SI: Wastewater disposal and earthquake swarm activity at the southern end of the Central Valley, California

T. H. W. Goebel1*, S. M. Hosseini2, F. Cappa3,4, E. Hauksson1, J. P. Ampuero1, F. Aminzadeh2, and J. B. Saleeby1

1Division of Geological and Planetary Sciences, CA Institute of Technology, 91125 Pasadena, CA, USA. 2Department of Chemical Engineering and Material Sciences, University of Southern CA, 90089 Los Angeles, CA, USA. 3Geoazur Laboratory, University of Nice Sophia-Antipolis, Nice, France. 4Institut Universitaire de France, Paris, France *now at University of California, Santa Cruz

Contents

1 Tectonic setting at the southern end of the Central Valley 4

2 Geologic structures involved in rupture and fluid migration processes 6

3 FMD, b-value and confidence interval 10

4 Earthquake cluster relocation 11

5 Additional earthquake detection using the template matching method 13

6 Moment tensor inversion and moment magnitudes 20

1 7 Hydrogeological model of fluid injection induced fluid pressure pertur- bations 25

7.1 Intro: Crustal permeability structure close to injection well WD05 . . 25 7.2 Theoretical background ...... 26 7.3 Sensitivity analysis of permeability and fault zone width ...... 29

2 Additional Supporting Information (Files uploaded separately)

File Name Description data.zip Seismicity catalogs and injection rates in well WD01, WD04 & WD05 WF_new.zip Waveform plots of newly detected events and tem- plates modelResults.zip Results and initial conditions of pore-pressure mod- eling WWF_2D_v2.gif 2D animation of WWF swarm epicenter locations WWF_3D_v1.gif 3D animation of WWF swarm hypocenter locations

3 1 1 Tectonic setting at the southern end of the Central

2 Valley

3 In order to elucidate the complex structure in the area of the injection well and

4 to discuss the plausible fluid pathways that could induce seismicity, we present a

5 simplified fault map of the Tejon area (Figure 1), and generalized cross sections that

6 show fault depth relations and fault inter-relationships (Figure 2). Figure 2 shows

7 the position of the injection well above the approximate surface traces of buried,

8 Early-Miocene, normal faults. A comparison of Figure 2 with the seismicity map in

9 the main text (Figure 1a) shows a band of background seismicity along one of the

10 principal buried normal faults, which along with geomorphic observations along

11 the Tehachapi foothills where the fault is observed at basement levels, indicates

20 12 Holocene fault-remobilization (J.B. Saleeby, unpub. mapping). Recognizing the

13 dominate north-south directed thrust or reverse sense to the Mw4.6 mainshock, we

14 show in Figure 2 a south-north cross section that crosses the mainshock focal point

10,11,15 15 (synthesized from ; and J.B. Saleeby, unpub. mapping). The focal point of the

16 Mw4.6 mainshock is deep within the footwall domains of the Pleito and Wheeler

17 Ridge north-directed thrust faults, but lies within the depth projected White Wolf

18 fault zone. On the south-north cross section we also denote the focal point of the

19 north-directed reverse dominated 1952, Mw7.3 Kern County earthquake, which

20 also lies along the depth projected White Wolf fault, at 19 km depth. These rela-

21 tions lead us to hypothesize that the Mw4.6 mainshock is associated with the White

22 Wolf fault.

4 119.2°W 119.1°W 119.0°W 118.9°W 118.8°W 118.7°W 118.6°W 35.2°N

35.1°N

35.0°N

34.9°N

34.8°N

Figure 1: Generalized fault map for Tejon area showing approximate surface traces of an active blind thrust and several reverse faults, buried early Miocene normal faults, and ar- eas where faults are exposed in adjacent exhumed basement (sources:6,14,20,21, J.B. Saleeby, unpub. mapping. Final drafting by Z.A. Saleeby.)

23 The principal basement structure of the White Wolf fault formed in the Late

24 Cretaceous in continuity with the early-phases of the Breckenridge-Kern Canyon

6 25 system to the north . Tens of kilometers of spatially varying oblique slip on the in-

26 tegrated system led to severe basement damage zones, numerous subsidiary fault

31 27 breaks, and rapid differential basement exhumation of up to ∼15 km . The typi-

28 cal width of the ductile to brittle basement damage zone, where exposed, is shown

29 on the south-north cross section in Figure 2 . From Early-Miocene to Early-Pliocene

30 the White Wolf segment of the system functioned primarily as a north-down nor-

10,11,33 31 mal fault , resulting in its profound north wall sediment accommodation

32 space (Figure 2, south-north cross section). With the late Pliocene-Quaternary

5 33 growth of the Tehachapi-San Emigdio fold thrust belt the White Wolf zone has

8,15 34 inverted along much of its length to a north-directed reverse/thrust zone .

35 2 Geologic structures involved in rupture and fluid mi-

36 gration processes

37 Several plausible tectonic structures exist that could be associated with the Mw4.6

38 mainshock such as: 1) Rupture processes along a Riedel shear within the principal

39 basement damage zone; 2) slip near the intersection of a hypothetical blind thrust

40 fault zone, suggested by Davis and Lagoe, (1988) and Gordon & Gerke (2009), and

41 approximated in depth as the hypothetical blind thrust on the Figure 2 south-north

42 cross section; or 3) slip along a zone of stress concentration at the basement surface

43 footwall cut-off of the White Wolf fault (Figure 2 south-north cross section).

44 Potential fluid migration paths from the injection wells into the White Wolf

1 45 fault zone can be visualized by projecting the structure of the Figure 2 west-east

46 cross section northwestward onto the fault zone. Most notable are remobilized

47 Early-Miocene normal faults. Fault damage zone permeability and hanging wall

48 brecciation provide potential direct fluid pathways.

49 Our geologic model is supplemented by detailed reservoir models based on

50 standard petroleum industry data such as seismic profiles and well log data, avail-

3,4 51 able from the CA Division of Oil, Gas and Geothermal Resources (DOGGR) . The

1In Figure 2 , we included an uncertainty ellipse for the injection position shown on the west-east cross section. The uncertainty is derived from: 1) Geological uncertainty in subsurface stratigraphic position resulting from having only a mud log, and no supporting electric log nor core data for the injection well; 2) Rapid south to north facies changes in the Neogene section from the basin margin to interior 10,14,20; 3) Northwards projection of the structure across relatively small offset NE–SW trending normal faults that are transverse to the principal NW–SE trending normal faults that the projection follows; and 4) The effect of the ∼ 1500 m long NNW trending horizontal well segment for which fluids are incrementally injected over the last ∼ 520 m.

6 S N Tehachapi W-E section - San Emigdio . Wheeler foothills flt San Joaquin Basin 1 Pleito Ridge 1 km MSL MSL ? -1 -1 n -2 -2 Ridge flt. -3 Wheeler -3

-4 sedimentatio -4

Quaternary alluvium -5 Base of Pleistocene Tulare Fm. -5 fault

Base of up. Pliocene San Joaquin Fm. -6 Base of up. Miocene Santa Margarita Fm. White -6 Base of up. Miocene Monterey Fm. Wolf growth

-7 -7 Base of lw. Miocene Tunis-Tecuya volcanics (Tv) fault Basement ? approx. depth of Tv -8 -8 Pre-Cenozoic White Wolf Hypothetical normal isochronous surface fault damage zone -9 Blind Thrust M 4.7 -9 ? ? -10 1952 M 7.3 -10 reverse event -11 at 16 km depth 0 1 2 3 km -11 0 1 2 mi -12 -12 km W S-N sectio n E 1 injection well projected ~6 km 1 km northward along normal fault strike

MSL MSL

uncertainty on -1 injection position N - plunging turbiditic -1 Holocene sand lenses in “Monterey” remobilization -2 -2

Lw. Miocene Tunis -3 normal growth volcanics -3 faults

-4 -4

-5 0 1 2 3 km -5

0 1 2 mi -6 -6 km

Figure 2: Simplified south to north, and west to east geologic cross sections for area of injection well and hypothesized induced seismicity. Locations given in Figure 1. Selected stratigraphic horizons are shown as structural form lines. Sources given in Supplementary text. Final drafting by Z.A. Saleeby.

7 52 industry data highlights many fracture and fault zones located between injection

53 site and the White Wolf fault (Figure 3). The WNW orientation of these faults is in

54 agreement with a linear feature in the seismicity catalog highlighting that at least

55 one of these faults is seismically active. This fault is referred to as ’Tejon fault’ in

56 the main text. The seismicity catalog indicates that the Tejon fault deepens toward

57 the White Wolf fault which is also seen within some of the interpreted well-logs

4 58 that extent to 3.7 km depth . The closest fault zones identified in the DOGGR data

59 is located less than 0.5 km from injection site WD05. Thus, these faults likely in-

60 fluenced the nearby permeability structure and fluid flow path ways of injected

61 wastewater.

8 M4.7 White Wolf Fault

Tejon, North

Pleito Fault

White Wolf Fault

Fault and Fracture Zones

0 1

WD05

Figure 3: Mapped faults and fractures within the Tejon, North oilfield. The top plot shows the approximate boundaries of the oil field (blue region) and earthquake locations. Seis- micity likely associated with the Tejon fault is highlighted in black and background seis- micity in gray. The bottom plot shows the more detailed oilfield boundaries (gray shaded area) based on a DOGGR technical report3. Faults and fracture zones were identified based on industry data such as seismic profiles, geological mapping and well logs (Modified af- ter California Division of Oil, Gas & Geothermal Resources, Technical Report3). The dis- played seismicity was predominantly recorded before the 2005 swarm and highlights the approximately linear trend of the Tejon fault which connects the injection site and largest magnitude epicenter. 9 62 3 FMD, b-value and confidence interval

63 Frequency-magnitude distributions (FMD) of earthquakes within the study area

64 generally followed a power-law of the form:

65 log N = a − b · M (1)

66 where b is the power-law exponent, N and M are the event number and magnitude

17 67 and a is a constant related to the overall seismic productivity within the area . To

1,39 68 compute b-values, we used the maximum likelihood approach .

1 69 b = log(e) (2) M − Mc

39 70 where Mc is the magnitude of completeness, corrected for bin-size and M is the

71 mean magnitude of events above Mc. The lower power-law bound, Mc, was de-

72 termined by minimizing the Kolmogorov-Smirnoff distance between the observed

7 73 and modeled power-law distributions . We compared the observed FMD with ex-

13 74 pectations for FMDs with a b-value of unity using Monte Carlo simulations . The

75 corresponding confidence limits as function of magnitude are reported as the 2.5

76 and 97.5 percentiles of 1,000 randomly sampled FMDs with the same parameters

77 (a, b, Mc) as the observed distribution.

78 In the main manuscript, we show that b-values show significant variations that

79 coincide with peak injection rates in well WD05. b-values are close to unity be-

80 fore and after peak injection but reach values as low as b=0.6 during the highest

81 injection rates in 2005. In addition, we investigate long-term temporal variations

82 in b-value within a 10 km radius of well WD05 between 1995 and 2011 (Figure 4).

83 b-values show strong variations between 0.6 and 1.4. We observed a systematic

10 84 decrease in b starting in 2004 which is when one of the high-rate injection wells

85 became active. This first order correlation between injection rates and temporal

86 b-value variations may indicate a connection between pressure changes and the

87 tendency of earthquakes to grow to larger sizes resulting in lower b-values. How-

88 ever, variations in b-value should be interpreted carefully because of the inherent

89 uncertainties in estimating power-law exponents over a limited number of decades

90 and from seismicity records with changing magnitude of completeness over time.

91 Moreover, a precise correlation between b-value variations and other time-series,

92 e.g. injection rates, is complicated by different temporal resolutions. Thus, the

93 most robust features within our data are generally low b-values during the time of

94 peak injection rates.

95 4 Earthquake cluster relocation

96 In addition to the standard single event locations within the Southern California

97 Seismic Network (SCSN) earthquake catalog, we use a state-of-the-art waveform-

19 98 relocated catalog . The relocated catalog is based on a detailed, 3D velocity model

99 and precise, travel-time differences determined by waveform cross-correlations of

26,36 100 earthquakes within clusters .

101 The relocated seismicity catalog highlights that most of the earthquakes that

102 occurred during the time of peak injection in WD05 occurred at depths between

103 the injection site and the Mw4.6 hypocenter (Figure 5). The seismic activity that

104 deepened toward the White-Wolf fault was likely a key component in maintaining

105 a high-permeability pathway that transmitted pressure changes to large depths.

11 800

700

01 + 04 + 05 WD05

Figure 4: Temporal b-value variations within a 10 km radius around well WD05 and injec- tion rates in wells WD01, WD04 and WD05.

12 0

5

10

15 Depth [km]

20

25 0 10 20 30 40 50 60 70 Number of Earthquakes

Figure 5: Focal depth distributions of events within a 10 km radius of well WD05 between 04/2005 to 09/2005. The red star highlights the focal depth of the Mw4.6 hypocenter.

106 5 Additional earthquake detection using the template

107 matching method

108 We extend the available earthquake catalog by cross-correlating event template

109 waveforms with the continuous waveform record. The waveform templates are

110 created from the earthquake record within the SCSN catalog. We use event wave-

111 forms as templates that were recorded at the closest station with high signal-to-

112 noise ratio, i.e. station MPI. For this study, we selected 14 template event wave-

113 forms with magnitudes between 0.6 and 1.8, which occurred within a ten kilome-

114 ter radius of well WD05 and were recorded and produced high-quality template

115 waveforms on all three components at station MPI. This station was installed in

116 2001. Our implementation of the template-matching method largely follows Meng

30 117 et al., (2013) and consists of 4 main steps:

118 1. Template selection and processing: We down-sample all waveforms to 20 Hz

119 to match the continuous, broadband waveform record which is available af-

120 ter June 2005 and bandpass-filter all waveforms between 5 to 10 Hz. This fre-

13 121 quency band is generally above the largest, coherent noise sources, providing

122 the most stable results for event detection. After bandpass-filtering, the tem-

123 plate waveforms are cut from 1 s before to 3 s after P-arrival on the vertical

124 component. Waveforms on the radial components are selected between 2 s

125 before and after the S-phase arrivals accounting for larger uncertainties in

126 phase picks.

127 2. Cross-correlation: The template waveforms are then cross-correlated with

128 the continuous waveform record between June 30th 2005 until the mainshock

129 occurrence on September 22nd 2005. Cross-correlation coefficients (CC) be-

130 tween templates and continuous waveforms are computed for a 4 sec sliding

131 window that is advanced by one sample steps for all three traces.

132 3. Event detection: An event detection is declared if the individual and stacked

133 cross-correlation coefficients exceed a certain threshold. For the present ap-

134 plication, we chose a conservative CC threshold to minimize false detection.

135 We tested different CC thresholds and find that a factor of 7 times the stan-

136 dard deviation provides the best results.

137 4. Earthquake-catalog creation: For the newly-detected events, we use the times

138 of highest correlation coefficients as origin times and adopt the locations and

139 magnitudes of the template events for the new event.

140 We test our implementation of the template matching method by first evaluating

141 its ability to ’self-detect’ events within the earthquake catalog that were recorded

142 between June 2001 and October 2005. Expectedly, the corresponding correlation-

143 coefficients (CC) across all traces are close to unity for these events (Figure 6).

144 We minimize false-detection by requiring relatively high CC values that are at

145 least 7 times larger than the standard deviation of noise correlations. In addition,

14 Figure 6: Example of waveform cross-correlations for a test-run of the template matching algorithm to ’self-detect’ a catalog event. Top: Template (blue) and continuous seismo- grams (gray) for the vertical, and the two horizontal components. CC values are shown in upper left corner of each subplot. Bottom Left: Time series of different CC values (black), detection threshold (red line) and event detection (red dot). Bottom Right: Histogram of CC values (black), detection threshold (red line) and event detection (red dot)

146 we test if S-P times and event durations are in approximate agreement between

147 template and newly detected events for each of the 21 new detection. Lastly, we

148 check if the first motion polarities agree between templates and new detection. Fig-

149 ure 8 to 10 show three examples of successfully detected events including wave-

150 form records and CC values. The waveform plots for the other detected events are

151 part of the Online Supplement.

152 Seven of the 14 template waveforms were connected to additional seismic event

153 detection resulting in a total of 21 additional event detection between the start of

154 injection in well WD05 and the occurrence the mainshock (Figure 7).

15 Newly Detected Events Template Locaon

MPI

Figure 7: Map-view of template (blue dots and waveforms) and newly-detected (red dots and gray waveforms) events based on cross-correlating waveforms at station MPI (red triangle). The White-Wolf swarm is highlighted by red, orange, yellow and green dots analogous to Figure 1a in the main manuscript.The injection site is highlighted by a blue triangle and the largest magnitude swarm event by a red star.

16 Figure 8: Same as Figure 6 but now showing an example of waveforms and CC values of a newly detected event.

155 Template matching is generally superior to simple phase picking algorithms,

156 which rely on a notable amplitude or frequency difference between signal and

29,30,37 157 noise, allowing for event detections even in high-noise environments . How-

158 ever, the limited availability of template events due to only one nearby station

159 with continuous waveforms records that was recording over several years before

160 and after the White Wolf swarm in 2005, prevents a systematic lowering of the

161 completeness threshold within the area. Nevertheless, the template matching and

162 catalog extension allow us to test if part of the Tejon fault was active during the

163 high-rate injection period in WD05 and provides information about possibly sys-

164 tematic migration patterns (see main manuscript).

17 Figure 9: Same as Figure 6 but now showing an example of waveforms and CC values of a newly detected event.

18 Figure 10: Same as Figure 6 but now showing an example of waveforms and CC values of a newly detected event.

19 165 6 Moment tensor inversion and moment magnitudes

166 We test the reliability of magnitude estimates in the upper tail of the FMD through

167 determining moment magnitudes of events with ML ≥ 4.0. We find that the local

168 magnitudes of ML = 4.5, 4.7 and 4.3 within the SCSN earthquake catalog exceed

169 moment magnitude estimates of Mw = 4.1, 4.6 and 4.0. However, three events

170 above Mw4 are in good agreement with the expected number of M≥4 events for

171 the determined power-law parameters (b=0.6, a=2.8) and further support a signif-

172 icant deviation from a b-value of unity.

173 Moment magnitudes were computed by fitting long-period waveforms in a 10

174 to 20 sec window immediately after P and S-phase arrivals using the Cut-And-

40,41 175 Paste method for pure, double-couple source tensors . The synthetic far-field

176 displacement for a double-couple source can be described as follows:

3 177 s(t) = M0 ∑ Ai(φ − θ, δ, λ)Gi(t), (3) i=1

178 here, i = 1,2,3 correspond to three fundamental faults, i.e. vertical strike slip, verti-

179 cal dip slip and 45° dip slip, Gi’s are the Green’s functions, φ is the station azimuth,

180 θ, δ, λ are the strike, dip and rake of the source, and M0 is the seismic moment.

181 The parameters describing the source tensor can be determined by minimizing the

182 misfit between observed and synthetic seismograms using a grid-search method

183 within the limited parameter space. The CAP method fits both body and surface

184 wave phases allowing for small time shifts (here 2 to 8 sec for P and S phases)

185 between different phases, which account for unmodeled velocity structures and

186 resulting uncertainties in Green’s function estimates.

187 We use a maximum fitting bandwidth of 0.02 to 0.2 Hz with a slightly narrower

188 band for the smaller magnitude events between 0.08 to 0.2 Hz. We perform another

20 189 grid-search to solve to the focal depth of the synthetic source that minimizes the

190 waveform misfits. For the focal depth inversion, we require reduction in waveform

191 misfits of at least 10% and use the depth within the relocated catalog otherwise. For

192 the largest magnitude event with Mw4.6, we find a focal depth of 9 km which is in

193 good agreement with the relocated catalog depth. The following Figures 11 to 13

194 show inversion results and waveform misfits for the three events with Mw ≥ 4.0.

21 M 4.6 Mainshock, w September 22 , 2015nd

M4.4 M4.5 M4.5 M4.5 M4.5 M4.5 M4.5 M4.5 M4.6 M4.6 M4.6 strike = 89 dip = 30 rake = 72

sec 0 10 20

Distance Staon Azimuth Time Shi Correlaon Coefficient

Figure 11: Focal mechanism (upper left), results of focal depth grid search including mo- ment magnitude (upper right) and waveforms misfits (bottom) for the largest magnitude event that was part of the 2005 White Wolf swarm. The best-fitting focal mechanism is highlighted in red, observed waveforms are shown in black and synthetic waveforms in red.

22 M 4.1 Forehock, September w 22 , 2015nd

M4.1 M4.1 M4.1 M4.2 M4.1 M4.1 M4.1 M4.1 M4.2 M4.0 M4.0 M4.1 M4.0 M4.0 M4.1 strike = 110 dip = 32 rake = 90

sec 0 10 20

Distance Staon Azimuth Time Shi Correlaon Coefficient

Figure 12: Same as Figure 11 for an earthquake above magnitude 4 that occurred ∼ 44 sec before the Mw4.6 event.

23 M 4.0 Aershock, w September 22 , 2015nd

M3.9 M3.9 M3.9 M4.0 M4.0 M4.0 M4.0 M4.0 M3.9 M3.9 M3.9 M4.0 M4.0 M4.0 M4.0 strike = 89 dip = 40 rake = 72

sec 0 10 20

Distance Staon

Azimuth Time Shi Correlaon Coefficient

Figure 13: Same as Figure 11 for an earthquake above magnitude 4 that occurred ∼ 6 min after the Mw4.6 event.

24 195 7 Hydrogeological model of fluid injection induced

196 fluid pressure perturbations

197 7.1 Intro: Crustal permeability structure close to injection well

198 WD05

199 We assess injection induced fluid pressure changes as a function of distance and

200 time from injection operations in well WD05 by modeling pressure diffusion in

201 three dimensions. The 3-D numerical diffusion model is based on the most com-

202 plete available datasets within the upper ∼2–3 km of sedimentary basins and in-

203 cludes seismicity records, geologic mapping results, and industry data (i.e. well-

204 logs, stratigraphic columns and interpreted reservoir structure). Below 3 km depth

205 little data is available except for seismicity catalogs. The model includes three prin-

206 cipal stratigraphic zones, in addition to the high-permeability portion of the Tejon

207 fault which is implemented as a vertical zone of elevated permeability. These three

208 zones are: 1) The injection zone, i.e. a 20-30 m thick turbiditic sand lens in the Mon-

209 terey formation with a lateral extent of up to ∼1.5 km, labeled as "Transition zone"

4 210 in the industry data ; 2) the crystalline (gneissic) basement complex, and 3) the

10,11,15 211 Monterey formation (see ).

212 Permeability is generally high within the sand lenses (i.e. ∼1 D) and very low

−4 213 (∼ 10 mD) above injection depth which is one of the requirements for the se-

−4 214 lection of an injection site. Similarly, permeability is low (∼ 10 mD) within the

215 basement and Monterey formations outside of the injection zone (permeabilities

−15 2 216 are reported in milli-darcy, 1 mD ≈ 10 m ). High permeability within the in-

217 jection zone is supported by publicly available well-log data, i.e., low Gamma-ray

4 218 and high resistivity values .

25 219 7.2 Theoretical background

220 In our model, injection induced pore-pressure diffusion is described by the un-

221 coupled diffusivity equation for slightly compressible fluids for which changes in

28,35 222 pressures do not affect the elastic deformation of the rock matrix :

∂2 p ∂2 p ∂2 p ∂p 223 k + k + k = φµc , (4) x ∂x2 y ∂y2 z ∂z2 ∂t

224 where kx, ky and kz are permeability in x, y and z directions, p is pore-pressure, φ

225 is porosity, µ is fluid viscosity and c is rock matrix compressibility.

226 To present the diffusivity equation in the presence of sources and sinks, we

227 derive the mathematical description of single-phase fluid flow in porous media.

228 We start with the continuity equation, Darcy’s law for flow in 3D and the equation

229 of state. The continuity equation in Cartesian coordinates with added source terms

25,28 230 can be written as :

∂ ∂ ∂ ∂x (ρqx) + ∂y (ρqy) + ∂z (ρqz) + ...

231 N ∑i=1 [ρQwδ(x − xw)δ(y − yw)δ(z − zw)] (5) ∂ = − ∂t (φρ),

232 where qx, qy and qz are volumetric rates of flow per unit cross-sectional area, ρ is

233 fluid density, xw, yw and zw are the injection locations, Qw is the flow rate per unit

234 volume, N is the total number of injection wells in the domain, δ(x) is the Dirac

235 delta function and φ is porosity. Darcy’s law for flow in the x, y and z directions

26 28 236 can be written as :

kxρ ∂p 237 q = (6) x µ ∂x kyρ ∂p 238 q = (7) y µ ∂y   kzρ ∂p 239 qz = + ρg (8) 240 µ ∂z

241 where kx, ky and kz are permeability in x, y and z directions, p is pore-pressure, µ

242 is fluid viscosity and ρ is fluid density. Using Darcy’s flow law and Eq. 5, we can

243 determine diffusion in the presence of sources and gravitational effects:

      ∂ kxρ ∂p ∂ kyρ ∂p ∂ kzρ ∂p ∂x µ ∂x + ∂y µ ∂y + ∂z µ ( ∂z + ρg) − ... 244 (9) N ∂ ∑i=1 [ρQwδ(x − xw)δ(y − yw)δ(z − zw)] = ∂t (φρ),

245 In order to study isothermal single-phase flow of fluids with small and constant

18 246 permeability, we use the following expression for fluid compressibility, c:

1 ∂ρ 247 c = (10) ρ ∂p

248 After integration of Eq. 10, we obtain the equation of state for slightly com-

249 pressible fluids:

c(p−p0) 250 ρ = ρ0e . (11)

251 The combined compressibility of fluid (c) and rock matrix (cr) can be expressed

252 as:

253 cc = c + cr, (12)

254 The rock or formation compressibility can be described as change in porosity as a

27 18 255 function of change in pore pressure:

1 ∂φ 256 c = , (13) r φ ∂p

257 where φ again is porosity.

258 Using the equation of state (Eq. 11) and Eq. 9, 12 & 13, we get:

2 2 2 ∂ p + ∂ p + ∂ p + ∂p − kx ∂x2 ky ∂y2 kz ∂z2 2kzcρg ∂z ... 259 (14) N ∂p ∑i=1 [ρQwδ(x − xw)δ(y − yw)δ(z − zw)] = φµct ∂t ,

260 which is the diffusivity equation used in our model. This description of the dif-

261 fusive process assumes that pressure gradients and compressibility are small, and

262 porosity does not change with time. This diffusivity equation is solved numeri-

32,34 263 cally using the finite-difference reservoir simulator ECLIPSE .

264 Numerical model set-up

265 For the present study, we used the single-phase reservoir simulator module of

34 266 ECLIPSE (’black-oil simulator’) . The initial conditions of the numerical model

267 are constrained by the available industry and geologic data described in Section

268 7.1 and include the high-permeability part at the top of the Tejon fault, identi-

269 fied through a combination of geologic mapping, seismicity locations and industry

270 data. We assume a pressure gradient of 12 MPa/km. We use an average value for

−10 −1 271 the porosity, φ = 0.2, rock compressibility, cr = 4 · 10 Pa and fluid compress- −9 −1 3,18 272 ibility, c = 1.1 · 10 Pa . The water formation volume factor at a reference

3 3 273 pressure of 30 MPa is 1.13 (reservoir m / standard condition m ). The water vis-

2 274 cosity at reference pressure is 0.5 cP. The size of the injection layer of 2.1 km is

275 determined from the publicly available data-sets on the California Division of Oil,

28 3 276 Gas and Geothermal Resources (DOGGR) website .

277 For the present study, we assign no-flux boundary conditions. We chose a large

278 modeling domain (x=30 km, y=5 km, z=18 km) and placed the injection well at the

279 center of this domain to minimize potential effects of boundary conditions on the

280 pressure solutions. The model domain is discretized in the following grid sizes:

281 dx = 109.75 m, dy = 500 m and dz = 100 m. At the vicinity of injection point

282 and high permeability pathway, we use local grid refinement down to dx = 5.78,

283 dy = 9.55 and dz = 1.58 m. The injection well is modeled as a vertical injector with

284 a perforation zone of 30 m that spans the entire extent of the injection zone and

4 285 exact monthly injection schedule is obtained from DOGGR , plotted in Figure 4.

286 7.3 Sensitivity analysis of permeability and fault zone width

287 Crust and fault zone permeability vary non-linearly over several orders of mag-

288 nitude both laterally and with depth so that permeability is one of the modeling

289 parameters most difficult to constrain. The permeability within fault and frac-

290 ture zones is generally higher than in the fault core and protolith and can be

291 even higher in the presence of rupture induced damage, for example, toward

12,23,27,38 292 the up-dip end of blind faults . The interplay between fault motion and

293 permeability increase has repeatedly been observed in controlled injection exper-

294 iments and is essential in maintaining relatively high fault permeability at seis-

2,5,9,16 295 mogenic depth . This is also in agreement with observations at the conti-

296 nental deep drilling project (KTB), Germany where zones of elevated permeability

297 were associated with fracture zones preferably oriented to slip within the local

38,42,43 298 stress field . These zones of elevated permeability persisted down to depth

42 299 of 9.1 km . Similarly, we expect regions with systematically higher seismicity

300 density toward the upper limit of the Tejon fault to exhibit higher permeability.

29 301 In our model, we vary both permeability (k) and width (w) of the upper por-

−6 302 tion of the Tejon fault over a wide range of values (i.e. k=10 to 1 D and w=100

303 to 1000 m) to determine a plausible range of pore-pressure changes at the Mw4.6

304 hypocenter (Table 1 & 2). The sensitivity analysis showed that differences in per-

305 meability have a stronger influence on pore-pressure variations; however both

306 higher fault zone permeability and narrower fault zone width can lead to larger

307 pore-pressure changes at the Mw4.6 hypocenter. For fault zone permeability above

308 ∼200 mD and fault width below ∼1000 m, we observe a pressure increase at the

309 Mw4.6 hypocenter of more than 0.1 MPa which is sufficient to trigger earthquakes 22,24 310 on faults close to failure .

311 The modeled pore-pressure increase at the Mw4.6 hypocenter is lower for a

312 fault zone with homogeneous permeability, i.e. without the high-permeability

313 pathway toward the top of the fault. For fault zones with a width between w=300

314 and 600 m and permeability k >400 mD, we expect an increase in pore-pressure

315 at Mw4.6 hypocenter of less than 0.01 MPa (Figure 14). This further highlights

316 that a narrow, high permeability pressure channel is expected to have the largest

317 seismogenic consequences for the White Wolf fault.

30 Table 1: Overview of model runs, initial conditions and pore pressure increase at the Mw4.6 hypocenter for a wide range of permeabilities.

Model run ki kf w IZL ∆Pp [mD] [mD] [m] [km] [MPa] 1 1000 0.01 200 1.5 <0.0001 2 1000 0.01 300 1.5 <0.0001 3 1000 0.01 400 1.5 <0.0001 4 1000 0.01 500 1.5 0.0002 5 1000 0.01 600 1.5 <0.0001 6 1000 0.01 800 1.5 <0.0001 7 1000 0.1 200 1.5 0.0008 8 1000 0.1 300 1.5 0.0005 9 1000 0.1 400 1.5 0.0005 10 1000 0.1 600 1.5 0.0004 11 1000 0.1 800 1.5 0.0005 12 1000 1.0 200 1.5 0.001 13 1000 1.0 300 1.5 0.001 14 1000 1.0 400 1.5 0.0009 15 1000 1.0 600 1.5 0.0007 16 1000 1.0 800 1.5 0.0007 17 1000 10 200 1.5 0.0012 18 1000 10 300 1.5 0.0013 19 1000 10 400 1.5 0.0012 20 1000 10 600 1.5 0.0012 21 1000 10 800 1.5 0.0012 22 1000 100 200 1.5 0.0085 23 1000 100 300 1.5 0.01119 24 1000 100 400 1.5 0.0127 25 1000 100 600 1.5 0.0117 26 1000 100 800 1.5 0.0105 27 1000 1000 200 1.5 1.3732 28 1000 1000 300 1.5 1.0537 29 1000 1000 400 1.5 0.8462 30 1000 1000 600 1.5 0.6045 31 1000 1000 800 1.5 0.47 ki - injection zone permeability; kf - fault zone permeability; w - fault zone width; IZL - injection zone lateral extent; ∆Pp - pore pressure change at the Mw4.6 hypocenter after 150 days of high-rate injection

31 Table 2: Overview of model runs, initial conditions and pore pressure increase at the Mw4.6 hypocenter for a narrow range of permeabilities.

Model run ki kf w IZL ∆Pp [mD] [mD] [m] [km] [MPa] 32 1000 200 200 1.5 0.0332 33 1000 200 400 1.5 0.0374 34 1000 200 600 1.5 0.0317 35 1000 200 800 1.5 0.0271 36 1000 200 1000 1.5 0.0232 37 1000 400 200 1.5 0.3015 38 1000 400 400 1.5 0.2405 39 1000 400 600 1.5 0.1848 40 1000 400 800 1.5 0.1489 41 1000 400 1000 1.5 0.1252 42 1000 600 200 1.5 0.6846 43 1000 600 400 1.5 0.4756 44 1000 600 600 1.5 0.3516 45 1000 600 800 1.5 0.2788 46 1000 600 1000 1.5 0.2312 47 1000 800 200 1.5 1.0527 48 1000 800 400 1.5 0.679 49 1000 800 600 1.5 0.492 50 1000 800 800 1.5 0.385 51 1000 800 1000 1.5 0.3171 27 1000 1000 200 1.5 1.3732 29 1000 1000 400 1.5 0.8462 30 1000 1000 600 1.5 0.6045 31 1000 1000 800 1.5 0.47 52 1000 1000 1000 1.5 0.385 ki - injection zone permeability; kf - fault zone permeability; w - fault zone width; IZL - injection zone lateral extent; ∆Pp - pore pressure change at the Mw4.6 hypocenter after 150 days of injection

32 Pp [MPa] 0.002 0.004 0.006 0.008

Figure 14: Expected pore-pressure increase at distances similar to Mw4.6 hypocentral distance for pressure diffusion along a fault with homogeneous permeability structure. The resulting pressure perturbations are significantly smaller than in the case of a high- permeability pathway at the top of the Tejon fault.

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