 rates in that depth range would be high even if seismic rupture of the main

876 shock did not extend that deep, so these observations allow, but do not require,

877 dynamic rupture below the long-term average depth of microearthquakes.

54 878 Appendix Tables

Table A.1: Models from Kanamori and Anderson (1975) for the relationship of fault size, stress drop, and MW . 1 Case M0 Implied magnitude relations 16 3 2 1. Buried, circular 7 ⌧SRE MW = log AE + 3 log ⌧S +3.0089 2 If LE =2RE: MW = 2 log LE + 3 log ⌧S +2.904 ⇡ 2 2 4 2 2. Strike-slip, long 2 ⌧SWELE MW = 3 log LE + 3 log WE + 3 log ⌧S +3.1359

⇡(+2µ) 2 2 4 2 3. Dip-slip, long 4(+µ) ⌧SWELE MW = 3 log LE + 3 log WE + 3 log ⌧S +3.3141

2 2 1. Fault area, AE = ⇡RE,inkm,faultradiusRE, width WE,andlengthLE in km, and stress drop ⌧S in bars.

55 879 Appendix Figures

W =15 km; C =1 8 max ld 7

W C =10 bars 6 M C =30 bars

5 C =100 bars

4 101 102 L, km

W =15 km; =30 bars 8 max C 7

W C ld=1 6 M C ld=2

5 C ld=4

4 101 102 L, km

C =1, =30 bars 8 ld C

7

W Wmax =10 6 56 M Wmax =15

5 Wmax =20

4 101 102 L, km

Figure A.1: Model for MW based on Chinnery (1964) scaling as given in Equa- tion A.18. Top: effect of changing the stress drop ⌧C . Center: effect of changing the aspect ratio of the fault. Bottom: effect of changing the limiting rupture width Wmax. Supplemental Material (Main Page) Click here to download Supplemental Material (Main Page, Tables, Figures) Online Supplement +DataTableNotes_r2.docx

Online Supplement for Fault Scaling Relationships Depend on the Average Geological Slip Rate by John G. Anderson, Glenn P. Biasi, Steven G. Wesnousky This supplement provides a table giving a complete summary of the data used in this study. Earthquakes from Anderson et al. (1996; “AWS96”) and Biasi and Wesnousky (2016; “BW16”) were reviewed for inclusion. Relative to the list in AWS96, the 1811 New Madrid, 1848 Marlborough, 1952 Kern County and 1986 N. Palm Springs earthquakes were not used because uncertainties in one or more parameters were considered too great to usefully constrain the regressions. All parameters for events in AWS96 were reviewed and several were updated where results were available from more recent studies. BW16 focused on surface rupturing events. Their event set overlaps with AWS96, but contributes earthquakes post-dating AWS96, and older events where new geologic study has developed length, magnitude, and/or fault slip rate data. New and revised events in BW16 include a rupture map and a narrative listing all studies considered for magnitude, length, and rupture configuration. For events in BW16 adopted from Wesnousky (2008), the reader is referred to the latter paper. Table A1 has been developed with the goal of not introducing systematic bias in parameter estimates. In fitting for regressions, one hopes that the errors are randomly distributed, such that an unknown overestimate of a parameter for one earthquake is countered by an underestimate somewhere else. Where individual parameters could exert a strong influence on the regression, a review of the original data and sensitivity tests of that influence were conducted. Sources of estimates of earthquake magnitude, rupture length and fault slip rate are listed in the references column of Table A1. References are divided into three sections. “Mag” includes the citations for seismic moment (Mo) and moment magnitude. The first listed citation is normally the source for the preferred estimate. Instrumental magnitudes are available for most ruptures after 1900. Moment magnitude estimates based on waveform fitting are given priority over body wave-based estimates. Magnitudes based only on geologic measurements have been avoided. Uncertainty ranges are taken from the original sources where a single source reference is available. Where multiple sources provide parameter estimates, the uncertainty range reflects that range, with some judgment applied to apparent outliers. For parameters estimated in more than one study, later study estimates have been preferred, as they normally bring more advanced methods and broader research to the problem. First cited references in a section generally provide the preferred parameter estimate. Rupture length estimates for events in Biasi and Wesnousky (2016) are measured as a total from primary surface rupture. Lmin and Lmax in Table A1 refer to minimum and maximum length estimates, respectively. Length uncertainty synthesizes mapping uncertainty where multiple maps are available. Where recognized as such, secondary and sympathetic fractures have not been included. Six events were retained from AWS96, all instrumentally recorded strike-slip events in California, that had little or no surface

1 rupture. For these events, totaling about 11% of the strike slip set, length is estimated from early aftershocks and other geophysical considerations. They were retained to improve data coverage at shorter lengths, and for continuity with AWS96. For some ruptures a simple length estimate on a main fault trace does not capture the complexity of the event. For these cases or where the length has been estimated by other means, brief notes of explanation have been added. Fault slip rate estimates have been selected to represent the recent, time-independent slip rate where slip took place. In the literature, fault slip rates may be developed from paleoseismic offsets from one or a few discrete events, from larger offsets representing longer-term fault activity, or from geodetic estimates, which measure essentially the current rate with any transients. Geologic slip rate estimates from offsets of dated 10ky to 100 ky features were preferred where available. Paleoseismic slip rates measured from one or a few individual earthquake offsets have been avoided where possible, because it is not normally clear how the offsets relate to long-term fault behavior. In Table A1 the first listed method of estimating slip rate relates to the preferred estimate. Where other methods are also listed, they indicate alternate sources of slip rate estimates, and inform the uncertainty estimate. The timeframes of geologic offsets are also indicated in the notes. For a few events (21, 42, 52, and 77) the preferred fault slip rate depends on geodetic measurements. The circumstances of each event differ, but each was considered reasonable in light of other available geologic information. It will also be seen below that regressions for the effect of fault slip rate are least sensitive to uncertainties in slip rate. Faults were also reviewed for the possible influence of creep on the slip rate estimate. Creep aseismically releases fault stresses, so that only some fraction of the total would be attributed to coseismic release. In our present database creep only 2 or 3 faults are known to have a creep component. Also, examination of Figure 5 and similar figures in the main text shows that results are least dependent on uncertainties in slip rate. As a result, we did not attempt creep-related corrections.

List of Table Captions Table A1. Surface rupturing earthquakes considered in this study.

References cited in Table A1.

Abe, K. (1975). Re-examination of the fault model for the Niigata earthquake of 1964, Journal of Physics of Earth 23 349-366. Akyuz, H. S., R. Hartleb, A. Barka, E. Altunel, G. Sunal, B. Meyer, and R. Armijo (2002). Surface rupture and slip distribution of the 12 November 1999 Duzce earthquake (M 7.1), North Anatolian fault, Bolu, Turkey, B Seismol Soc Am 92 61- 66. Allen, C. R., Z. L. Luo, H. Qian, X. Z. Wen, H. W. Zhou, and W. S. Huang (1991). Field- Study of a Highly-Active Fault Zone - the Xianshuihe Fault of Southwestern China, Geol Soc Am Bull 103 1178-1199.

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Table S1, Earthquakes, parameters, and references

Ev Date Earthquake Fault Mw (min Seismic Fault Length References Num yyyy/mm Name (mechanism) - max) Moment, Slip Rate (Min - /dd * Mo (min (min- Max), - max), max) km dyne-cm mm/yr 2 Fukushima Yunotake, 6.7 (6.7- 1.45 0.02 15 (15 - Mag: Tanaka et al., 2014, Kobayashi, 2014, GCMT; 2011/04/ -Hamadori, Idosawa, (N) 6.7) (1.20 - (0.01 - 15) Length: Surface rupture, Anderson et al., 2013; Slip rate: 11 Japan 1.55) 0.03) Geologic (120-130ka), estimated from 125 ka/2 m per E+26 event 4 2010/04/ Yushu, Garze- 6.8 (6.8- 2.30 12 (10 - 52 (32 - Mag: Yakota et al., 2012; max from GCMT; Length: 14 China Yushu, 6.9) (2.30 - 14) 52) Lmin: surface rupture; L, Lmax include 20 km gap from Ganzi–Yushu 2.53) E epicenter to nearest surface rupture, Li et al., 2012; Slip (SSL) +26 rate: Geologic (<50ka), Wen et al., 2003. 5 2010/04/ El Mayor Laguna 7.3 (7.2- 9.90 2.5 (1 - 117 (117 Mag: Wei et al., 2011, GCMT; Length: L, Lmin: Surface 04 Cucapah, Salada, 7.3) (7.62- 5) - 120) rupture, Fletcher et al., 2014, Oskin et al., 2012; Slip rate: Mexico Pescadores, 9.90) Geologic (Holocene), Mueller and Rockwell, 1995. Borrego and E+26 Indiviso faults (SSR) 6 2008/05/ Wenchuan, Longmenshan 7.9 (7.9- 8.19 1.3 (0.9 - 240 (232 Mag: Yu et al., 2010, GCMT; Length: Lmin surface 12 China (R) 7.9) (8.19 - 1.5) - 330) rupture; Lmax includes 90 km coseismic subsurface 8.90) rupture to NE, Lin et al., 2009; Slip rate: Geologic (late E+27 Pleistocene), Yu et al., 2010, Zhang, 2013. 7 2005/10/ Kashmir, Balakot– 7.6 (7.6- 2.82 3.1 (1.6 - 70 (70 - Mag: Avouac et al., 2006, GCMT; Length: Surface 08 Pakistan Bagh (R) 7.6) (2.82- 4.7) 70) rupture, Kaneda et al., 2008; Slip rate: Geologic 2.94) (Pleistocene), Kaneda et al., 2008, Kondo et al., 2008. E+27 8 2003/09/ Chuya,Rus Har-us-Nuur 7.2 (7.2- 9.38 0.5 (0.2 - 70 (60 - Mag: GCMT; Length: Lmin: surface rupture; Lmax: 27 sia (Gorny Fault (SSR) 7.2) (9.38- 1.0) 80) seismicity, Rogoshin et al., 2007; Dorbath et al. 2008; Slip Altay) 9.38) rate: Geologic (latest Holocene), Dorbath et al., 2008. E+26 Min rate uses 1 event/5 ky, and 1 m/event. 9 2002/11/ Denali, Denali Fault 7.8 (7.8- 7.48 12.4 340 (340 Mag: Dreger et al., 2004; GCMT. Length: Surface 03 Alaska (SSR) 7.9) (7.28 - (11.1 - - 340) rupture, Haeussler et al., 2004. Slip rate: Geologic (latest 8.10) 13.7) Pleistocene), Meriaux et al., 2009; Matmon et al., 2006. E+27 10 2001/11/ Kunlun, Kunlun 7.7 (7.7- 4.90 10 (8.5 - 450 (426 Mag: Wen et al., 2006; GCMT. Length: Surface rupture; 14 China mountain 7.8) (4.90- 11.5) - 475) Lmax: InSAR, Xu et al., 2006; Lassere et al., 2005. Slip (SSL) 5.90) rate: Geologic (Holocene, late Pleistocene), Van Der E+27 Woerd et al., 2002; Haibing et al., 2005; Fu and Awata, 2007. 11 1999/11/ Duzce, Duzce- 7.1 (7.0- 5.40 15 (11.8 40 (40 - Mag: Ayhan et al., 2001; Tibi et al., 2001. Length: 12 Turkey Karadere 7.1) (4.50 - - 18.2) 40) Surface rupture, Akyuz et al., 2002. Slip rate: Geologic fault (SSR) 6.70) (Holocene), Pucci et al., 2008. E+26 12 1999/10/ Hector Lavic Lake 7.1 (7.1- 6.28 0.6 (0.2 - 48 (48 - Mag: Li et al., 2003; Jonsson et al., 2002; Length: 16 Mine, fault (SSR) 7.2) (5.93 - 1.0) 48) Surface rupture, Treiman et al., 2002. Slip rate: Geologic California Bullion fault 6.28) (Quaternary), Treiman et al., 2002. E+26 13 1999/09/ Chi-Chi, Chelungpu 7.7 (7.6- 4.10 12.9 (8.1 72 (72 - Mag: Chi et al., 2001; GCMT. Length: Surface rupture, 21 Taiwan Fault (R) 7.7) (3.38 - - 17.7) 72) Lin et al., 2001; Slip rate: Geologic (Holocene), Simoes et 4.10) al., 2007. E+27 14 1999/08/ Izmit, North 7.5 (7.5- 2.18 12 (10 - 145 (145 Mag: Tibi et al., 2001; Reilinger et al., 2000; GCMT; 17 Turkey Anatolian 7.6) (2.18 - 14) - 145) Length: Surface rupture, Lin et al., 2001. Slip rate: fault zone 2.88) Geologic (Holocene), Armijo et al., 1999; Gasperini et al., (SSR) E+27 2011; Polonia et al., 2004. 15 1998/03/ Fandoqa, Gowk Fault 6.6 (6.5- 9.09 2 (1.5 - 22 (12 - Mag: Berbarian et al., 2001; GCMT; USGS NEIC. Length: 14 Iran zone (SSR) 6.6) (7.07 - 2.4) 23) Surface rupture; Lmax: InSAR, Berbarian et al., 2001. Slip 9.43) rate: Geologic (Quaternary, mid-Holocene), Walker and E+25 Jackson, 2002; Walker et al., 2010. 16 1997/11/ Manyi, Manyi (SSL) 7.4 (7.4- 1.73 3 (1 - 5) 170 (165 Mag: Funning et al., 2014; GCMT; USGS NEIC. Length: 08 China 7.5) (1.40 - - 175) Surface rupture, Wang et al., 2007; Wen and Ma, 2010. 2.23) Slip Rate: Bell et al., 2011. E+27 17 1995/05/ Sakhalen Upper Pil'tun 7.0 (7.0- 4.20 4 (3.5 - 40 (40 - Mag: Katsumata et al., 2004; GCMT. Length: Surface 27 Island (SSR) 7.0) (4.20 - 4.5) 40) rupture, Ivashchenko, 1997; Arefiev et al., 2000. Slip rate: (Neftegors 4.32) Geologic (Holocene), Tsutsumi et al., 2005; Tsutsumi, k), Russia E+26 2014. 18 1994/01/ Northridge, Northridge 6.7 (6.6- 1.20 0.4 (0.3 - 21 (18 - Mag: USGS NEIC; GCMT. Length: Aftershocks, 17 California (R) 6.7) (1.00 - 1.7) 24) waveform modeling, Jones et al., 1994; Wald et al., 1996. 1.40) Slip rate: Geologic (Holocene), Marshall et al., 2013; E+26 Davis and Namson, 1994; Dolan et al., 1997; Huftile and Yeats, 1996. 19 1992/06/ Landers, Johnson 7.2 (7.2- 7.70 0.4 (0.2 - 77 (77 - Mag: Wald and Heaton, 1994. Length: Surface rupture, 28 California Valley, 7.2) (6.90 - 0.6) 77) Sieh et al., 1993. Slip rate: Paleoseismic (<20 ka), Homestead 8.00) Rockwell et al., 2000. Valley, E+26 Emerson, and Camp Rock Faults (SSR) 20 1990/07/ Luzon, Digdig fault 7.7 (7.7- 4.07 15 (12 - 112 (112 Mag: Velasco et al., 1996; Yoshida and Abe, 1992; 16 Philippines (SSL) 7.7) (3.90 - 35) - 112) GCMT. Length: Surface rupture, Nakata et al., 1990; 4.20) Wesnousky, 2008. Slip rate: Geologic ( 40 ka), Beavan et E+27 al., 2001; Daligdig, 1997. 21 1990/06/ Rudbar, Rudbar fault 7.4 (7.3- 1.40 1 (0.1 - 80 (80 - Mag: Berbarian and Walker, 2010; GCMT. Length: 20 Iran (SSL) 7.4) (1.26 - 2) 80) Surface rupture, Berbarian and Walker, 2010. Slip rate: 1.54) Geodetic, Berbarian and Walker, 2010; Djamour et al., E+27 2011; Walker, 2014. 22 1989/10/ Loma Loma Prieta 6.8 (6.8- 2.20 3.2 (2.4 - 35 (30 - Mag: Choy and Boatwright, 1996; GCMT. Length: L is 17 Prieta, (SSR) 6.9) (2.20 - 4.2) 60) mean from finite-fault modeling; Lmax: aftershocks, California 2.69) Beroza, 1991; Dietz and Ellsworth, 1990. Slip rate: E+26 Geologic (105-120 ka), Anderson and Menking, 1994. 25 1987/11/ Superstitio Superstition 6.6 (6.6- 1.08 3.0 (1.7 - 25 (25 - Mag: Bent et al., 1989. Length: Surface rupture, Sharp et 24 n Hill, Hills Fault 6.6) (1.08- 5.5) 25) al., 1989. Slip rate: Geologic (330 yr), Field et al., 2014; California (SSR) 1.08) Hudnut and Sieh, 1989. E+26 26 1987/03/ Edgecumbe Edgecumbe 6.4 (6.2- 4.30 2 (1.3 - 15.5 (7 - Mag: Anderson and Webb, 1989. Length: Lmin: surface 02 , New Fault (N) 6.5) (2.30 - 2.8) 16) rupture; Lmax: geodesy, Beanland et al., 1989; Darby, Zealand 6.30) 1989. Slip rate: Geologic (Quaternary), Anderson et al, E+25 1996; Nairn and Beanland, 1989. 28 1986/03/ Marryat Marryat Fault 5.8 (5.7- 5.80 0.005 13 (13 - Mag: Fredrich et al., 1988. Length: Surface rupture, 30 Creek, Zone (R) 5.8) (4.30 - (0.001 - 13) Machette et al., 1993. Slip rate: Geologic (>100 ka), Australia 7.30) 0.01) Machette et al., 1993. E+24 29 1984/04/ Morgan Calaveras 6.1 (6.1- 2.10 5.2 (3 - 20 (16 - Mag: Hartzel and Heaton, 1986; Bakun et al., 1984. 24 Hill, Fault (SSR) 6.1) (1.90 - 7) 25) Length: Lmin: Waveform modeling; Lmax: aftershocks, California 2.10) waveform modeling, Bakun et al., 1984; Hartzell and E+25 Heaton, 1986. Slip rate: Geologic (Holocene), Machette et al., 1993; Field et al., 2014. 30 1983/10/ Borah Lost River 6.8 (6.8- 2.30 0.15 (0.1 36 (36 - Mag: Mendoza and Hartzell, 1988; Doser and Smith, 28 Peak, Idaho (N) 6.9) (2.10 - - 0.2) 36) 1985; GCMT. Length: Surface rupture, Crone et al., 3.12) 1987. Slip rate: Geologic (late Pleistocene, Holocene), E+26 Haller and Wheeler, 1995; Hanks and Schwartz, 1987. 31 1983/05/ Coalinga, Coalinga (R) 6.4 (6.3- 4.70 1.4 (1 - 25 (25 - Mag: Sipkin and Needham, 1990; GCMT. Length: 02 California 6.4) (4.00 - 4) 25) Aftershocks, Eaton, 1990. Slip rate: Geologic 6.00) (Quaternary), Wakabayashi and Smith, 1994; Stein and E+25 Ekstrom, 1992; Field et al., 2014. 32 1981/07/ Sirch, Iran Gowk Fault 7.1 (7.1- 3.67 4.3 (3.1 - 65 (65 - Mag: Berbarian et al., 2001; GCMT. Length: Surface 29 system (SSR) 7.2) (3.67 - 5.7) 65) rupture, Berbarian et al., 2001; Berbarian et al., 1984. Slip 9.1) rate: Geologic (latest Pleistocene, Holocene), Fattahi et E+26 al., 2014; Walker et al., 2010. 33 1981/02/ Corinth, South 6.1 (6.1- 1.68 1.7 (1 - 14 (12 - Mag: Jackson et al., 1982; GCMT. Length: Surface 25 Greece Alkonydes 6.3) (1.68- 2.3) 15) rupture, Jackson et al., 1982; Slip rate: Paleoseismic (late (SSR) 3.75) Holocene), Collier et al., 1998; Pantosti et al., 1996. E+25 34 1981/03/ Corinth, Kaparelli (N) 5.9 (5.9- 9.70 0.3 (0.2 - 15 (14 - Mag: Jackson et al., 1982; GCMT. Length: Surface 04 Greece 6.2) (9.70 - 0.3) 15) rupture, Jackson et al. 1982; GCMT. Slip rate: 27.0) Paleoseismic (late Pleistocene, Holocene), Benedetti et al., E+24 2003; Chatzipetros et al., 2005. 35 1981/01/ Daofu, Xianshuihe 6.7 (6.5- 1.60 12 (8 - 44 (44 - Mag: Zhou et al., 1983; GCMT. Length: Aftershocks, 24 China (SSL) 6.7) (0.73 - 16) 44) Tang, 1984; Molnar and Deng, 1984. Slip rate: Geologic 1.60) (Holocene), geodesy, Yu et al., 2010; Allen, 1991; Wang E+26 et al., 2009. 36 1980/10/ El Asnam Oued Fodda 6.9 (6.9- 2.50 0.8 (0.25 36 (36 - Mag: Yielding et al., 1981; GCMT. Length: Surface 10 (Ech (R) 7.1) (2.50 - - 1.6) 36) rupture, Yielding et al., 1981. Slip rate: Geologic Cheliff), 5.00) (Quaternary, mid-late Holocene), Swan, 1988; Meghraoui Algeria E+26 et al, 37 1979/10/ Imperial Imperial 6.4 (6.4- 5.00 17 (15 - 36 (36 - Mag: Hartell and Heaton, 1983; Kanamori and Reagan, 15 Valley, Valley (SSR) 6.5) (5.00 - 20) 36) 1982; GCMT. Length: Surface rupture, Trifunac, 1972; California 7.23) Wesnousky, 2008. Slip rate: Geologic (late Holocene), E+25 Thomas and Rockwell, 1996; Bennett et al., 1996; Genrich and Bock, 1997. 38 1979/08/ Coyote Calaveras 5.8 (5.7- 6.00 11.9 (3 - 14 (6 - Mag: Buchon, 1982; Bakun et al., 1984; GCMT. Length: 06 Lake, (SSR) 6.1) (5.06 - 15) 18) Lmin: waveform modeling; L: aftershocks < 1 day; Lmax: California 16.0) aftershocks, Bouchon, 1982; Liu and Helmberger, 1983; E+24 Reasenberg and Ellsworth, 1982. Slip rate: Geologic (Holocene), Kelson et al., 1996; Simpson et al., 1999; Field et al., 2014. 40 1978/09/ Tabas, Iran Tabas - 7.4 (7.3- 1.50 1.3 (1.2 - 90 (85 - Mag: Hiazi and Kanamori, 1981; GCMT. Length: Lmin: 16 Nayband 7.4) (1.32 - 1.4) 95) surface rupture; Lmax: waveform modeling, Berbarian, fault system 1.50) 1979; Hartzell and Mendoza, 1991. Slip rate: Geologic (R) E+27 (late Pleistocene, Holocene), Walker et al., 2013. 41 1977/12/ , Iran Bob-Tangol 5.8 (5.8- 6.60 4 (2 - 4) 19.5 Mag: Talebian et al., 2006; GCMT. Length: Surface 19 segment, Kuh 5.9) (6.60 - (19.5 - rupture, Berbarian et al., 1979. Slip rate: Vernant et al., Banan fault 7.65) 19.5) 2004; Allen et al., 2011. (SSR) E+24 42 1976/02/ Motagua, Motagua 7.5 (7.4- 2.60 12 (10 - 230 (230 Mag: Kanamori and Stewart, 1974. Length: Surface 04 Guatemala Fault (SSL) 7.5) (1.55 - 20) - 230) rupture, Plafker, 1976. Slip rate: Geodetic, Schwartz et al., 3.30) 1979; Lyon-Caen et al., 2006. E+27 43 1973/02/ Luhuo, Xianshuihe 7.7 (7.4- 1.90 14 (12 - 90 (90 - Mag: Zhou et al, 1983; Papadimitriou et al., 2004. 06 China (SSL) 7.5) (1.50 - 16) 90) Length: Surface rupture, aftershocks, waveform modeling, 1.90) Zhou et al., 1983. Slip rate: Geologic, Honglin et al., E+27 2006; Yu et al., 2010. 44 1971/02/ San San Fernando 6.8 (6.7- 1.70 1.8 (1 - 19 (19 - Mag: Heaton, 1982; Wyss, 1971. Length: Surface 09 Fernando, (R) 6.8) (1.50 - 5) 19) rupture, Proctor et al., 1972. Slip rate: Geologic (late California 1.70) Pleistocene, Holocene), Treiman, 2000; Field et al., 2014. E+26 45 1970/01/ Tonghai, Qujiang 7.2 (7.2- 8.70 2 (1 - 60 (48 - Mag: Zhou et al., 1983. Length: Lmin: surface rupture; 04 China (SSR) 7.2) (7.00 - 2.1) 90) Lmax: waveform modeling, Zhou et al., 1983. Slip rate: 8.70) Geologic (2 Ma), geodetic, Zhu, 1985; Shen et al., 2005. E+26 46 1968/08/ Dasht-e- Dasht-e- 7.1 (7.1- 5.90 5 (2.5 - 80 (80 - Mag: Walker et al., 2004. Length: Surface rupture, 31 Bayaz, Iran Bayaz (SSL) 7.1) (5.90 - 10) 80) Ambraseys and Tchalenko, 1969. Slip rate: Geologic 5.90) (Holocene), Berbarian and Yeats, 1999; Walker et al., E+26 2004. 47 1968/04/ Borrego Coyote Creek 6.6 (6.5- 1.12 6.7 (1 - 33 (33 - Mag: Burdick and MEllman, 1976; Heaton and 09 Mountain, (San Jacinto), 6.6) (0.70 - 6.7) 33) Helmberger, 1977. Length: Surface rupture, Clark, 1972; California (SSR) 1.12) Slip rate: Geologic (Holocene), Treiman and Lundberg, E+26 1999; Field et al., 2014. 48 1967/07/ Mudurnu North 7.3 (7.3- 1.10 18 (13 - 80 (60 - Mag: Pinar et al., 1996. Length: Surface rupture, 22 Valley, Anatolian 7.3) (1.10 - 23) 80) Ambraseys and Zatopek, 1969; Barka, 1996; Wesnousky, Turkey (SSR) 1.10) 2008. Slip rate: Geologic (late Pleistocene, Holocene), E+27 Hubert-Ferrari, 2002. 49 1966/06/ Parkfield, San Andreas 6.2 (6.2- 2.32 30 (21.9 28 (25 - Mag: Segall and Du, 1993; Archuleta and Day, 1980. 28 California (SSR) 6.4) (2.32 - - 32.6) 30) Length: Surface rupture, Lindh and Boore, 1981; Segal 4.40) and Du, 1993. Slip rate: Geologic (late Holocene), Toke E+25 et al., 2011; Field et al., 2014. 51 1963/04/ Alake Kunlun (SSL) 7.0 (6.9- 3.60 12 (10 - 40 (30 - Mag: Guo et al., 2007; Molnar and Deng, 1984; Shen et 19 Lake, 7.0) (2.70 - 14) 50) al., 2003. Length: Surface rupture, Guo et al., 2007; Biasi China 3.60) et al., 2013. Slip rate: Geologic (Holocene), geodetic, E+26 Guo et al., 2007; Van Der Woerd et al., 2002; Fu and Awata, 2007; Wang et al., 2001; Chen et al., 2000. 52 1962/09/ Ipak, Iran Ipak (SSL) 7.0 (6.9- 3.68 1 (1 - 2) 100 (95 - Mag: Priestly et al., 1994; range=+-20%. Length: 01 7.0) (2.80 - 105) Surface rupture, Ambraseys, 1963; Berbarian and Yeats, 3.68) 2001. Slip rate: Geodetic (Quaternary), Bachmanov et al., E+26 2004. 53 1959/08/ Hebgen Hebgen and 7.3 (7.2- 1.20 0.5 (0.2 - 25 (25 - Mag: Barrientos et al., 1987; Doser, 1985. Length: 18 Lake, Red Canyon 7.3) (0.92 - 5.3) 25) Surface rupture, Witkind, 1964. Slip rate: Geologic (late Montana (N) 1.20) Pleistocene), geodetic, Puskas et al., 2007; Haller, 1994; E+27 Zreda and Noller, 1998. 54 1957/12/ Gobi-Altai, Bogd (SSL) 8.1 (7.9- 1.80 1 (0.5 - 260 (260 Mag: Okal, 1976. Length: Surface rupture, Kurushin et 04 Mongolia 8.2) (0.84 - 1.2) - 260) al., 1997; Biasi et al., 2013. Slip rate: Geologic (<80 ka), 2.20) Rizza et al., 2011; Ritz et al., 1995. E+28 55 1956/02/ San San Miguel 6.6 (6.5- 1.00 0.3 (0.1 - 20 (20 - Mag: Doser, 1992; Thatcher and Hanks, 1973. Length: 14 Miguel, (SSR) 6.7) (0.80 - 0.4) 25) Surface rupture, Shor and Roberts, 1958; Harvey, 1985; Mexico 1.20) Doser, 1992; Anderson et al., 1996. Slip rate: Geologic E+26 (Holocene), Hirabayashi et al., 1996. 56 1954/12/ Fairview Fairview to 7.1 (6.9- 5.30 0.14 46 (35 - Mag: Doser, 1996; Caskey et al., 1996. Length: Surface 16 Peak, Louderback 7.3) (2.90 - (0.09 - 46) rupture, Caskey et al., 1996. Slip rate: Geologic (late Nevada (N) 11.0) 0.22) Pleistocene), Bell et al., 2004. E+26 57 1954/12/ Dixie Dixie Valley 6.6 (6.2- 9.04 0.5 (0.4 - 47 (36 - Mag: Doser, 1986; Caskey et al., 1996. Length: Surface 16 Valley, (N) 6.6) (2.89 - 0.6) 47) rupture, Caskey et al., 1996. Slip rate: Geologic Nevada 9.80) (Holocene), Bell et al., 2004. E+25 58 1953/03/ Gonen- Yenice- 7.3 (7.2- 1.00 6.8 (5.1 - 60 (53 - Mag: Eyodigan, 1988; Jackson and McKenzie, 1988. 18 Yenice, Gonen (SSR) 7.4) (0.77 - 8.4) 80) Length: Lmin: surface rupture; Lmax: aftershocks, Kurcer Turkey 1.53) et al., 2008; Herece, 1990; Emre et al., 2011. Slip rate: E+27 Geologic (Holocene), Kurcer et al., 2008. 60 1944/02/ Gerede- North 7.3 (7.3- 1.33 18 (14.5 155 (155 Mag: Barka, 1996; Wesnousky, 2008. Length: Surface 01 Bolu, Anatolian 7.4) (1.33 - - 21.5) - 180) rupture, Barka, 1996. Slip rate: Paleoseismic, geologic Turkey (SSR) 1.40) (Holocene), Kondo et al., 2010; Hubert-Ferrari et al., 2002. E+27 61 1943/11/ Tosya, N. Anatolian 7.6 (7.5- 2.86 19 (12 - 275 (260 Mag: Barka, 1996; Wesnousky, 2008. Length: Surface 26 Turkey (SSR) 7.6) (2.40 - 26) - 275) rupture, Ketin, 1969 (in German); Barka, 1996; 2.86) Wesnousky, 2008. Slip rate: Geologic (Holocene), E+27 Kozaci et al., 2007; Kozaci et al., 2009; Hubert-Ferrari et al., 2002. 62 1943/09/ Tottori, Shikano- 6.9 (6.9- 3.00 0.3 (0.1 - 33 (11 - Mag: Kanamori, 1973. Length: Lmin: surface rupture; L, 10 Japan Yoshioka 6.9) (3.00 - 0.4) 33) Lmax: geodesy, Kanamori, 1973; Kaneda, 2003. Slip rate: (SSL) 3.00) Geologic (Pleistocene,Holocene), Kanamori, 1973; Okada, E+26 1981; Kaneda, 2003. 63 1942/12/ Niksar- North 6.8 (6.8- 2.30 19 (12 - 50 (28 - Mag: Barka, 1996; Wesnousky, 2008. Length: L, Lmax: 20 Erbaa, Antolian 6.9) (1.80 - 26) 50) surface rupture; Lmin from slip distribution measurements, Turkey (SSR) 3.20) Barka, 1996; Ambraseys, 1970; Wesnousky, 2008. Slip E+26 rate: Geologic (Pleistocene), paleoseismic (Holocene), Hubert-Ferrari et al., 2002; Kozaci et al., 2007; Kozaci et al., 2009; Kondo et al., 2010. 64 1940/05/ Imperial Imperial 7.1 (6.8- 5.60 17 (15 - 60 (60 - Mag: Doser, 1990; King and Thatcher, 1998; Kanamori 19 Valley, (SSR) 7.1) (2.25 - 20) 60) and Regan, 1982. Length: Surface rupture, Trifunac, 1972 California 5.60) from field notes by J. Buwalda. Slip rate: Geologic (300 E+26 yr), geodetic, Thomas and Rockwell, 1996; Bennett et al., 1996. 65 1939/12/ Erzincan, North 7.8 (7.7- 6.60 19 (12 - 330 (300 Mag: Barka, 1996. Length: Surface rupture, Barka, 1996; 25 Turkey Antolian 7.8) (4.15 - 26) - 360) Wesnousky, 2008. Slip rate: Geologic (Holocene), (SSR) 6.60) geodetic, Hubert-Ferrari et al., 202; Kozaci et al., 2007; E+27 Kozaci et al., 2009; Kondo et al., 2010; Tatar et al., 2012. 66 1937/01/ Tuosuo Kunlun Fault 7.6 (7.6- 3.70 11 (10- 150 (145 Mag: Geologic, from parameters in Guo et al., 2007; 07 Lake (SSL) 7.7) (3.40 - 12) - 155) Molnar and Deng, 1984 considered overestimate of Mo. (Huashixia) 4.30) Length: Surface rupture, Guo et al., 2007. Slip rate: , China E+27 Geologic (late Quaternary, Holocene), geodetic, Chen et al., 2000; Wang et al., 2001; Van Der Woerd et al., 2002; Fu and Awata, 2007; Guo et al., 2007. 67 1934/06/ Parkfield, San Andreas 6.2 (6.2- 2.30 30 (21.9 25 (25 - Mag: Archuleta and Day, 1980; Segall and Du, 1993. 08 California (SSR) 6.4) (2.30 - - 32.6) 25) Length: Assumed from 1966 event and waveform 4.40) modeling. Slip rate: Geologic (late Holocene), Toke et E+25 al., 2011; Field et al., 2014. 68 1933/03/ Long Newport- 6.4 (6.4- 5.00 1.1 (1 - 22 (13 - Mag: Hauksson and Gross, 1991. Length: Lmin: 10 Beach, Inglewood 6.4) (5.00 - 5) 25) waveform modeling; Lmax: aftershocks, Hauksson and California (SSR) 5.00) Gross, 1991. Slip rate: Geologic, geodetic, Treiman and E+25 Lundberg, 1999; Field et al., 2014. 69 1932/12/ Changma, Changma 7.6 (7.4- 2.80 5 (3.2 - 149 (149 Mag: Molnar and Deng, 1984. Length: Surface rupture, 25 China (SSL) 7.7) (1.40 - 7.5) - 149) Xu et al., 2010. Slip rate: Geologic (late Pleistocene, 5.60) Holocene), Peltzer et al., 1988. E+27 70 1931/08/ Fuyun, Fuyun (SSR) 7.9 (7.8- 8.50 (7.0 0.3 (0.1 - 160 (160 Mag: Molnar and Deng, 1984. Length: Surface rupture, 10 China 8.0) - 11.5) 0.52) - 180) Shi et al., 1984; Baljinnyam et al., 1993; Klinger et al., E+27 2011. Slip rate: Geologic (Holocene), Xu et al., 2012. 71 1930/11/ North Izu, Tanna (SS) 6.9 (6.9- 2.70 2.4 (2 - 28 (28 - Mag: Abe, 1978; Matsuda, 1972; Wesnousky, 2008. 25 China 6.9) (2.70- 2.9) 28) Length: Surface rupture, Matsuda, 1972. Slip rate: 3.00) Geologic (Quaternary), paleoseismic (Holocene), Research E+26 Group for Active Faults, 1991; Kimura, 2011. 72 1928/01/ Laikipia, Laikipia– 6.8 (6.8- 2.32 0.18 38 (38 - Mag: Doser and Yarwood, 1991. Length: Surface 06 Kenya Marmanet 6.8) (2.32 - (0.15 - 38) rupture, Ambraseys, 1991. Slip rate: Geologic (N) 2.32) 0.20) (Pleistocene), Zielke and Strecker, 2009. E+26 73 1927/03/ Tango, Gomura 7.0 (7.0- 4.60 0.3 (0.2 - 35 (14 - Mag: Kanamori, 1973. Length: Surface rupture; Lmax: 07 Japan (SSL) 7.0) (4.60- 0.4) 35) geodesy, Okada and Matsuda, 1997; Kanamori, 1973; 4.60) Kaneda, 2003. Slip rate: Geologic (late Pleistocene, E+26 Holocene), Kaneda, 2003. 74 1923/03/ Luoho- Xianshuihe 7.3 (7.1- 1.20 10 (8 - 80 (60 - Mag: Molnar and Deng, 1984; Pacheco and Sykes, 1992. 24 Qiajiao (SSL) 7.4) (0.62 - 16) 100) Length: Surface rupture; Lmax based on ground (Daofu), 1.27) fracturing, Allen et al., 1991. Slip rate: Geologic China E+27 (Holocene), geodetic, Allen, 1991; Wang et al., 2009. 75 1920/12/ Haiyuan, Haiyuan 8.0 (7.8- 1.20 7 (3.4 - 237 (200 Mag: Chen and Molnar, 1977; Deng et al., 1984. Length: 16 China (SSL) 8.2) (0.60 - 10) - 260) Surface rupture, Geologic (Quaternary, late Pleistocene, 2.40) Holocene), Chen and Molnar, 1977; Deng et al., 1984; E+28 Zhang et al., 1987; Burchfiel et al., 1991; Deng, 1989. Slip rate: Peizhen, 1988; Burchfiel et al., 1991; Li et al., 2009. 76 1915/10/ Pleasant Pleasant 7.3 (7.1- 1.03 0.1 (0.01 61 (61 - Mag: Doser, 1988; Wesnousky, 2008. Length: Surface 03 Valley, Valley 7.3) (0.66 - - 0.2) 61) rupture, Wallace et al., 1984; Wesnousky, 2008. Slip rate: Nevada (Pearce, 1.03) Geologic (late Pleistocene, Quaternary), Anderson and Tobin, China E+27 Machette, 2000. Mtn, Sou Hills) (N) 77 1911/01/ Chon- Kemin-Chilik 8.0 (7.9- 1.35 2 (2 - 10) 177 (169 Mag: Kulikova and Kruger, 2015. Length: surface 03 Kemin and Aksu (R) 8.1) (0.85 - - 260) rupture; Lmax: waveform modeling, Delvaux et al., 2001; (Kebin), 1.85) Chen and Molnar, 1977; Crosby and Arrowsmith, pers. Krygystan E+28 comm. Slip rate: paleoseismic evidence, geodesy. 78 1906/04/ San San Andreas 7.9 (7.8- 9.62 21 (16 - 497 (483 Mag: Wald et al., 1993; Thatcher et al., 1997; Biasi et al., 18 Francisco, (SSR) 8.0) (7.48 - 28) - 517) 2013. Length: surface rupture; geodesy, Thatcher et al., California 11.6) 1997; Biasi et al., 2013. Slip rate: Geologic (Holocene), E+27 Bryant and Lundberg, 2002. 79 1905/07/ Bulnay, Bulnay (SSL) 8.5 (8.3- 7.27 3 (2 - 375 (350 Mag: Okal, 1977; Schlupp and Cisternas, 2007; Okal, 23 Mongolia 8.5) (3.97 - 3.1) - 517) 1977. Length: Surface rupture Baljinnyam et al., 1993; 7.67) Schlupp and Cisternas, 2007. Slip rate: Geologic E+28 (Holocene), Baljinnyam et al., 1993; Prentice et al., 2010. 80 1892/02/ Laguna Laguna 7.2 (7.1- 8.00 2.5 (2 - 42 (42 - Mag: Mueller and Rockwell, 1995; Hough and Elliott, 23 Salada, Salada and 7.2) (6.00 - 3) 50) 2004. Length: Surface rupture, Mueller and Rockwell, Mexico Canon Rojo 8.00) 1995; Rockwell et al., 2010. Slip rate: Geologic (SSR) E+26 (Holocene), Mueller and Rockwell, 1995. 81 1896/08/ Rikuu, Senya (R) 7.2 (7.2- 9.0 (9.0 - 1.0 (0.5 - 40 (37 - Mag: Wesnousky et al., 1982. Length: Matsuda et al., 31 Japan 7.4) 14.0) 1.6) 50) 1980; Thatcher et al., 1980. Slip rate: Geologic (Holocene, E+26 Quaternary), Research Group for the Senya Fault, 1986; Imaizumi et al., 1997; Kagohara et al., 2009. 82 1891/10/ Nobi Neodani, 7.4 (7.4- 1.83 1.6 (1 - 80 (80 - Mag: Fukuhama et al., 2007; Mikumo and Ando, 1976. 28 (Mino- Nukumi, 7.5) (1.40 - 2) 80) Length: Surface rupture, Matsuda, 1974. Slip rate: Owari), Umehara 1.83) Geologic (late Pleistocene, Holocene), Kaneda and Okada, Japan (SSL) E+27 2008; Okada and Matsuda, 1992. 83 1888/09/ Canterbury, Hope (SSR) 7.1 (7.0- 5.62 14 (8 - 65 (40 - Mag: Khajavi et al., GSAB in press. Length: Surface 01 New 7.1) (3.80 - 17) 70) rupture, Kowan, 1991; Khajavi et al., in press. Slip rate: Zealand 6.10) Geologic (late Pleistocene, Holocene), Langridge and E+26 Berryman, 2010; Cowan, 1991; van Dissen, 1991; Khajavi et al., in press; slip rate varies along strike, middle segment rate used. 84 1887/05/ Sonora, Pitaycachi, 7.2 (7.2- 8.20 0.08 101.8 Mag: Suter, 2008. Length: Surface rupture, Sutur and 13 Mexico Otates, Teras 7.2) (8.20 - (0.02 - (86.3 - Contreras, 2002; Suter, 2008. Slip rate: Geologic (late (N) 8.20) 0.18) 101.8) Pleistocene, Quaternary), McCalpin, 1995; Suter and E+26 Contreras, 2002; Suter, 2008. 85 1872/03/ Owens Owens 7.4 (7.4- 1.62 3.5 (1 - 110 (107 Mag: Biasi et al., 2013. Length: Surface rupture, 26 Valley, Valley (SSR) 7.5) (1.46 - 4) - 140) Beanland and Clark, 1994; Bacon and Pezzopane, 2007; California 2.06) Amos et al., 2013. Slip rate: Geologic (late Pleistocene, E+27 Holocene), Bacon and Pezzopane, 2007; Field et al., 2014. 86 1868/10/ Hayward, Hayward 6.9 (6.8 - 3.0 (2.30 8 (7.3 - 61 (50 - Mag: Yu and Segal, 1996. Length: L, Lmax: Surface 21 California Fault (SSR) 7.0) - 3.70) 8.7) 61) rupture; Lmin: geodesy, Lienkaemper and Williams, 1999; E+26 Yu and Segall, 1996. Slip rate: Geologic (Holocene), Lienkaemper et al., 2012. 87 1857/01/ Fort Tejon, San Andreas 7.8 (7.8- 7.12 25 (24 - 339 Mag: Zielke et al., 2010; Sieh, 1978. Length: Surface 09 California (SSR) 7.9) (7.12- 35) rupture, Biasi et al., 2013. Slip rate: Geology (late 7.80) Pleistocene, Holocene), Sieh and Jahns, 1984; Field et al., E+27 2014.

* mechanisms: N = normal; R = reverse; SS = strike slip; SSR = strike slip right lateral; SSL = strike-slip left lateral