Millenary Mw>9.0 Earthquakes Required by Geodetic Strain in the Himalaya

1 2 GRL 3 Supporting Information for

4 Millenary Mw>9.0 earthquakes required by geodetic strain in the Himalaya 5 V. L. Stevens1, and J-P. Avouac1 6 1California Institute of Technology. 7 8 Contents of this file 9 10 Text S1 to S2 11 Figures S1 to S5 12 Tables S1 to S2 13 References 14 15 16 Introduction 17 Here we give more details of the methods and data used in the maintext. Figures S1 to S2 18 help clarify the method while figures S3 and S4 show the results of changing 19 assumptions. Figure S5 shows a comparison of moment build-up and release through 20 time. Tables S1 and S2 show original and binned data respectively for the historical and 21 paleoseismic earthquakes. 22 23

24 Text S1. METHOD 1 25 Text S1.1. Introduction 26 We use the instrumental, historical and paleoseismic earthquakes catalogs, along with the total 27 moment build-up rate each year, to find the maximum likely earthquake size. 28 In this first method, we assume earthquakes follow a GR distribution, 29 30 (1) 31 32 where a and b are constants, Mw is the magnitude, and N is the number of earthquakes above 33 magnitude Mw. a is the number of earthquakes above Mw=0, and can be thought of as the 34 productivity. We also assume the b value is 1.1±0.1, the largest aftershock is 1.2±0.1 below the 35 mainshock, and the seismic moment build-up is 15.1±1.1 x1019 Nm/yr. 36 37 38 The total moment line is found from the integration of the number and magnitude of earthquakes, 39 assuming the GR law as above, and the relation between moment (M0) and magnitude: 40 41 (2) 42

43 where = 2/3 and = 10.7. 44 45 (3) 46 47 where is the number of earthquakes below magnitude . 48 49 (4) 50 51 So we get 52 . (5) 53 54 55 56 Since we have estimates of and b we can use this equation to find the relation between and the 57 recurrence time, if were to be the maximum sized earthquake. 58 59 60 Text S1.2. Data 61 Instrumental Seismicity 62 We use the NSC catalog (from 1995 to 2001), which covers five years of microseismicity in 63 Nepal, and contains 12,201 earthquakes with magnitudes 0.3 to 5.5. These magnitudes are

64 reported in local magnitudes (ML), and we use the method of Ader et al. 2012 who used a subset 65 of events reported also in the CMT catalog, to convert into moment magnitude (MW): 66 67 (6) 68 69 Since this catalog contains only earthquakes recorded in Nepal, we scale up by a factor of 3, 70 assuming the microseismicity is consistent along the arc. 71 72 We use the NEIC catalog between 1976 and August 2015. We take earthquakes within 100 km of 73 the surface trace of the Main Frontal Thrust. To account for the fact that some of these 74 earthquakes are not on the MHT, we use the CMT catalog covering the same area to find the 75 percentage of the total that are thrust events. We find that 75% are thrusts, so we scale the NEIC 76 catalog by 0.75. Large earthquakes are reported as Mw in the NEIC catalog, however for those 77 reported as mb we use [Scordilis, 2006] 78 79 (7) 80 81 The catalog we use then contains 1,465 earthquakes between magnitudes 4.9 and 7.8. 82 Figure 2B shows lateral variations of the seismicity rate of derived from the NEIC catalog from 83 1976 to present after declustering. The earthquakes were declustered using ZMAP [Wiemer, 84 2001] and Reasenberg‘s method [Reasenberg, 1985] with the optimum parameters obtained by 85 Ader and Avouac for this catalog [Ader and Avouac, 2013]. The magnitude of completeness is 86 estimated to be MW4.9. 87 88 Historical and Paleo- Earthquakes 89 The historical earthquakes considered in this study are listed in Table S1. This list is based on the 90 historical catalogs of Ambraseys and Douglas [2004], Bilham [2004] and Pant [2002]. We 91 revised the magnitudes of the 1934 Bihar Nepal and 1950 Assam earthquakes to M w 8.4 and 8.7 92 respectively, based on the moment determined from the long period seismic waves [Chen and

93 Molnar., 1977; Molnar and Deng., 1984]) assuming a dip angle of 5°-10° consistent with the 94 estimated dip angle of the seismogenic portion of the MHT. 95 The magnitudes of the 1344 and 1505 earthquakes are debated. We have assigned Mw 8.4 to the 96 1505 event. Some authors argue that this earthquake was in fact more minor [Rajendran et al., 97 2013] and that the major event in western Nepal is actually the 1344 earthquake [Mugnier et al., 98 2011]. This earthquake could match the paleoseismic event in the Kumaon-Garwal Himlaya 99 dated to 1400 AD [Kumar et al., 2006]. A recent study (Schwanghart et al. 2016) confirms the 100 probability of significant earthquakes in 1110, 1255 and 1344 from catastrophic valley infilling 101 events corresponding to these dates. 102 103 Based on Table S1 we constituted a possible model of the long-term averaged rate of large 104 earthquakes in the Himalaya (Table S2). For earthquakes >= Mw9, there are two earthquakes 105 which could be in this range – the 1100AD and 1400AD earthquakes (see Table S1), however 106 these could both be below Mw 9. So we choose the range 0-2 earthquakes >= Mw9 in the past 1000 107 years to be the 1σ uncertainties. 108 109 For earthquakes >=Mw8.5 we consider the two above, 1100AD and 1400AD earthquakes, which 110 have a larger certainty of being above 8.5 than 9. We also consider the 1255 and 1950 111 earthquakes, though we are less certain if the 1255 earthquake was over magnitude 8.5, so we 112 assign the 1σ range as 3-4 in the past 1000 years. 113 114 For earthquakes >=Mw8, we have the four potentially above 8.5 and the 1505 and 1934 events. 115 We consider these six events to be a lower bound on the 1σ uncertainty, but we may be missing 116 some, for example if the 1100 and 1400 earthquakes were actually two earthquakes of around 8 117 instead of nine, so we consider 9 as an upper 1σ bound. 118 119 For the earthquakes in the range Mw7.5-8, we used only the past 220 years of data (with the oldest 120 earthquake being the 1803 Garwhal earthquake). This is because for these smaller earthquakes, 121 the historical record deteriorates more quickly than for the larger earthquakes as the shaking 122 created is lesser and over a smaller area, so may more easily be missed. We then assume a 123 similar rate of earthquakes for the past 220 years as for the past 1000 years. There have seen six 124 recorded earthquakes of size Mw7.5-8 in the past 220 years (Table 1). We take this as the 1σ 125 lower bound, and assuming perhaps at least 3 missed earthquakes in this size range, take nine as 126 the 1σ upper bound, so there is a chance that there were between six and nine earthquakes in 127 this magnitude range. 128 129 The data used is summarized in table S2. 130

132 Text S1.3. b Value and moment released by aftershocks 133 The b value is used in calculating the slope of the line that takes up the seismic moment buildup, 134 in simulating the aftershocks and in calculating the equivalent a value for the pieces of data. The 135 latter is the most affected by the uncertainty in the b value. 136 137 We find the b value using the NSC catalog. We use the maximum likelihood method [Aki, 1965] 138 to find the b value, after choosing Mc (the lower cutoff value) using a bootstrap method, 139 implemented in ZMAP [Wiemer, 2001]. We find Mc = 3.2 and b = 1.1±0.04. We increase the 140 formal uncertainty on the b value to 1.1±0.1, as the NSC catalog only contains one third of the arc 141 and only contains magnitudes up to 5.5 so the uncertainty may be more than the actual value 142 obtained from the NSC catalog alone. 143 3 4

144 We are missing aftershocks of large earthquakes in the instrumental catalogs, as there have been 145 no great (>Mw8) earthquakes since instrumental records began. 146 We simulate aftershocks simply by assuming they follow a GR distribution with b value 1.1±0.1, 147 and that they follow Bath’s law, with the largest aftershock 1.2±0.1 below the mainshock. 148 For example, every time we have a magnitude 8 in the record, we assume an aftershock sequence 149 with largest aftershock 6.8, with smaller earthquakes with frequency in accordance with GR. If 150 the magnitude 8 occurred once every 100 years, this aftershock sequence would also occur every 151 100 years. In this way, we add missing aftershocks to the current catalogue. We add missing 152 aftershocks for magnitudes 7.5, 8, 8.5 and 9. 153 Adding aftershocks increases uncertainties due to b value uncertainty and uncertainty in 154 magnitude-frequency relations of the larger earthquakes. The addition of the aftershocks does not 155 change the maximum predicted earthquake size significantly, but it shows that the full earthquake 156 catalog may follow more closely the GR law. 157 158 We can compare our aftershock model with aftershocks seen elsewhere. For the Gorkha 2015 159 earthquake, the first aftershock sequence had the largest aftershock 1.1 below the mainshock, 160 whilst the second larger earthquake was only 0.5 below. Using the same method as described 161 above, we find the b value for the Gorkha aftershock sequence to be 1.08. For the Kashmir 2005 162 earthquake, the largest aftershock was 1.2 below the mainshock. 163 164 165 Text S1.4. Finding the Maximum Earthquake 166 Instrumental earthquakes 167 If we use the NSC catalog, by simply extending the line using the b value found to the line that 168 takes up the maximum moment, we find the results would be very high (Mw10.4) as we’re 169 missing aftershocks. If we add aftershocks it becomes Mw9.8. There are large uncertainties on 170 this because of the large uncertainties in the number of aftershocks and b value uncertainties have 171 the largest effect for extending smallest earthquakes. The answer gives us a magnitude of 172 between 8.5 and 10.5 with 60% probability. 173 We can do the same for the NEIC catalog, which gives a magnitude 9.1 without aftershocks and 9 174 with. The aftershocks here have less of an affect here because the earthquakes are larger, so there 175 will be fewer added earthquakes of this size. 176 177 Larger earthquakes 178 We then look at four points – the average recurrence times seen of magnitudes 7.5, 8, 8.5 and 9, 179 which is discussed in the data section. We use Monte Carlo analysis using b = 1.1±0.1, Baths 180 Law = 1.2±0.2, the earthquake recurrence time data in Table 2 and a seismic moment buildup rate 181 of 15.1±1x1019 Nm/yr. We run 40 million simulations to get a probability density function (pdf) 182 of the probable maximum earthquake, and its recurrence time, predicted by each point (shown in 183 Figure S1). 184 185 186 Text S1.5. Afterslip 187 Afterslip is a large unknown in the model. Aside from the Gorkha 2015 and Kashmir 2005 188 earthquakes (afterslip respectively ~10 % and ~56% as mentioned in the main text), we see that 189 for other large earthquakes, afterslip has varied between 10% and up to 70%. For the Chile M w8.8 190 earthquake in 2010, 20-30% of the moment was released as afterslip [Lin et al., 2013]. In 191 Sumatra Mw9.1 earthquake, about 30% was released as afterslip (Chlieh et al. 2008). However in 192 the Chichi Mw7.6 earthquake, only 13% was released postseismically [Hsu et al., 2006]. For the 193 Tohoku-Oki earthquake, about 20% of the moment was released as afterslip [Yamagiwa et al.,

194 2010]. For the seismogenic portion of the Central Peru megathrust, 50-70% of the moment may 195 be released aseismically [Perfettini et al., 2010]. 196 If we assume no afterslip at all, we get a maximum magnitude of roughly 9.5 (grey line in Figure 197 S2). 198 199 200 Text S2. METHOD 2 201 202 For the second method we relax the assumption of the GR distribution. We use the observation of 203 one Mw8.7 and possibly one Mw9.0 in the past 500 and 1000 years respectively, along with the 204 assumption that independent earthquakes follow a Poisson distribution. The probability of 205 observing k event over a time given the seismicity rate is: 206 207 , (8) 208 209 where = occurrence rate, = time window considered, = number of occurrences. 210 Knowing that we have seen one Mw8.7 in 500 years, and one Mw>9.0 in 1000 years, we can work 211 out the probability of not observing a possible larger magnitude event with a given return period 212 (. 213 214 We then find the probability that these different sizes of earthquakes and recurrence times would 215 take up the moment needed (P2). 216 217 We then multiply these two probabilities together to find the probability that the earthquake 218 occurs and that all earthquakes combined (including this largest event with its specific magnitude 219 and return time, and all smaller earthquakes) balance the interseismic moment deficit. 220 221 For example, P1 for one Mw8.5 event in 500 years is close to 1, and P1 for four Mw8.5 events in 222 500 years is only about 7%. P2 for the first event is almost zero, whilst P2 for the second event is 223 95%. This leads to their final probabilities both being low (almost zero in the former case and 224 roughly 7% in the latter case). 225 226 We also test alternative assumptions. 227 As well as assuming here that the maximum earthquake is the largest in a catalog of earthquakes, 228 we also show the end member where the largest earthquake is the only earthquake. With the 229 former assumption, two-thirds of the moment is taken up in the largest earthquake, and one-third 230 in all the other earthquakes. As expected, having no other earthquakes decreases the chance that a 231 certain magnitude can take up all the moment (purple line in Figure S3). 232 233 We also test the method assuming zero afterslip (green line), and assuming we have 50% less 234 seismic moment build-up on the MHT (due to distributed deformation) as well as 50% afterslip 235 (also shown in Figure S4). Distributed deformation could occur if faults or folds north of the 236 MFT took up some of the slip. 50% is an upper bound, we expect only up to 10% of the 237 deformation to be distributed (Stevens and Avouac 2015).

Final distributions 2 . 5 N S C N E I C 7 . 5 8 8 . 5 2 9

1 . 5 F D P

0 8 8 . 5 9 9 . 5 1 0 1 0 . 5 1 1 238 M a x i m u m M a g n i t u d e 239 Figure S1. All data sets used separately to predict the maximum moment. 240 241 3 N S C N E I C 7 . 5 8 2.5 8 . 5 9 n o a f t e r s l i p

D 1.5 P

0 8 8.5 9 9.5 10 10.5 11 242 Maximum Magnitude 243 Figure S2. Data sets combined. Grey line shows the case with zero afterslip.

244 245

248 249 Figure S3. The red line shows 50% afterslip and this is used in the main text. The green line 250 assumes zero afterslip. The purple line shows the probabilities if we assume the largest 251 earthquake releases all the moment, with 50% afterslip. The blue line shows 50% afterslip and a 252 50% decrease in moment build-up due to distributed deformation.

255 256 Figure S4. Same as Figure 3 in the main text, but now assuming anelastic shortening of the 257 Himalayan wedge takes up all the shortening across the Himalaya. The underlying MHT is still 258 assumed seismic but long-term slip rate tapers linearly to zero at the surface. The rate of seismic 259 moment build-up is halved. 260

1 6 M o m e n t b u i l d - u p

1 4 M o m e n t r e l e a s e

1 2 ) m N

2 1 0 0 1 (

n 8 e m o

0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0 261 Y e a r , A D 262 Figure S5. Seismic moment released from major earthquakes along the Himlayan Front 263 compared to moment accumulation since 1000 AD. Blue lines show moment build-up calculated 264 from the coupling model of Stevens and Avouac (2015). The solid line shows the mean, the two 265 dashed lines show the one-sigma errors. The dotted line shows the mean reduced by 50% - used 266 in most of the calculations. The black lines show moment release. The solid line shows the 267 preferred model, whilst the dashed lines show the highest and lowest reasonable magnitudes for 268 past earthquakes.

269 270 271 272 273 Magnitud Date Location Reference e 1100 >8.5 Eastern Himalaya (2, 4) 1255 8-8.5 Nepal (35) 1344 >8.0 Nepal (28) 1400 >8.5 Western Himalaya (3) 1505 8.2 Western Nepal (34) 1555 7.6 Kashmir (34) 1720 7.5 N Uttar-Pradesh (34) 1803 7.5 Garwhal (34) 1806 7.7 Samye (34) 1833 7.7 Nepal (34) 1905 7.7 Kangra (34) 1934 8.4 Bihar-Nepal (1, 37) 1950 8.7 Assam (1, 37) 2005 7.6 Kashmir (40) 2015 7.8 Gorkha-Nepal (24)

274 Table S1. Earthquakes above magnitude 7.5 for the past 1000 years from paleoseismic,historical 275 and instrumental catalogs.

277 Magnitud Number per 1000 years e >=9 0-2 >=8.5 3-4 >=8 6-9 >=7.5 33-50

278 Table S2. Proposed rate of large earthquakes estimated based on the data of Table S1. Range of 279 number of earthquakes at the 1- igma confidence level. For magnitude 7.5, we use the past 200 280 years of data, and scale up to 1000 years.

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