Confidential manuscript submitted to JGR Solid Earth

1 A Geology and Geodesy Based Model of Dynamic Earthquake Rupture on the 2 Rodgers Creek-Hayward-Calaveras Fault System, California 3

4 R. A. Harris1, M. Barall2, D. A. Lockner3, D. E. Moore3, D. A. Ponce1, R. W. Graymer1, G. 5 Funning4, C. A. Morrow3, C. Kyriakopoulos5, and D. Eberhart-Phillips6,7

6 7 1U.S. Geological Survey, Moffett Field, California. 8 2Invisible Software, San Jose, California. 9 3U.S. Geological Survey, Menlo Park, California. 10 4University of California, Riverside, Riverside, California. 11 5University of Memphis, Memphis, Tennessee. 12 6University of California, Davis, Davis, California 13 7GNS Science, Dunedin, New Zealand. 14 15 Corresponding author: Ruth A. Harris ([email protected])

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17 Key Points: 18 • We simulated large earthquakes on the Rodgers Creek-Hayward-Calaveras fault system, 19 California. 20 • Our spontaneous rupture (dynamic rupture) simulations included the 3D fault geometry, 21 3D rock properties, and creeping fault patches. 22 • The resulting earthquakes are most affected by which fault they start on, the fault 23 geometry, and the pattern of interseismic fault creep. 24 25

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26 Abstract 27 The Hayward fault in California’s San Francisco Bay area produces large earthquakes, with the 28 last occurring in 1868. We examine how physics-based dynamic rupture modeling can be used 29 to numerically simulate large earthquakes on not only the Hayward fault, but also its connected 30 companions to the north and south, the Rodgers Creek and Calaveras faults. Equipped with a 31 wealth of images of this fault system, including those of its 3D geology and 3D geometry, in 32 addition to inferences about its interseismic creep rate pattern and rock-friction behavior, we use 33 a finite-element computer code to perform 3D dynamic earthquake rupture simulations. We find 34 that the rock properties affect the locations and amount of slip produced in our simulated large 35 earthquakes. Crucial factors that control rupture behavior in our modeling are the earthquake 36 nucleation locations, the fault geometry, and the data that reveal where the fault system is 37 creeping or locked. Our findings suggest that large Rodgers Creek-Hayward-Calaveras-Northern 38 Calaveras (RC-H-C-NC) fault-system earthquakes may result from dynamic rupture that starts in 39 a locked part of the fault system, but is then stopped by the creeping parts, leading to high- 40 magnitude-6 earthquakes; or, from dynamic rupture that starts in a locked part of the fault 41 system, then cascades through some of the creeping parts, leading to magnitude-7 earthquakes. 42 43 Plain Language Summary 44 The San Francisco Bay area has experienced large earthquakes in the past and is likely to 45 experience large earthquakes in the future. Although the San Andreas fault is the best-known 46 earthquake generator, other San Francisco Bay area faults, including some that slowly move 47 (creep) all of the time are also known to be hazardous. We use computer modeling to simulate 48 large earthquakes on the Hayward fault, and its connected companions to the north and south, the 49 Rodgers Creek and Calaveras faults. In our computer simulations we include information about 50 the rock properties, rock friction, and fault geometry, in addition to inferences about where the 51 faults creep. We find that the earthquake nucleation location, the fault geometry, and the pattern 52 of fault creep, are most important. Our findings suggest that large earthquakes on these faults 53 may result from a fast-slipping rupture that starts in a locked part of the faults, but is then 54 stopped by the slowly slipping parts of the faults, leading to high-magnitude-6 earthquakes, or, 55 from fast slipping rupture that starts in a locked part of the faults, then cascades through some of 56 the creeping fault parts, leading to magnitude-7 earthquakes. 57 58

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59 1 Introduction 60 The San Andreas fault system is the primary boundary between the Pacific and North 61 American tectonic plates in most of California (e.g., Atwater, 1970; Wallace, 1990). In the San 62 Francisco Bay Area, the San Andreas fault system consists of numerous faults (Figure 1), 63 including its namesake, the San Andreas fault. Although the San Andreas fault is the best 64 known, the faults with the highest calculated likelihood of producing large earthquakes in the 65 San Francisco Bay Area during the years 2014-2043 are the Hayward and Rodgers Creek faults 66 with a 33% probability of a magnitude 6.7 or larger, and the Calaveras and Northern Calaveras 67 faults with a 26% probability (Aagaard et al., 2016, based on information from Field et al., 68 2013). A large earthquake on the Hayward fault alone will likely affect more than a million 69 people and cause billions of dollars in economic losses, due to the fault's proximity to critical 70 lifelines, homes, and businesses (e.g., Hudnut et al., 2018). 71 72 Geologic and historical observations provide abundant evidence of previous large 73 earthquakes in this region. Paleoseismic studies have exposed geologic features caused by 12 or 74 more ground surface rupturing Hayward fault earthquakes, and document an average large- 75 earthquake recurrence interval of 161+/-65 years on the southern Hayward fault for the years 91- 76 1868 A.D. (Lienkaemper et al., 2010). The last large earthquake on the Hayward fault occurred 77 in 1868, and some of its features have been revealed through geodetic analyses (Yu and Segall, 78 1996) and engineering and felt-report intensity investigations (e.g., Boatwright and Bundock, 79 2008). The 1868 Hayward earthquake has been assigned a magnitude of M6.8 based on shaking 80 intensity data (Bakun, 1999). 81 82 The Calaveras fault too has produced moderate to large earthquakes in the past, with the 83 largest well-recorded event a magnitude M6.2 earthquake in 1984. The Northern Calaveras fault 84 produced a M5.8 in historical times, in 1861 (Bakun, 1999), and paleoseismic evidence reveals a 85 M6.5-6.8 earthquake that ruptured the Northern Calaveras fault around the year 1740 (1692- 86 1776) (Schwartz et al., 2014; Kelson et al., 2008). Geologic studies by Hecker et al. (2005) 87 infer the most recent large earthquake on the Rodgers Creek fault to have occurred sometime 88 during the years 1716-1775; this earthquake produced at least 2 meters of slip at their two study 89 sites on the south-central portion of that fault. 90 91 Geodetic and geologic observations provide information about the fault system’s short- 92 term (years to decades) to long-term (centuries to millions of years) slip rates. These 93 observations indicate that the San Francisco Bay region’s faults will produce large earthquakes 94 in the future. However, aside from the aforementioned well-recorded M6.2 Morgan Hill 95 earthquake in 1984, the large earthquakes on these faults were so long ago that our views of how 96 large earthquakes in this region might operate are unclear. To solve this problem, we implement 97 the tool of dynamic rupture computational simulations to investigate physics-based scenarios of 98 large earthquakes on the Rodgers Creek, Hayward, Calaveras, and Northern Calaveras faults. 99 100 In contrast to the approach that we present in this paper, previous computational studies 101 of large earthquakes in the San Francisco Bay region have primarily centered on kinematic 102 (prescribed) rupture simulations. These include kinematic rupture simulations of large Hayward 103 fault earthquakes (e.g., Larsen et al., 1997; Harmsen et al., 2008; Aagaard et al., 2010a, b; 104 Rodgers et al., 2018, 2019), and kinematic rupture simulations of large earthquakes starting on

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105 the Hayward fault and continuing on to part of the Rodgers Creek fault or part of the Calaveras 106 fault (e.g., Aagaard et al., 2010a, b). Some advantages of kinematic rupture simulations are 107 their computational efficiency, and thereby, their ability to compute higher-frequency ground 108 shaking caused by scenario large earthquakes and actual smaller earthquakes in the San 109 Francisco Bay region (e.g., Hirakawa and Aagaard, 2019). However, kinematic rupture 110 simulations do not intrinsically simulate physically self-consistent features of earthquake 111 behavior. Kinematic rupture simulations have already pre-decided the along-strike and along-dip 112 extents of the earthquakes, along with the resulting fault slip-rate patterns, all before the 113 simulations start, and kinematic rupture simulations are unaffected by interactions of a 114 propagating earthquake rupture with the fault geometry, fault friction, and the physical properties 115 of the rocks surrounding faults. 116 117 A feature of our targeted faults is that all four of the faults creep (slip) aseismically at a 118 measurable rate equal to a significant part of the faults’ slip budgets (e.g., McFarland et al., 119 2016). The Hayward fault’s creep has been noted, analyzed, and discussed for decades (e.g., 120 Radbruch and Lennert, 1966; Cluff and Steinbrugge, 1966; Lienkamper et al., 1991; 121 Burgmann et al., 2000; Simpson et al., 2001; Malservisi et al., 2003; 2005; Schmidt et al. 122 2005; Funning et al., 2007; Burgmann, 2007; Shirzaei and Burgmann, 2013; McFarland et 123 al., 2016; Lienkaemper et al., 2012; 2014; Chaussard et al., 2015b; Harris, 2017). The 124 Calaveras fault also creeps (e.g., McFarland et al., 2016; Oppenheimer et al., 2010; 125 Chaussard et al., 2015b), as does the Northern Calaveras fault (e.g., Chaussard et al., 2015b; 126 McFarland et al., 2016). The Rodgers Creek fault exhibits evidence of creep, but this creep 127 primarily occurs north of our study area (e.g., Jin and Funning, 2017). This ongoing, slow 128 aseismic fault creep may reduce the amount of fast coseismic slip (earthquakes) that occurs 129 during large earthquakes, by gradually releasing some of the plate boundary's tectonic strain 130 during interseismic and postseismic times. However, the relation between the aseismic fault 131 creep and the punctuated bursts of large coseismic slip in this region is not well understood. For 132 example, it has been noted (e.g., Lienkaemper et al., 1991; Simpson et al., 2001; Lienkaemper 133 et al., 2014; Chaussard et al., 2015b) that despite the existence of Hayward fault creep, there is 134 still ample stored energy available to produce and drive large coseismic moment-release 135 earthquakes. 136 137 This study uses information about the aseismic creep-rate patterns on the fault surfaces to 138 assign the initial stresses on the fault system. We then construct fully dynamic three- 139 dimensional (3D) earthquake rupture models that include the complex geometry of the multi- 140 fault system, the 3D rock structure, and the laboratory-inferred frictional strengths of the rocks 141 that surround and comprise the fault zone. We thereby present a physics-based portrait of 142 scenario large earthquakes on the RC-H-C-NC fault system, which is constrained as much as 143 possible by what is currently known about earthquake and fault properties. Our study is the first 144 that we know of to dynamically simulate large-earthquake rupture propagation on this longer 145 fault system. In addition, in contrast to the previously mentioned kinematic-rupture earthquake 146 simulations, we are the first to conduct this work using physics-based dynamic (spontaneous) 147 earthquake rupture simulations (e.g., Harris, 2004) that incorporate the detailed geological and 148 geophysical information for this region. 149 150 151

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153 154 155 FIGURE 1. Map showing the setting of major faults of the San Andreas fault system 156 in California’s San Francisco Bay area. Our 196-km-long modeled fault system (the 157 orange and blue lines) includes the southern Rodgers Creek fault, the Hayward fault, 158 the Central Calaveras fault, and the Northern Calaveras fault (NoCal). Our fault 159 system model also includes the connector (cf) between the Hayward and Rodgers 160 Creek faults, inferred by Watt et al. (2016). Point Pinole (PP), the location where the 161 Hayward fault meets the edge of San Francisco bay, is 0-km along-strike distance in 162 our other figures. Yellow stars show the cities of San Francisco (left star), and 163 Oakland (right star). SR, SJ, and G are the cities of Santa Rosa, San Jose, and Gilroy, 164 respectively. Map created using the U.S. Geological Survey (USGS) Quaternary 165 Active Faults database (U.S. Geological Survey and California Geological Survey, 166 2019). 167

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168 2 Methods 169 We computationally simulate dynamic (spontaneous) rupture propagation on the right- 170 lateral strike-slip Rodgers Creek-Hayward-Calaveras-Northern Calaveras fault system. Our 3D 171 finite-element computer code, FaultMod (Barall, 2009), has been extensively tested using code 172 verification exercises (e.g., Harris et al., 2009; 2018). The code simulates dynamic earthquake 173 rupture on complex 3D fault geometry set in complex 3D rock properties. The simulations are 174 fully dynamic in that the time-dependent stresses in the system drive the earthquake rupture 175 extent. Inertia of the host rock, and consequently, seismic wave propagation throughout the 3D 176 medium are fully accounted for in the simulations. 177 178 Dynamic (spontaneous) rupture simulations have many advantages and also many 179 burdens. The advantages are that they allow the user to include everything known about 180 earthquake and fault physics and wave production. These advantages are also burdens. That is, 181 many assumptions are needed to produce the simulations, including the geometry of the faults 182 involved, the material properties of the rocks that comprise and surround the faults, the initial 183 stresses on the faults, and the friction criterion that determines when the faults are or are not 184 allowed to slip (e.g., Harris, 2004) (Figure 2). The spontaneous rupture numerical tool 185 therefore not only allows one to include everything that one knows about earthquake physics, but 186 also requires that one include everything. 187 188 Spontaneous Earthquake Rupture Simulation

Fault Rock Initial Frictional Geometry Properties Stresses Behavior

Spontaneous Rupture Code

Earthquake Ground Source Motions 189 190 191 FIGURE 2. (Modified from Harris, 2017). The ingredients for a spontaneous rupture 192 simulation include the fault geometry, the on- and off-fault rock properties, the initial 193 stresses (shear and normal stresses), and the friction behavior that determines if and 194 when the faults are allowed to slip. A computer code that simulates dynamic, 195 spontaneous (unforced) rupture can be used to calculate the resulting wave 196 propagation and the progress of the simulated earthquake. Earthquake extent and 197 size, time-dependent images of fault-slip, and seismograms (ground shaking) are all 198 results of these types of simulations. 199

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200 Fortunately, the Rodgers Creek-Hayward-Calaveras-Northern Calaveras fault system is 201 one of the few regions of the world where information is available about the nature of the faults 202 and the surrounding rocks. The "known" elements include a 3D geologic model that provides 203 details about the 3D fault geometry and reveals which rocks abut and surround the faults. There 204 are laboratory friction studies on surface-samples of Hayward fault rocks, and there are geodetic 205 and seismological data that shed light on the faults’ creep-rate patterns that are occurring during 206 the current interseismic period between large earthquakes.

207 2.1 Fault Geometry 208 The 3D geologic model of the Hayward fault (Graymer et al., 2005; Phelps et al., 2008) 209 and the USGS 3D Geologic Model of the San Francisco Bay Area (subsequently referred to as 210 the “Big Bay Model”) (Jachens et al., 2006) provide a picture of the 3D geometry of the 211 Rodgers Creek-Hayward-Calaveras-Northern Calaveras fault zone. This geometry, from the 212 Earth's surface to the base of the brittle fault zone, is inferred from surface-geology analyses, 213 double-difference relocated earthquake hypocenters, and gravity and magnetics studies 214 (Waldhauser and Ellsworth, 2002; Ponce et al., 2003; Simpson et al., 2004; Manaker et al., 215 2005; Graymer et al., 2005; Watt et al., 2008). Whereas some previous (kinematic) 216 simulations of large Hayward fault earthquakes have assumed that the Hayward fault and its 217 neighbor the Calaveras fault are separated geometrically, much evidence points to these two 218 faults being connected at depth (e.g., Ponce et al., 2004; Simpson et al., 2004; Manaker et al., 219 2005; Hardebeck et al., 2007; Chaussard et al., 2015a). Therefore, our simulations assume the 220 fault geometry to be a continuous Hayward/Central Calaveras three-dimensional fault surface, 221 rather than distinguishing the Central Calaveras fault as a separate entity. This is a simplification 222 of the multiple strands observed at the Earth's surface that appear to connect to a single fault at 223 depth (e.g. Ponce et al., 2004), a simplification that we make due to computational constraints. 224 We also include in our fault geometry the Northern Calaveras fault as a branch from the 225 Hayward and Central Calaveras faults. 226

227 In addition, we assume, as inferred by Watt et al. (2016) (who used ultrahigh-resolution 228 seismic-reflection cross sections and shipborne magnetometer data to image shallow fault zone 229 structure), that the Hayward fault does not stop at San Pablo Bay, but rather that there is a direct 230 connection between the northern end of the Hayward fault and the southern end of the Rodgers 231 Creek fault. Figure 3 shows the 3D fault geometry that we use for our dynamic earthquake 232 rupture simulations. Our modeled fault zone is 196-km long, from its northwest end on the 233 Rodgers Creek fault at the city of Santa Rosa to its southeast end on the Central Calaveras fault 234 east of the city of Gilroy. The faults themselves continue farther along strike. The Calaveras 235 fault reaches farther southeast as it gets closer to the San Andreas fault (see Figure 1), the 236 Rodgers Creek fault reaches farther northwest, as it transitions into the Healdsburg section 237 northwest of Santa Rosa (Hecker and Randolph Loar, 2018), and the Northern Calaveras fault 238 transitions into a complex zone of distributed faulting as it reaches farther north. Due to 239 computational constraints, we truncate the along strike fault geometry. 240

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241 242 243 244 FIGURE 3. The geometry of the strike-slip faults used for our dynamic rupture 245 simulations. We include complexities such as the non-planar fault surfaces, the 246 merging of the Central Calaveras fault with the Hayward fault, the branching of the 247 Northern Calaveras from the connected Hayward and Central Calaveras faults, and, 248 from 0 to 21 km along strike, the Watt et al. (2016) connector between the Hayward 249 and the Rodgers Creek faults. 0 km along strike is Point Pinole, California 250 (38.0030N, 122.3670W). The NW end of our model is on the Rodgers Creek fault at 251 the city of Santa Rosa (SR). The fault itself continues farther northwest, but we end 252 our model at this location to keep the simulations computationally feasible. Circles 253 with stars indicate our simulated earthquake nucleation locations on each of the four 254 faults. Lower figure shows the entire 3D finite-element mesh, including the fault 255 trace (black lines). The denser blue area on the top of the 3D finite-element mesh 256 shows that the elements are smaller in the fault region. For ease of viewing, both the 257 fault surface mesh and the 3D mesh are depicted with 700 m elements, rather than the 258 250 m elements that we used in our simulations. We created these figures with the 259 software ParaView (Ahrens et al., 2005). 260

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261 2.2 Rock Properties 262 We use the 3D geologic model (Figure 4) based on information from the Hayward fault 263 model (Graymer et al., 2005; Phelps et al., 2008) and the Big Bay model (Jachens et al., 2006) 264 to assign the rock units for our 3D simulations. Since we are performing numerical experiments 265 that include wave propagation and fault slip, we need to know the properties, including the P- 266 wave speeds, S-wave speeds, and densities of this 3D geologic rock structure. Fortunately, 267 Brocher (2008) constructed mathematical relationships between northern California rock types 268 (and their depths) and their material-property values. We adopt his equations and apply them at 269 the locations of the rock-units in the 3D geologic model to construct the 3D material property 270 structure. One modification is that we impose a minimum P-wave velocity of 3600 m/s, a 271 minimum shear-wave velocity of 1950 m/s, and a minimum density of 2550 kg/m3. This is 272 because our 3D computer simulations cannot capture the propagation of waves through very 273 slow-velocity and low-density media, although they perform well for wave propagation through 274 material with faster velocities and higher densities. 275

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276 4a)

277 278

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279 4b)

280 281

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282 4c)

283

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284 4d)

285 286 287 288 FIGURE 4. Rock units in the region of the Calaveras-Hayward-Rodgers Creek- 289 Northern Calaveras fault system. Geologic information is from the Hayward model 290 (Graymer et al., 2005; Phelps et al., 2008) and the Big Bay Model (Jachens et al., 291 2006). Point Pinole (PP) is at (0,0) in map views, and at 0-km along-strike in fault- 292 surface views. Positive distances along strike are to the N35W direction. Santa Rosa 293 is at 60-km along strike. Rock units inside the gray rectangle are from the detailed 294 Hayward geologic model (Phelps et al., 2008). Rock units outside the gray rectangle 295 are from the less detailed but larger Big Bay geologic model (Jachens et al., 2006). 296 a) Horizontal map slice at 140 meters below the Earth’s surface. White lines are our 297 modeled faults. 298 b) Horizontal map slice at 7 km depth. White lines are our modeled faults. 299 c) View of the rock units on each face (side) of the fault surfaces. 300 d) The resulting shear-velocity (Vs) structure on each face (side) of the fault surfaces, 301 assuming the 1950 m/s low-velocity cutoff. The 3D velocity structure is derived from 302 the geologic model’s rock units, e.g., shown in c), using Brocher et al.’s (2008) 303 relations. 304

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305 2.3 Fault Friction 306 Unlike prescribed kinematic earthquake ruptures that propagate at pre-determined speeds 307 and have pre-defined rupture extents, dynamic (spontaneous) earthquake rupture simulations 308 need a friction formulation to determine the fault's frictional resistance to sliding. The dynamic 309 rupture simulation code then calculates the resulting time-dependent fault rupture and slip. The 310 friction formulation that we use, slip-weakening (Figure 5), is similar in some aspects to the 311 more-familiar static Coulomb failure criterion, except that slip-weakening is also time-dependent 312 and slip-dependent. The slip-weakening friction formulation is a macroscopic representation of 313 the dynamic rupture process (Okubo, 1989; Cocco et al., 2008). It is inferred from laboratory 314 experiments of rock-friction (Ida, 1972; Dieterich, 1981), soil response (Palmer and Rice, 315 1973), and kinematic studies of strong ground motion seismograms (e.g., Beroza and Mikumo, 316 1996; Day et al., 1998) to be a viable mathematical formulation of coseismic friction. Slip- 317 weakening is shown to be equivalent to some forms of rate- and state-dependent friction for 318 coseismic rupture simulations if the fracture energy, which is the amount of energy needed to 319 keep a rupture propagating on a fault (Bizzarri, 2010a), is assigned to be equivalent (Ryan and 320 Oglesby, 2014). The slip-weakening friction formulation allows the tip of a crack in a 321 computationally simulated earthquake rupture to behave well numerically (e.g., Andrews, 1976; 322 Day, 1982), and therefore has been used for more than three decades. The slip-weakening 323 formulation may also act as a proxy for simulating the effects of off-fault damage, in that a 324 sizeable slip-weakening distance leads to a sizeable fracture energy that the rupture needs to 325 overcome to advance. In our slip-weakening friction formulation, the coefficients of friction 326 themselves are normal-stress independent, but we allow both the shear and normal stresses to 327 vary as a function of time and space. 328 329 For the slip-weakening friction formulation (Figure 5), we need to assign three values at 330 every location on the fault surfaces. These are the static coefficient of friction, the dynamic- 331 sliding coefficient of friction, and the slip-weakening critical distance, the latter of which is the 332 amount of fault slip over which the friction decreases from static to dynamic-sliding values 333 (Figure 5). We assume a constant slip-weakening critical distance of 0.30 m for all fault 334 surfaces. This choice of 0.3 m allows the breakdown zone at the rupture's front to be resolved 335 with the 250-meter on-fault elements of our 3D finite-element models, as evidenced by a few 336 tests that we conducted using 125-m-on-fault elements, which produced similar results. While 337 larger than the rate-state distance Dc inferred from laboratory experiments, the slip-weakening 338 critical distance is inferred to be on the order of 0.1-5 meters, as determined from seismological 339 observations (e.g., Kaneko et al., 2017). We could vary the slip-weakening critical distance 340 over the fault surface, but we have no observations to tell us how to do so for this fault system, 341 so instead we take the simplest approach and assume that it is constant. 342 343

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344

345 346 347 FIGURE 5. Slip-weakening friction (e.g., Andrews (1976)) defines the strength of a 348 location on a fault surface as a function of the amount of slip at that location. Initially 349 the strength is the static yield strength (the static coefficient of friction (µs) x the time- 350 dependent normal stress). As the location on the fault-surface starts to slip, its 351 strength linearly decreases until it reaches the dynamic-sliding friction stress (the 352 dynamic-sliding coefficient of friction (µd) x the time-dependent normal stress). The 353 fault-slip distance over which this strength-breakdown occurs is the slip-weakening 354 critical distance, d0. After a location on the fault surface has slipped this critical 355 distance, the fault strength at this location remains at its dynamic-sliding friction 356 stress level. The fracture energy, e.g., Bizzarri (2010a), the energy needed to keep a 357 rupture propagating on a fault, is snd0(µs-µd)/2, where sn is the normal stress. 358 359 360 361 To select the dynamic-sliding coefficients of friction for our slip-weakening friction 362 formulation, we rely on laboratory experiments that have measured the constitutive properties of 363 rocks collected at the Earth's surface in the vicinity of the Hayward fault (Morrow et al., 2010). 364 The Morrow et al. (2010) experiments were conducted at effective normal stress of 50 MPa on 365 water-saturated unweathered rock samples at room temperature. Morrow et al. (2010) found 366 that strong gabbro and quartzo-feldspathic protoliths have higher frictional sliding strengths than 367 phyllosilicates that are typically weaker. In addition to the Morrow et al. (2010) experiments, 368 Moore et al. (2016) conducted rock friction studies on samples from similar kinds of rocks along 369 the San Andreas fault, collected at the San Andreas Fault Observatory at Depth (SAFOD). 370 371 To simplify the friction parameters, we assume that the fault-bounding rocks are divided 372 into three categories with respect to their dynamic-sliding coefficients of friction values. The 373 Coast Range Ophiolite’s San Leandro gabbro is the strongest of the fault zone rocks, and it is 374 assigned a dynamic-sliding coefficient of friction of 0.65. This is weaker than the 0.8 value 375 presented in Morrow et al.’s (2010) Figure 3, but we assign the value of 0.65, due to the 376 assumed alteration of pyroxene to chlorite at depth on the Hayward fault, which reduces the 377 friction from the pristine laboratory-sample value of 0.8, but does not change its velocity 378 weakening behavior, particularly at depth (He et al., 2007; Swiatlowski et al., 2017). Following 379 Morrow et al. (2010), the Coast Range Ophiolite’s serpentinite, which includes the low- 380 temperature serpentine mineral chrysotile, is assigned a dynamic-sliding coefficient of friction of

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381 0.3. This also agrees with the findings for serpentinites summarized by Viti et al. (2018), and is 382 consistent with their strengths in the presence of crustal fluids at temperatures ≥ 250°C (Moore 383 and Lockner, 2013). The rest of the fault rocks, including considerable amounts of Franciscan 384 mélange, are assigned dynamic-sliding coefficients of friction of 0.5, based on the studies by 385 Morrow et al. (2010) and Moore et al. (2016). Moore et al. (2016) showed that gouges 386 prepared from Great Valley and Franciscan mélange materials (the Franciscan gouge is the same 387 stock as used by Morrow et al., 2010) began transitioning to velocity-weakening behavior at 388 150°C, with stick-slip behavior at 250°C. Table 1 summarizes these assumptions. 389 390 In cases where our 3D geologic model involves rock units of different types meeting 391 across the faults, if the two rock units have different dynamic-sliding coefficients of friction, we 392 use the lower of the two values, as Collettini et al. (2009) show to be appropriate. Figure 6 393 shows these dynamic friction values on the fault surfaces in our model. 394 395 In addition to the aforementioned dynamic-sliding coefficients of friction, our slip- 396 weakening friction formulation (Figure 5) needs us to assume values for the static coefficients of 397 friction. Wong (1986) compiled data from laboratory experiments, including those of Scholz et 398 al. (1972), and showed a 20 percent difference between static and dynamic-sliding coefficients 399 of friction. Therefore, we choose static coefficients of friction that are 1.2 times the dynamic- 400 sliding coefficients of friction for the fault surfaces in the RC-H-C-NC fault system. 401 402

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403

404 405 406 FIGURE 6. Dynamic-sliding coefficient of friction values on the Rodgers Creek- 407 Hayward-Calaveras fault surface and the Northern Calaveras fault surface, based on 408 Morrow et al.’s (2010) Hayward fault laboratory experiments on field-collected 409 Hayward fault samples, and Moore et al.’s (2016) SAFOD laboratory experiments on 410 rock samples collected from deep drilling at SAFOD. We use the Phelps et al. (2008) 411 Hayward geologic model set in the (Jachens et al., 2006) Big Bay geologic model and 412 assign friction values to each general type of rock unit (red/0.65/San Leandro gabbro, 413 purple/0.3/serpentinite, green/0.5/Franciscan Complex mélange or other). PP is Point 414 Pinole. The ‘combined’ dynamic friction coefficients are the lower of the two 415 dynamic-sliding coefficient of friction values on the east and west faces of the fault 416 surfaces. We use these ‘combined’ dynamic friction coefficients at each point on the 417 fault surface for our dynamic rupture simulations. From top to bottom of the figure: 418 The dynamic-sliding coefficients of friction on the east face of the main RC-H-C fault 419 surface, the dynamic-sliding coefficients of friction on the west face of the RC-H-C 420 fault surface, the combined dynamic-sliding coefficients of friction for the east and 421 west RC-H-C faces, and the dynamic-sliding coefficient of friction for the Northern 422 Calaveras fault surface. The Northern Calaveras fault surface contains neither gabbro 423 nor serpentinite, so it is assigned a single dynamic-sliding coefficient of friction value 424 of 0.5 over its entire length and depth for the east face of the fault surface, for the west 425 face of the fault surface, and for its combined dynamic friction coefficient that we use 426 in our dynamic rupture simulations. 427

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428 2.4 Initial Stress Conditions and Creeping Faults 429 We use observations of the Rodgers Creek-Hayward-Calaveras-Northern Calaveras fault 430 system’s interseismic creep-rate pattern to help inform our choices of initial (time=0) stress 431 conditions for our dynamic rupture simulations. Because we are working with spontaneous 432 (dynamic) rupture models, after time=0, the stresses are time-dependent and freely allowed to 433 vary. In addition, because we are assuming an elastic model for the deformation of the 434 surrounding rock, we only need to assign the initial shear and normal stresses on the fault 435 surfaces themselves, rather than throughout our 3D model. 436 437 There is still, however, the question of how to incorporate the information that some parts 438 of our fault system creep interseismically, thereby releasing at least part of the tectonic strain 439 budget at times other than during large earthquakes. Geodetic observations and abundant 440 microseismicity have been used to infer the rates and locations of interseismic fault creep at 441 depth along the Hayward, Calaveras, and Northern Calaveras faults (e.g., Burgmann et al., 442 2000; Simpson et al., 2001; Waldhauser and Ellsworth, 2002; Malservisi et al., 2003; 443 d'Alessio et al., 2005; Schmidt et al., 2005; Burgmann, 2007; Funning et al., 2007; Funning 444 et al., 2009; Shirzaei and Burgmann, 2013; Lienkaemper et al., 2014; Chaussard et al., 445 2015a;b; Lozos and Funning, 2020). We use this information to infer which parts of the fault 446 surfaces are closer to or farther from their static yield strength, at the start of each dynamic 447 rupture simulation. 448 449 None of the previously published, detailed interseismic creep-rate patterns encompass the 450 entire length of our 196-km long fault system, so we use the available information and merge it 451 where appropriate. Funning et al. (2009) provide an interseismic creep-rate model for most of 452 the Hayward fault and part of the connector fault. Chaussard et al. (2015b) provide an 453 interseismic creep-rate model for the southern Hayward and central and northern Calaveras 454 faults. For the southern Hayward, there is overlapping information, so we transition from the 455 Funning et al. (2009) to the Chaussard et al. (2015b) interseismic slip-rate models between 60 456 and 70-km south of Point Pinole. On the Rodgers Creek fault south of Santa Rosa, there is a 457 dearth of both geodetic data (Jin and Funning, 2017) and microseismicity (Xu et al., 2018; 458 Shakibay Senobari and Funning, 2019), so we assume that the Rodgers Creek fault is 459 predominantly locked (Jin and Funning, 2017) during the current interseismic period, from 460 south of Santa Rosa all of the way to the bend at the connector that links the Rodgers Creek fault 461 with the Hayward fault (Figures 1 and 3). This reach of the Rodgers Creek fault south of Santa 462 Rosa is inferred to have been involved in large earthquakes in the past (Budding et al., 1991; 463 Hecker et al., 2005). South of this bend in the fault geometry, we assume a short taper to, then a 464 continuation of, the interseismic creep rate values that are inferred for the northern end of the 465 Funning et al. (2009) interseismic creep-rate model. Our interseismic creep-rate pattern for the 466 Calaveras-Hayward-Connector-Rodgers Creek fault system that incorporates all this information 467 is shown in Figure 7. For the Northern Calaveras fault, we adopt the Chaussard et al. (2015b) 468 interseismic creep-rate pattern, also shown in Figure 7. 469 470 We next use our newly constructed interseismic creep rate pattern on the fault surfaces 471 (Figure 7) to assign where the initial shear stresses on the fault surfaces are higher or lower, and 472 thereby closer to or farther from the static yield strength at the beginning of each of our dynamic 473 rupture simulations (Table 1). We examine three options: In option one, we ignore the fact that

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474 any of these faults creep interseismically and we assign, to all locations on the fault surfaces, 475 initial shear stresses that are solely related to the rocks’ friction values. In option two, we assign 476 to all locations on the fault surfaces with interseismic creep rates of 3 mm/yr or faster (Figure 7), 477 a lower initial shear stress. This makes it more difficult for those parts of the fault surfaces to 478 spontaneously rupture. In option three, we repeat option two, except that we instead use the 479 locations of 1 mm/yr or faster interseismic creep rates (Figure 7), as the criterion for the 480 locations of lower initial shear stress in our dynamic rupture models. These assumptions are 481 summarized in Table 1. 482 483 For the whole fault system, the initial S value, defined by Andrews (1976) and Das and 484 Aki (1977) as (µssn-so)/(s0-µdsn), where the denominator is the stress drop and s0 is the initial 485 shear stress, is 1.5 for the locked portions of the fault surfaces, and 4.0 for the creeping portions 486 of the fault surfaces (Table 1). The S value of 1.5 produces primarily subshear (slower than the 487 shear-wave velocity) rupture speeds in our simulations, as expected from theoretical 488 considerations (e.g., Dunham, 2007). The S value of 4.0 is less likely to allow rupture, because 489 it represents the situation where the initial shear stress is further from the static yield strength, 490 relative to the stress drop. This 4.0 value, which has one-half the stress drop of the 1.5 value, 491 was chosen based on the idea that the tectonic stress on the interseismically creeping portions of 492 the faults has not been fully released during the interseismic timeframe, so that one-half of the 493 stress drop is still available to drive coseismic rupture. 494

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495

496 497 498 Figure 7. Top) The interseismic slip-rate (creep-rate) pattern on the Calaveras- 499 Hayward-connector-Rodgers Creek fault surface. This creep-rate pattern is obtained 500 by our merging of the partially overlapping Calaveras and Hayward interseismic 501 creep-rate models from Chaussard et al. (2015b) and Funning et al. (2009), then 502 using additional information (see text) for the creep-rate pattern on the connector fault 503 (Watt et al., 2016) and on the Rodgers Creek fault. PP is Point Pinole, SR is Santa 504 Rosa. Bottom) The interseismic creep-rate pattern on the Northern Calaveras fault 505 surface, from Chaussard et al. (2015b). The left edge of the Northern Calaveras 506 fault merges with the Hayward fault at an angle, so the left edge of the Northern 507 Calaveras fault is non-vertical. White areas below each fault surface indicate the 508 bottom of the seismogenic zone, which is inferred to be slipping at the faults’ long 509 term rates. White areas along strike indicate that the fault surface is creeping very 510 slowly, or is locked in these locations during the interseismic period. We use the 511 depicted 1 mm/yr and 3 mm/yr creep-rate contours (white curves) from these 512 interseismic creep-rate images to assign the locations of the transition from higher 513 initial shear stress to lower initial shear stress in our spontaneous (dynamic) rupture 514 simulations. 515

516

517 2.5 Nucleation Method 518 We nucleate our simulated earthquakes by forcing a portion of the fault surface to 519 rupture, within a 6-km-radius circular area surrounding the hypocenter. Outside this nucleation 520 zone, fault friction is governed by slip-weakening. Inside this nucleation zone, fault friction is 521 governed by a combination of slip-weakening and time-weakening (Supplement Text S1). 522 With slip-weakening (Andrews, 1976), the coefficient of friction decreases from its static value 523 to its dynamic value as a function of how far the fault has slipped (as shown in Figure 5). In 524 contrast, with time-weakening (e.g., Bizzarri, 2010b; Hu et al., 2017) the coefficient of friction 525 decreases with the passage of time, without regard to fault slip. We combine the two by

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526 calculating the coefficient of friction using both slip-weakening and time-weakening, and taking 527 whichever result is smaller. This procedure leads to a smooth nucleation process, and to final 528 slip in the nucleation area that is consistent with the final slip on the rest of the fault surface. 529 530 At the hypocenter, time-weakening is initiated at the start of the simulation, t=0. At other 531 points in the nucleation zone, time-weakening is initiated at progressively later times, increasing 532 with distance from the hypocenter. This means that the initiation of time-weakening occurs in a 533 gradually expanding circle surrounding the hypocenter. At first, the radius of the circle increases 534 at a rate that approximates the expected rupture propagation speed. As the circle gets larger, the 535 rate of expansion slows, eventually reaching zero at the outer edge of the nucleation zone. This 536 process allows a smooth transition from a forced rupture driven by time-weakening to a 537 spontaneous rupture driven by slip-weakening. 538 539 When the rupture has traveled beyond the nucleation zone on the fault surface, there is no 540 longer any forcing. The rupture is then required to spontaneously propagate on its own, and if 541 unable to do so, it stops. For our RC-H-C-NC fault system study, we assume that the artificial 542 nucleation zone has a radius of 6 km. 1-km smaller nucleation radii also suffice for some of the 543 nucleation locations, in that they also lead to subsequent spontaneous rupture propagation, but 544 much smaller radii do not suffice and those ruptures are then unable to propagate beyond the 545 forced-nucleation area.

546 2.6 Finite Element Mesh 547 Our 3D model of the Rodgers Creek-Hayward-Calaveras-Northern Calaveras fault 548 system is a finite-element mesh that is 260 km long (fault parallel) x 166 km wide (fault 549 perpendicular) x 84 km deep. The elements are primarily hexahedra, with some wedge elements 550 used to construct the fault branch. Our mesh uses 250-meter elements on the fault surface. 551 Outside of the near-fault 3D fault-surface region, for computational efficiency we use the grid- 552 doubling technique described in Barall (2009). Table 1 summarizes many of the assumptions 553 used in our modeling. 554

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555 TABLE 1. ASSUMPTIONS FOR THE DYNAMIC RUPTURE SIMULATIONS 556 557 Model dimensions: 260 km (fault parallel) x 166 km (fault perpendicular) x 84 km deep 558 559 Rock properties (density, Vp, Vs): 560 Phelps et al. (2008) 3D Hayward model inside 3D Big Bay model (Jachens et al., 2006) 561 inside 1-D SCEC velocity model (Kanamori and Hadley, 1975). (Big Bay model is 285 562 km N-S x 133 km E-W) 563 Brocher (2008) equations 564 565 Locked regions: Fault surface areas with inferred slip-rate < 1 or 3 mm/yr 566 Creeping regions: Fault surface areas with inferred slip-rate >=1 or 3 mm/yr 567 568 Nucleation method: within nucleation area, gradual forcing (see supplement) 569 Nucleation area: 6-km-radius circle 570 Nucleation depth: 7 km 571 Nucleation Locations: Rodgers Creek, Hayward, Calaveras, Northern Calaveras faults 572 573 Element-size: 250 m for fault-surface elements 574 Simulation time-step: 0.01 second 575 Simulation duration: up to 120 seconds (until the faults have stopped moving) 576 577 Friction Formulation slip-weakening 578 Dynamic friction coefficient: lower value on each side of fault surface 579 0.65 for San Leandro gabbro 580 0.3 for serpentinite 581 0.5 for everything else 582 583 Static friction coefficient: 1.2 x dynamic friction coefficient 584 Slip-weakening critical distance: 0.3 m 585 S value: 1.5 for locked regions, 4.0 for creeping regions 586 Initial (assumed only at t=0) normal stress: 75 MPa 587 Initial (assumed only at t=0) shear stress: 588 in locked regions: 52.65 MPa for San Leandro gabbro 589 24.3 MPa for serpentinite 590 40.5 MPa for everything else 591 in creeping regions: 50.7 MPa for San Leandro gabbro 592 23.4 MPa for serpentinite 593 39.0 MPa for everything else 594 Initial (assumed only at t=0) stress-drop: 595 in locked regions: 3.90 MPa for San Leandro gabbro 596 1.80 MPa for serpentinite 597 3.00 MPa for everything else 598 in creeping regions: 1.95 MPa for San Leandro gabbro 599 0.90 MPa for serpentinite 600 1.50 MPa for everything else

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601 a 602 Fault Depths (from Field et al., 2013): 603 Rodgers Creek: 12.0 km 604 Hayward: 11.1 km for north part, 13.4 km for south part 605 Central Calaveras: 11.0 km 606 Northern Calaveras: 14.0 km b 607 Hayward-Rodgers Creek connector : 11.1 km in the south to 12.0 km in the north 608 ______a 609 in locations where Field et al. (2013) has fault depth changing, either between faults, or along 610 strike on one fault, we taper the depth over a 20-km along-strike distance that is centered where 611 the depth change occurs. b 612 this fault section is not included in Field et al. (2013), so we choose its depth as a smooth 613 tapering of the depth from the northern part of the Hayward fault to the Rodgers Creek fault. 614

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615 3 Results 616 Our simulations of large earthquakes on the RC-H-C-NC fault system incorporate many 617 complex features. These include the 3D fault system geometry, the 3D geology that comprises 618 this fault system, and our assumptions about the initial stresses, the frictional behavior of the 619 fault system's rocks, and the locations and sizes of the locked parts of the fault system. For most 620 of the simulations, we assume that at the beginning of the simulation the locked parts of the fault 621 have higher initial shear stresses and thereby higher initial stress drops than the creeping parts of 622 the faults. Since the shear and normal stresses are time-dependent, as time progresses from 623 time=0, the stresses are not fixed at their initial values, but instead are allowed to change. This 624 implies that the simulated earthquake rupture may, if there is sufficient strain energy to do so at 625 each time-step, propagate from locked into creeping parts of the faults. This also implies that the 626 simulated earthquake rupture may, if it runs out of strain energy, stop before completely filling a 627 locked fault patch. This is one of the key differences between the spontaneous dynamic rupture 628 simulations that we are doing here, and kinematic rupture-simulations by others (e.g., Aagaard 629 et al., 2010a, b; Rodgers et al., 2018, 2019); in our work the earthquake rupture extent on the 630 fault system is not prescribed, but instead the simulated earthquake rupture only propagates when 631 and where there is sufficient strain energy to do so (e.g., Husseini et al., 1975).

632 3.1 Nucleation Locations 633 Large earthquakes have occurred on each of the RC-H-C-NC faults in the past, so we 634 know that each of these four faults has the potential to produce a large earthquake in the future. 635 We do not, however, know where any of these large earthquakes might start (nucleate). We 636 therefore choose an earthquake nucleation site for each of the four faults. Ponce et al. (2003) 637 proposed that the San Leandro gabbro (Figure 4) focuses stress and could be a rupture initiation 638 area for large earthquakes on the Hayward fault. Boatwright and Bundock (2008) proposed, 639 based on intensity observations from the 1868 M6.8 Hayward earthquake, that the 1868 640 earthquake started just northwest of the city of Hayward, between the cities of Hayward and San 641 Leandro. We therefore choose our Hayward fault nucleation site to be in the vicinity of the San 642 Leandro gabbro, in the region beneath the cities of Hayward, Castro Valley and San Leandro. 643 For our other three faults, we have fewer suggestions as to where large earthquakes might start, 644 so the choices of those nucleation locations are more arbitrary. The Rodgers Creek nucleation 645 site is northeast of Petaluma. The Central Calaveras fault nucleation site is northeast of Morgan 646 Hill. The Northern Calaveras fault nucleation site is near Pleasanton. All nucleation sites 647 (Figure 3) are centered at 7 km depth.

648 3.2 Fully Locked Rupture Scenarios 649 We start the presentation of our results by showing what happens if the entire fault 650 system is assumed to be locked before large ruptures nucleate; that is we assign higher initial 651 shear stress and thereby higher initial stress drop (Table 1) over the entire fault system. These 652 ‘fully locked’ simulations produce the maximum rupture extent and maximum slip that can occur 653 in our models, and thereby, the maximum-magnitude simulated earthquakes. We examine this 654 ‘fully locked’ scenario for each of our four nucleation locations: the Rodgers Creek fault (40-km 655 along strike), the Hayward fault near the San Leandro gabbro (-40-km along strike), the Central 656 Calaveras fault (-110-km along strike), and the Northern Calaveras fault (-50-km along strike). 657 Snapshots of the rupture progress on the fault surfaces and the final slip pattern are shown for

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658 each of these four locked-fault scenarios in Figure 8, and the final moment magnitude and 659 rupture length of each scenario is listed in Table 2. 660 661 For the locked fault scenarios (Figure 8, Table 2), we see that earthquakes nucleating in 662 any one of the four locations are able to propagate through the Rodgers Creek-Hayward- 663 Calaveras three-fault system. The earthquake nucleating on the Northern Calaveras fault is able 664 to rupture the entire Northern Calaveras, then dynamically trigger and rupture the entire Rodgers 665 Creek-Hayward-Calaveras fault system, thereby producing a four-fault rupture. The earthquake 666 nucleating on the Calaveras fault ruptures the three-fault system, and also triggers a small part of 667 the Northern Calaveras fault. The pattern of fault rupture timing is different for each nucleation 668 location, as are the time-dependent slip and slip rate patterns, and the resulting ground shaking at 669 the Earth’s surface (Figure 8). 670

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671 672 8a) Rupture Front Contours in 0.5 second intervals 673 674

675 676

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677 8b) Final Slip (m) 678

679

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680 8c) Shaking (3D Velocity in m/s) at Earth’s Surface 681

682 683 684

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685 Figure 8. Locked-fault scenario earthquakes that nucleate on each of the four faults. 686 687 a) Contours of the earthquake ruptures’ progress, in 0.5 second intervals on the fault 688 surfaces, starting from the center of the circular nucleation area. From top to bottom of 689 the figure: The earthquake nucleating (at 40-km along strike) on the Rodgers Creek fault 690 propagates along the entire Calaveras-Hayward-connector-Rodgers Creek main fault but 691 is unable to trigger Northern Calaveras rupture. The earthquake nucleating (at -40-km 692 along strike) on the Hayward fault propagates over the entire main fault, and is also 693 unable to trigger rupture on the Northern Calaveras fault. The earthquake nucleating (at - 694 110 km along strike) on the Calaveras fault is able to propagate over the entire main-fault 695 surface and it also triggers small rupture on the Northern Calaveras fault. The earthquake 696 nucleating (at -50-km along strike) on the Northern Calaveras fault propagates over its 697 entire area, and jumps onto the Calaveras-Hayward portion of the main fault, then 698 ruptures the main fault in its entirety. 699 700 b) Final slip on the fault surfaces, after the ruptures have finished propagating. From top 701 to bottom, nucleation on the Rodgers Creek fault, Hayward fault, Calaveras fault, and 702 Northern Calaveras fault. The earthquake nucleating on the Calaveras fault also produces 703 very minor slip on the Northern Calaveras fault (not shown). The earthquake nucleating 704 on the Northern Calaveras fault produces sizable slip on both the Northern Calaveras 705 fault and the main fault, although there is a small stress shadow effect (e.g., Harris and 706 Simpson, 1996) on the Hayward fault across from the Northern Calaveras fault branch. 707 708 c) Snapshot of shaking (3D velocity, m/s) at the Earth’s surface, at 15 seconds (left) and 709 30 seconds (right) after nucleation. From top to bottom: the earthquake nucleates on the 710 Rodgers Creek fault, Hayward fault, Central Calaveras fault, and Northern Calaveras 711 fault. 712

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713 3.3 Creeping Fault Rupture Scenarios 714 Next, we examine the effect of having a lower initial shear stress, and thereby, lower 715 initial earthquake stress drop in the creeping regions of the fault surfaces. We assume that 716 patches on the fault surfaces that are creeping during the current interseismic period at rates of 3 717 mm/year or faster (Figure 7) have lower initial shear stress than the parts of the fault surfaces 718 that are creeping more slowly or are locked during the interseismic period. We examine this 719 ‘creeping faults’ scenario for the same four nucleation locations: Hayward fault near the San 720 Leandro gabbro, the Central Calaveras fault, the Rodgers Creek fault, and the Northern 721 Calaveras fault. Snapshots of the rupture progress at the Earth’s surface and on the fault surfaces 722 themselves, for the ruptures that are able to spontaneously propagate beyond their nucleation 723 areas, are shown in Figure 9.

724 We then repeat this exercise, using the 1 mm/yr creep-rate contour (Figure 7) to define 725 the lower initial shear stress region. The results for the ruptures that are able to spontaneously 726 propagate beyond their nucleation areas are shown in Figure 10. The simulated earthquake 727 magnitudes and rupture lengths for all these simulations are summarized in Table 2. 728 729 Earthquake rupture nucleating at our site on the Hayward fault is able to propagate a 730 considerable along-strike distance, 173 km, when we use the 3 mm/yr creep-rate contour 731 (Figures 7 and 9a) to define where the fault has a lower initial shear stress. In contrast, when 732 we use the 1 mm/yr contour (Figures 7 and 10a) to define where the fault has a lower initial 733 shear stress, the rupture has insufficient energy to drive its propagation beyond the nucleation 734 area, so the rupture spontaneously stops. 735 736 Earthquake ruptures nucleating at our site on the Calaveras fault are stopped by the lower 737 shear stress portions of the fault, and unable to propagate beyond the nucleation area when using 738 either the 3 mm/yr or the 1 mm/yr slip-rate contour to define the lower shear stress portions of 739 the fault. This is because the higher shear stress part of the fault is not sufficiently big to allow 740 for the transition from nucleation to spontaneous rupture propagation. 741 742 Earthquake rupture nucleating at our site on the Northern Calaveras fault is able to 743 propagate on the Northern Calaveras fault itself, when we use either the 3 mm/yr or the 1 mm/yr 744 contours to define the lower initial shear stress portions of the fault. This is because these lower 745 shear stress portions do not encompass the entire fault surface, for either the 3-mm/yr or the 1- 746 mm/yr creep-rate contour, as shown in Figures 9a and 10a, respectively. The Northern 747 Calaveras’s 14-km depth helps contribute to this larger fault surface area being available to 748 rupture. The earthquake nucleating at our site on the Northern Calaveras fault also triggers small 749 rupture on the main fault when we use the 3 mm/yr creep-rate contour to define the lower shear 750 stress region, but this triggering does not occur when we use the larger lower shear stress area 751 defined by the 1 mm/yr creep-rate contour. 752 753 Earthquake rupture nucleating at our site on the Rodgers Creek fault propagates more 754 than 100-km along strike of the Rodgers Creek-Hayward-Calaveras system, for both the 3 mm/yr 755 (Figure 9) and the 1 mm/yr (Figure 10) low shear stress cases, with the former propagating 192- 756 km, and the latter propagating 105-km. The 1 mm/yr case stops sooner than does the 3 mm/yr

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757 case, when it encounters the lower shear stress parts of the Hayward fault. Table 2 provides a 758 summary of these results. 759 760 In addition to details about the dynamic rupture simulation results, Table 2 includes 761 predictions of the earthquakes’ magnitudes and the fault traces’ maximum and mean slip that are 762 calculated using Hanks and Bakun’s [2008] and Wesnousky’s [2008] empirical relations, 763 respectively. The simulated earthquake magnitude values for the earthquakes that nucleate on 764 the Rodgers Creek, Hayward, and Central Calaveras faults are generally smaller than the 765 predicted magnitudes using the Hanks and Bakun (2008) equations. The exceptions are the 766 cases of nucleation on the Northern Calaveras fault, where only the locked fault dynamic rupture 767 simulation has a smaller magnitude than predicted. This appears to indicate that the Hanks and 768 Bakun (2008) equation for smaller rupture area earthquakes relates to our results differently than 769 the Hanks and Bakun (2008) equation for earthquakes with larger rupture areas (Table 2). The 770 Northern Calaveras fault also reaches deeper into the Earth’s crust than the other faults (see 771 Table 1), and this too may play a role. Whereas the differences between the magnitude-log area 772 empirical relations and the simulation results may be understandable, and perhaps are explained 773 by the shallow seismogenic depths of the modeled faults, there are less-consistent differences 774 between the predicted maximum and mean fault trace slip values using the Wesnousky (2008) 775 equations (see Table 2) and the simulated earthquakes’ corresponding slip values. 776 777

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778 779 780 9a) Rupture Front Contours in 0.5 second intervals 781

782 783 784

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785 9b) Final Slip (m) 786

787

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788 9c) Shaking (3D Velocity in m/s) at Earth’s Surface 789

790 791

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792 Figure 9. Creeping fault scenario earthquakes that use the 3 mm/yr interseismic slip-rate 793 contour (Figure 7) to define the creeping region, and thereby the lower initial shear stress 794 region. 795 796 a) Contours of the earthquake ruptures’ progress, in 0.5 second intervals on the fault 797 surfaces, starting from the center of the circular nucleation area. The 3 mm/yr interseismic 798 creep-rate contour is indicated by the red curves; gray shading indicates creeping area as 799 defined by the 3 mm/yr contour. From top to bottom of the figure: The earthquake 800 nucleating (at 40-km along strike) on the Rodgers Creek fault propagates along the majority 801 of the main fault and makes it most of the way along the Calaveras, but is unable to trigger 802 Northern Calaveras rupture. The earthquake nucleating (at -40-km along strike) on the 803 Hayward fault propagates over most of the main-fault surface, but is stopped along the 804 Calaveras, and is also unable to trigger rupture on the Northern Calaveras fault. The 805 earthquake nucleating (at -50-km along strike) on the Northern Calaveras fault propagates 806 over its entire area, and jumps onto the main fault to rupture a very small part of that fault. 807 The earthquake nucleating (at -110 km along strike) on the Central Calaveras fault is unable 808 to propagate beyond the nucleation area, so it is not shown. 809 810 b) Final slip on the fault surfaces, after the ruptures have finished propagating. From top to 811 bottom, nucleation on the Rodgers Creek fault, on the Hayward fault, and on the Northern 812 Calaveras fault. The earthquake nucleating on the Northern Calaveras fault also produces a 813 small amount of triggered slip on the main fault. 814 815 c) Snapshot of shaking (3D velocity, m/s) at the Earth’s surface, at 15 seconds (left) and 30 816 seconds (right) after nucleation. From top to bottom: the earthquake nucleates on the 817 Rodgers Creek fault, Hayward fault, and Northern Calaveras fault. 818 819

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820 10a) Rupture Front Contours in 0.5 second intervals 821 822

823 824 825 826 827 10b) Final Slip (m) 828

829 830 831

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832 10c) Shaking (3D Velocity in m/s) at Earth’s Surface 833

834 835 836 837 838

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839 Figure 10. Creeping fault scenario earthquakes that use the 1 mm/yr interseismic 840 creep-rate contour (Figure 7) to define the creeping region, and thereby the lower 841 initial shear stress region. 842 843 a) Contours of the earthquake ruptures’ progress, in 0.5 second intervals on the fault 844 surfaces, starting from the center of the circular nucleation area. The 1 mm/yr 845 interseismic creep-rate contour is indicated by the red curves, gray shading indicates 846 creeping area as defined by the 1 mm/yr contour. From top to bottom of the figure: 847 The earthquake nucleating (at 40-km along strike) on the Rodgers Creek fault 848 propagates along the main fault before it is stopped along strike by the Hayward fault 849 lower-initial-shear-stress region. The earthquake nucleating (at -50-km along strike) 850 on the Northern Calaveras fault propagates over its entire area, then stops. Neither the 851 earthquake nucleating (at -40-km along strike) on the Hayward fault nor the earthquake 852 nucleating (at -110 km along strike) on the Central Calaveras fault is able to propagate, 853 so neither are shown. 854 855 b) Final slip on the fault surfaces, after the ruptures have finished propagating. From 856 top to bottom, nucleation on the Rodgers Creek fault and on the Northern Calaveras 857 fault. 858 859 c) Snapshot of shaking (3D velocity, m/s) at the Earth’s surface, at 15 seconds (left) and 860 30 seconds (right) after nucleation. From top to bottom: the earthquake nucleates on 861 the Rodgers Creek fault, and the Northern Calaveras fault. 862 863

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864 Table 2. Earthquake Scenarios 865 Max Mean Predicted Predicted Locked (L) Slip on Slip on Predicted Max Slip Mean Slip or Co- Rupture Earthquake Rupture Figure Rupture Fault Fault Earthquake on Fault on Fault Nucleation Creeping hesion Length Moment Duration in this Area Trace Trace Moment Trace Trace Sitea (Cr) (Y/N) (km) Magnitude (sec) Paper (km2) (m) (m) Magnitudeb (m)c (m)d RC L No 196 7.42 79 8 2368.1 6.7 4.3 7.57 6.5 3.0 H L No 196 7.39 49 8 2368.1 5.4 3.7 7.57 6.5 3.0 CC L No 196 7.38 74 8 2368.1 5.4 3.5 7.57 6.5 3.0 6.83+7.36= 481.0 3.8 3.3 NC L No 36+196 7.47 90 8 +2368.1 +4.7 +3.3 7.68 6.9 3.2 RC Cr (3 mm/yr) No 192 7.29 101 9 2301.9 4.5 2.8 7.55 6.4 3.0 H Cr (3 mm/yr) No 173 7.24 60 9 2047.4 3.6 2.4 7.48 6.2 2.9 CC Cr (3 mm/yr) No 0 0 0 0 0 0 0 0 NC Cr (3 mm/yr) No 36 6.78 19 9 481.0 3.5 2.8 6.66 2.8 1.3 RC Cr (1 mm/yr) No 105 7.04 57 10 1169.4 3.3 2.5 7.16 5.1 2.4 H Cr (1 mm/yr) No 0 0 0 0 0 0 0 0 0 CC Cr (1 mm/yr) No 0 0 0 0 0 0 0 0 0 NC Cr (1 mm/yr) No 36 6.74 19 10 481.0 3.3 2.3 6.66 2.8 1.3 RC Cr (3 mm/yr) Yes 156 7.19 90 11 1924.3 3.1 1.9 7.45 6.0 2.8 H Cr (3 mm/yr) Yes 79 6.94 42 11 932.8 2.2 1.4 7.03 4.5 2.1 CC Cr (3 mm/yr) Yes 0 0 0 0 0 0 0 0 0 NC Cr (3 mm/yr) Yes 36 6.75 19 11 481.0 2.5 1.8 6.66 2.8 1.3 866 a RC: Rodgers Creek fault, H: Hayward fault, CC: Central Calaveras fault, NC: Northern Calaveras fault 867 b Predicted magnitude using Hanks & Bakun (2008) Magnitude-Log Area Equations: M=logA+3.98 (A≤537km2) and M=4/3logA+3.07 (A>537 km2) 868 c Predicted maximum slip on fault trace (m) using Wesnousky (2008) equation: Maximum Surface Slip (m) = -C + C log Length (km), where C=5.02 869 d Predicted mean slip on fault trace (m) using Wesnousky (2008) equation: Mean Surface Slip (m) = -C + C log Length (km), where C=2.31 870

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871 4 Discussion 872 This paper examines scenario earthquake ruptures on the RC-H-C-NC fault system. We 873 have incorporated information about the fault geometry, geology, friction, and locking conditions 874 of the fault system. We find that simulated large earthquakes may propagate over the entire fault 875 system, or just a part of the fault system. 876 877 Our simulations are physically self-consistent, in that the stresses, friction, material 878 properties, and fault geometry all interact. This is a desirable feature that is in contrast to 879 kinematic rupture simulations that are not, by design, self-consistent. Unlike kinematic rupture 880 simulations we need to make assumptions about how fault friction works, and what the initial 881 stresses are. 882 883 Fault geometry plays a role in our simulation results. An example of the effect of fault 884 geometry is the change in the final slip pattern along strike at the southern end of the connector 885 fault where it meets the Hayward fault (0-km along strike) and at the northern end of the 886 connector fault, where it meets the Rodgers Creek fault (21-km along strike) (Figures 8b, 9b, 887 10b). An important fault geometry aspect of our fault system model is that we include the 888 connector fault segment linking the Hayward fault to the Rodgers Creek fault (Watt et al., 889 2016). As shown by Oglesby (2005) and Lozos et al. (2011) for fault geometry cases in general, 890 linking faults play an important role in determining the feasibility of rupture propagation across 891 fault stepovers. Without the connector, our simulated ruptures that nucleate on the Rodgers 892 Creek fault would have terminated on the Rodgers Creek fault, as a result of a more 893 geometrically segmented fault system (e.g., Schwartz and Sibson, 1989; Manighetti et al., 894 2007; Perrin et al., 2016). Similarly, without the connector, our simulated ruptures that 895 nucleate on the Hayward fault would have been unable to reach the Rodgers Creek fault. This 896 fault geometry detail was discussed in Harris and Day (1993) where it was mentioned that 897 rupture propagation from the Rodgers Creek fault to the Hayward fault (and vice versa) appears 898 possible only if there are connecting fault structures between the two faults. 899 900 Another significant geometrical feature in our model is the manner in which the Northern 901 Calaveras branch fault is connected to the main fault (e.g., DeDontney et al, 2012; Pelties et al., 902 2014; Harris et al., 2018; Douilly et al., 2020). In our finite-element model, the Northern 903 Calaveras branch fault is effectively disconnected from the Hayward portion of the main RC-H- 904 C fault surface by one element. This occurs because in the type of finite-element code that we 905 use, each split-node within the fault surface is constrained to slide along the fault surface, which 906 means that the node’s slip, slip-rate, and slip-acceleration are always tangent to the fault surface 907 (Barall, 2009). At the RC-H-C and NC fault intersection, the two fault surface tangents are 908 incompatible, so we must choose between them. We choose to allow split-nodes at the 909 intersection to slip tangent to the main fault R-H-C fault surface, and disallow slip tangent to the 910 Northern Calaveras fault surface. This effective disconnect between the Northern Calaveras 911 branch fault and the main fault makes it more difficult for rupture to propagate between the 912 Northern Calaveras fault and the main fault. This is evidenced in the 3 mm/yr creeping fault 913 case (Figure 9), where a Northern Calaveras rupture is only able to trigger a small patch on the 914 Hayward portion of the main fault, which is subsequently unable to spontaneously propagate on 915 the main RC-H-C fault. The locked fault case (Figure 8) is the exception. In the locked fault

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916 case, rupture nucleating and spontaneously propagating on the Northern Calaveras branch fault 917 triggers a small rupture on the Hayward portion of the main fault, which subsequently 918 spontaneously propagates along the entire main fault. In the locked fault case, rupture nucleating 919 on the Central Calaveras part of the main fault triggers a patch on the Northern Calaveras fault 920 branch, which is unable to spontaneously propagate on the Northern Calaveras branch. 921 922 To make it easier for the Northern Calaveras fault branch and at least part of the main 923 fault to rupture together, an alternative choice would have been to allow split-nodes at the 924 intersection to slip tangent to the Northern Calaveras fault surface and the portion of the 925 Hayward fault surface lying south of the intersection. However, this would have created an 926 effective gap between the portions of the Hayward fault lying to the south and to the north of the 927 intersection. This would have disagreed with geophysical studies that infer the entire Hayward 928 fault and the Central Calaveras fault to be one fault surface that is fully connected (e.g., Ponce et 929 al., 2004; Simpson et al., 2004; Manaker et al., 2005; Graymer et al., 2007; Hardebeck et 930 al., 2007; Chaussard et al., 2015a). A more realistic approach to the fault geometry might be to 931 include the many small transfer faults that are observed geologically (e.g., Graymer et al., 932 2006), or to assume non-elastic behavior in the vicinity of the fault junction (e.g., DeDontney et 933 al., 2012). 934 935 We have used the slip weakening constitutive formulation for the faults’ frictional 936 strength. This allows us to include interfacial cohesion (e.g., Paterson and Wong, 2005). We 937 now examine the effect of including the constant of cohesion in the upper kilometers of the 938 faults, because this is frequently done by dynamic rupture modelers to suppress large amplitude 939 slip and slip rates and supershear rupture at the Earth’s surface. We find that when we include 2 940 MPa of cohesion from the Earth’s surface with a taper down to zero cohesion at 3-km depth, 941 rupture propagation is affected, the resulting earthquake magnitudes are reduced, and the ground 942 shaking is reduced compared to simulations that do not include cohesion. Figure 11 shows the 943 results of including cohesion in our 3 mm/yr (lower initial shear stress) simulations, and these 944 results can be compared with those from Figure 9 that presents results without cohesion. The 945 cohesion particularly affects our earthquake simulation that nucleates on the Hayward fault, with 946 the resulting rupture length reduced from 173 km to 79 km, and the resulting earthquake 947 magnitude reduced by 0.3, from M7.24 to M6.94 (Table 2). When including the cohesion, the 948 earthquake nucleating on the Rodgers Creek fault shortens by about 36 km, and its magnitude is 949 reduced by about 0.1, whereas the Northern Calaveras simulated earthquake rupture is less 950 affected by whether or not cohesion is included. These earthquake-magnitude reductions 951 primarily occur because the combination of our reduced initial shear stress at the locations of 952 fault creep and the cohesion in the upper kilometers of the faults act in tandem to suppress the 953 rupture propagation along-strike. Therefore, although the primary simulation results that we 954 present in our paper (Figures 8-10) do not include cohesion, more discussion about whether or 955 not to include it might be warranted. The answer also ties to ongoing discussions about how best 956 to forecast values of coseismic fault slip at Earth’s surface, particularly in creeping fault regions 957 (e.g., Aagaard et al., 2012). 958

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959 11a) Rupture Front Contours in 0.5 second intervals 960 961

962 963 964 965

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966 11b) Final Slip (m) 967

968 969 970

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971 11c) Shaking (3D Velocity in m/s) at Earth’s Surface 972

973 974 975

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976 Figure 11. Creeping fault scenario earthquakes that use the 3 mm/yr interseismic 977 creep-rate contour (Figure 7) to define the creeping region, and thereby the lower 978 initial-shear stress region, and also use interfacial cohesion, tapered from 2 MPa at the 979 Earth’s surface down to 0 MPa at 3-km depth. Compare this figure to Figure 9 that 980 does not use cohesion. 981 982 a) Contours of the earthquake ruptures’ progress, in 0.5 second intervals on the fault 983 surfaces, starting from the center of the circular nucleation area. The 3 mm/yr 984 interseismic creep-rate contour is indicated by the red curves, gray shading indicates 985 creeping area as defined by the 3 mm/yr contour. From top to bottom: The earthquake 986 nucleating (at 40-km along strike) on the Rodgers Creek fault, the earthquake 987 nucleating (at -40-km along strike) on the Hayward fault, and the earthquake 988 nucleating (at -50-km along strike) on the Northern Calaveras fault. The earthquake 989 nucleating on the Northern Calaveras fault is least affected by the cohesion. The 990 earthquake nucleating on the Central Calaveras (at -110 km) fault is unable to 991 propagate beyond the nucleation area, so it is not shown. 992 993 b) Final slip on the fault surfaces, after the ruptures have finished propagating. From 994 top to bottom, nucleation on the Rodgers Creek fault, on the Hayward fault, and on the 995 Northern Calaveras fault. The earthquake nucleating on the Northern Calaveras fault 996 also triggers a small amount of slip on the main fault. 997 998 c) Snapshot of shaking (3D velocity, m/s) at the Earth’s surface, at 15 seconds (left) 999 and 30 seconds (right) after nucleation. From top to bottom: The earthquake 1000 nucleates on the Rodgers Creek fault, on the Hayward fault, and on the Northern 1001 Calaveras fault. 1002 1003 1004 1005

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1006 Aside from the decision about whether or not to include cohesion (Figure 11) in our 1007 simulations, variations in friction coefficients appear to play a role in affecting our results. The 1008 results differ between dynamic rupture simulations assuming the same coefficients of friction for 1009 all of the fault surfaces, and dynamic rupture simulations assuming that the gabbro and 1010 serpentinite have different friction coefficients (Figure 12). An important caveat is that we 1011 assumed slip-weakening friction is adequate for simulating the coseismic behavior of both the 1012 interseismically creeping portions of the fault system and the interseismically locked portions of 1013 the fault system, as was done for a coseismic study of the creeping Bartlett Springs fault farther 1014 north in California (Lozos et al., 2015). If we had instead had simulated both the coseismic 1015 period and the postseismic period (e.g., Lozos and Funning, 2020), or if we had simulated full 1016 seismic cycles that include coseismic, postseismic and interseismic periods (e.g., Lapusta et al., 1017 2000; Kaneko et al., 2010; Erickson et al., 2020; Liu et al., 2020), then slip-weakening is 1018 likely inadequate, and as was done for those other studies, we too would have needed to 1019 implement another friction formulation, such as rate-dependent friction. 1020 1021 Using slip-weakening friction for our coseismic rupture simulations, we have accounted 1022 for the behavior of the creeping portions of the fault surfaces by assuming that they have already 1023 expended some of their tectonic strain by slipping during the interseismic period. How creeping 1024 faults act during an earthquake is, however, still a topic of scientific discussion (e.g., Harris, 1025 2017; Chen and Burgmann, 2017). Well-recorded evidence to date, from events such as the 1026 M6 earthquakes on the creeping section of the San Andreas fault at Parkfield (e.g., Bakun et al., 1027 2005; Murray and Langbein, 2006), and from large earthquakes in settings such as the 1028 Longitudinal Valley fault in Taiwan (e.g., Chen et al., 2008; Thomas et al., 2014), show that 1029 fast-creeping fault regions may sometimes control along-fault earthquake rupture, depending on 1030 where the earthquake nucleates. For the Longitudinal Valley fault, Thomas et al. (2014) 1031 proposed that the presence of the clay-rich Lichi Mélange affected the along-strike and along-dip 1032 rupture extent of the 2003 Mw6.8 Chengkung earthquake. 1033 1034 Alternatively, some have hypothesized that mechanisms such as thermal pressurization 1035 dominate during earthquake rupture, and that coseismic propagation through fast-creeping 1036 regions is quite feasible (e.g., Noda and Lapusta, 2013). Based on their laboratory 1037 observations, McLaskey and Yamashita (2017) have proposed that slowly creeping fault 1038 patches can quickly transition to earthquake production, if the stressing rate is suddenly 1039 increased. They suggest that this earthquake production becomes feasible because the increased 1040 stressing rate on the fault patches acts to decrease the minimum required earthquake nucleation- 1041 patch size. 1042 1043 Our simulations assume elastic deformation, and aside from accounting for the rock types 1044 and creeping versus locked patches, we have assumed that the initial shear and normal stresses 1045 are uniform along strike and dip. Another approach for assigning the initial shear and normal 1046 stresses on the fault surfaces could involve resolving a regional stress field onto the 3D geometry 1047 of the RC-H-C-NC fault system. However, this has been shown from past experience (e.g., 1048 Oglesby et al., 2014) to rarely result in stress conditions that lead to reasonable simulated 1049 earthquake ruptures, especially for cases such as ours with complex fault geometry. Most 1050 sophisticated simulations that replicate the dynamic rupture details of past earthquakes (e.g., 1051 Wollherr et al., 2018; Ulrich et al., 2019) implement initial stresses that have been altered from

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1052 a pure regional stress field. And, given that ours are scenario large-earthquake simulations, 1053 rather than an effort to match well-recorded large earthquakes that have already occurred, we 1054 cannot know in advance which complicated initial stress conditions might be most appropriate. 1055 Similarly, although there is abundant information from stress-drop studies of many smaller 1056 earthquakes in this region (e.g., Hardebeck and Aron, 2009; Taira et al., 2015), it has been 1057 shown that smaller earthquakes are not an indicator of larger earthquake stress-behavior 1058 (Hardebeck, 2020). We therefore chose to avoid these complications by starting with 1059 independently derived simple values for the initial shear and normal stresses (Table 1). 1060 1061 Our dynamic rupture simulations all included the 3D geology, and thereby the 3D rock 1062 properties (Figure 4). To examine the effect of our 3D rock properties assumptions, we compare 1063 simulations that incorporate a 1D velocity and density structure with those that incorporate a 3D 1064 velocity and density structure. For our 1D structure (Figure 12a), we use the depth-dependent 1065 rock properties of one of the common rock units in our 3D geologic model, KJfN (Figure 4). We 1066 incorporate the same velocity and density cutoffs in our 1D structure as are used in our 3D 1067 structure. An advantage of comparing results using 3D versus 1D structures is that this also 1068 permits a look at how along-strike versus along-dip rock property changes affect the results. 1069 With the 3D structure, there appears to be an inverse relationship between the varying shear 1070 modulus near the Earth’s surface and the amount of slip near the Earth’s surface. This along- 1071 strike variability is not as strong in the simulations that assume a 1D structure (Figure 12). As 1072 another example, one might consider a potential bimaterial effect (e.g., Harris and Day, 2005) 1073 where the San Leandro gabbro abuts lower shear modulus rocks at depth across the Hayward 1074 fault, a feature that is only present in our 3D rock property structure. The result is that a change 1075 from using a 1D to a 3D rock property structure does affect the rupture pattern, final slip pattern, 1076 and on-fault slip-rates (Figure 12), but it would be difficult to attribute this difference as being 1077 primarily due to a bimaterial effect, rather than being due to the variety of along-strike and 1078 along-dip rock properties in our geologic model. 1079 1080 We find that the 3D velocity structure adds complexity that is not seen for simulations 1081 conducted with a one-dimensional velocity structure. A comparison of the velocity structure 1082 near the Earth’s surface (e.g., Figure 4d) with the final slip patterns, particularly for earthquakes 1083 nucleating on the Rodgers Creek fault, shows that the velocity structure does affect the results. 1084 Due to computational constraints, although we did incorporate considerable 3D velocity structure 1085 complexity, we were unable to include the lowest velocities near the Earth’s surface. Rodgers et 1086 al. (2019) performed kinematic rupture simulations rather than the physics-based dynamic 1087 rupture simulation method that we used. The computational efficiency of their kinematic rupture 1088 simulations permitted them to include the lower velocities in the region’s 3D velocity structure, 1089 and Rodgers et al. (2019) showed that these lower velocities did make a difference for their 1090 ground shaking simulations, particularly in low-velocity basin structures. When more 1091 computational power becomes available, a future dynamic rupture project could include these 1092 lower velocity features in conjunction with the long fault system that we examined. In the 1093 meantime, the 3D velocity structure that we were able to use demonstrates that the dynamic 1094 rupture propagation is affected by this rock property. 1095 1096 Factors that make even more of a difference to our dynamic rupture results than assuming 1097 a 3D versus 1D rock property structure, or variable slip-weakening friction coefficients

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1098 depending on rock type, are the pattern of locked (higher initial shear stress) versus creeping 1099 (lower initial shear stress) fault surface patches, and whether or not cohesion is incorporated in 1100 the models. Some of our simulated ruptures are unable to propagate beyond their nucleation 1101 areas if features such as creeping patches (lower initial shear stress regions) or cohesion are 1102 included. Figures 9-11 show the effects of including some combinations of these different 1103 features, relative to the locked fault cases (Figure 8) that include neither creeping patches nor 1104 cohesion. Omitted plots in Figures 9-11 indicate that although those simulated ruptures were 1105 nucleated, they were unable to spontaneously propagate. These include the cases of nucleation 1106 on the Central Calaveras fault, where the transition to spontaneous rupture propagation and 1107 thereby, earthquakes much larger than magnitude 6, is unable to occur if the feature of creeping 1108 patches (lower initial shear stress regions) is included in our simulations. Similarly, nucleation 1109 on the Hayward fault is unable to transition beyond the nucleation region into spontaneous 1110 rupture propagation, if the larger creeping region defined by the 1 mm/yr interseismic creep rate 1111 contour is considered (Figures 7 and 10). 1112 1113 In contrast to the Central Calaveras fault nucleation site and the Hayward fault nucleation 1114 site, earthquakes nucleating on the Northern Calaveras fault are less affected by its creeping 1115 patches (lower initial shear stress regions) and by cohesion. This is likely due to the Northern 1116 Calaveras fault extending deeper than the other faults (Table 1), so that the creeping patch does 1117 not cover as much of the Northern Calaveras fault’s surface area (Figure 7). Ruptures 1118 nucleating on the Northern Calaveras fault primarily remain confined to the Northern Calaveras 1119 fault with only a small dynamic triggering of the main fault. As mentioned earlier, it is only in 1120 the locked fault case (Figure 8) that rupture on the Northern Calaveras fault is able to 1121 dynamically trigger and then spontaneously propagate along the main Central Calaveras- 1122 Hayward-Rodgers Creek main fault surface. 1123 1124 Dynamic ruptures nucleating on the Rodgers Creek fault transition to spontaneous 1125 rupture propagation and produce sizeable earthquakes for all the tests that we performed. The 1126 rupture length, final slip, and slip-rates do vary, depending on the included features (Figure 12). 1127 An important assumption for our simulations of the Rodgers Creek fault is that it is primarily 1128 locked from southeast of Santa Rosa to the connector fault segment. Due to computational 1129 limits, we truncated the Rodgers Creek fault at Santa Rosa. The fault does however continue 1130 farther north, and exhibits considerable creep in this northern extent (e.g., Jin and Funning, 1131 2017). Future simulations of dynamic earthquake rupture on the Rodgers Creek fault could 1132 include these additional portions of the fault, and also consider the possibility of rupture 1133 nucleating near Santa Rosa (Hecker et al., 2016). 1134

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1135 1136 12a) 1D velocity and density structure for rock unit KJfN 1137

1138

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1139 12b) Rupture Front Contours in 0.5 second intervals 1140 1141

1142 1143

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1144 12c) Final Slip 1145

1146

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1147 12d) Horizontal slip-rate (m/s) at on-fault stations 1148 1149

1150 1151

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1152 Figure 12. Comparisons among results that implement a 3D versus 1D velocity and 1153 density structure, results that implement uniform slip-weakening friction coefficients and 1154 results that implement interfacial cohesion, for both locked and 3 mm/yr creeping models. 1155 The 1D structure uses the same parameters as are used for rock unit KJfN in our 3D rock 1156 property structure. The uniform friction coefficients assume dynamic and static values of 1157 0.5 and 0.6, respectively. All eight dynamic rupture simulations nucleate at 40-km along 1158 strike on the Rodgers Creek fault. 1159 1160 a) The 1D velocity and density structure for rock unit KJfN are used for our 1D model. As 1161 for the 3D structure, the shear wave velocity cutoff is 1.95 km/s. The density for this rock 1162 unit always exceeds 2.55 g/cm3, so no density cutoff is needed. 1163 1164 b) Contours of the dynamic earthquake rupture fronts’ progress, in 0.5 second intervals on 1165 the fault surfaces, starting from the center of the circular nucleation area on the Rodgers 1166 Creek fault, for each of the eight dynamic rupture simulations. 1167 1168 c) Final slip patterns for each of the eight dynamic rupture simulations. 1169 1170 d) Horizontal slip-rate versus time (lowpass filtered at 1 Hz) produced by each of the eight 1171 simulations, at on-fault stations (shown by the stars in the inset) 30, 10, -10, -30, -50, -70, 1172 -90, -110, -130 km along strike, at 0 km depth (left column), and at 7 km depth (right 1173 column). 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183

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1184 One aspect of dynamic rupture simulations that we briefly discussed in the context of 1185 geometrical fault junctions, is the inclusion of non-elastic rock response. To avoid requiring 1186 assumptions about the entire 3D initial stress field for our model, our simulations have assumed 1187 that the rock response is purely elastic. This meant that we just needed to choose the initial shear 1188 and normal stresses on the fault surfaces themselves. Inelastic deformation can, however, play 1189 an important role in earthquake behavior, and some authors have calculated that off-fault damage 1190 generated during a propagating earthquake rupture can perturb the energy balance, ground 1191 motion, and even rupture path, compared to calculations done in a perfectly elastic medium (e.g., 1192 Andrews, 2005; Duan, 2008; Ma, 2008, Templeton et al., 2008; Gabriel et al., 2013; 1193 Wollherr et al., 2018). We leave this topic of including inelastic deformation in our four-fault 1194 system for future investigations. 1195 1196 Lastly, we have presented simulations of large earthquakes on a simplified and truncated 1197 geometry of the Rodgers Creek-Hayward-Calaveras-Northern Calaveras fault system. There are 1198 other nearby faults (e.g., Graymer et al., 2006) that have the potential to participate in large 1199 earthquakes in this region. How and when this occurs is an important issue for understanding the 1200 likelihood of multi-fault earthquake rupture and the resulting ground shaking. We leave these 1201 points for future investigations when more data become available.

1202 5 Conclusions 1203 We have conducted 3D spontaneous rupture simulations of large earthquakes nucleating 1204 in four locations on the Rodgers Creek- Hayward-Calaveras-Northern Calaveras fault system. 1205 Our simulations model this geometrically complex fault system set in a 3D rock structure that 1206 bounds and surrounds the faults. We have incorporated the on-fault interseismic creep-rate 1207 information for the fault system and examined how different patterns of lowered initial shear 1208 stress due to the creeping parts of the faults might affect propagating earthquake ruptures. 1209 Depending on where the earthquakes nucleate, the location of fault creep and thus the location of 1210 lower initial shear stress plays an important role in controlling the resulting ruptures. We have 1211 also incorporated field and laboratory information about rock friction for our simulations. We 1212 find that large earthquakes nucleating on the Rodgers Creek fault may propagate long distances, 1213 if, as inferred by others, the Rodgers Creek and Hayward faults are connected beneath San Pablo 1214 Bay, and if these faults are not fully relieving their tectonic strain through interseismic fault 1215 creep. We find that simulated earthquakes nucleating on the Northern Calaveras fault may 1216 remain confined to the Northern Calaveras if this fault is not well connected to the Hayward and 1217 Central Calaveras faults. Simulated earthquakes nucleating on the Central Calaveras fault appear 1218 to remain on the Central Calaveras fault, if the creeping fault portions play a dominant role in 1219 confining earthquakes on this fault. Simulated Hayward fault earthquakes present multiple 1220 possibilities. These include the situation where rupture is able to propagate over the entire fault 1221 length, and continue propagating along the connector fault to the Rodgers Creek fault in the 1222 north and to part of the Central Calaveras fault to the south, before stopping. Additional 1223 simulated Hayward fault earthquake possibilities for the same nucleation site adopt cohesion in 1224 the upper reaches of the faults or larger creeping areas on the faults, in which case simulated 1225 Hayward rupture either produces a large earthquake or is unable to propagate a meaningful 1226 distance, respectively. Our simulations serve as a reminder that there is still much to learn about 1227 how coseismic fault friction works for both locked-fault and creeping-fault settings, and that

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1228 more information about the nature of faults, rocks, and stress at depth in the Earth’s crust will 1229 help us move forward.

1230

1231 Acknowledgments 1232 The fault surfaces’ modeled geometries and on-fault creep rate patterns are provided in the 1233 supplement. The finite element dynamic rupture code is available on request from coauthor 1234 Barall. 1235 Google Earth was used to create the base layer for the movies. The topographic data in the 1236 Google Earth file were from California State University Monterey Bay, the California Ocean 1237 Protection Council, Monterey Bay Aquarium Research Institute, Scripps Institution of 1238 Oceanography, the National Oceanic and Atmospheric Administration, the U.S. Navy, the 1239 National Geospatial-Intelligence Agency, and the General Bathymetric Chart of the Oceans. The 1240 images were from Landsat and Copernicus. 1241 This research project was originally inspired by thoughtful science suggestions from Art 1242 McGarr, and earlier versions of this work greatly benefited from the contributions and ideas of 1243 Bob Simpson. Thank you to Luke Blair for creating Figure 1. Thank you to Jim Lienkaemper, 1244 John Langbein, and Jeanne Hardebeck for constructive and insightful comments on early 1245 versions of this manuscript, to Roland Burgmann for helpful insights about Hayward fault 1246 behavior, and to (in alphabetical order) Brad Aagaard, Ralph Archuleta, Nick Beeler, Mike 1247 Blanpied, Jack Boatwright, Tom Brocher, Roland Burgmann, Estelle Chaussard, Eric Daub, 1248 Steve Day, Jeanne Hardebeck, Steve Hickman, Bob Jachens, John Langbein, Jim Lienkaemper, 1249 Robert McFaul, Andy Michael, Carolyn Morrow, Jessica Murray, Geoff Phelps, David 1250 Schwartz, Bill Stuart, and Janet Watt for educational conversations about this work over the 1251 years. Thank you to Evan Hirakawa, Jessica Murray, Keith Knudsen, Suzanne Hecker, and 1252 Mike Diggles for thoughtful USGS internal reviews of the manuscript, and to Isabelle 1253 Manighetti, Sylvain Barbot, Martijn van den Ende, and two anonymous reviewers for thoughtful 1254 JGR journal reviews. Partial funding for this project was provided by Pacific Gas and Electric 1255 Company through the USGS-PGE CRADA. 1256 Any use of trade, firm, or product names is for descriptive purposes only and does not imply 1257 endorsement by the U.S. Government.

1258

1259 References 1260 Aagaard, B. T., Lienkaemper, J. J., & Schwartz, D. P. (2012). Probabilistic estimates of surface 1261 coseismic slip and afterslip for Hayward fault earthquakes, Bull. Seism. Soc. Am., 103(3), 961- 1262 979, doi:10.1785/0120110200. 1263 1264 Aagaard, B. T., Blair, J. L., Boatwright, J., Garcia, S. H., Harris, R. A., Michael, A. J., Schwartz, 1265 D. P., & DiLeo, J. S. (Edited by Jacques, K., & C. Donlin, C.) (2016). Earthquake outlook for 1266 the San Francisco Bay region 2014-2043, U.S. Geological Survey Fact Sheet 2016-3020, 1267 doi:10.3133/fs20163020. 1268

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