Journal of Geophysical Research: Solid Earth

High fluid pressure and triggered earthquakes in the enhanced geothermal system in Basel, Switzerland

Authors


Corresponding author: T. Terakawa, Earthquake and Volcano Research Center, Nagoya University, Nagoya 464–8601, Japan. (terakawa@seis.nagoya-u.ac.jp)

Abstract

[1] We analyzed 118 well-constrained focal mechanisms to estimate the pore fluid pressure field of the stimulated region during the fluid injection experiment in Basel, Switzerland. This technique, termed focal mechanism tomography (FMT), uses the orientations of slip planes within the prevailing regional stress field as an indicator of the fluid pressure along the plane at the time of slip. The maximum value and temporal change of excess pore fluid pressures are consistent with the known history of the wellhead pressure applied at the borehole. Elevated pore fluid pressures were concentrated within 500 m of the open hole section, which are consistent with the spatiotemporal evolution of the induced microseismicity. Our results demonstrate that FMT is a robust approach, being validated at the meso-scale of the Basel stimulation experiment. We found average earthquake triggering excess pore fluid pressures of about 10 MPa above hydrostatic. Overpressured fluids induced many small events (M < 3) along faults unfavorably oriented relative to the tectonic stress pattern, while the larger events tended to occur along optimally oriented faults. This suggests that small-scale hydraulic networks, developed from the high pressure stimulation, interact to load (hydraulically isolated) high strength bridges that produce the larger events. The triggering pore fluid pressures are substantially higher than that predicted from a linear pressure diffusion process from the source boundary, and shows that the system is highly permeable along flow paths that allow fast pressure diffusion to the boundaries of the stimulated region.

1. Introduction

[2] Hydraulic stimulation is one of the fundamental methods to increase the permeability at depth in the enhanced geothermal system (EGS). From 2 to 8 December, 2006, a private/public consortium in Basel, Switzerland (Figure 1), attempted to stimulate a geothermal reservoir by injecting approximately 11,500 m3 of water at high pressure into a 5 km deep well [Häring et al., 2008]. Thousands of induced seismic events were recorded by a six-sensor borehole array installed at depths between 317 m and 2740 m around the well. At a peak wellhead pressure of almost 30 MPa, a seismic event of ML 2.6 occurred, that surpassed the safety threshold and which resulted in a termination of the injection. It was followed a few hours later by an ML 3.4 event. Seismic activity in the stimulated rock volume declined rapidly over the following three weeks, but increased again in January and February 2007, including three additional events with ML > 3.

Figure 1.

Topographic map of Switzerland and surroundings with regional seismic stations that contributed data to the focal mechanisms. For the locations of the seismic stations in the region of Basel see Deichmann and Giardini [2009] or Deichmann and Ernst [2009].

[3] Determining the pore fluid pressure field in the stimulated region of EGS is essential for the long-term management of geothermal resources. Focal mechanisms of seismic events reflect the pore fluid pressure and the friction coefficient on the fault as well as the tectonic stress pattern, because fault strength is controlled by Coulomb failure criterion (Coulomb friction law). Several studies [e.g., Zoback, 1992b; Cornet and Yin, 1995; Plenefisch and Bonjer, 1997; Rivera and Kanamori, 2002] estimated a uniform stress pattern from a variety of focal mechanisms of seismic events, and investigated levels of the pore fluid pressure and the friction coefficient using the following two end-member models. One end-member model assumes hydrostatic pore fluid pressure, and attributes focal mechanism variations to variations in friction coefficients of pre-existing faults. The other end-member model assumes a constant standard friction coefficient (0.6), as suggested by Byerlee's law [Byerlee, 1978]. This model attributes the observed variation of focal mechanisms to fault strength heterogeneity controlled by variations in pore fluid pressures acting on faults. Using Byerlee's law as well as Bayesian statistical inference and Akaike's Bayesian Information Criterion (ABIC) [Akaike, 1980], Terakawa et al. [2010] developed an analysis technique, termed focal mechanisms tomography (FMT), to estimate the 3D pore fluid pressure field from focal mechanisms. Application of this technique to the 2009 L'Aquila earthquake in Italy showed that overpressured fluid reservoirs at hypocentral depths likely contributed to that sequence. The results of Terakawa et al. [2010] were consistent with other seismic studies that showed the involvement of high pressure fluids [Lucente et al., 2010], but there was no independent way to validate the pore fluid pressures determined using FMT.

[4] The Basel fluid-injection experiment provided an excellent opportunity to validate the FMT approach because of the well-constrained regional stress field, the known fluid pressure history applied at the open section of the borehole, and numerous well-constrained focal mechanisms with relocated hypocenters [e.g., Häring et al., 2008; Valley and Evans, 2006, 2009; Deichmann and Giardini, 2009]. In this paper, we apply FMT to the Basel experiment to estimate the pore fluid pressure in the stimulated region and quantitatively demonstrate the validity of the FMT method. We also discuss how the results provide additional insight into the role of high pressure fluids and their interaction with tectonic stress to earthquake generation.

2. Methodology of Focal Mechanism Tomography

[5] Focal mechanism tomography is an analysis technique to estimate pore fluid pressures at depth from focal mechanisms of seismic events [Terakawa et al., 2010]. The primary assumptions in this approach are; 1) fault strength is controlled by the Coulomb failure criterion with a constant standard friction coefficient [Byerlee, 1978], and 2) seismic slip occurs in the direction of the resolved shear traction acting on pre-existing faults [Wallace, 1951; Bott, 1959]. We further assume that 3) the vertical stress is the weight of the overburden, and 4) seismic slip on optimally oriented faults relative to the prevailing regional stress pattern occurs under hydrostatic pressure. The following sections describe basic ideas and the procedure of the method.

2.1. Basic Ideas

[6] We assume that earthquakes are governed by the Coulomb failure criterion (assumption 1). The fault strength τs is described by

display math

where σn and Pf are the normal stress (compression is positive) and the pore fluid pressure, respectively, and μ is the friction coefficient. Within a uniform stress pattern and hydrostatic pore fluid pressure, the variety of earthquake focal mechanisms can be attributed to variations in friction coefficients of pre-existing faults. Conversely, in a uniform stress pattern with constant friction coefficients, variations in focal mechanisms can be attributed to fault strength heterogeneity controlled by variations in pore fluid pressures acting on pre-existing faults. Based on laboratory experiments of rock friction [e.g., Byerlee, 1978] and in situ stress measurements in deep boreholes [e.g., Zoback and Healy, 1992; Zoback and Townend, 2001], heterogeneity of friction coefficients within the rock mass is normally be substantially smaller than the pore fluid pressure heterogeneity in the study region. In FMT we estimate pore fluid pressure with a constant friction coefficient.

[7] The theory of FMT can be explained using the 3D Mohr diagram (Figure 2). This diagram represents the stress state on any plane within a uniform stress field, designated by a point in the region surrounded by the three Mohr circles. The horizontal and vertical coordinates of the point show the normal and shear stresses acting on the plane, while the relative position of the point shows the orientation of the fault relative to the stress pattern [e.g., Zoback, 2007]. Since seismic slip occurs when shear stress reaches the fault strength, the intersection of the Mohr-Coulomb failure line passing through this point and the horizontal axis shows the pore fluid pressure Pf activating the event. Thus elevated fluid pressure initiates seismic slip on unfavorably oriented faults relative to the regional stress pattern even in the absence of shear stress build-up, and the fault orientation within that stress field is a measure of pore fluid pressure. It should be noted that pore fluid pressure activating seismic slip must be theoretically less than the least principal stress, otherwise hydraulic fracture occurs [e.g., Zoback, 1992b; Rice, 1992; Hardebeck and Michael, 2004].

Figure 2.

Theory of FMT in 3D Mohr diagram. The horizontal and vertical axes show normal and shear stresses; σ1, σ2, and σ3 are the maximum, intermediate, and minimum compressive principal stresses; Pf, Ph, ρw, g, z, and μ are the pore fluid pressure, the hydrostatic pore fluid pressure, density of water, gravity, depth of hypocenter, and the friction coefficient. A stress state acting on a plane (σ0: normal stress, τ0: shear stress) is shown with a point within the shadow zone surrounded by the three Mohr circles. The solid line labeled H0 shows the fault strength controlled by Coulomb failure criterion under hydrostatic pressure. Assuming that rock tensile strength is negligible, the fluid pressure can increase to the minimum principal stress, and the fault strength is shown by the solid line labeled Hmax. Elevated pore fluid pressure reduces fault strength and triggers seismic slip on faults unfavorably oriented relative to the regional stress pattern.

2.2. The Procedure of FMT

[8] In the first step we estimate the tectonic stress pattern, which is usually represented by the 3 directions of the principal stress axes and the R value, R = (σ1 − σ2)/(σ1 − σ3) (i.e., the relative dimensions of the Mohr circles), through stress inversion of seismic events [e.g., Gephart and Forsyth, 1984; Michael, 1984, 1987; Horiuchi et al., 1995; Terakawa and Matsu'ura, 2008]. The signs of σ1, σ2, and σ3 show maximum, intermediate, and minimum (compressive) principal stresses, respectively.

[9] In the second step we identify which of the two nodal planes is a geometrically possible slip plane. We calculate expected moment tensors from the orientation (strike and dip angles) of both nodal planes [Terakawa and Matsu'ura, 2008], based on the assumption 2 (the Wallace-Bott hypothesis). We measure the closeness of the observed and expected moment tensors (CT) with inner tensor product as defined by Michael [1987]:

display math

where mijo and mije are components of the observed and expected moment tensors. The CT value ranges from −1 ≤ CT ≤ 1, where +1 indicates that the observed moment tensor exactly coincides with the expected moment tensor, and −1 indicating that the observed moment tensor is opposite to that expected. We choose the nodal plane with the higher CT value as the true fault plane. It should be noted that this criterion for selection of true fault planes depends only on the stress pattern but not on the absolute stress tensor.

[10] In order to determine absolute pore fluid pressures, we need to know all the six components of the stress tensor. In the third step we determine the deviatoric and isotropic stress levels (i.e., the actual diameters and the center of the largest Mohr circle, respectively) with assumptions 3 and 4. We can determine the isotropic level by assumption 3 that the vertical stress is the weight of the overburden. Assumption 4 requires that the Mohr-Coulomb failure line (under hydrostatic pore fluid pressure) must connect with the largest Mohr circle, which enables a determination of the diameters of the Mohr circles.

[11] Finally, from Cauchy's relation and given an absolute stress tensor and fault orientations (determined from focal mechanisms in step 2), we can estimate normal and shear stresses acting on the fault plane. Pore fluid pressures are then determined by solving equation (1). Determining pore fluid pressure from this method results in a pore fluid pressure measurement at the discrete points of the hypocenters. By applying an inversion technique developed by Yabuki and Matsu'ura [1992] to the excess (above hydrostatic) pore fluid pressures pn (n = 1, ⋯, N) of the data set, we can estimate the 3D excess pore fluid pressure field as a continuous function with estimation errors (see Appendix). This technique is based on Bayesian statistic inference and Akaike's Bayesian Information Criterion (ABIC) [Akaike, 1980].

3. FMT Analysis in the Basel Geothermal Reservoir

[12] We applied the FMT method to focal mechanisms based on first-motion polarities (Figure 3) determined for 118 events with local magnitudes (ML) between 1.0 and 3.4, which occurred from 3 December 2006 to 30 November 2007. The focal mechanisms were computed as described in Deichmann and Ernst [2009]. According to the classification of Zoback [1992a], of the 118 focal mechanisms, 101 are strike-slip, 5 are oblique strike-slip with a normal component, and 12 are normal faulting mechanisms (Figure 4b). Hypocentral locations of the events analyzed in this study were determined using a master-event relocation technique. As documented in Deichmann and Giardini [2009] mean and standard deviations of the calculated relative location errors for the x, y, and z coordinates are 49 ± 4 m, 54 ± 6 m, and 72 ± 8 m. In Section 3.1, following the procedure described in Section 2.2, we first determined the tectonic stress field from the data set. Next, in Section 3.2, we estimated the pore fluid pressure distribution at depth by examining the fault orientation relative to the tectonic stress pattern.

Figure 3.

Hypocenter maps of 118 induced events and focal mechanisms of the 42 events with ML ≥ 1.7. (a) Map of epicenters (gray dots). Focal mechanisms are represented as lower-hemisphere stereographic projections, scaled with magnitude. The color of the focal spheres corresponds to focal depth. (b) Vertical distribution of hypocenters (E-W section). (c) Vertical distribution of hypocenters (N-S section). The color of the dots corresponds to focal depth. The focal depth is measured from sea level.

Figure 4.

The tectonic stress pattern and focal mechanisms of the triggered seismicity. (a) The tectonic stress pattern. (b) Stereographic projection (equal area, lower hemisphere) of the orientation of the P-axes (white circles) and T-axes (black circles) of the 118 focal mechanisms of the triggered Basel events. The diagonal lines correspond to the average azimuths of the P- and T-axes. (c) Symmetric polar histogram of the strike of all nodal planes, together with the overall strike of the macroscopic structure defined by the hypocenter locations. The arrows in Figures 4b and 4c point in the direction of the maximum and minimum horizontal compressive stress estimated in the present study. The red line in Figure 4c shows the orientation of the macroscopic plane of microseismic cloud.

3.1. Tectonic Stress Field in the Basel Geothermal Reservoir

[13] Using the computer code of Terakawa et al. [2010], from the data set we searched the best fitting stress pattern which minimizes the difference between the expected and observed moment tensors. We chose the nodal planes with the higher CT values between the observed and expected moment tensors as the true fault planes (Table 1).

Table 1. Focal Mechanism Parametersa
Event NumberLatLonZMPlane 1ϕ1CT 1Pf1Plane 2ϕ2CT 2Pf2
  • a

    Z: focal depth (km); M: local magnitude; Plane1 and Plane 2: strike/dip/rake; ϕ1 and ϕ2: expected rake angles from the best fit stress pattern; CT1 and CT2: CT values between theoretical and observed moment tensors, Pf1 and Pf2: excess pore fluid pressures (MPa).

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19547.587.5974.21.690/73/1531680.96714188/65/17/−160.82219

[14] Figure 4a shows the tectonic stress pattern and the estimation errors of the three principal stress axes estimated in the present study. We evaluated the estimation errors of the stress pattern using a bootstrap method. The number of re-sampling was 500. The stress pattern is characterized by strike-slip faulting, where the maximum and minimum principal stress axes are almost horizontal in the directions of N38°W and N48°E and the value of R is 0.36. The 67% confidence regions of maximum and minimum horizontal principal stress axes are N30°W-N45°W and N41°E-N59°E. R-values in the confidence region vary from 0.3 to 0.6. This stress pattern is entirely consistent with that deduced by Valley and Evans [2006, 2009] from borehole measurements (maximum horizontal principal stress: N36°W ± 14°, minimum horizontal principal stress: N54°E ± 14°). For the Basel data set, the average CT is 0.98, which corresponds to an average misfit angle between observed and expected slip vectors of about 9.7 degrees. Seismic events with high CT values can be explained as reactivation of pre-existing faults in a uniform stress field, while those with low CT may be indicative of local stress heterogeneities and/or very weak fault strengths. The horizontal orientation of the principle stress axes coincides to within 4 degrees with the average azimuth of the P- and T-axes (Figure 4b).

[15] With the known stress pattern, and assumed friction coefficient of 0.85 [Byerlee, 1978] and rock density of 2540 kg/m3 [Häring et al., 2008], we determined the absolute stress tensor (Figure 5). The absolute values of σ1, σ2, and σ3 at the depth of 5 km are 144 MPa, 117 MPa and 69 MPa, respectively. These values are consistent with those determined by Häring et al. [2008], whose values of σ1, σ2, and σ3 at the same depth are 160 MPa, 122 MPa and 84 MPa. One of the reasons of the slight difference between the two studies is that, contrary to our approach, Häring et al. [2008] assumed σ2 to be perfectly vertical. The other reason is that, in the absence of any evidence for the occurrence of hydrofracking during the injection, Häring et al. [2008] constrained the value of σ3 to be slightly higher than the maximum injection pressure at the bottom of the well.

Figure 5.

The depth distribution of absolute stresses. We assume that the density of rock is 2540 kg/m3 [Häring et al., 2008]. Seismic events used in the present study occurred in the depth range from 3.77 km to 4.93 km.

3.2. The Distribution of the Pore Fluid Pressure in the Basel Fluid-Injection Experiment

[16] Given the absolute stress tensor and true fault planes, we estimated pore fluid pressures necessary to trigger the observed seismic events. Assuming errors of focal mechanisms to be within 10–15 degrees, we chose a tight constraint of CT ≥ 0.965 for events to be included in the analysis to estimate the pore fluid pressure field. This corresponds to misfit angles between the observed and expected slip vectors less than about 15 degrees. Figure 6a shows the distribution of 96 excess pore fluid pressures plotted in the 3D Mohr diagram. The maximum value of the excess pore fluid pressures is about 31 MPa (Event 46, Table 1), which is consistent with the maximum wellhead pressure. Figures 6b and 6c show the temporal and spatiotemporal evolutions of excess pore fluid pressures, respectively. Figure 6b shows that temporal change of excess pore fluid pressures before the shut-in is consistent with the history of wellhead pressures. Figure 6c shows that overpressured fluids are concentrated within 500 m from the injection point.

Figure 6.

The pore fluid pressures formed by the fluid injection in Basel. (a) The excess pore fluid pressure for each event (with CT ≥ 0.965) in the 3D Mohr diagram. The horizontal and vertical axes show normal and shear stresses which are normalized by the maximum shear stresses, defined by (σ1σ3)/2. σ1, σ2, σ3 and Ph show positions of the 3 principal stresses and the hydrostatic pressure in the horizontal axis. The color indicates the excess pore fluid pressure, and the size scales with magnitude. The line labeled H0 indicates fault strength under hydrostatic pressure, and the other two lines (H1, and H2) under supra-hydrostatic pore fluid pressures. The inlet figure is the histogram of excess pore fluid pressures. (b) The temporal evolution of pore fluid pressures. The diamonds show excess pore pressures, and the solid line shows the history of the wellhead pressure of the injection experiment. (c) The spatiotemporal evolution of pore fluid pressures. The color circles are the same as in Figure 6a.

[17] The hypocenters of the events are localized along a near-vertical plane that strikes approximately N18°W (Figures 3a and 4c). We took this macroscopic plane of the microseismic cloud with lengths of 2800 m and 3600 m along strike and in depth, respectively, as the model region. We divided it into 14 × 18 subsections, and distributed 165 (11 × 15) bi-cubic B splines (basis functions) with 200 m equally spaced local support (grid interval) to represent the distribution of the pore fluid pressure on this macroscopic plane. In this case, since the variation of pore fluid pressures within each grid interval is represented by the superposition of four local cubic functions, the theoretical limit of spatial resolution is 50 m. These values are smaller than the average resolution length expected from the distribution of seismic events (Figure 3), and so the present choice of grid intervals will not affect the results of inversion analysis. Then, determining the best estimates of the expansion coefficients (model parameters) and the covariance matrix with the Yabuki-Matsu'ura inversion formula [Yabuki and Matsu'ura, 1992], we estimated the pore fluid pressure field as a continuous function with estimation errors. Figure 7a shows the distribution of excess pore fluid pressures on the macroscopic plane, and Figure 7b shows the estimation errors. Figures 7a and 7b show that elevated pore fluid pressures with a peak of 17 MPa are concentrated within about 500 m of the open hole section with the estimation errors (the standard deviation) of 2–5 MPa. Figure 8 shows that the hypocenters mainly migrated upward in the direction of S18°E.

Figure 7.

The distribution of pore fluid pressures formed by the fluid injection in Basel. (a) The excess pore fluid pressure field projected onto the macroscopic plane defined by the overall hypocenter distribution. The circles show hypocenters of events projected on the plane, whose excess pore fluid pressures are included in the analysis to estimate the pore fluid pressure field. The color and the size of circles are the same as in Figure 6a. (b) The distribution of estimation errors of pore fluid pressures. The size of the circles is the same as in Figure 7a.

Figure 8.

The spatiotemporal evolution of seismicity. Excess pore fluid pressure for each event is plotted on the excess pore fluid pressure field in Figure 7a. The color and size of the circles are the same as in Figure 6a. (a) 3–6 December 2006, (b) 7 December 2006, (c) 8 December 2006, (d) 9–24 December, and (e) Jan. to Nov. 2007.

4. Discussion

[18] In FMT we estimate the pore fluid pressure field from a given set of focal mechanisms of seismic events by examining the fault orientation relative to the tectonic stress field, based on an end-member model that the friction coefficient is constant for each event. This assumption is suggested by laboratory experiments of rock friction [e.g., Byerlee, 1978] and in situ stress measurements in deep boreholes [e.g., Zoback and Healy, 1992; Zoback and Townend, 2001]. The other end-member model that pore fluid pressure is hydrostatic everywhere, and the variation in focal mechanisms can attributed to variations in friction coefficients does not apply in our case because large volume of fluids were injected at high pressures, so we can assume that the effect of possible variations of friction coefficients is small in comparison.

[19] In the present study we make the simplifying assumption that the tectonic stress pattern is spatiotemporally uniform in the geothermal reservoir, although pore fluid pressures should be coupled with the stress fields. The most influential stress perturbation seems to be stress changes due to seismic events triggered by increase of pore fluid pressures, although an excess pore fluid pressure will deform porous rock and cause stress perturbations. From seismic observations, the stress drop in the source region is scale independent, and it is at most 5 MPa on average [e.g., Kanamori and Anderson, 1975; Goertz-Allmann et al., 2011]. As shown in studies on Coulomb stress changes [e.g., King et al., 1994; Stein, 1999], stress changes due to a seismic event rapidly vanish with distance from the source. The stress perturbation due to seismic events is at most 10% of the absolute stress level at the depth of 4–5 km, and therefore the uniform stress pattern assumption is reasonable. In the Basel case, more than 80% of the slip vectors were consistent with those expected under the estimated uniform stress pattern, but in order to apply FMT to seismic data in a broader region, we have to consider spatial variation of stress fields. The formulation described in Section 2 is also applicable to the heterogeneous stress field, and it would be useful to combine FMT with stress inversion methods that can infer spatial variation of stress fields [e.g., Terakawa and Matsu'ura, 2008, 2010].

[20] The excess pore fluid pressure for each event in the data set (Figures 6a–6c), and the distribution of pore fluid pressures (Figure 7a) are consistent with the conditions of the wellhead pressure of the injection experiment [Häring et al., 2008] and the spatiotemporal evolution of the induced microseismicity. In addition to the analysis in Section 3.2, we performed nine additional numerical experiments to examine the robustness of FMT. The conditions of these analyses are listed in Table 2. In Experiments 1–3 we estimated pore fluid pressure fields, varying the friction coefficients (Figures 9a–9c). These results show that the shape of the inferred fluid reservoir does not depend on the friction coefficient, although the absolute value of pore fluid pressures (in the upper part of the reservoir) tends to increase slightly with increasing friction coefficients. These results show that FMT can reproduce reliable pore fluid pressure distributions at depth. As discussed in the next paragraph, reliability of results in the deeper parts of the reservoir is unreliable because of limited data (one data point) in this region.

Table 2. Parameters of the Numerical Experimentsa
 Data SetT. F. P.μBasis FunctionFigure
  • a

    Data set: The data set used in the present study; T. F. P: The criterion for selecting the true fault plane; μ: The friction coefficient; Basis function: The number of basis functions; Figure: Figure number.

The standard analysisoriginalCT0.85165Figure 7a
Experiment 1originalCT0.4165Figure 9a
Experiment 2originalCT0.6165Figure 9b
Experiment 3originalCT1.0165Figure 9c
Experiment 4original + random errors (±5°)CT0.85165Figure 10a
Experiment 5original + random errors (±10°)CT0.85165Figure 10b
Experiment 6original + normal random errorsCT0.85165Figure 10c
Experiment 7originalCT + random0.85165Figure 11
Experiment 8originalCT0.85513Figure 12a
Experiment 9originalCT0.8599Figure 12b
Figure 9.

Dependence of the pore fluid pressure distribution on the friction coefficient: (a) μ = 0.4 (Experiment 1), (b) μ = 0.6 (Experiment 2), and (c) μ = 1.0 (Experiment 3). The color and size of the circles are the same as in Figure 6a.

[21] Some of the excess pore pressures in Figures 6a–6c exceed the maximum wellhead pressure (29.6 MPa). This may be caused by observation errors of focal mechanisms and/or incorrect selection of true fault planes. In order to check the error propagation, we applied FMT to three data sets of focal mechanisms, each of which is rotated from the original focal mechanism around an arbitrary vector. In Experiments 4 and 5 we determined rotation angles using uniform random numbers. Rotation angles vary from −5 degrees to 5 degrees, and from −10 degrees to 10 degrees in Experiments 4 and 5, respectively. In Experiment 6 we determined rotation angles using a normal distribution (mean: 0 degree, standard deviation: 5 degrees). Figures 10a–10c show the distributions of excess pore fluid pressures in the three cases. In all the cases we can see two large fluid pockets with peak pore fluid pressures of about 20 MPa, indicating that the pore fluid pressure field inferred from FMT is robust. It is expected that the distribution of excess pore fluid pressures (Figure 7a) would not be affected by random errors of the data set because we statistically obtained this result using an inversion technique [Yabuki and Matsu'ura, 1992]. However, the deepest fluid pocket in Figure 7a does not appear in Experiments 5 and 6 (Figures 10b–10c) because there are few data in the vicinity of the deepest parts of the stimulated rock volume. The estimation error of pore fluid pressures in the deeper part (> 4.5 km) is larger than in the region of the two large shallower pockets of high fluid pressure (Figure 7b). The existence of the deepest concentration of high fluid pressure may be less reliable.

Figure 10.

Influences from the error propagation on the distribution of pore fluid pressures. We show the excess pore fluid pressure fields inferred from three data sets of (a) Experiment 4, (b) Experiment 5, and (c) Experiment 6. The data sets consist of focal mechanisms each of which was rotated around an arbitrary vector. Rotation angles were determined by uniform random numbers in Experiment 4 (−5° ≤ θ ≤ 5°) and Experiment 5 (−10° ≤ θ ≤ 10°), and by normal random numbers in Experiment 6 (mean: 0 degree, standard deviation: 5 degrees). The color and size of the circles are the same as in Figure 6a.

[22] We determined true fault planes by choosing the higher CT of the observed and expected moment tensors. As long as the B-axis does not coincide with that of the intermediate principal stress, this criterion can identify the true fault plane [Gephart, 1985]. However, some incorrect selections may be caused by focal mechanism errors and/or by local stress-field heterogeneities. To determine the effect of choosing CT values that are close to each other, we used a criterion that for CT values within 0.05 (33 events), the true fault plane was chosen at random between the two possibilities (Experiment 7). The criterion of 0.05 was used because that corresponds to the uncertainty in the focal mechanisms. The distribution of pore fluid pressures (Figure 11) has a few fluid pockets. This feature is similar to that in Figure 7a, although we randomly chose true fault planes for a third of the data set. This indicates that the selection of true fault planes using CT does not result in systematic errors, and so the pore fluid pressure field inferred through FMT is unbiased.

Figure 11.

Influences from incorrect selection of true fault planes with CT on the distribution of pore fluid pressures. We show the excess pore fluid pressure field of Experiment 7 (in text).

[23] The distribution of pore fluid pressures peaks (17 MPa) in a large fluid pocket south of the well, and the peak value is 56% of the applied maximum wellhead pressure. There should be a pressure gradient from borehole to the triggering location with the peak value, and so the estimate seems to be rational. But on the other hand this may be related to resolution of the present analysis. In order to check dependence of the number of the basis function (model parameters), we estimated the distributions of the pore fluid pressure using 513 (19 × 27) and 99 (9 × 11) bi-cubic B splines with 100 m and 300 m equally spaced local support, respectively (Experiments 8 and 9). The estimated pore fluid pressure fields are independent of the number of the basis function (Figures 12a–12b), although the peak value of pore fluid pressures (18 MPa in Experiment 8, 16 MPa in Experiment 9) was slightly higher with smaller size of basis function. This can be improved with additional data that would result in higher resolution of the pore pressure field.

Figure 12.

Dependence of the number of the basis functions on the distribution of pore fluid pressures. (a) Experiment 8, and (b) Experiment 9. We used 513 and 99 basis functions in Experiments 8 and 9, respectively.

[24] Figures 6a, 6b, and 7a indicate that many events occurred at intermediate pore fluid pressures with an average of about 10 MPa ± 6 MPa. Such earthquake triggering pressures are significantly larger (by several orders of magnitude) than earthquake triggering pressures inferred from linear diffusion models of porous rock media [e.g., Dinske and Shapiro, 2010; Goertz-Allmann et al., 2011]. This is significant because it shows that the system is highly permeable along flow paths, allowing fast pressure transfer and substantially elevated fluid pressures within the stimulated region. The large change in local permeability at the onset of slip [e.g., Miller and Nur, 2000] should be included in numerical modeling efforts of EGS systems. In addition, the observation that the injected fluids mainly migrated upward in the direction of S18°E (Figure 8) indicates that future modeling efforts include the effective stress-dependence of permeability as used in previous models of fluid-rock interactions [Rice, 1992; Miller et al., 2004].

[25] The strike of the macroscopic plane of the microseismic cloud formed by the injection experiment is roughly N18°W, although only a small fraction of the available focal mechanisms have nodal planes whose strike is more or less parallel to it (Figure 4c). The orientation is very consistent with that of one of the optimally oriented planes for shear faulting with the friction coefficient of 0.85 (N13°W). This indicates that the macroscopic plane formed in response to shear faulting due to overpressured fluids. Although formation of the macroscopic plane appears to be controlled by the tectonic stress field, the evolution of this system includes many individual seismic events occurring along unfavorably oriented faults due to elevated pore fluid pressures (Figure 6a).

[26] Figure 13a shows the relationship between event magnitudes and the degree of overpressure, which is defined by the overpressure coefficient, C = (Pf − Ph)/(σ3 − Ph), and Figure 13b shows the relationship between event magnitudes and shear stress normalized by the maximum shear stress at hypocentral depth. These figures show that many small events (M < 3) occurred on unfavorably oriented faults with relatively low values of shear stress, which we attribute to triggering by elevated fluid pressure. However, the 3 largest events occurred along faults with relatively high shear stress and with overpressure coefficients indicative of near hydrostatic pore pressure at the time of failure. Because of insufficient data set, an unambiguous conclusion is difficult, but we note that a similar tendency was found in the case of the 2009 L'Aquila earthquake (auxiliary material), although the critical magnitude of events triggered by fluids in L'Aquila is larger than that in Basel [Terakawa et al., 2010]. It has also been reported for natural earthquakes that focal mechanisms of large earthquakes directly represent the regional tectonic stress field, although those of small earthquakes are diverse [e.g., England and Jackson, 1989; Amelung and King, 1997; Terakawa and Matsu'ura, 2010].

Figure 13.

Roles of pore fluid pressure and tectonic stress. (a) Relationship between magnitudes of seismic events and pore fluid pressures (Pf) activating the events. The vertical axis shows the over-pressure coefficient, C, which is defined by C = (Pf − Ph)/(σ3 − Ph), where Ph, and σ3 are the hydrostatic pressure and the minimum principal stress. (b) Relationship between magnitudes of seismic events and shear stress acting on fault planes. The vertical axis shows shear stress normalized by the maximum shear stress.

[27] The implication of this observation is that small-scale triggering by reduction of fault strength due to overpressured fluids provides a mechanism for an evolving interconnected network, but whether events grow into larger ones or not appears to be controlled by tectonic stress field. The overpressured fluid reservoir may play a role as the non-asperity, slip on which would cause tectonic loading at the asperity around them [Kanamori, 1981]. How this evolving interconnected network influences larger-scale seismicity requires additional study.

5. Conclusions

[28] We estimated the distribution of pore fluid pressures developed within the reservoir of the enhanced geothermal system in Basel Switzerland. The injection of high-pressure fluids induced thousands of earthquakes, and we applied focal mechanism tomography to 118 well-constrained focal mechanisms to infer the pore fluid pressure field at depth. The inferred pore fluid pressure distribution is consistent with the known fluid pressure history applied at the borehole. Our analysis demonstrates that focal mechanism tomography is a viable method for inferring pore fluid pressures, and their distribution, at depth. Our results show that triggering pressures of about 10 MPa are orders of magnitude larger than would be inferred using a simple linear diffusion model. The results demonstrate that high fluid pressures trigger earthquakes on non-optimally oriented faults, but that larger events are primarily controlled by shear failure in response to the tectonic stresses. The complex interaction between high pore pressure and shear failure [e.g., Miller et al., 1996] requires that future modeling efforts include evolving crack networks coupled to pressure diffusion and fluid flow. A further coupling between the evolving fluid pressure field and its poro-elastic consequences will be the focus of future studies.

Appendix A

[29] Determining pore fluid pressure from FMT results in a fluid pressure measurement at the discrete points of the hypocenters. In order to estimate the 3D excess fluid pressure field we apply an inversion technique developed by Yabuki and Matsu'ura [1992] to the excess (above hydrostatic) fluid pressures pn(n = 1, ⋯, N) of the data set. First, we represent the excess fluid pressure field p(x) by the superposition of a finite number of tri-cubic B-splines:

display math

where Φm are the tri-cubic B-splines, and am (m = 1, ⋯, M) are the expansion coefficients (model parameters). Then, we obtain system linear equations to be solved for the expansion coefficients am (m = 1, ⋯, M),

display math

where N is the number of data, xn is the position vector of the hypocenter of the n-th event, and en is the observation error for pn. These observation equations can be rewritten in vector form as

display math

where p is a N × 1 data vector, a is a M × 1 model parameter vector, F is a N × M coefficient matrix, and e is a N × 1 error vector. Assuming the errors to be Gaussian with zero mean and a covariance σ2, we obtain a stochastic model that relates the data p with the model parameter a as

display math

[30] In addition to observed data we can use the physical consideration that the pore fluid pressure field must be smooth to some degree because fluids are connected within a porous network. We thus impose prior constraint on the roughness of the pore fluid pressure field, which is expressed in the form of probability density function with an unknown scale factor ρ2 as

display math

where inline image denotes the absolute value of the product of (nonzero) eigenvalues of G. Here G is a M × M roughness matrix defined in Terakawa and Matsu'ura [2008]. Combining the prior constraint inline image in equation (A5) with the stochastic model inline image in equation (A4) by Bayes' rule, and introduce a new hyper-parameter α2(=σ2/ρ2) instead of ρ2, we can obtain a hierarchic, highly flexible model controlled by the hyper-parameters σ2 and α2:

display math

with

display math

[31] Here, it should be noted that the hyper-parameter α2 controls the relative weight of observed data to the prior information. Now, our problem is to find the values of a, σ2 and α2 that maximize the posterior pdf in equation (A6) for a given data set of excess fluid pressures. To find the optimum values of hyper-parameters, we can use Akaike's Bayesian Information Criterion (ABIC) [Akaike, 1980]. The explicit expression of ABIC is given in Yabuki and Matsu'ura [1992] as

display math

where a* denotes a maximum likelihood solution for a given α2. Once the optimum value inline image2, which minimizes ABIC in equation (A8), has been found, the best estimates inline image of the model parameters a and the covariance matrix C( inline image) of their estimation errors are given by

display math
display math

where inline image2 is the optimum value of the hyper-parameter σ2, and it's obtained by:

display math

[32] The best estimate of the excess fluid pressure at an arbitrary point xo can be calculated by substituting inline image = [ inline imagem] in equation (A9) into equation (A1) as

display math

and so the variance of its estimation errors is given by

display math

where Clk inline image denotes the lk-element of the covariance matrix C inline image in equation (A10). We can use the square root of variances (the standard error) to measure the uncertainty of estimated excess fluid pressure fields.

Acknowledgments

[33] We thank GeoPower Basel for permission to publish these results. We also thank the Editor Robert Nowack, one of the reviewers Thomas Plenefisch, and the anonymous Associate Editor and reviewer. Thoughtful comments from them were helpful to improve the manuscript. This work was supported by grant-in aid for scientific research C (23540493).