Modeling Injection-Induced Seismicity with the Physics-Based Earthquake Simulator RSQSim by James H. Dieterich, Keith B. Richards-Dinger, and Kayla A. Kroll
INTRODUCTION physics-based simulations include McClure and Horne (2011), who investigated the effects of fluid injection on a 1D fracture. Although the phenomenon of earthquakes induced by the sub- Here, we present a modeling approach for simulating seismicity surface injection of fluids has been recognized, and the basic induced by fluid injection in 3D over multiple earthquake mechanisms understood, for many decades (e.g., Healy et al., cycles. 1968), the recent increase in seismicity associated with oil and gas development, including large damaging events (e.g., Ells- worth, 2013; Keranen et al., 2013; Hough, 2014; Rubinstein INDUCED-SEISMICITY SIMULATIONS et al., 2014) makes clear the need to better understand the processes controlling such seismicity and to develop techniques We developed a method to simulate injection-induced seismicity to mitigate the associated seismic hazard. that couples the regional scale, multicycle earthquake simulator, The relationship of fault stress, fault strength, and fluid RSQSim, to reservoir models that give changes of effective pressure at the onset of fault slip in the most basic form is given stresses acting on the modeled faults due to fluid injection. by the modified Coulomb criterion, RSQSim is a computationally efficient 3D boundary-element code that incorporates rate–state fault friction to simulate long τ μ σ − P; 1 sequences of earthquakes in interacting fault systems. Although RSQSim (Dieterich and Richards-Dinger, 2010; Richards- Dinger and Dieterich, 2012) was specifically developed for ef- τ σ in which and are the shear and normal stress, respectively, ficient simulations of earthquakes and other fault slip processes P μ acting on the fault surface, is the pore-fluid pressure, and is in geometrically complex fault systems, our initial investigation σ − P the coefficient of fault friction. The term ( ) is the effec- reported here focuses on the characteristics of induced earth- tive normal stress (Terzaghi, 1925). From equation (1), a fault quakes arising from injection near a single isolated planar fault. can be brought to a critical state through an increase of shear RSQSim is a boundary element code in which faults are τ σ stress , a decrease of the normal stress , an increase of fluid represented by arrays of rectangular or triangular elements. Be- P pressure , or some combination of the three. Increase of pore- cause fully dynamic models of the rupture process are computa- fluid pressure is the most widely cited cause of earthquakes in- tionally intensive, the great efficiency of this code derives in part duced by human activities (National Research Council, 2012). from use of a quasi-dynamic approximation of rupture dynamics Consequently, investigations and models of induced seismicity wherein slip speed during an earthquake is fixed at a constant have tended to focus mainly on spatial changes of fluid pressures value consistent with the elastic shear impedance and earthquake (Hsieh and Bredehoeft, 1981; Shapiro and Dinske, 2009). stress drop. Slip on the fault elements is governed by a rate- and Although the immediate cause of injection-induced earth- state-dependent constitutive formulation of friction, quakes is the increase of fluid pressure that brings a fault to a critical stress state, models of the spatial changes of fluid pres- δ_ θδ_ sure alone are insufficient to either predict or understand the τ σ − P μ a b – 0 ln ln 2 space time characteristics of induced earthquakes. Compre- δ_ Dc hensive system-level models that couple physics-based simula- tions of seismicity with reservoir simulations of fluid pressure a changes can provide an experimental capability to investigate (Dieterich, 1978, 1979; Ruina, 1983; Marone, 1998), in which and b are experimentally determined dimensionless constants topics related to induced seismicity. These include (1) investi- − gation of the system-level interactions controlling the space– (with typical laboratory values of 10 2 ), δ_ is the instantaneous δ_ μ time characteristics of induced seismicity; (2) characterization slip speed, is a reference slip speed, 0 is the steady-state co- of the relationships among injection parameters, reservoir char- efficient of friction at the reference slip speed and constant nor- acteristics, and induced seismicity; (3) development of best- mal stress, Dc is a characteristic distance over which θ evolves, practice protocols for injection projects; (4) site-specific models and θ is a state variable (with dimensions of time) that evolves of injection-induced earthquakes; and (5) probabilistic hazard according to the aging law (with the variable normal stress modi- evaluations of the potential for inducing earthquakes. Previous fication of Linker and Dieterich, 1992): doi: 10.1785/0220150057 Seismological Research Letters Volume 86, Number 4 July/August 2015 1 τ θδ_ aθ min, then no events will ever nucleate. An analagous argument θ_ 1 − − α σ_; 3 Dc bσ to that leading to equation (4), but including the effect of the changing effective normal stress on the state variable, gives α in which is an additional empirical constant and overdots in- dicate time derivatives. A key property of rate–state friction is θ δ_ τ ≈ σ − P μ b − a 0 that nucleation of unstable slip is highly time dependent (Diet- min 0 max 0 ln D c erich, 1992), which results in earthquake clustering, foreshocks, b − a P and aftershocks that follow the Omori aftershock decay law (Di- − α − max ; b ln 1 σ 5 eterich, 1994). 0 For the simulations of injection-induced seismicity de- P scribed below, tectonic stressing rates are set to zero in order in which max is the largest pore-fluid pressure perturbation at to simulate regions that were formerly tectonically active but the location of a given fault element. are now completely or nearly inactive. We construct models Figure 1 illustrates the fault model and some features of a with two different patterns of initial shear stress heterogeneity: typical simulation. The fault is a 3km× 5kmplanar surface and (1) Gaussian white noise with a standard deviation of 5 MPa consists of 37,500 20 m × 20 m elements. The upper edge of the (Figs. 3 and 4) or 15 MPa (Figs. 1 and 6) smoothed with a 3 × fault is buried at 3 km depth. The injection point is even with the 3 running mean filter (so that stresses are correlated over a top edge of the fault and 200 m from the nearest point on the maximum distance of ∼170 m ) and (2) the remnant pattern fault. The injection rate is 0:01 m3=s (26:9 × 103 m3=month), M > after an w 5 rupture from a previous simulation (Figs. 2 which is roughly comparable to injection rates associated with and 5). The effective normal stress on the fault elements (initially the Rocky Mountain Arsenal induced earthquakes (7:5 × 103 set to 100 MPa) is controlled by fluid pressure histories from an to 17 × 103 m3=month; Healy et al.,1968) and Paradox external reservoir simulation of fluid injection. The earthquake simulator can accept pore-fluid pressure (and/or poroelastic Event A: 2.9 years Event B: 9.4 years Event C: 15.5 years stressing) histories from arbitrarily sophisticated reservoir models, (a) 3 20 but all the results presented here use pressure histories generated 5 from the simple analytic Green’s function for pore-fluid pressure 15 due to injection at a point source into a uniform, isotropic half- 4 8.19 60 6.19 (b) Closest point on the space immediately below an impermeable layer, based on Wa ng 0 4.19 50 fault from well 2.19 (2000). Because of the unbounded nature of the medium we use 40 10 30 Depth (km) Shear Stress (MPa) Δ
5 Time (years) here, the pressure perturbation due to an infinitely long, constant 0.19 20 500 m –5 rate injection will approach a steady-state value at large times. In 10 5 1800 m
Pore Pressure Change (MPa) 0 contrast, injection into a bounded compartment will lead to ever- 0 51510 20 Time (years) 6 increasing pore-fluid pressures once the pressure front begins to 12345 interact with the boundaries of the compartment. Distance Along Strike (km)
Even with zero tectonic stressing rates and zero pore-fluid (c) 4 Event A: Event B: Event C: pressure perturbation, earthquakes will nucleate spontaneously 2.9 years 9.4 years 15.5 years τ if the initial shear stress 0 is high enough. Specifically, this will 3 occur if the initial shear stress on any fault element is greater τ than some max, which is offset above the steady-state stress by an Magnitude 2 amount controlled by the critical element stiffness for instability (Ranjith and Rice, 1999), which in turn is inversely proportional 1 to Dc. In these simulations, we use Dc 10 μm, which results in very large values for the critical stiffness compared with the 0 5 10 15 20 25 τ Time (years) element stiffness. In this case, the offset is very small and max is nearly the steady-state friction, giving ▴ Figure 1. Fault model and an example of simulation results. (a) Fault surface (gray) with hypocenter locations (colored by time θ δ_ τ ≈ σ μ b − a 0 ; since injection began and scaled by magnitude). The injection well max 0 0 ln 4 Dc is located at 1.5, −0:2,and−3kmin the along-strike, out of plane, and depth directions, respectively. The contours indicate pressure σ θ in which 0 is the initial normal stress and 0 is the initial value of change (in MPa) at the end of the 20-year injection interval. The back- the state variable on that element. In the results we show here, we ground gray scale gives the pattern of initial shear stress with a mean τ τ 50 MPa use initial shear stresses strictly less than max,sothatanyearth- 0 . (b) Inset shows pressure histories at three locations quakes in the simulations would not have occurred in the absence indicated by matching colored stars. Distances are measured along of the injection-induced pore-fluid pressure perturbations. strike from closest point on the fault to the well. (c) Magnitude versus Similarly, if the tectonic stressing rates are zero and the time for the simulation shown in (a). Beginning and end of injection initial shear stresses are everywhere less than a critical value period shown by the blue and red dashed lines, respectively.
2 Seismological Research Letters Volume 86, Number 4 July/August 2015 Valley, Colorado, induced earthquakes (∼37:6 × 103 to • the magnitude of the first event increases, 56:4 × 103 m3=month; King et al., 2014). The diffusivity, • the magnitude of the largest event in the sequence porosity, and compressibility of the medium are 0:005 m2=s, increases, 0.05, and 5 × 10−4 Pa−1, respectively. With this model, the • the cumulative number and total moment of induced M ≈ minimum simulated magnitude is w 1, and the maximum earthquakes increases, M ≈ • magnitude is w 5. In this simulation, there were six earth- the distance from the injection point to the most distant M > quakes with w 3, in addition to the many smaller events. earthquake increases, and Generally, the magnitudes of the largest events increase with • the seismicity following shut-in increases. time and the areal extent of induced earthquakes expands. Additionally, the fraction of the earthquake moment due τ In this simulation, two small earthquakes occurred after injec- to fluid injection decreases as 0 increases (compare the red tion was halted at 20 years. and black curves in Fig. 2a–c). In these zero tectonic stressing τ < τ rate simulations with 0 max, no events would have taken EFFECT OF INITIAL STRESS ON INDUCED place without the pore-fluid pressure perturbations due to the SEISMICITY injection, so in some sense the injection is responsible for all of the events. However, it also is true that without some pre- τ existing shear stress, no shear-failure events would have oc- The average initial shear stress 0 strongly affects the character- istics of induced seismicity. Figure 2 shows results from three curred no matter how much fluid was injected. To quantify simulations with different average initial shear stresses between the fraction of the total moment to be attributed to fluid in- τ τ τ min and max. Consistently, in simulations with increasing 0 , jection versus pre-existing shear stress, we define the portion • the delay between the start of injection and onset of seis- of the earthquake moment that is due to the increase of fluid micity decreases, pressure as
τ = 36 MPa τ = 48 MPa τ = 56 MPa (a) o (b) o (c) o 8·1015 4·1013 6·1014 6·1015 4·1014 2·1013 4·1015 Cumulative Cumulative Moment 2·1014 2·1015 0 0 (d) 80 0 (e) 250 700 60 200 (f) 500 40 150 100 300 of Events 20 Cumulative # # Cumulative 50 100 (g) 0 0 4 (h) 4 (i) 4 3 3 3
Magnitude 2 2 2
1 1 1 –5 0 5 10 15 20 25 –5 0 5 10 15 20 25 0102030 40 Time (years) Time (years) Time (years) (j) 20 (k) 20 (l) 30 50 15 14 2 15 50 25 38 26 14 26 2 38 20 50 10 10 2 15 14 26 38 5 10
Time (years) 5 5 0 0 0 0 1 2 3 45 012345 012345 Distance along strike (km) Distance along strike (km) Distance along strike (km)
▴ Figure 2. Effect of initial shear stress on induced seismicity. Columns show simulation results for a range of mean preinjection initial shear-stress values τ0 in the range of acceptable values between τmin and τmax. The pattern of initial shear stresses is that which results following an Mw > 5 earthquake in a previous simulation. The cumulative moment, number of events, and event magnitudes are shown in (a–c), (d–f), and (g–i), respectively. The black curve in panels (a–c) is the total cumulative moment released by all events in the simulation, whereas the red curve represents the moment release that can be ascribed to the change in pore-fluid pressure (see text). The along- strike rupture lengths (black horizontal lines) of all events are shown, projected onto the surface of the fault, in (j–l). Gray contours in the lower panels show the pore-fluid pressure with time. Blue and red dashed lines indicate the beginning and end of the injection period in all panels, respectively.
Seismological Research Letters Volume 86, Number 4 July/August 2015 3 Δτ M M p ; crust over which the pressure is increased sufficiently. This vol- 0ΔP 0 Δτ 6 ume, in turn, is proportional to the injected volume (at least during the initial injection period before the pressure field ap- M Δτ in which 0 is the total earthquake moment, is the earth- proaches its steady state). This relationship can be derived with quake stress drop, and Δτp is the average reduction of fault simple scaling laws. M strength due to the increase in fluid pressure on the fault sur- The scaling of earthquake magnitude w with rupture face, which is area A can be derived from the definition of earthquake mo- ment M , coupled with the assumption of self-similarity (i.e., Δτ μΔP; 0 p 7 constant stress drop) and the moment–magnitude relation. The seismic moment is defined by in which μ is the nominal coefficient of friction, which we μ ΔP equate to 0 in equation (2) and is the average fluid pressure M GAd;¯ 8 change on the rupture surface of a given event. 0 The fraction of the moment of individual events that is G d¯ due to increased fluid pressure decreases with increasing event in which is the elastic shear modulus and is the average slip. magnitude (Fig. 3a). By our measure, for this particular simu- Assuming constant stress drop, the average slip will scale with M ∼ rupture length L,asd¯ ∼ L, and therefore (because A ∼ L2) lation at magnitude w 3, more than half of the earthquake = moment is a consequence of the increase in fluid pressure due with A as d¯ ∼ A1 2. Thus, the moment will scale with area as M ∼ A3=2 – to injection, but at M ≥5:0 as little as 1% of the moment is 0 . Because the moment magnitude relation (Hanks w M = M − due to injection. As suggested by Figure 2a–c, the fraction of and Kanamori, 1979)is w 2 3 log10 0 6, the mag- the total moment released by an entire induced sequence that nitude will scale with area as can be attributed to injection decreases with increasing initial shear stress (Fig. 3b). 2 2 M ∼ log M ∼ log A3=2 ∼ log A: 9 w 3 10 0 3 10 10 RELATION OF MAXIMUM MAGNITUDE TO M ∼ A INJECTED VOLUME This same w log10 scaling is also observed in empirical scaling studies (e.g., Wells and Coppersmith, 1994). V If the average initial shear stress is sufficiently high, then once For a given volume of pressurized crust , the linear di- L an earthquake rupture initiates, it will propagate over the entire mension of a fault that will fit in this volume will scale as L ∼ V 1=3 A fault surface. In that case, the maximum possible earthquake , and hence the area of such a fault will scale as A ∼ L2 ∼ V 2=3 – magnitude is controlled by the fault dimensions. However, . Combining this with the above magnitude τ τ area scaling gives a scaling of magnitude with volume of pres- over a wide range of subcritical stresses ( 0 well below max), induced-earthquake ruptures are able to propagate only over a surized crust of sufficiently pressured portion of the fault (Fig. 2). In those 2 cases, the maximum limits of earthquake ruptures (and there- M ∼ log V 2=3 ∼ log V ; 10 fore maximum magnitudes) are related to the volume of the w 10 3 10
(a)0.6 (b)
0.5 0.8 ) ) EQ EQ /Mo /Mo 0.4 P 0.6 P Δ Δ
0.3 0.4
0.2 0.2 Moment Ratio (Mo Moment Ratio (Mo 0.1 0.2 35 40 45 50 55 60 65 0.0 Mean initial shear stress (MPa) 3.5 4.0 4.5 5.0 5.5 Magnitude
▴ Figure 3. (a) Ratio of seismic moment due to the change in pore-fluid pressure to the total seismic moment release as a function of magnitude for individual events within a single simulation. (b) Moment ratio for the cumulative moment released in an entire simulation as a function of mean initial shear stress in the simulation.
4 Seismological Research Letters Volume 86, Number 4 July/August 2015 and, as mentioned above, during the initial injection period the flow back out of the reservoir. Although the flow-back pro- volume of pressurized crust will be roughly proportional to the cedure reduced the rate of seismicity, microseismicity was still injected volume so that the scaling of magnitude with injected detected two years later (Häring et al., 2008; Deichmann and volume will be the same. Using a different line of reasoning, Giardini, 2009). This phenomenon is quite important because M ∼ = V McGarr (2014) also obtains scaling of w 2 3 log10 . it means that induced earthquakes cannot necessarily be turned Our argument depends on the pore-fluid pressure being domi- off immediately by termination of injection to manage the risk nated by 3D bulk diffusion. If the pressure is instead domi- of a possible future damaging event. nated by fracture permeability along the fault(s) on which the There appear to be two possible mechanisms for contin- induced seismicity occurs, a similar argument would, in the uing seismicity following cessation of injection. First, following simplest case, give the scaling of injected volume with fault area shut-in, fluid pressures continue to increase, and therefore to (times a fixed fault width and porosity) of V ∼ A, resulting trigger events, until the shut-in signal reaches progressively dis- M ∼ V in w log10 . tant points from the injection well. Second, delayed nucleation Both observations from secondary recovery and waste resulting from the rate–state properties of faults, can result in water disposal wells (National Research Council, 2012) and continuing aftershocks from both previously induced events simulation results show a general agreement with the relation- and the effective stress perturbation. τ τ ship of equation (10) (Fig. 4). Additionally, in the simulations Figure 5 illustrates a simulation with a 0 close to max that there is a dependence on initial stress. This arises because results in many events following shut-in. A few post-shut-in higher pressures (larger volumes of injected fluids) are needed events occur as the pressure continues to increase at points to bring the fault to failure for lower initial stresses. some distance from the injection well. However, most events occur as the pressure is falling, which indicates that delayed POST-SHUT-IN SEISMICITY nucleation is responsible. Additionally, we find that the post- shut-in events show a power-law decay (Fig. 5b) with slope Continuing seismicity following shut-in is a common charac- near −1, which is characteristic of delayed nucleation and after- teristic of injection-induced seismicity. For example, elevated shocks. Once this delayed nucleation process is underway, it is levels of seismicity continued for nearly two years following largely self-driven and relatively insensitive to the subsequent shut-in of wells in the Rocky Mountain Arsenal near Denver, stressing history (Dieterich, 1992). Colorado (Hsieh and Bredehoeft, 1981). Furthermore, injec- tion for reservoir stimulation at an enhanced geothermal field M EFFECTS OF WELL SHUT-IN ON SUBSEQUENT in Basel, Switzerland, was halted after an L 2.6 event oc- curred, which exceeded the safety threshold for the stimulation SEISMICITY (Deichmann and Giardini, 2009). Several hours following M To manage risk associated with induced seismicity, the use of shut-in, an L 3.4 event occurred, the largest earthquake of the sequence (Deichmann and Giardini, 2009). This resulted traffic-light procedures has been advocated to progressively in measures to reduce reservoir pressure by allowing water to scale back or halt injection, based on measures of increasing risk from the recorded seismicity (Majer et al., 2012, 2014; Na- tional Research Council, 2012). As an initial examination of 8 the possible utility of this approach, we conduct a set of 7 numerical experiments to determine how far in advance of in- Secondary recovery and duced earthquakes shut-in must occur to prevent those particu- 6 waste water disposal (NRC, 2013) lar earthquakes. For this test, we use the simulation shown in 5 Figure 1 as the starting point. We choose three moderate M – 4 Initial Shear Stress ( w 3 4) events from that simulation, labeled A, B, and C in 58 MPa Figure 1, that occur at increasingly later times and distances 54 MPa 3 1.5M from the well. In these experiments, the simulation of Figure 1 ∝ 10 50 MPa 2 V 46 MPa is repeatedly restarted, and injection is halted at various times 10x40 km fault Maximum Induced Magnitude 1 before each of the chosen impending earthquakes. Results of 3x5 km fault the shut-in experiments are shown in Figure 6. 0 2 394 5 6 7 8 10 In general, the farther the earthquake from the well, the 3 Log10[Vol of Fluid Injected (m )] further in advance of the event that shut-in has to occur to prevent the moderate earthquake. In the case of earthquake ▴ Figure 4. The volume of injected fluid needed to pressurize (by A (260 m from the well; Fig. 6a), shut-in any time in the last M some fixed amount) the volume of crust that embeds an induced- 14 days before the time of occurrence of the original w 3.8 earthquake rupture, scales by 101:5M , which has a slope of 2= 3 on event leads to essentially the same event (nearly equal magni- M this plot (dashed line). Results from simulations are indicated by tude and rupture area) as the original w 3.8, with slightly data points in color (see legend). Additional parameters that affect delayed origin times (not shown). There is a sudden transition maximum magnitude include reservoir storage capacity and nor- such that turning off injection more than 14 days in advance of M mal stress, which controls earthquake stress drop. the original w 3.8 is effective in preventing the occurrence of
Seismological Research Letters Volume 86, Number 4 July/August 2015 5 (a) (b) 102 Events with delayed nucleation 60 1 10
40 Peak pressures
2 2.5 yrs after shut-in 100 Time (years) 20 Shut-in Slope = –1 50 @ 20 years 14 38
26
Earthquake Rate (events/year) −1 0 10 −1 0 1 2 012345 10 10 10 10 Distance Along Strike (km) Time Following Shut-in (years)
▴ Figure 5. Seismicity following shut-in. (a) Rupture length with time (as in Fig. 2j–l). The pore pressure continues to increase at distances far from the well for as much as 2.5 years (blue dashed line) after shut-in. Events with delayed nucleation are shown in red and their rate of occurrence is plotted in (b). (b) Earthquake rate following shut-in. Slope of −1 shown for reference. Results are from a simulation with an evolved pattern of shear stress with mean τ0 58 MPa.
M any event similar to the original w 3.8, with the largest post- abundance, expand more rapidly, and post-shut-in seismicity M ≤ : injection event having w 2 0. Neither of the other two is enriched. Additionally, the portion of seismic moment re- events undergoes such a sharp discontinuity in behavior with lease that can be attributed to changes in pore-fluid pressure M the variation of shut-in time. Event B ( w 3.2, 680 m from the decreases as both earthquake magnitudes and the mean value τ well) displays a continuous reduction of rupture area and mag- of 0 increases. Although the fluid pressure moment may be- nitude as the well is shut-in earlier, such that it requires cessa- come very small under these circumstances, the earthquakes tion of injection nearly 5 months in advance of the original would nonetheless not have occurred without the perturbation M w 3.2 to keep the magnitude of the largest postinjection of fluid pressure. Furthermore, for faults with initial stresses be- M M event below w 2.0. Similarly, for event C ( w 4.1, 690 m low a near-critical value, the maximum magnitude of induced M ∼ = V from the well), shut-in approximately 5 months before the earthquakes increases roughly as w 2 3log10 .Thisscal- original event is required to keep the post-shut-down seismicity ing is characteristic of bulk 3D fluid diffusion. Fracture diffusion M M ∼ V below w 2.0. For all three of these events, the time after shut- along the fault would yield scaling by w log10 .Contin- in at which the pore-fluid pressure begins to decrease at the uing seismicity following shut-in appears to be driven primarily eventual hypocenter (5, 39, and 36 days for events A, B, and by delayed nucleation and decays by the Omori aftershock law. C, respectively) is much shorter than the length of time before Preliminary tests of traffic-light procedures, where injection the original event that injection must be halted to significantly wells are shut-in to prevent future events, indicate that earth- reduce the magnitude of the induced event: the aforemen- quake magnitudes can continue to increase following shut-in tioned self-driven nature of the rate-and-state nucleation proc- due to both the delay time before the shut-in pulse reaches the ess can make it more difficult than might be expected to halt most distant sites of impending earthquakes and the self-driven the induced seismicity. nature of the earthquake nucleation process. The initial work presented uses an extremely simple fault DISCUSSION and injection system. But even within this simple framework, much work remains to be done, for example, on the effects of We presented a modeling approach to investigate the seismic more complex injection histories and the efficacy of producing response to fluid injection by coupling RSQSim to a reservoir from, instead of merely shutting in, an injection well for pre- model. RSQSim is an earthquake simulator that accepts highly venting subsequent induced seismicity. Beyond that, more real- complex, 3D fault systems and inputs from geomechanical res- istically complex fault geometries and reservoir models need to ervoir models. Such simulations provide a means to conduct be explored in order to attempt to successfully model specific experiments to understand the processes controlling induced observed induced-seismicity sequences. If such sequences can, seismicity under a variety of circumstances. in fact, be modeled, there is some hope that such simulations The results presented here indicate that the space–time could be used in a predictive fashion. Insufficient knowledge of patterns of simulated injection-induced seismicity are quite the initial state of stress on the faults will likely be the most sensitive to preinjection fault stresses. For example, with in- serious obstacle, but it may be that comparing the early part of creasing preinjection shear stress, induced events increase in the seismic response to results of many simulations run ahead
6 Seismological Research Letters Volume 86, Number 4 July/August 2015 (a) 3.0 3.5 3.2
Event A: 3.4 2.5 M3.8; 2.92 yrs 3.6 Depth (km) Magnitude 3.8 1.5 4.0 2.80 2.85 2.90 2.95 0.5 1.0 1.5 2.0 2.5
(b) 3.0 3.0 3.2
3.4 2.5 Event B: M3.2; 9.4 yrs 3.6 Magnitude 2.0 Depth (km) 3.8
4.0 8.9 9.0 9.1 9.2 9.3 9.4 0.5 1.0 1.5 2.0 2.5 (c) 3.0
3.5 3.2 3.4 2.5 Event C: M4.1; 15.5 yrs 3.6 Magnitude Depth (km) 1.5 3.8
4.0 14.6 14.8 15.0 15.2 15.4 15.6 0.5 1.0 1.5 2.0 2.5 Shut−In Time (years) Distance Along Strike (km)
▴ Figure 6. Effect of shut-in time on post-shut-in earthquakes. Earthquakes A, B, and C are the events shown in Figure 1. (Left) The magnitude of the largest post-shut-in event as a function of the time at which injection was halted (note the different time scales). For shut-in times shortly before the impending moderate event, this largest post-shut-in event is essentially the same event as that which occurred in the original simulation; however, for early enough shut-in times, it is a much smaller and/or completely different event. For example, shutting in the well any time before ∼15:2 years, that is at any time more than ∼0:3 years prior to event C, results in the largest earthquake to occur after shut-in having a magnitude Mw ≤1:9 (Fig. 6c, left). (Right) The nucleation positions (colored circles) and rupture areas (colored outlines) of the largest post-shut-in ruptures; colors correspond to those of the data points in the left panels. of time using a suite of initial stress states may provide infor- Dieterich, J. H (1978). Time-dependent friction and the mechanics of 116, – mation on the state of stress and enable forecasting of the sub- stick-slip, Pure Appl. Geophys. 790 806. Dieterich, J. H. (1979). Modeling of rock friction, 1. Experimental results sequent seismicity. and constitutive equations, J. Geophys. Res. 84, 2161–2169. Dieterich, J. H. (1992). Earthquake nucleation on faults with rate- and state-dependent strength, Tectonophysics 211, 115–134. ACKNOWLEDGMENTS Dieterich, J. H. (1994). A constitutive law for rate of earthquake produc- tion and its application to earthquake clustering, J. Geophys. Res. 99, We thank Paul Segall, an anonymous reviewer, and Associate 2601–2618. Editor Justin Rubinstein for thoughtful reviews that improved Dieterich, J. H., and K. B. Richards-Dinger (2010). Earthquake recurrence in simulated fault systems, in Seismogenesis and Earthquake Forecasting: this manuscript. All authors contributed equally to this work. The Frank Evison Volume II,Springer,Basel,Switzerland,233–250. Ellsworth, W. L. (2013). Injection-induced earthquakes, Science 341, no. 6142, doi: 10.1126/science.1225942. REFERENCES Hanks, T., and H. Kanamori (1979). A magnitude moment scale, J. Geo- phys. Res. 84, 2348–2351. Deichmann, N., and D. Giardini (2009). Earthquakes induced by the Häring, M. O., U. Schanz, F. Ladner, and B. C. Dyer (2008). Character- stimulation of an enhanced geothermal system below Basel (Switzer- isation of the Basel 1 enhanced geothermal system, Geothermics 37, land), Seismol. Res. Lett. 80, no. 5, 784–798. no. 5, 469–495.
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