As early as 1988, Mastin and Heinemann, 1998 analysed the data from 4-arm caliper and ultrasonic televiewer (BHTV) logs in GPK1 and concluded that the direction of the maximum horizontal principal stress, SHmax was N169° ± 21°. Rummel and Baumgärtner, 1991 applied the HTPF stress determination technique to just five hydraulic tests performed between 1458 and 1989 m depth in GPK1 and found SHmax was oriented N155° ± 3°. However, given the few number of data, this cannot be considered a reliable estimate (Cornet et al., 2007). Tenzer et al., 1992 analysed breakouts and DITFs for the same depth range in the same well and found an SHmax orientation of N169° ± 11°. Nagel, 1994 analyzed vertical DITFs in GPK1 after its extension to 3600 m and found an SHmax orientation of 181° ± 22°. Brudy and Zoback, 1999 extended Nagel's study by adding en échelon DITFs and found the same SHmax orientation. Hydrofracture stress tests performed in 1993 between 2195 and 3506 m as reported by Klee and Rummel, 1993 provide stress magnitude but no orientation information. Heinemann-Glutsch, 1994 analysed all stress data collected up to 1993 and proposed linear variations of stress magnitude with depth and an SHmax orientation of N170°E. Bérard and Cornet, 2003 identified breakouts in GPK1 between 2850 m and 3465 m and indicated an SHmax orientation of N5°E ± 7°. Genter and Tenzer, 1995 identified vertical DITFs in GPK2 in the depth range 1420–3880 m and reported SHmax orientation of N175° ± 17°.

Stress orientation in the deeper reservoir as revealed by breakouts and DITFs in the two 5 km deep wells, GPK3 and GPK4, was studied by Valley and Evans, 2005; Valley and Evans, 2007a. DITFs dominate above 3 km whereas breakouts dominate below 3.5 km. Axial DITFs in GPK3 above 3257 m MD² depth indicate a mean SHmax direction of N167° ± 12°. Below 3257 m MD in GPK3, the numerous breakouts indicate an SHmax orientation of N162° ± 20°. The large standard deviation is partly due to the presence of a fault that cuts the borehole at 4770 m MD (Hettkamp et al., 2004), and perturbs the stress orientation by up to 90° over several hundred meters (Valley and Evans, 2007b). In GPK4, the DITFs in the upper part of the well indicate an SHmax orientation of N172° ± 12°. Below 3.7 km MD, the breakouts are numerous and show two large-scale systematic changes in orientation associated with fracture zones. They suggest that the mean SHmax orientation over the lowermost 1.5 km of hole is N174° ± 17°.

Maximum pressures at the casing shoes during the stimulation of the three deep wells appeared to be limited by jacking (Valley and Evans, 2007a), and lay on the Shmin magnitude trend proposed by Cornet et al., 2007. The profiles of the presence or absence of breakouts and DITFs along the wells GPK3 and GPK4 suggest SHmax lies between 0.9 and 1.05 times the value of the vertical principal stress Sv (Valley and Evans, 2007a), indicating a quasi uniaxial extensive stress regime.

We used the seismological data recorded during the 2000 and 2003 hydraulic stimulations of the lower reservoir in GPK2 and GPK3 respectively to estimate the stress field about the lower sections of these holes. The study used 100 well-constrained focal mechanisms from the six days long injection stimulation of GPK2, from 30th June to 5th July 2000 (Weidler, 2000), and 96 from the 10 days long injection stimulation of GPK3, from 27th May to 7th June 2003 (Baria et al., 2004; Hettkamp et al., 2004). All of these are compatible with a double couple model of slip. No evidence for tensile rupture within the geothermal reservoir has been noticed, which means that the tensile component is weak or non-existent. This is in agreement with the purpose of the stimulation, that is large water injections induce shearing on pre-existing fractures favourably oriented in the regional stress field since the increasing pore fluid pressure is likely to reduce the effective normal stress on the fractures. The determination of seismic moment tensor for induced seismic events in GPK3 results in the absence of any NDC (non double couple) component in the source mechanisms (Horálek et al., 2008).

The GPK2 events all occurred during the first two days of the injection, whereas the GPK3 events occurred throughout the injection. Consequently, hypocenters of the GPK2 events tend to be located near the injection whereas those from GPK3 spread over a larger volume. The seismological data recorded during the 2004 and 2005 stimulation injections of GPK4, the third 5 km deep well at Soultz, do not allow sufficiently well-constrained focal mechanisms to be derived. Thus we restrict the analysis to the GPK2 and GPK3 data. The focal mechanism solutions (FMSs) for GPK2 are constrained by at least 12 P-wave first-motion polarities recorded on both surface and downhole instruments, and the GPK3 events with at least 15. The FMSs are determined automatically with the code FPFIT (Reasenberg and Oppenheimer, 1985) and fine-tuned by hand without any wrong polarity. The azimuthal coverage is usually good, so that there are always at least three covered quadrants and there is no need to use the S-wave to constrain the focal planes (see Cuenot et al., 2006), for more details on the seismic array deployed at Soutz-sous-Forêts during the stimulation tests. The location of the microearthquakes used in this study has been obtained through a local tomography method which allows to determine the 3-D velocity model together with the hypocenters coordinates (Charléty et al., 2006; Cuenot et al., 2008). The uncertainties have been estimated to 50 m and 70 m on the horizontal and vertical position respectively. The uncertainties on the azimuth and dip of the planes (or, at least, one of them) are around 10°.

We inverted the focal mechanism solutions for stress using the Slickenside Analysis Package of Michael, 1984; Michael, 1987a; Michael, 1987b. Initially, for each injection, the full collection of FMSs was inverted with a priori fixed fault planes. The results showed that the discrepancies between the ‘observed’ and predicted slip vectors in the fault plane, the misfit, for several mechanisms were unacceptably large, sometimes greater than 50°. Thus, for the next inversion run, the fault and auxiliary planes were switched for mechanisms that had a misfit greater than 30°. In many cases, the misfit decreased significantly, and so the new planes were retained. However, in some cases the misfit remained large. These events were thus excluded from the calculation. The process was then repeated with the maximum misfit angle reduced by 5°, and so on until the maximum misfit angle reached 10°, which is comparable to the uncertainty in the ‘observed’ slip angle. At the end of this process, we obtained a stress tensor and a set of mechanisms which are compatible. We also checked that the misfit of the mechanisms which were excluded in the process remained large. For GPK2, 66 mechanisms out of 100 were found to have a misfit less than 10°, and 21 mechanisms showed a misfit higher than 15°. For GPK3, the numbers are 62 and 23, respectively. As suggested by Michael, 1987a; Michael, 1987b, we bootstrap resample the data set 1000 times flipping the selected fault and slip direction 10% of the time. As the fault planes were selected in the previous step, the resampling is only performed on the fault planes. We thus calculated 1000 stress tensors for each set of mechanisms. The principal directions of the tensors are presented in Fig. 1a (GPK2) and 2a (GPK3). On the same figures are shown the focal mechanisms used for the inversion (1b, 1c and 1d for GPK2; 2b, 2c and 2d for GPK3).

The principal directions of the stress tensor are reasonably well-determined for GPK2. σ₃, which is Shmin, is well constrained, and is near-horizontal with an orientation of N68° ± 5°. Inverting the whole data set of 100 events yields an average Shmin direction of N68.3°, whereas for the 79 events with a misfit threshold less than 15°, the orientation is N69.9°. The vast majority of solutions for σ1 cluster near vertical, consistent with the predominant normal faulting component in the FMSs. The deviation of this axis from true verticality might be ascribed to local stress heterogeneity whose existence is demonstrated by the variations in orientation of breakouts and DITFs on scales of a hundred metres or more (Valley and Evans, 2007b). Alternatively, it might be due to near-equivalence of the magnitudes of σ1 and σ2, implying a uniaxial extensional stress state, which would also explain the scattering of a few inclined solutions across the plane normal to σ3. However, the shape factor F, defined as (σ2-σ3)/(σ1-σ3) is ∼0.75, rather than the value of 1.0 that would define a uniaxial extensional regime. Normal faulting is dominant among the focal mechanism solutions. If we consider the west-dipping plane as the fault plane (even if it is actually not), then an azimuth for this plane of around 140°/150° would imply the shear component is dextral, while it would be senestral for azimuths of the order of 170°/180°. This is completely in agreement with the direction of extension. On Fig. 1c and d, we can notice strike-slip mechanisms with a normal component on N120° faults.

The distribution of principal axis orientations for the GPK3 data (Fig. 2a) also shows that σ3 (i.e. Shmin) is well constrained to be horizontal, but is oriented at N77° ± 4°. The solutions for the other two principal stress axes form a continuous band across the stereoplot, indicating the stress state has cylindrical symmetry consistent with a uniaxial extension regime. The shape factor value of ∼0.9 estimated for the shape factor with the 62 events data set is reasonably consistent with uniaxial extension. The mechanisms (Fig. 2 b–d) are more or less very similar to those observed in GPK2. Nevertheless, close scrutiny reveals that the dextral strike-slip movements occur on planes whose strike is larger than in the GPK2 examples. This would be consistent with a slight rotation in the orientation of σ3. We also observe more mechanisms with a dominant strike-slip feature.

4.1 GPK2

4.2 GPK3

In the lower part of GPK3, Valley and Evans, 2007a found an Shmin orientation of N71° ± 20° from breakouts, which is consistent with the inversion results for both GPK2 and GPK3, the standard deviation being too large to discriminate. The large standard deviation is due in large part to a large-scale disturbance of the stress field extending along the GPK3 well between 4.5 and 4.8 km (true vertical depth) that is associated with a fault that dips at 50–60° towards N250° (Valley and Evans, 2007b). This perturbation results in changes in Shmin-orientation of up to 90°. The presence of such large perturbation is the principal justification for the process of removing focal mechanism solutions from the inversion that high large misfit since these are likely to be occurring within a stress perturbation. On Fig. 3, we show the location of the 23 seismic events for which the misfit between the observed and the calculated slip direction is higher than 15°. It can be seen that 11 of the 23 focal mechanisms are clustered within the cloud close to GPK3 (on this projection view) at depths between 4800 m and 5100 m.

In conclusion, direct observation of breakouts and DITFs in the boreholes appears to be the most accurate method to determine the linear-with-depth state of stress, and quantify the deviations from this (i.e. the heterogeneity). Nevertheless the inversion of focal mechanisms can yield useful characteristics of the stress field, and has the advantage that it samples a much larger volume. The results obtained in the present study show that, for the well-constrained stresses, the discrepancy between the results of the focal mechanism and the wellbore failure observations is less than the uncertainty range. The approach of selecting compatible mechanisms produces simultaneously a set of rejected mechanisms, which can, in some favourable cases, highlight zones of strong stress heterogeneities.