We estimate Coulomb stress variations (ΔCFS) by considering interactions among 163 earthquakes (ML ≤ 3.4) that occurred during the hydraulic stimulation of the enhanced geothermal system in Basel, Switzerland, in 2006. We observe that overall 75% of event locations are consistent with positive ΔCFS. The performance of the model increases with time and distance from injection, accordingly with the presumed less dominant role of the pore pressure further from the injection well and after shut-in. We analyze the sensitivity of results to location and focal mechanism uncertainties, the fault-plane ambiguity, and the friction coefficient. We find that ΔCFS are highly sensitive to location accuracy but robust with regard to uncertainties of the other parameters. Our results suggest that (i) the Coulomb model may complement conventional pore-pressure triggering models and (ii) implementing it for time-dependent seismic hazard assessment during fluid injection may improve the forecasting ability but will require highly accurate hypocenter estimates.
 Between 2 and 8 December 2006, approximately 11,500 m3 of water were injected at high pressure into a 5 km deep well in the enhanced geothermal system (EGS) of Basel, Switzerland [Häring et al., 2008]. Such stimulation produces fractures in the rock where the fluid flows through and heats up to produce heat and power. During this process, more than 10,500 earthquakes were induced close to the injection point [Häring et al., 2008, Figure 5]. Most of the seismicity occurred during the water injection that was first reduced and then stopped after the occurrence of the ML 2.6 event of 8 December [Häring et al., 2008]. The overall time behavior of the seismicity followed the flow-rate and wellhead pressure trend, with a gradual increase in seismicity during the injection (both in rate and magnitudes) and a rapid decrease over the 3 weeks after bleed off [Bachmann et al., 2011]. However, three additional events with ML > 3 occurred 1–2 months later, and sporadic micro-seismicity was being detected even more than 5 years later. The bulk of seismicity is located on a near-vertical lens-shaped structure at a depth around 4.5 km with a maximum radial distance from the casing shoe of about 900 m.
 The triggering effect of the pore pressure change ΔP due to the fluid injection is well established: an increase of the pore pressure reduces the effective normal stress and promotes slip along pre-existing subcritical ruptures [Rutledge et al., 2004]; as pore pressure increases, differential stress needed to trigger an event decreases. Several studies [e.g., Shapiro et al., 2010, and references therein] examine the link between the rate, the total number as well as the magnitudes of expected induced events on one hand, and the rate of fluid injection and the volume of the stimulated area on the other. Goertz-Allmann and Wiemer  and Bachmann et al.  present and apply a simple geomechanical model of induced seismicity that is able to reproduce the first-order variations of the source parameters (relative earthquake size distribution and stress drop) with time and space, including the occurrence of the largest event shortly after shut-in. Statistical models applied in a pseudo-prospective test are able to forecast the overall induced seismicity in Basel quite well [Bachmann et al., 2011; B. Mena et al., Building robust materials to forecast the induced seismicity related to geothermal enhancement, submitted to Bulletin of the Seismological Society of America, 2012], however, the process that caused the events with ML ≥ 3 long after bleed off is poorly understood [Baisch et al., 2009].
 Coulomb stress changes, ΔCFS, associated to earthquake interactions have been commonly seen as a powerful tool for forecasting subsequent seismicity in a tectonic regime [e.g., Steacy et al., 2005, and references therein]. The concept that underlies the Coulomb model is simple but effective: positive shear, Δτ, and normal effective (extensive), Δσ, stress changes favor the generation of future events; negative ones inhibit them, following the relation ΔCFS = Δτ + μ′Δσ, where μ′ is the apparent friction coefficient [Harris, 1998]. The Coulomb model has mainly been used to explain aftershock sequences after large or intermediate sized events and also to study the generation process of fluid related phenomena such as magmatic dike progression and the accompanying earthquake swarm [Toda et al., 2002]. Moreover, it has been used to examine mining induced seismicity [Orlecka-Sikora, 2010, and references therein] finding positive correlations between locations of events and positive stress variations. Orlecka-Sikora  concluded that the static stress transfer can accelerate the mining induced seismicity generation because even a small ΔCFS can have a significant effect on faults already loaded by mining stress. Schoenball et al.  estimated co-seismic Coulomb stress transfers due to 715 earthquakes occurred after the stimulation of the EGS at Soultz-sous-Forêts (France). They neglected any poro-elastic interaction of stress and pore fluid pressure and found that static stress changes alone play a minor role for injection-induced seismicity but might trigger events after shut-in. Baisch et al.  used the Coulomb model to investigate to what extent the induced perturbation in an EGS might trigger larger magnitude events on pre-existing faults beyond the injection volume. They find that the triggering effect is predominantly caused by the thermal contraction of the Basel reservoir and that the cumulative shear deformation plays a secondary role.
 In this work, we estimate cumulative stress variations and intentionally ignore the pore pressure change, in order to investigate whether elastic stresses alone play a role in the triggering process during the Basel sequence.
2 Dataset and Methodology
 The Coulomb stress variation is a function of the relative position of the source and receiver faults, their relative focal mechanisms, and the magnitude of the source event. We use focal mechanisms, moment magnitudes MW (obtained from the operators of the down-hole monitoring network) [T. Spillmann, Geothermal Explorers Ltd., personal communication, 2012] and hypocenter locations of 163 earthquakes that occurred from 3 December 2006 to 30 November 2007, in the EGS close to the city of Basel (Figure 1a) to calculate ΔCFS with the isotropic poro-elastic Coulomb model as defined by, for example, Harris . We limit our analysis to these events because they have well-constrained focal mechanisms, which were determined as documented in Deichmann and Ernst . This subset includes all the largest events that occurred (0.7 ≤ ML ≤ 3.4). Parameters of 118 of these focal mechanisms are listed in Terakawa et al. . Additional focal mechanisms of smaller events with fewer first-motion polarities are constrained by the fact that these events have nearly identical signals as stronger events with independently determined fault-plane solutions, so that their focal mechanisms must be identical as well. We use relocated hypocenters by Deichmann and Giardini . For clusters of similar events, these relocations have been refined using relative arrival times determined from signal cross-correlations.
 We estimate dimensions and mean slip of extended square fault patches based on the relations of Hanks and Kanamori  and Keilis-Borok  assuming a constant stress drop of 2.3 MPa on the faults, which is the median value found for Basel by Goertz-Allmann and Wiemer .
 Using focal mechanism data to infer fault orientations requires a choice of which of the two possible nodal planes corresponds to the fault that most probably ruptured. This identification process is never straightforward. The induced seismicity in Basel shows a preferred strike orientation of the focal mechanism nodal planes that is mainly NS-EW (see inset in Figure 1a). In principle, both directions NS and EW of nodal planes could fit with the regional stress field [Deichmann and Ernst, 2009]. We call “NS” the catalog where we selected each nodal plane as the closest to the NS direction and “EW” the catalog where the nodal planes are the closest to the focal mechanism with strike oriented towards EW. We calculate ΔCFS using both catalogs “NS” and “EW” and find that the percentage of events in the two cases, which receive a positive ΔCFS, that is the Coulomb index (CI) as introduced by Hardebeck et al. , is almost the same (1% difference). This is a consequence of the symmetry that characterizes the stress change pattern due to the simple uniform slip model that we imposed in our calculations. When considering a uniform slip model, if the strike of both source and receiver is changed by 90°, the positive and negative lobes of ΔCFS have almost the same total area, but different orientation, as those without rotation. This implies that the choice between the “NS” or the “EW” catalog is not crucial for this study. In the following, if not specified otherwise, all results are based on the “EW” catalog. However, in all the sensitivity analyses presented in a later part of this study, we take the nodal plane ambiguity into account by considering CI distributions of a set of test catalogs where fault planes are selected randomly.
 For the stress change computations, we used a modified version of the code developed by Wang et al., . A cross-validation of results was made by using the code of Nostro et al., . We used a friction coefficient μ = 0.8, which is a value common to almost all the type of rocks [e.g., Segall, 1991], a Skempton ratio B = 0.5, and a rigidity value of 30 GPa.
 We treat each event of the sequence consecutively as both source and receiver. For each event, we compute the cumulative stress change that all previous events caused on its hypocenter before it occurred. We exclude all source-receiver combinations with inter-event distances of less than one source length. ΔCFS values of event pairs too close to each other are not reliable because of their sensitivity to details of slip distributions [Steacy et al., 2004], which are poorly understood with current data. We therefore take the side length of the slip model as a proxy for the slip model resolution and use it as an exclusion threshold.
 Each point of the map in Figure 1b represents a cumulative ΔCFS estimate for a specific triplet of x, y, and z coordinates relative to each receiver event location and focal mechanism. For quantifying the success of the model to explain the observed seismicity, we use the CI as defined before.
3 Coulomb Stress Changes: Discussion of Results
 Figures 1a and 1b show the maps of cumulative ΔCFS for each of the 163 studied events, by highlighting their focal mechanisms and stress change magnitudes, respectively. The estimated overall CI is 75%, which indicates a correlation between event hypocenters and positive ΔCFS. One can notice in Figures 1b and 1d that the correlation between positive ΔCFS and locations occurs preferably further away from the casing shoe and the injection time.
 For all computations shown in Figure 1, we assume square source models and a fixed stress drop to calculate fault dimensions and mean slip, as described in the previous section. We also tried to use spatially variable stress drops calculated by Goertz-Allmann and Wiemer  for Basel, finding that ΔCFS are not sensitive to stress drop variations in this area (the difference in CI is <1%).
 In Figure 2, we focus on the trend of ΔCFS, which are more often positive at larger distances and later times from the injection, as observed also in Figures 1a, 1b, and 1d. Figure 2a illustrates this trend in terms of a moving average over the CI time series. The CI increase is particularly pronounced when the sequence starts to develop and after shut-in. A similar behavior applies to ΔCFS as a function of distance from the casing shoe (Figure 2b).
 Overpressure at the injection point and during the time of maximum flow rate reaches values of up to 30 MPa, which are several orders of magnitudes higher than the estimated ΔCFS. Therefore, we can reasonably suppose that close to the well and before shut-in, ΔP, rather than ΔCFS, is the dominant triggering process. However, even for these events, we observe a correlation between earthquakes and stress changes (Figure 2). This suggests that also the pore-pressure-induced events may have been accelerated by static shear stress changes. Moreover, pore fluid pressure as a function of distance to the injection point is badly constrained, and different models lead to a huge variety of ΔP estimates [K. Evans, personal communication, 2012]. According to linear pore-pressure diffusion models [e.g., Goertz-Allmann and Wiemer, 2012, and references therein], ΔP might decrease to the order of KPa within 200 m away from the well. Nonlinear diffusion models [e.g., Murphy et al., 2004], on the other hand, predict a smoother decrease of ΔP with distance, finding values of the order of tens MPa even away from the well. Hence, at some distance in space and time from the injection, ΔP is expected to decrease to values comparable to ΔCFS or below, but this distance is hard to quantify. Besides, we observe a continuous increase of the performance of the Coulomb model with increasing distance (Figures 2a and 2b), suggesting that Coulomb interactions may lead the triggering process further away from the injection time and place.
 Before the leak-off of the well, we observe a dense generation of seismicity, which experience both positive and negative ΔCFS; in this phase, when ΔP reaches 30 MPa at the maximum injection rate, we can partially explain the presence of seismicity also in stress shadows by considering that (i) under high–pore pressure changes, even faults not optimally oriented can easily slip [Terakawa et al., 2012] and (ii) we have larger uncertainties for the larger number of smaller events [Goertz-Allmann and Wiemer, 2012; Bachmann et al., 2011].
4 Sensitivity Analysis
 We analyze the sensitivity of our results by considering wide testing ranges for uncertainties of strike, dip, rake and locations. For this purpose, we perturb the original catalog by (i) adding von Mises distributed errors to strike, dip and rake of each original focal mechanism from 0° to 170° and (ii) adding normal distributed errors to all the hypocenter locations from 0 to 300 m. We perform these perturbations 1000 times for each event to obtain a set of 1000 test catalogs, and we evaluate a distribution of CI, a mean value, and a standard deviation for each set. In addition, we analyze the sensitivity of the methodology to the friction coefficient parameter, μ, by considering a range of its values from 0 to 2 in our ΔCFS computations. In this case, we obtain distributions of CIs only by randomly selecting the fault plane. The results of this sensitivity analysis are summarized in Figure 3. In Figure 3a, we show the effect of uncertainties of strike, dip, and rake: when we perturb strike, dip, and rake of each focal mechanism of the catalog, we observe that the trend of mean CI is not substantially affected by these errors within a range of about 0°–45°. Only for errors larger than 45° is the CI decrease sharper and not negligible. In Figure 3b, we show the effect of uncertainties of hypocentral location (x, y, z). The panel shows that the trend of mean CI depends strongly on locations: for an uncertainty of 20 m, the model looses already 10% of its performance.
 For Basel, we consider 10° as 2 standard deviations (2σ) for strike, dip, and rake by following [Deichmann and Giardini, 2009]. As 10° is a conservative error for the estimated focal mechanisms in Basel [N. Deichmann, personal communication, 2012], we took it as 2σ. On the other hand, uncertainties of locations for the whole dataset are 50 and 70 m as 1σ for x, y, and z directions, respectively. For relative locations of hypocenters within individual clusters of similar events, based on signal cross-correlations, the errors are less than 10 m. The distributions of CI considering these specific uncertainties are also shown on the left side of Figures 3a and 3b. In Figure 3a, the distributions of CI evaluated by considering the focal mechanism of the original catalog and the focal mechanisms perturbed with the uncertainties of the catalog do not depart considerably from each other. From Figure 3a, it is clear that estimates of ΔCFS in Basel are robust within the error of 10° assumed for the focal mechanism parameters. In the extreme case of random focal mechanisms, the distribution shifts to around CI = 50%. On the contrary, Figure 2b shows that distributions of CI estimated for perturbed hypocentral locations within the catalog uncertainties and for locations of the original catalog depart considerably from each other. This departure in a strike-slip regime is mainly governed by the uncertainties of the horizontal locations [Catalli and Chan, 2012]. The model performance is hence sensitive to location uncertainties, in particular to the epicentral ones.
 In Figure 3c, we analyze the model sensitivity to the friction coefficient μ. For this sensitivity analysis, we considered an extended range of μ values from 0 to 2 and observe that in the range 0.0 < μ < 0.8, the trend shown in Figure 3c confirms that ΔCFS values are only moderately influenced by the choice of μ [e.g., Harris, 1998]. In addition, we observe that the best performance of the model corresponds to values of μ close to 0. This is in agreement with the conclusion of Kagan and Jackson  that either μ is close to zero or both tectonic and earthquake static stress are self-organizing into a pattern that mimics μ = 0. This could also explain why the choice of μ is not crucial in applying the Coulomb model.
5 Conclusions and Outlook
 In a context where one would expect that the triggering process is mostly dominated by the large increase of the ΔP alone, in all our computations we observe a significant correlation between event locations and positive ΔCFS during the Basel sequence. Surprisingly, we observe that the Coulomb Index is already high (80%) even before the reduction of the pumping rate, suggesting that earthquake-earthquake interaction is an important contributor to the evolution of the micro-seismicity cloud. The Coulomb Index is highest for events that occurred after shut-in and at larger distances from the well, when and where ΔP decreases and the relative importance of earthquake-earthquake interaction increases. The degree of the correlation depends on the following parameters: accuracy of source/receiver hypocenter locations and focal mechanism parameters, as well as physical source characteristics (such as μ, B, and slip model). Our analysis shows that we can constrain most of the modeling parameters sufficiently well and our results are robust with respect to their uncertainties. In fact, the value of CI, which represents the degree of correlation between model and observations, is stable at around 75% for most model settings (i.e., for choice of fault planes, for a range of reasonable μ values, for fault plane uncertainties). On the other hand, the methodology shows a substantial sensitivity to uncertainties of hypocentral location. We do not expect that by considering a larger number of events, the overall CI would increase, because uncertainties would then also be larger.
 Our study also shows that the model reaches highest values of CI for values of μ close to 0. In the context of a hydro-stimulation, this observation may also suggest that while the seismically induced shear stresses seem to control the triggering process, the seismically induced normal stress changes are negligible. The unclamping would then be caused predominantly by the injection-related pore pressure changes, rather than by the normal stress due to earthquake interaction. However, subsequent events preferentially occur where previous earthquakes raised the static shear stresses. In this sense, the Coulomb model may probably complement a conventional ΔP triggering model. We conclude that the correlation between positive ΔCFS and locations of events suggests that static stress changes from previous small-induced earthquakes are actively involved in the triggering process. For this reason, ΔCFS in principle is an important parameter for a comprehensive assessment of the hazard associated with man-induced seismicity. In practice, we observed in this study that the possible contribution of ΔCFS for the hazard assessment is strongly limited by the high accuracy of hypocenter locations needed in real time.
 Special thanks to N. Deichmann for the refined event relocations and for the unpublished focal mechanisms, and to T. Spillmann, Geothermal Explorers Ltd, for the MW values.