Seismotectonic state of reservoirs inferred from magnitude distributions of fluid-induced seismicity

J Seismol (2013) 17:13 25 DOI 10.1007/s10950-012-9292-9 ORIGINAL ARTICLE Seismotectonic state of reservoirs inferred from magnitude distributions of fluid-induced seismicity Carsten Dinske Serge A. Shapiro Received: 30 June 2011 / Accepted: 1 March 2012 / Published online: 22 March 2012 Springer Science+Business Media B.V. 2012 Abstract Fluid injections in geothermal reservoirs usually induce small magnitude earthquakes (M < 2). Sometimes, however, earthquakes with larger magnitudes (M 4) occur. Recently, we have shown that under rather general conditions, the probability of an event having a magnitude larger than a given one increases proportionally to the injected fluid mass. The number of earthquakes larger than a given magnitude also depends on the tectonic conditions of an injection site. A convenient parameter for the characterisation of the seismotectonic state of a reservoir location is the seismogenic index. It combines four, generally unknown, site-specific seismotectonic quantities. Using this index, we comparatively analyse the seismotectonic state of several geothermal as well as non-geothermal reservoir locations. The seismogenic indices of the considered locations are in the range of 10 < < 0.5. Although the number of reservoirs under examination is limited, we see a clear separation between hydrocarbon and geothermal reservoirs with respect to the seismotectonic state. In addition to a higher seismogenic index, geothermal reservoir locations are characterised C. Dinske (B) S. A. Shapiro FR Geophysik, Freie Universität Berlin, Malteserstr. 74-100, 12249 Berlin, Germany e-mail: carsten@geophysik.fu-berlin.de by a lower b value. It means that fluid injections in geothermal reservoirs have a higher probability to induce an earthquake with a significant magnitude. Our formulation provides a basis for estimating expected magnitudes of induced earthquakes. This can potentially be used to avoid the occurrence of large magnitude earthquakes by correspondingly planning fluid injections. Keywords Fluid-induced seismicity Magnitude Seismogenesis Geothermal Hydrocarbon Pore pressure Seismic hazard 1 Introduction Inducing fracture shear slippage and dilatation is, to some extent, intended by hydraulic fracturing and hydraulic stimulation operations. A potential hazard associated with the seismic activity has so far received less consideration. The hydraulic stimulation of the Basel geothermal reservoir in 2006, however, caused several significant events which were felt by the population (Majer et al. 2007; Häring et al. 2008). It led to the awareness that a more in-depth knowledge of seismic hazard associated with fluid injections is required. By the development of enhanced geothermal systems, the bottom hole injection pressure is often less than the minimum principal stress. For such situations, the behaviour of the seismicity

14 J Seismol (2013) 17:13 25 triggering in space and in time is controlled by the process of relaxation of stress and pore pressure perturbations initially created at the injection source. This relaxation process can approximately be described by a diffusion of fluid pressure in the pore space of the reservoir rock (e.g. Nur and Booker 1972; Pearson 1981; Shapiro et al. 1997). Tectonic stresses at some locations in the Earth s crust are close to a critical stress causing brittle failure of rocks. The fluid pressure in the connected pore space of rocks increases due to the injection of fluid into the reservoir rock. The pore space includes pores, cracks, fractures, grain contacts and all other possible voids in rocks. Such an increase in the pore pressure consequently causes a decrease of the effective normal stress, usually acting compressionally on internal rock surfaces. This leads to sliding along pre-existing, favourably oriented and near-critically loaded fractures. Shapiro et al. (2007) described the magnitude distribution of fluid-induced seismicity in case of linear pressure diffusion and constant fluid injection rates. Shapiro and Dinske (2009) expanded this description to the case of non-linear diffusion and a power-law increase with time of the injection rate. In this paper, we further generalise this approach. We extend it to a general type of a non-decreasing injection source, and we give a full description of the derivation of our model. The process of fluid rock interaction can be strongly non-linear in the sense of a strong impact of a fluid injection on the rock permeability. Such situations like a hydraulic fracturing of rock or a shearcaused dilatational permeability enhancement are taken into account. Furthermore, we continue to investigate the seismotectonic state of reservoir locations. Shapiro et al. (2010) introduce the seismogenic index and provide a formalism which allows for quantifying and evaluating the seismotectonic reservoir conditions. Here, we compute the seismogenic index for eight different reservoir locations (and 15 different injection experiments). We show that the seismogenic index is nearly time-independent. It is clear from our analysis that the seismogenic index has a characteristic range of values for geothermal reservoirs on the one hand and hydrocarbon reservoirs on the other hand. Furthermore, we analyse correlations between seismogenic index and other injection-, reservoirand seismicity-related parameters. We propose to collect a database of seismogenic indices for different geological settings. The presented work here is a first step towards such a database. 2 Theoretical model of magnitude distribution of fluid-induced seismicity The presented theoretical model here hypothesizes that the frequency magnitude distribution of fluid-induced seismicity is in accordance with the Gutenberg Richter scaling law (Gutenberg and Richter 1954). In spite of its simplicity and schematic character, our model indicates important parameters which control magnitudes of fluid-induced seismicity. 2.1 Cumulative number of induced earthquakes We consider a point-like injection source of monotonically increasing or constant strength at the origin of a Cartesian coordinate system. The injection-induced pressure relaxation alters the insitu pore pressure p 0 throughout the pore space and hence modifies the effective normal stress. We further assume that a random set of noninteracting, pre-existing fractures with volume concentration ζ is statistically homogeneously distributed in the medium. Each of the fractures is characterised by a critical pore pressure value C necessary for the occurrence of a slip event along the fracture in accordance with the Coulomb failure criterion (e.g. Scholz 2002). These critical pressures are randomly selected from a uniform distribution between a minimum value, C min, and a maximum value, C max. C min and C max address most unstable and most stable fractures, respectively. A fracture location r = (x, y, z) (and defined by its distance r = x 2 + y 2 + z 2 to the source point) will now become the hypocenter of an earthquake with occurrence time t 0,ifthe pore pressure perturbation p(r, t) exceeds the local value of critical pressure C(r) at time t 0.For simplicity, we assume that once an earthquake occurred at a certain fracture location, then no further earthquakes are possible at this position. This condition is confirmed by the observation that recharging of fractures to a near-critical state by

J Seismol (2013) 17:13 25 15 tectonic loading takes longer than the diffusionprocess of relaxation of a pore pressure perturbation (Shapiro et al. 2007). These preliminary considerations lead to the following. The probability W ev (r, t) that an earthquake occurs at a given fracture location r and in the time interval from the injection start until time t is equal to the probability that the critical pressure at position r is smaller than or equal to the maximum pore pressure perturbation reached at this position until time t. It means, the probability is equal to W(C(r) max{p(r, t)}). Withthe condition of non-decreasing injection pressures, we obtain the following: p(r,t) W ev (r, t) = f (C)dC, (1) C min where f (C) is the probability density function (PDF) of critical pressures C(r) of pre-existing fractures. Since uniformly distributed critical pressures are assumed, the PDF is given by the following: 1 f (C) = (C max C min ) 1. (2) C max The latter, approximated term in this equation takes into account the observation that C max is generally several orders of magnitude larger than C min,i.e.c max 10 6 and C min 10 2 10 4 (Rothert and Shapiro 2007). With the assumption that the maximum of critical pressures in the medium is larger than the pore pressure perturbation (excluding the very near borehole area) and the minimum of critical pressures is nearly equal to zero (the so-called reference case, Langenbruch and Shapiro 2010), Eq. 1 yields for the earthquake occurrence probability a direct proportionality to the pore pressure perturbation: p(r, t) W ev (r, t) =. (3) C max The total number of earthquakes N(t) induced in the time interval (0, t) can now be computed by multiplying the event probability with the fracture bulk concentration ζ, followed by spatial integration of the product: N(t) = A δζ p(r, t)r δ 1 dr. (4) C max R The factor A δ is a geometrical constant with values corresponding to the dimension δ of the problem under consideration, which means, if δ = 1, 2 or 3 then A δ = 2A r, 2πh or 4π, respectively (A r is the normal cross section of an infinite straight rod in the case of a 1D filtration, h is the height of a homogeneous plain layer, where a cylindrically symmetric 2D filtration takes place, and 4π is for a filtration in a 3D medium). The quantity R describes the radius of an effective injection source cavity (see Rothert and Shapiro 2007). In the following, we show that the spatial integral of pore pressure perturbation (Eq. 4) can be solved under rather general conditions including also a strongly non-linear interaction of the injected fluid with the reservoir rock. A universally valid principle, independent of any injection impact on the rock permeability, represents the continuity equation which expresses the fluid mass conservation: ρφ t = Uρ, (5) where ρ is the density of a pore fluid, U is its filtration velocity and φ is the rock porosity. Under realistic conditions (by neglecting irrotational deformation and stress dependence of elastic properties of drained rocks), the time-dependent part of the quantity φρ is proportional to the pore pressure perturbation p and can be substituted by ρ 0 ps. ρ 0 is a reference fluid density and S = α 2 (1/M dr + 1/(K gr K dr ) + φ(1/k f 1/K gr )) is a poroelastic compliance related to porosity φ and defined by the bulk modulus of pore fluid, K f, bulk moduli of grain material, K gr and drained rock skeleton, K dr, P-wave modulus of drained rock skeleton, M dr and Biot coefficient α = 1 (K dr /K gr ) (see also Detournay and Cheng 1993). We then obtain the following: ρ 0 S p t = Uρ. (6) We examine situations where borehole fluid injections can be approximated by a point pressure source switched on at time t = 0. We can therefore consider a spherically symmetric problem in a

16 J Seismol (2013) 17:13 25 δ-dimensional space. The continuity equation then takes the following form: ρ 0 S rδ 1 p = t r rδ 1 U r ρ, (7) where r is the radial distance from the injection point, and U r denotes the radial component of the filtration velocity U. Equation 7 is solved with the initial condition of zero pore pressure perturbation and zero filtration velocity before the injection starts, p = 0 and U r = 0 for t < 0, and with the two following boundary conditions. The first one gives the mass flow rate m i of the fluid injection at the surface of the injection cavity: m i (t) = A δ r δ 1 ρu r r=r. (8) The second boundary condition states that filtration velocity becomes vanishingly low at infinity. Integrating Eq. 7 over the distance r gives the following: ρ 0 S r δ 1 pdr = r δ 1 U r ρ r=r. (9) t R Subsequent integration over time and substitution of the boundary condition given in Eq. 8 results in: A δ ρ 0 S R r δ 1 pdr = t 0 m i (t)dt t = m c (t) ρ 0 Q i (t)dt. (10) Here, m c (t) is the cumulative injected fluid mass until time t. In the last approximated term, we have neglected any pressure dependence of the fluid density and have introduced the volumetric flow rate of the fluid injection, Q i (t). FromEqs.4 and 10, we further obtain: N(t) = m c(t)ζ C max ρ 0 S. (11) We notice that the cumulative number of fluidinduced earthquakes is proportional to the injected fluid mass. An important validity condition for this statement is a non-decreasing pore pressure perturbation in the whole space. If we neglect possible alterations of fluid density, then 0 this result will correspondingly simplify: N(t) = ζ C max S t 0 Q i (t)dt = ζ Q It I+1 C max S, (12) where the last term represents the case of a powerlaw fluid injection rate, Q i (t) = (I + 1)Q I t I,with constant parameters Q I and I. In situations where the fluid injection rate is kept constant over time I = 0 and Q i (t) = Q 0, it gives: N(t) = Q 0ζ t C max S. (13) This result shows that the cumulative event number grows proportionally to the injection time with a constant rate equal to Q 0 ζ/c max S. Furthermore, for a constant fluid injection rate and linear pressure diffusion, Q 0 /S is equal to 4π Dp I R, where p I is the injection pressure (see Rothert and Shapiro 2007). This relation provides an alternative interpretation of Eq. 13 already derived by Shapiro et al. (2007): N(t) = 4π Dp I Rζ t. (14) C max 2.2 Magnitude statistics of induced earthquakes The question arises on how can we now describe the statistics of magnitude distributions of fluidinduced earthquakes. In order to determine the probability of an event having a magnitude larger than a given magnitude M during the time interval (0, t), W ev ( M, t), we assume that this probability is independent of the number of events. It means that the relation of the number of events with a magnitude larger than a given one to the complete number of events is a constant. Furthermore, as mentioned before, we suppose that magnitudes of fluid-induced seismicity follow a Gutenberg Richter type statistics (see e.g. Turcotte et al. 2007). Precisely, the logarithm to the base ten of the number of earthquakes having a magnitude larger than magnitude M is equal to a bm where a and b are regional seismicity constants. The a value describes the probabilistic productivity of earthquakes with magnitude larger than zero, whereas the b value is the ratio of small to large events. Such a scaling of fluidinduced seismicity might be a consequence of a power-law type size distribution of pre-existing

J Seismol (2013) 17:13 25 17 fractures. These assumptions provide the following equation. The product of the cumulative number of events given by Eq. 11 and the probability W ev ( M, t) yields the cumulative number of events with a magnitude larger than a given magnitude M: N M (t) = W ev ( M, t) N(t). (15) Introducing the Gutenberg Richter type probability, that is: W ev ( M, t) = 10 a b M, (16) results in the following expression: N M (t) = m c(t)ζ C max ρ 0 S 10a bm, (17) and in logarithmic scale, respectively: log 10 N M (t) ( ) mc (t)ζ = log 10 + a bm. (18) C max ρ 0 S If we consider a power-law fluid injection rate instead of cumulative injected fluid mass, then Eqs. 17 and 18 accordingly change: We notice from the derived formalism that the probability of inducing an earthquake with a significant magnitude increases with the injected cumulative fluid mass. Strictly speaking, the cumulative number of earthquakes with a magnitude larger than a given one and the cumulative injected fluid mass are linearly related in the double logarithmic scale, obeying a proportionality factor equal to one. This theoretical finding is confirmed by observations from fluid-induced seismicity induced during hydraulic stimulation as well as hydraulic fracturing (Fig. 1). Apart from injection engineering parameters, we can identify a second group of magnitudecontrolling factors from the derived formalism. These are site-specific characteristics of the reservoir-building rock and fracture system. Precisely, they are so-called seismotectonic parameters, including the constants a and b of the Gutenberg Richter probability, the tectonic potential F t and the poroelastic compliance S. For the assessment of seismic hazard due to fluid injections, knowledge of the site-specific seismotectonic parameters is required. N M (t) = Q I t I+1 ζ C max S 10a bm, (19) ( ) QI ζ log 10 N M (t) = log 10 C max S +(I + 1) log 10 t + a bm. (20) The ratio C max has previously been introduced ζ as the tectonic potential F t (Shapiro et al. 2007). It is defined by two seismotectonic parameters of an injection site: the maximum of the critical pressures of pre-existing fractures, C max, and the bulk concentration of these fractures, ζ. The tectonic potential has critical implications for the seismic activity caused by a fluid injection. If, for instance, injection flow rates are equal at two injection sites but the locations are characterised by a different tectonic potential, then the one having a lower tectonic potential will experience a higher rate of seismicity. In other words, the larger the tectonic potential, the more efforts are necessary to induce seismicity. Fig. 1 Cumulative number of microearthquakes having a magnitude larger than M, N M, induced during injections in geothermal (Basel (M = 0.7), Soultz (M = 1.2)) and hydrocarbon (Barnett Shale (M = 2.9), Cotton Valley (M = 2.1)) reservoirs as function of cumulative injected fluid volume, V I, in double logarithmic scale. Shortly after beginning the injections, the two quantities are linearly related with a proportionality coefficient equal to one

18 J Seismol (2013) 17:13 25 3 Characterisation of seismogenesis of fluid-induced seismicity In the following, we will address the question how one can utilise the theoretical model described above for developing a predictive tool. The achievement of such a tool should be a mitigation of a possible seismic hazard. Here, we provide a first step towards a prediction. Let us rearrange Eq. 18 and substitute the tectonic potential F t = C max. Additionally, we replace the cumulative injected fluid mass with the cumulative injected ζ fluid volume V I (t) = m c(t) ρ 0. We then obtain: = log 10 N M (t) log 10 V I (t) + bm, (21) where known or measurable quantities are on the right-hand side. On the left-hand side of this equation, we introduce a new quantity, the seismogenic index (Shapiro et al. 2010), which combines the site-specific seismotectonic parameters of an injection location: ( 10 a ) a log 10 (F t S) = log 10. (22) F t S The seismogenic index has physical units of log 10 m 3 which expresses the potential of a reservoir location to induce seismicity per injected unit fluid volume. Notably, the seismogenic index has the following meaning. Once it is known for a particular injection site, it provides, together with the b value of the Gutenberg Richter scaling law, a tool to predict the number of earthquakes with a magnitude larger than M, for a future fluid injection at the same location: log 10 N M (t) = log 10 V I (t) bm+, N M (t) = V I (t) 10 b M. (23) This equation is valid under the assumption that the b value and the seismogenic index are constant quantities. We notice from the last equation that the larger the seismogenic index, the larger is the probability of the occurrence of an earthquake having a significant magnitude. In order to avoid such significant magnitude events, one can accordingly adjust the cumulative injected fluid volume or the volumetric injection flow rate for a given injection time. Besides the prediction of expected seismic activity due to a fluid injection (Eq. 23), the seismogenic index provides us with a tool for quantitatively comparing the seismotectonic state at different injection sites. Here, we consider fluidinduced seismicity from 15 injection experiments at different reservoir locations. The study is a continuation of previously presented work by Shapiro et al. (2010). We add seismicity catalogues from the KTB injection site (two injection experiments), from Soultz-sous-Forêts (four) and from Ogachi (one) to the existing database. We calculate the seismogenic index for all reservoir locations according to Eq. 21 using the parameters summarised in Table 1. These include the cumulative injected fluid volume, V I (t), which is known from the hydraulic treatment data, the b value, which has been derived from the frequency magnitude distribution of earthquakes induced during periods of non-decreasing injection flow rates, and a given representative magnitude of interest M i above the magnitude of completeness. In most cases, magnitudes of earthquakes are given in the moment magnitude scale. Exceptions are data from Cooper Basin, Ogachi, Soultz 2000 and KTB 2004/2005. Although the use of different magnitude scales yields a bias in the estimate of, we assume that this bias is small and is expected to be of the same order as the statistical fluctuations. Thus, this bias should be insignificant for our conclusions. The calculated seismogenic indices of all considered injection experiments are given in Table 1 and illustrated in Fig. 2. We see from the figure that estimates of arestablewithtime apart from statistical fluctuations regardless of the injection duration or the cumulative injected fluid volume. Let us briefly discuss the obtained indices. We easily notice the difference in seismotectonic parameters between hydrocarbon and nonhydrocarbon reservoirs. Seismogenic index and b value derived from seismicity in the sandstone and shale gas reservoirs in Cotton Valley and Barnett significantly differ from corresponding quantities in geothermal reservoirs. The gas reservoirs are characterised by a low seismogenic index, 10 < < 4 and a high b value. The rather large diversity of at Cotton Valley has the following reasons. The fracturing stages were not only

J Seismol (2013) 17:13 25 19 Table 1 Summary of a comparative analysis of seismotectonic state of injection locations Reservoir Location/experiment Injection Event Mi b Time Volume (m 3 ) number Geothermal Basel (SUI) (Häring et al. 2008) 5.5 days 10,800 2,313 1.0 1.65 0.4 ± 0.1 Cooper Basin (AUS) 2003 (Soma et al. 2004) 9 days 14,600 2,834 0.0 0.75 0.95 ± 0.05 Ogachi (JP) 1991 (Kaieda et al. 1993) 11 days 10,100 1,504 2.0 0.74 2.65 ± 0.1 Ogachi (JP) 1993 (Kaieda et al. 1993) 16 days 20,700 762 1.2 0.81 3.2 ± 0.3 Soultz (FR) 1993 (Baria et al. 1999) 16 days 25,900 9,550 1.0 1.38 2.0 ± 0.1 Soultz (FR) 1995 (Baria et al. 1999) 11 days 28,500 3,950 1.2 2.18 3.8 ± 0.1 Soultz (FR) 1996 (Baria et al. 1999) 48 h 13,500 3,325 1.2 1.77 3.1 ± 0.3 Soultz (FR) 2000 (Dyer 2001) 6 days 23,400 6,405 0.6 1.1 0.5 ± 0.1 Miscellaneous KTB (GER) 1994 (Jost et al. 1998) 9h 86 54 1.3 0.93 1.65 ± 0.1 (hard rock) KTB (GER) 2004/2005 (Haney et al. 2011) 223 days 64,130 2,405 1.0 1.1 4.2 ± 0.3 Paradox Valley (USA) (Ake et al. 2005) 1,050 days 1.7 10 6 2,566 1.0 0.98 2.6 ± 0.1 Hydrocarbon Barnett Shale (USA) (Maxwell et al. 2009) 6 h 2,840 844 3.0 2.86 9.25 ± 0.05 Cotton Valley (USA) A (Rutledge et al. 2004) 2.5 h 1,020 628 2.1 2.67 6.25 ± 0.05 Cotton Valley (USA) B (Rutledge et al. 2004) 2.5 h 950 888 1.8 2.16 4.42 ± 0.02 Cotton Valley (USA) C (Rutledge et al. 2004) 3.5 h 333 369 2.0 4.12 9.42 ± 0.06 Parameters for calculating the seismogenic index include injected fluid volume VI(t), a representative magnitude Mi, and Gutenberg Richter b value (compare with Eq. 21). Note that the diversity of the seismogenic index at one particular injection location but for different years can be explained by the fact that fluid were injected in different depth intervals and/or in different boreholes (see also discussion in the text)

20 J Seismol (2013) 17:13 25 Fig. 2 Seismogenic index as function of normalized time (elapsed injection time/total injection time) for several injection locations in geothermal and hydrocarbon environments performed in different boreholes but also with different treatment fluids: a gel-proppant mixture was injected in stages A and B, whereas water was used in stage C. Note that also for the fracturing in Barnett Shale water was injected. In both Barnett Shale and stage C, the value of is of the same order. In stage B, the propagating hydraulic fracture intersected and consequently opened a natural fracture system as shown in Fig. 3 (Dinske et al. 2010) which, in our opinion, may have resulted in the highest value of seismogenic index for the Cotton Valley reservoir. In addition to the different characteristics of the pre-existing fractures, the gel-proppant mixture used in stages A and B may also affect the geomechanical properties, particularly the poroelastic compliance S. In case of injection of gel-proppant instead of water, one alters the compliance S because the pore fluid is replaced by the gel-proppant. It means that the rock gets stiffer resulting in a higher seismogenic index. In contrast, geothermal reservoirs and the KTB, as well as the Paradox Valley injection site, have seismogenic indices > 4. The highest value is found for the Basel reservoir where the seismogenic index is of the order of = 0.4. This result is coherent with the occurrence of several earthquakes with a significant magnitude during and shortly after the fluid injection in Basel. For reservoir locations where multiple fluid injections had been carried out, such as in Soultz or at the KTB, we obtain several different indices. This observation is coherent since fluid were injected in either different wells and/or different depths of the reservoir location. For example, at the KTB site, the 1994 injection was performed at a depth of about 9 km using the main borehole to stimulate the SE1 fault zone, whereas in 2004/2005, fluid Fig. 3 Map view of source locations of stage B of hydraulic fracture treatments in Cotton Valley gas reservoir marking the intersection of the hydraulic fracture with a pre-existing natural fracture. About 40% of induced earthquakes occurred along the natural fracture

J Seismol (2013) 17:13 25 21 were pumped into a reservoir depth of 4 kmusing the pilot borehole. In this experiment seismicity occurred along the less prominent fault zone SE2 (see Fig. 4). Additionally, there was a longterm fluid extraction phase (1 year) preceding the last injection. Also in Soultz, the various injections have stimulated different parts of the whole reservoir. We address the differences in the derived seismogenic indices to different characteristics of the fracture systems. In general, geothermal reservoirs and the KTB, as well as the Paradox Valley reservoirs, are not only characterised by a higher seismogenic index but also by a lower b value (if compared to hydrocarbon reservoirs). These findings lead to the conclusion that fluid injections in geothermal reservoirs have a higher potential to induce an earthquake with a significant magnitude which is in agreement with the observed earthquake magnitudes (Majer et al. 2007). This potential is further enhanced due to the injection of a larger fluid volume. Finally, we analyse possible correlations between the seismogenic indices and other parameters of injection, reservoir and seismicity (see Table 2). In spite of the low data statistics due to the limited number of catalogues, we observe the following general tendencies. We notice from Fig. 5a that the seismogenic index is higher the greater is the depth of a reservoir. Such an observation is understandable since the shear strength of rock closer to the surface is lower, which inhibits the occurrence of significant events. Figure 5b shows the correlation between seismogenic index and the seismic hazard indicator PGA for naturally occurring seismicity. The PGA values for the reservoir sites are taken from the global seismic hazard map prepared in frame of the Global Seismic Hazard Assessment Program (Giardini et al. 2003). Usually, seismic hazard indicators depict the level of ground motion that will likely be exceeded in a given time span. Here, we use seismic hazard specified as the peak ground Fig. 4 Left: tectonical sketch of the KTB injection site showing the major fault zones SE1 and SE2 (from Gräsle et al. 2006). Right: depth migrated image ISO89-3D. The seismic reflection intensities are shown in blue-white colour on one vertical slice. Light colours correspond to large reflection intensities and darker colours to lower ones, respectively. The SE1 reflector is clearly visible as a steeply dipping event. Additionally, seismicity induced by injection experiments of years 1994 (blue), 2000 (green) and 2004/2005 (red) are shown. Locations of the main and pilot boreholes are marked by black and green lines, respectively (from Shapiro et al. 2006)

22 J Seismol (2013) 17:13 25 Table 2 Set of parameters used in a correlation analysis of seismogenic index Reservoir Location/experiment Reservoir depth Hydraulic Cumulative seismic Hydraulic efficiency Hazard indicator (m) (midpoint) energy Eh [J] moment M0 (N m) Es/Eh 10 4 PGA (m/s 2 ) Geothermal Basel 0.4 ± 0.1 4,400 2.7 10 11 8.6 10 13 159.3 1.47 Cooper Basin 2003 0.95 ± 0.05 4,200 8.8 10 11 0.67 Ogachi 1991 2.65 ± 0.1 1,000 1.8 10 11 2.66 Ogachi 1993 3.2 ± 0.3 1,000 3.9 10 11 2.66 Soultz 1993 2.0 ± 0.1 2,790 2.6 10 11 2.5 10 12 4.8 0.81 Soultz 1995 3.8 ± 0.1 3,400 3.3 10 11 1.7 10 11 0.3 0.81 Soultz 1996 3.1 ± 0.3 3,400 1.7 10 11 2.1 10 11 0.6 0.81 Soultz 2000 0.5 ± 0.1 4,740 2.7 10 11 0.81 Miscellaneous KTB 1994 1.65 ± 0.1 9,100 3.5 10 9 2.5 10 8 0.04 0.54 (hard rock) KTB 2004/2005 4.2 ± 0.3 4,000 6.4 10 11 0.54 Paradox Valley 2.6 ± 0.1 4,600 5.6 10 13 4.4 10 15 39.3 0.4 Hydrocarbon Barnett Shale 9.25 ± 0.05 2,365 4.9 10 10 8.2 10 7 0.0008 0.2 Cotton Valley stage A 6.25 ± 0.05 2,650 1.5 10 10 8.2 10 8 0.03 0.2 Cotton Valley stage B 4.42 ± 0.02 2,800 1.5 10 10 1.8 10 9 0.06 0.2 Cotton Valley stage C 9.42 ± 0.06 2,620 6.6 10 9 2.7 10 8 0.02 0.2 Parameters include mean reservoir depth (i.e. injection depth midpoint), hydraulic injection energy Eh, total cumulative released seismic moment M0,seismic injection efficiency Es/Eh (Es = 6 10 5 M0) and seismic hazard indicator peak ground acceleration (Giardini et al. 2003)

J Seismol (2013) 17:13 25 23 (a) (b) (c) (d) (e) (f) Fig. 5 Result of a correlation analysis between seismogenic index and other reservoir and seismicity parameters. a Seismogenic index versus reservoir depth (midpoint of open borehole section). b Seismogenic index versus peak ground acceleration (seismic hazard indicator). c Gutenberg Richter b value versus seismogenic index. d Cumulative released seismic moment versus seismogenic index. e Cumulative released seismic moment versus peak ground acceleration. f Seismic injection efficiency versus seismogenic index. Correlation functions (solid lines) are obtained by least squares linear fitting acceleration with 10% probability of exceedance in 50 years, corresponding to a return period of 475 years (Giardini et al. 2003). We see from the figure that the seismotectonic quantification parameter derived from fluid-induced seismicity well correlates with the logarithm of PGA. An exception is the Ogachi reservoir in Japan. Because of its location in a seismically active region, the area is characterised by a high PGA value expressing the potential seismic hazard. The b value of the Gutenberg Richter scaling which describes the ratio of small to large earthquakes is also a site-specific seismotectonic quantity. We have shown before that reservoirs which are characterised by a low seismogenic index tend to produce a frequency magnitude distribution of induced events with a high b value. This general trend is confirmed by a correlation analysis as presented in Fig. 5c. Furthermore, we also consider the cumulative seismic moment in our analysis since it is to some extent a measure of released energy (strictly speaking, under the assumption of self-similarity of earthquake rupture processes, the released seismic energy E s of an earthquake scale constant with the seismic moment M 0,i.e. E s /M 0 = 6 10 5 (e.g. Gutenberg and Richter 1956; Ide and Beroza 2001; Shearer 2009)). We calculate the seismic moment from the given

24 J Seismol (2013) 17:13 25 moment magnitudes of induced earthquakes according to M 0 = 10 1.5 M+9.1. The correlation analysis shows that the logarithm of the total cumulative released seismic moment linearly scales with the seismogenic index and with the logarithm of PGA (Fig. 5d, e). In both cases, we observe an expected increase in the cumulative seismic moment with higher seismogenic indices and higher PGA values, respectively. A more significant parameter by fluid injections is the seismic injection efficiency which normalises the total released seismic energy (E s = 6 10 5 M 0 ) with the hydraulic injection energy E h. The hydraulic injection energy is equivalent to the work done during an injection defined by the time integral of injection pressure and flow rate. We see from Fig. 5f that the seismic injection efficiency well correlates with the seismogenic index. Hydrocarbon reservoir locations which are characterised by lowest seismogenic indices have extremely low efficiency, meaning that nearly the complete injection energy has been converted to potential and frictional energy. Aseismic fracture opening may also largely contribute to the energy budget (Hill 1977;Baisch and Harjes 2003). On the other hand, we observe a much higher seismic energy release per unit injection energy for reservoir locations which have a high seismogenic index. For example, the ratio of total released seismic energy to hydraulic injection energy at the Basel geothermal reservoir is approximately five to six orders of magnitude larger than at the Barnett Shale gas reservoir. 4 Conclusions Identifying the parameters that define the magnitude and its frequency is a key point for evaluating the seismic hazard by fluid injections. Apart from the injected fluid mass, parameters that control the magnitude distribution of fluid-induced seismicity are of seismotectonic nature. These parameters are site-specific. The seismogenic index which combines generally unknown quantities is a convenient parameter to quantify the seismotectonic state of an injection site. Our comparative study of the seismogenic index for several reservoir locations and various injection experiments lead to the following conclusions: Hydrocarbon reservoirs are characterised by lowest seismogenic indices and highest b values. This means, also in consideration of the small fluid volume required in fracturing operations, that earthquakes of significant magnitude are less likely to occur. It likewise means, however, that a seismic monitoring system at such locations has to have a high level of sensitivity in order to detect the induced events. In contrast, fluid injections which are aimed to develop geothermal systems have caused noticeable earthquakes at several locations (see e.g. Häring et al. 2008; Majer et al. 2007). These observations can again be explained by evaluating the seismotectonic state of corresponding reservoirs using the presented formalism. We found that geothermal reservoirs and the KTB and the Paradox Valley sites, which are in crystalline rock, are characterised by higher seismogenic indices and lower b values compared to hydrocarbon reservoirs, which typically are in sediments. In addition to its value in a comparative study of several injection locations, the seismogenic index can also be used in a predictive manner. If both seismogenic index and b value of Gutenberg Richter law are known for a specific location (for instance, from a shortterm injection), then our formalism allows to compute the expected number of induced earthquakes having a magnitude larger than a given one for a known fluid mass. From the correlation analysis between seismogenic index and parameters related to a fluid injection and the induced seismicity, we conclude that the seismogenic index provides a tool to specify and also to mitigate a possible seismic hazard by fluid injections. Acknowledgements We thank the Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (BMU) as sponsor of the MAGS project and the sponsors of the PHASE consortium project for supporting the research presented in this paper. Microseismic data from Cooper Basin and Ogachi are courtesy of Dr. H. Kaieda (CRIEPI, Japan); from Basel, of Dr. M. O. Häring (Geothermal Explorers LTD); from Paradox Valley, of Dr. K. Mahrer (formerly, Bureau of Reclamation, now at Weatherford); from Cotton Valley, of Dr. J. Rutledge (LANL); from Barnett Shale, of Dr. S. Maxwell (formerly, Pinnacle, now at Schlumberger); and microseismic data from Soultz experiments were kindly provided by Dr. A. Jupe and by the GEIE Exploration Minire de la Chaleur. We thank the two anonymous reviewers for their comments and suggestions.

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