JournalofGeophysicalResearch: SolidEarth

Transcription

1 JournalofGeophysicalResearch: SolidEarth RESEARCH ARTICLE Key Points: Fluid extraction induced seismicity conforms to reservoir compaction Fraction of seismic to reservoir strain increases with reservoir compaction Able to forecast future seismicity according to future reservoir compaction Correspondence to: S. J. Bourne, Citation: Bourne, S. J., S. J. Oates, J. van Elk, and D. Doornhof (2014), A seismological model for earthquakes induced by fluid extraction from a subsurface reservoir, J. Geophys. Res. Solid Earth, 119, , doi:. Received 3 OCT 2014 Accepted 14 NOV 2014 Accepted article online 18 NOV 2014 Published online 19 DEC 2014 A seismological model for earthquakes induced by fluid extraction from a subsurface reservoir S. J. Bourne 1,S.J.Oates 1,J.vanElk 2, and D. Doornhof 2 1 Shell Global Solutions International B.V., Rijswijk, Netherlands, 2 Nederlandse Aardolie Maatschappij (NAM) B.V., Assen, Netherlands Abstract A seismological model is developed for earthquakes induced by subsurface reservoir volume changes. The approach is based on the work of Kostrov (1974) and McGarr (1976) linking total strain to the summed seismic moment in an earthquake catalog. We refer to the fraction of the total strain expressed as seismic moment as the strain partitioning function, α. A probability distribution for total seismic moment as a function of time is derived from an evolving earthquake catalog. The moment distribution is taken to be a Pareto Sum Distribution with confidence bounds estimated using approximations given by Zaliapin et al. (2005). In this way available seismic moment is expressed in terms of reservoir volume change and hence compaction in the case of a depleting reservoir. The Pareto Sum Distribution for moment and the Pareto Distribution underpinning the Gutenberg-Richter Law are sampled using Monte Carlo methods to simulate synthetic earthquake catalogs for subsequent estimation of seismic ground motion hazard. We demonstrate the method by applying it to the Groningen gas field. A compaction model for the field calibrated using various geodetic data allows reservoir strain due to gas extraction to be expressed as a function of both spatial position and time since the start of production. Fitting with a generalized logistic function gives an empirical expression for the dependence of α on reservoir compaction. Probability density maps for earthquake event locations can then be calculated from the compaction maps. Predicted seismic moment is shown to be strongly dependent on planned gas production. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. 1. Introduction The increasing prevalence of earthquakes induced by human activities is leading to increased public awareness and concern about the potential risks. These activities include mining, the impounding of water reservoirs, geothermal energy production, and fluid injection or production, including hydrocarbon production. Most fluid extraction from the subsurface occurs without inducing any earthquakes. Nonetheless, there are many notable examples of earthquakes induced by fluid injection or extraction. Several recent reviews comprehensively summarize the worldwide evidence for seismicity induced by human activities [Majer et al., 2007; Suckale, 2009; Evans et al., 2012; Davies et al., 2013; Ellsworth, 2013; Klose, 2013; National Academy of Sciences, 2013; International Energy Agency Greenhouse Gas R&D Programme, 2013]. For example, earthquakes were induced by oil production from the Goose Creek field in South Texas [Pratt and Johnson, 1926], the Wilmington field in Long Beach, California [Kovach, 1974], and the Valhall and Ekofisk fields in the North Sea [Zoback and Zinke, 2002]. Earthquakes were also linked to gas production from, for example, the Rocky Mountain House seismic zone in Alberta, Canada [Wetmiller, 1986], the Lacq field in France [Grasso and Wittlinger, 1990], the War-Wink field in West Texas [Doser et al., 1991], several fields in the Rotliegendes basin in the Netherlands [e.g., van Eijs et al., 2006], a gas field in Oman [Bourne et al., 2006], and the Rotenburg field in Germany [Dahm et al., 2007]. Ground water extraction was also linked to a damaging earthquake in Lorca, Spain [Avouac, 2012]. The mechanism of poroelastic stress changes within and surrounding the region of pore pressure depletion explains the occurrence and spatial distribution of earthquakes induced by fluid extraction [Segall, 1989; Segall et al., 1994; Baranova et al., 1999]. Within these models, seismicity is expected when shear traction is sufficient to overcome frictional resistance to slip on the fault surface. Such critically stressed faults are unstable and prone to slip. Faults inside the region of pressure depletion may become critically stressed, despite an increase in effective normal stresses, due to an increase in shear stress. These conditions might arise due to uniform uniaxial compaction associated with uniform pressure depletion within a thin reservoir [e.g., Geertsma, 1966, 1973], or due to differential compaction associated with lateral changes BOURNE ET AL The Authors. 8991

2 in pressure depletion, reservoir thickness, reservoir compressibility, or offset across an existing fault [e.g., Mulders, 2003]. Equally, if preexisting faults cross the reservoir, fault slip may extend outside the region of pressure depletion [e.g., Bourne et al., 2006]. Alternatively, changes in the total stress outside the reservoir might initiate slip on preexisting faults located outside the region of pressure depletion [e.g., Segall, 1989; Zoback and Zinke, 2002]. Although these circumstances may give rise to induced seismicity, these assumed conditions are insufficient to determine the amount of earthquake deformation, if any, that results. Unstable, critically stressed faults may creep without any seismicity, or they may slip by such small amounts that each earthquake remains undetectable or poses only negligible hazard or risk. An additional mechanism is required to explain why some critically stressed faults yield more and larger earthquakes than other critically stressed faults. We will consider the amount of strain induced by fluid extraction as a mechanism for governing the amount of slip induced on critically stressed faults. This has the advantage that strains induced by fluid extraction or injection may be estimated using geodetic measurements of surface deformations [e.g., van der Kooij, 1997; Vascoetal., 2002; Du et al., 2008] or time-lapse changes in reflection seismic traveltimes [e.g., Hatchell and Bourne, 2005; Bourne and Hatchell, 2007]. Induced strains have previously been used to constrain the maximum magnitude of an induced earthquake [e.g., McGarr, 2014; Hallo et al., 2014]. However, the maximum magnitude is not a reliable proxy for seismic hazard as more frequent intermediate magnitude events are much more likely to cause extreme values in peak ground velocity or acceleration [e.g., Petersen et al., 2008; Giardini et al., 2013; S. J. Bourne, et al., A Monte Carlo method for probabilistic hazard assessment of induced seismicity due to conventional natural gas production, Bulletin of Seismological Society of America, under review, 2014] than the maximum magnitude earthquake. For this reason, probabilistic seismic hazard assessments require a seismological model that describes the numbers, locations, and magnitudes of possible earthquakes within a given future time interval [Cornell, 1968]. The purpose of this paper is to extend these strain-based methods for induced earthquakes to develop a seismological model for subsurface volume changes due to fluid extraction. This model is then applied to the case of earthquakes induced by natural gas extraction from the Groningen gas field in the Netherlands that are of sufficient frequency and magnitude to cause considerable public concerns [e.g., Muntendam-Bos and de Waal, 2013]. 2. A Seismological Model for Earthquakes Induced by Volume Changes Following Kostrov [1974], the incremental average irrotational seismic strain, ε s, due to a population of earthquakes that occurred within a given volume and a given time interval is proportional to the sum of their seismic moment tensors, ε s,ij (t) = 1 N(t) M k o 2μV mk ij, (1) k=1 where ε s,ij is the ijth component of the average seismic strain tensor, N is the number of events that occurred within the given volume, V, and the time interval, t, μ is the shear modulus, and M k o and mk are the scalar ij seismic moment and the unit symmetric moment tensor of the kth event, respectively. The scalar seismic moment is defined as [e.g., Kanamori, 2001] M o = μau, (2) where u is the average slip on the fault, A is the area of the fault slip, and μ is the shear modulus of the medium surrounding the fault. The unit symmetric moment tensor for a double-couple source depends on the unit fault slip vector, û i and the unit normal vector to the fault plane, n i according to [e.g., Kostrov, 1974] m ij = û i n j + û j n i. (3) Now consider a deformation process that starts at time t = 0 and induces an incremental strain field, ε ij (x, t), that varies with position x and time t. The average incremental strain within the volume is such that ε ij (x, t) =0 for t 0. ε ij (t) = 1 V V ε ij (x, t)dv, (4) BOURNE ET AL The Authors. 8992

3 As a first approximation to evaluate the total strain integral associated with a subsurface reservoir, we assume the reservoir has the geometry of a thin sheet, meaning that its lateral extents are significantly larger than its vertical extent. This geometry means that deformations induced by an internal body force, such as a change in reservoir pore fluid pressure, will be approximately uniaxial due to symmetry. That is, ε ij 0 with the exception that inside the reservoir ε zz 0, where z denotes the vertical coordinate. These approximations simplify the volume integral of strain to a surface integral over the area of the reservoir, S, ε zz (t) 1 V S Δh(x, t)ds, (5) where Δh = z 2 ε z 1 zz (x, t)dz is the change in thickness of the reservoir. Given fault slip is in the plane of the fault, the trace of the seismic moment tensor is zero. According to (1), the same is also true for the average seismic strain tensor, but not for the average induced strain tensor (5) due to the induced volume change. Decomposition of average induced strain tensor into its isotropic dilatation and shear strain components leads to ε ij = 1 3 ε zz ε zz ε zz ε zz ε zz ε zz. (6) The trace-free component of the induced strain field is then available for accommodation by slip on a population of faults. As not all incremental shear strain is necessarily accommodated as seismogenic slip on faults, it follows that the average seismic strain is some fraction of the average-induced shear strain. To represent the fraction of induced strain accommodated by seismogenic slip on faults, let α = ε s ε. (7) For earthquakes induced by this incremental strain, it follows that 0 α 1. This denotes the average partitioning of strain into its seismogenic part, α, and its nonseismogenic part, 1 α, which includes elastic strain and aseismic fault slip among others. Combining the last term of (6) and (7) leads to ε s,ij = 2 3 α ε zz (8) As the scalar seismic moment is the largest principal value of the seismic moment tensor [Kostrov, 1974], the total seismic moment, M o,t, follows from (1), (5), and (8) as M o,t (t) 4μ α Δh(x, t) ds. (9) 3 S The absolute value of the change in reservoir thickness, Δh, appears because the total seismic moment is by definition positive definite. The value of α will likely depend on site-specific geological conditions and may also differ for reservoir compaction caused by fluid production compared to reservoir dilation caused by fluid injection. In the limit that volume of interest tends to zero, i.e., V 0 and S 0, the average strain partitioning fraction becomes a local property, i.e., α α. Using this concept of a local strain partitioning fraction, the total seismic moment tensor, may be expressed by generalizing the previous equations as 1 2 M o,t (t) 4μ 3 S α Δh ds. (10) This result predicts the areal and temporal distribution of total seismic moment will be conformable to the areal and temporal distribution of reservoir thickness changes if α is a monotonically increasing function of thickness change. Earthquake and geodetic observations provide opportunities to test this prediction and estimate the strain partitioning, α. BOURNE ET AL The Authors. 8993

4 In general, α may depend on the cumulative-induced deformation as represented locally by the change in reservoir thickness, i.e., α = α(δh). However, if some fixed fraction of the strain is permanently accommodated by nonseismogenic processes, then the strain partitioning, α, would be a constant and so the total seismic moment would simply increase in proportion to the absolute bulk reservoir volume change, ΔV : M o,t (t) 4μ α ΔV(t). (11) 3 The upper bound on the total seismic moment corresponds to α = 1, meaning M o,t (t) 4μ ΔV(t). (12) 3 This expression is comparable to that obtained by McGarr [1976] for several particular deformation geometries associated with subsurface volume changes. The total seismic moment released during the time interval t 1 t < t 2 follows from (10) simply as ΔM o,t (t 1, t 2 )=M o,t (t 2 ) M o,t (t 1 ). (13) Similarly, the rate of total seismic moment released with time follows from (10) as M o,t (t) 4μ 3 S α Δḣ + α Δh ds, (14) where the dot symbol denotes differentiation with respect to time. The first term within the integral denotes the release of seismic moment due to the ongoing strain, whereas the second term denotes the release of previously accumulated elastic strain that is now destabilized and accommodated by seismogenic fault slip. In order to perform statistical significance testing of this model for a given set of observations and to quantify confidence bounds on estimates for the strain partitioning function, α, we must first consider the possibility of sample bias and stochastic variability in the seismic strain field that may be estimated from a finite sample of earthquakes Sample Bias in the Observed Earthquake Strain Field The number of observed earthquakes, N, of at least magnitude, M, within a given region and period of time follows the log linear frequency-magnitude relationship of the Gutenberg-Richter law [Gutenberg and Richter, 1954]: log 10 N(M) =a bm. (15) The b parameter, known as the b value, describes the relative decline in abundance of larger earthquakes relative to the smaller ones. The a value is simply the log of the number of M 0 earthquakes. The relationship between the magnitude, M, and the seismic moment, M o, takes the form [Hanks and Kanamori, 1979]. where typically c = 9.1 and d = 1.5. log 10 M o = c + dm, (16) The total seismic moment, M o,t, is simply the sum of all individual moments for a population of earthquakes. For a large population of observable earthquakes with seismic moments of at least M o,min and less than M o,max, the expectation value for the observable total seismic moment, M o,t,is M o,t = M o,max M o,min Combining these last three equations leads to the result [ M o,t = β 1 β M o,max 1 M o dn dm o dm o. (17) ( Mo,min M o,max ) 1 β ], (18) BOURNE ET AL The Authors. 8994

5 where β = b d.forβ<1, in the limit M o,min 0 the expected total seismic moment for the entire population of earthquakes, M o,t, is simply M o,t = β 1 β M o,max. (19) For an earthquake monitoring system which yields a catalog of events that is complete down to a seismic moment M o,min, the fraction of the total seismic moment that remains undetected is ( Mo,min ) M o,t M 1 β o,t =. (20) M o,t M o,max This means that the observed total seismic moment will be a biased underestimate of the total seismic moment. However this bias decreases as the ratio of the observed total seismic moment to the detection threshold increases. For a typical value of β = 2 3, 58% of the total seismic moment remains undetected for M o,t = 10M o,min, whereas for M o,t = 10 4 M o,min this bias reduces to 5.8% Stochastic Variability in the Earthquake Strain Field An observed set of earthquakes may be viewed as a finite random sample from an underlying asymptotic probability distribution. The role of chance means that departures from this distribution are possible, and for smaller earthquake populations larger departures are more likely. This stochastic variability must be included in the earthquake strain model if it is to properly describe a finite set of earthquakes. The probability that the seismic moment of the next event, X M o given X M o,min, follows from (15) and (16): ( ) β Mo Prob(X M o X M o,min )=F β (M o )=. (21) M o,min The probability density function, Φ(M o ), is then simply Φ(M o )= F β (M o ) M o, (22) Φ(M o )= β M o,min ( Mo M o,min ) 1 β. (23) This is a Pareto distribution. The total observed seismic moment for a population of earthquakes may then be modeled as the sum, S n, of independent random variables X i, i = 1,, n, drawn from a common Pareto distribution, i.e., n S n = X i. (24) i=1 Obtaining expressions for the Pareto sum distribution of S n is nontrivial for 0 <β<2 because X i has an infinite variance which precludes the use of the Central Limit Theorem. For an arbitrary quantile, z q (n),ofthe S n distribution such that Prob(S n < z q (n)) = q, (25) Zaliapin et al. [2005] obtained the following useful approximate expression for these quantiles given 0 <β<1, where Γ(x) is the Gamma function and x q solves the equation z q (n) C β x q n 1 β, (26) C β =[Γ(1 β) cos(πβ 2)] 1 β, (27) F β (x q )=1 q. (28) BOURNE ET AL The Authors. 8995

6 Figure 1. (a) Comparison between the Zaliapin et al. [2005] approximation to the Pareto sum distribution for M 1.5 events (red lines) and synthetic data obtained as 1000 stochastic simulations (thin grey lines). The lower and upper bounds denote the 1 in 1000 confidence interval. (b) As for Figure 1a except for the cumulative distribution of total seismic moment after 188 M 1.5 events. Combining these three expressions with (21) allows quantiles of the total observable seismic moment, M o,t,q(n) for N independent M o > M o,min events to be written as ( ) 1 β N M o,t,q (N) M o,min C β. 1 q (29) Results obtained from stochastic simulations of M 1.5 earthquake catalog randomly sampled from a frequency-moment distribution characterized by b = 1, d = 1.5 (Figure 1) are in good agreement with the Pareto sum approximation obtained by Zaliapin et al. [2005]. Perhaps, the most important characteristic of the Pareto sum distribution is the long tail of extreme values above the median. This is clearly evident in Figure 1a as the upper bound to the 1 in 1000 confidence interval is substantially further from the median than the lower bound. For example, from (29) the total observable seismic moment for a given quantile q depends on the median total seismic moment according to M o,t,q (2 2q) 1 β M o,t,0.5. (30) Given this expression, the lower bound witha1in10 2 or 1 in 10 3 chance of not exceeding is 0.36 and 0.35 times the median total seismic moment, respectively. However, the upper bound with a1in10 2 or 1 in 10 3 chance of exceeding is approximately and 10 4 times the median total seismic moment, respectively. This small but finite chance of encountering an extreme value relative to the median total seismic moment is a significant source of stochastic variability in the observed earthquake strain field. Clearly, this significant variability must be accounted for when testing the validity of the kinematic earthquake strain model for a given set of observed earthquakes. Also, this variability will cause uncertainty in the estimation of these model parameters which must be propagated into any seismicity predictions based on this model Estimation of the Strain Partitioning Function At lower levels of reservoir deformation, more of the induced strain may be accommodated by elastic deformation; however, as deformation increases more and more of the rock volume may exceed its elastic limit and so an increasingly large fraction must be accommodated as slip on faults. There is also evidence that seismic strain increases more quickly than bulk strain in laboratory experiments [Ojala, 2003; Heap et al., 2009] and prior to volcanic eruptions [Bell and Kilburn, 2011]. Induced seismicity within the Groningen field behaves in a similar fashion with an exponential-like trend. For these reasons let us consider the following exponential-trend model for the strain partitioning function, α α = ef+gδh, (31) 1 + ef+gδh BOURNE ET AL The Authors. 8996

7 where f and g are the model parameters, and Δh is the change in reservoir thickness. Notice for small changes in reservoir thickness such that f + gδh << 0 then α = e f+gδh and for large compaction such that f + gδh >> 0 then α = 1. In this way the exponential trend is truncated to ensure 0 α 1. Also, notice that for g = 0, this model also represents constant strain partition. The strain partitioning model parameters f, g may be estimated using observations of α obtained from the observed earthquakes and reservoir deformations. From (11), an average estimate for strain partitioning, α, may be obtained from the total seismic moment per volume change: α = 3 M o,t 4μ ΔV. (32) Dividing the deformation model into contiguous regions bounded by contours of reservoir thickness change and counting the total seismic moment and volume change within each region yields independent estimates of the strain partitioning, α i, for each region with a distinct average estimated reservoir thickness change, Δh i. A maximum likelihood estimate of model parameters f, g given the data α i, Δh i requires a procedure to maximize the joint likelihood of a sequence of Pareto sums. To achieve this, we approximate the Pareto sum distribution with a log normal distribution where the standard deviation is set equal to the approximation for Pareto sums obtained by Zaliapin et al. [2005]. This reduces parameter estimation to a standard weighted least-squares linear regression between log α and Δh according to α log = f + gδh, (33) 1 α where standard errors in the observations are based on the standard deviation of the log-pareto sum distribution estimated from (30) as the 68% interval centered on the median, i.e., σ 1 ( ) 1 2β log q1, (34) 1 q 2 where β = 2 3, q 1 = 0.159, and q 2 = and so σ = for natural logarithms. In practice, this method has led to a scale bias in the residuals such that the regions with the largest seismic moments were systematically underestimated. We attribute this bias to the log normal distribution that underrepresents the heavy upper tail of the Pareto sum distribution. Nonetheless, this scale bias can be corrected by also minimizing the least squares difference between the observed and computed total seismic moment for the entire reservoir and weighted in the same manner. Robust uncertainty bounds for this strain partitioning model were obtained using a Monte Carlo procedure. To represent stochastic variability in the finite set of observed α values, the observed total seismic moment within each region was resampled as a value drawn at random from the Pareto sum distribution with the same median value as the observed value. Values for the model parameters, f and g, were also selected at random. The probability, p, that this particular realization of the data might have occurred from this particular realization of the model was then computed according to standard chi-squared statistics. These model parameters were then retained as an acceptable model if q p where q is a number sampled at random from a uniform distribution between 0 and 1. Repeating this process many times yields a probability distribution of acceptable model parameter values Probability Distribution of Total Seismic Moment For a given deformation model and strain partitioning model, the total seismic moment may be computed according to (13) for any given time interval. This estimate is subject to variability due to the range of strain partitioning models that are consistent with the observed earthquakes within their stochastic variability. Each acceptable realization of the strain partitioning model discovered during the Monte Carlo estimation process yields an estimate of the total seismic moment within the given time interval. The relative frequency of total seismic moment estimates obtained from a sufficiently large number of acceptable strain partitioning models yields an estimate for the probability distribution of total seismic moment. This distribution possesses an upper bound corresponding to (12) but the probability of approaching this upper bound depends in detail on the probability distributions associated with the strain partitioning function. BOURNE ET AL The Authors. 8997

8 2.5. Probability Density for Event Locations Combining (29) and (11) yields an estimate for the median number of M o M o,min events per unit area ( ) β 4μα(Δh) Δh. (35) N d (x, t) 1 2 3C β M o,min Figure 2. The Groningen gas field is located directly to the east of the city of Groningen in the north-east of the Netherlands. The distribution of M L 2 earthquakes reported by The Royal Netherlands Meteorological Institute (KNMI) indicate natural seismicity (yellow) in the south-east of the Netherlands and induced seismicity (red) associated with onshore and offshore producing gas fields further north, the largest of which is the Groningen gas field. where Δh =Δh(x, t). The incremental event density map for the time interval from t 1 to t 2 follows as ΔN d (x) = N d (x, t 2 ) N d (x, t 1 ). The probability density of event locations is then simply the normalized event density distribution, i.e., ΔN d (x) s ΔN d (x)ds Stochastic Procedure for Simulating Events In order to assess seismic hazard or risk, the number, magnitude, and location of future earthquakes must be characterized. Monte Carlo simulation of earthquake catalogs (a list of earthquake locations and seismic moments) is perhaps the most general and easily adaptable method available. Three inputs are required to simulate a catalog of earthquakes for a given time interval, the probability distribution of total seismic moment (section 2.4), the relative event density map (section 2.4), and a b value which may be estimated from the observed earthquake population using the maximum likelihood method [Aki, 1965; Utsu, 1966; Gibowicz and Kijko, 1994; Marzocchi and Sandri, 2003]. Monte Carlo simulation of a single earthquake catalog may then be obtained according to the following procedure. 1. Total seismic moment. Choose a single random independent sample from the total seismic moment distribution. 2. Location. Choose a single random independent event location weighted by the expected event density map that characterizes a given production interval. This is achieved by selecting a random location, then selecting a random number to decide if an event occurs at this location according to the local event density. This process is repeated until an event location is identified. 3. Magnitude. Choose a single random independent event magnitude of M min or greater from the frequency-magnitude distribution. This distribution must be truncated so there is zero chance the event magnitude exceeds M max. The value of M max used for the first event corresponds to the total seismic moment obtained in step 1. Subsequently, M max is lowered by an amount corresponding to the total seismic moment of the events already simulated. 4. Catalog. Repeat steps 2 and 3 until the total seismic moment of the sampled population is equal to that obtained in step 1 to within some suitable small tolerance. The resulting earthquake catalog is one possible simulation of future-induced seismicity. Repeating this procedure many times allows the variability in these realizations to be assessed. For example, the probability of the maximum magnitude exceeding some threshold may be estimated as the relative frequency of such occurrences over many earthquake catalog simulations. This simulation procedure also provides the necessary input to any Monte Carlo seismic hazard assessment to estimate the peak ground motion map with a certain probability of exceedance. BOURNE ET AL The Authors. 8998

9 Figure 3. Location of surface accelerometer stations (squares) and near-surface borehole geophones (triangles) that comprise the earthquake monitoring network operated by KNMI in the vicinity of the Groningen field. 3. Application to the Groningen Gas Field The Groningen field is located in the north-east of the Netherlands (Figures 2 and 3) and is western Europe s largest gas field. The reservoir is a more than 100 m thick Slochteren sandstone of the Upper Rotliegend Group, at a depth of approximately 3000 m. It was discovered in 1959 and has been in production since Some 300 wells have been drilled, spread over 29 surface production clusters. The recoverable volume of gas is about 2800 billion cubic meters. As of November 2012 about 70% of this original recoverable volume has been produced leaving a further 800 billion cubic meters to be produced over about the next 70 years. During 2013, the 54 billion cubic meters of gas produced from the field accounted for over half of the total gas produced in the Netherlands Geological and Seismic Setting The Groningen field is located on the Groningen High, a tectonically stable block since the late Kimmerian uplift. The gas-bearing interval of the Groningen field comprises the Upper Rotliegend Group (Permian) and the Limberg Group (Carboniferous) sediments, separated by the Saalian unconformity (Figure 4). The depth of the Rotliegend reservoir is m. The field extent is controlled primarily by fault closures with occasional local dip closures. The top seal is the Zechstein salt. Reflection seismic surveys indicate a large number of natural faults within and around the reservoir interval (Figure 5). Fault density and fault strike are both variable throughout the field. These faults formed during a phase of extension during the Late Carboniferous and Early Permian. Most were reactivated during a subsequent phase of extension from the Triassic to the Late Jurassic and again during a phase of inversion from the late Jurassic to the early Tertiary. Zechstein salt movements during the Cretaceous will have also loaded these faults. Finally, the Alpine orogeny caused further fault reactivation associated with north-south compression lasting until the early Tertiary. Figure 4. Schematic cross section through the Groningen field. The Slochteren sandstone formation and the Ten Boer claystone are members of the Upper Rotliegend Group. BOURNE ET AL The Authors. 8999

10 Figure 5. The distribution of M L 1.5 earthquake epicenters from 1995 to 2012 is subject to a standard location error of 500 m (67% confidence). Due to these uncertainties it remains unclear if the earthquakes originate exclusively from faults mapped using reflection seismic surveys or are instead associated with unmapped faults. Grey lines denote fault traces mapped at the top of the Upper Rotliegend Group. Map coordinates are given as kilometers within the Dutch National Triangulation Coordinates System (Rijksdriehoek). Reservoir compaction now causes a further reactivation of these faults that results in the ongoing seismicity. The amount of compaction for a given depletion in reservoir gas pressure depends on the reservoir thickness and compressibility. Net reservoir thickness increases from zero in the south-east to 280 m in the north-west. Reservoir compressibility depends primarily on reservoir porosity which is largest in the Slochteren sandstone and smallest in the Ten Boer claystone. For the seismicity model developed for the Groningen field, tectonically triggered seismicity is excluded on the basis of the apparently very low natural seismicity, as revealed by both the instrumental and historical records for the region. Houtgast [1992] compiled a catalog of historical earthquakes in the Netherlands which lists only one possible earthquake event on 28 January 1262 in the north of the Netherlands prior to the first instrumentally recorded event in the area in The 1986 event is considered to be associated with gas production. The historical record is however unclear about the true nature of the 1262 event which may have been a meteorological event rather than an earthquake. This does not preclude the possibility of long-recurrence interval earthquakes, but it is assumed that the seismic moment budget derives entirely from the reservoir compaction process. That is we neglect any contribution from other deformation processes such as tectonics and postglacial rebound [see Main et al., 1999] that may also contribute to the magnitude of a triggered earthquake. Probabilistic seismic hazard analyses were carried out by KNMI, the authority responsible for meteorology and seismology in the Netherlands, based on various vintages of the Groningen and North Netherlands earthquake catalogs. A series of publicly available reports [de Crook et al., 1995, 1998; Wassing et al., 2004; van Eck et al., 2004, 2006; Dost et al., 2012] and the paper of van Eck et al. [2006] documents this work on earthquake monitoring and hazard analysis. A key element of these previous hazard analyses has been the estimation of the probabilities of shallow events with magnitudes above the threshold for the onset of damage to buildings at surface. The consensus between these numerous studies was that the maximum magnitude earthquake that could be induced by gas production in the north of the Netherlands was M = 3.9. A magnitude 3.6 earthquake on 16 August 2012 near Huizinge, above the central part of the Groningen field, claims that induced seismicity associated with the field is increasing triggered efforts to reassess the induced seismic hazard associated with gas production from the Groningen field [e.g., Muntendam-Bos and de Waal, 2013]. Moreover a significant amount of new data has become available since the previous hazard update by KNMI: the report of Dost et al. [2012] is based on analysis of the data up to and including 1 January 2010, whereas a major upgrade of the monitoring system was carried out during BOURNE ET AL The Authors. 9000

11 Figure 6. The time sequence of mean reservoir pressure depletion according to a dynamic reservoir simulation model that matches the history of gas production and reservoir pressure measurements in observation wells Production History Gas production started in 1963, and production rates increased rapidly until the oil crisis in After that time production rates reduced to conserve Groningen gas reserves, while smaller gas fields were able to meet the market demand. In recent years, increased market demand and decreased production capacity from these smaller gas fields led to an increase in Groningen gas production. This same trend is evident in the reduction in mean Groningen reservoir pressure with time (Figure 6) with increasing depletion rates into the 1970s followed by slower depletions rates until a return to faster depletion rates in recent years Subsidence History Geodetic monitoring of subsidence over the Groningen field (Figure 7) began in 1964 with optical leveling over a limited network of benchmarks sparsely covering the central and southern part of the field. The first repeat survey in 1972 expanded the coverage of this network to the entire field and also increased the density of benchmarks. Complete and partial repeat surveys of this network occurred in 1975 and 1985, respectively, followed by a further and significant increase in the density of benchmarks in Further complete or partial repeat surveys of this network occurred every 1 to 5 years until InSAR monitoring using the persistent scatterer technique began in These data were processed to yield the equivalent of repeat subsidence surveys every year with the exception of 2000, 2001, and This method relies on monitoring objects within the landscape that are typically related to buildings and yields a dense population of measurement locations that persist through time [Ketelaar, 2008, 2009]. During this period, leveling surveys were repeated in 1997, 1998, and 2008 to demonstrate consistency between the InSAR and leveling measurements [Nederlandse Aardolie Maatschappij (NAM), 2010]. Figure 8 shows subsidence, downward vertical displacement relative to the initial elevation, as a function of time and mean reservoir pressure for the subset of benchmarks that repeat the initial 1964 benchmark locations. There is clear evidence for increasing rates of subsidence during the period of increasing reservoir pressure depletion rates until about Thereafter, subsidence rates appear more constant. The trend of subsidence with reservoir pressure depletion is primarily linear, although there is some evidence for the rate of subsidence increasing with increasing pressure depletion Reservoir Compaction Model The model of reservoir compaction for the Groningen field is based on a dynamic reservoir simulation model that computes the distribution of reservoir pressure changes. This model is calibrated to match the history of gas production from each production well and the history of reservoir pressure depletion and limited aquifer influx measured by a network of observation wells [Nederlandse Aardolie Maatschappij (NAM), 2013, chapter 4.4]. Based on Figure 8b, the initial simple model considered for reservoir compaction in response to these pressure changes is linear poroelasticity where compaction is the product of reservoir pressure depletion, net reservoir thickness, and the uniaxial compressibility of the bulk reservoir. The distribution of net reservoir thickness was taken from a static reservoir model constrained by reflection seismic data and well control. The distribution of uniaxial compressibility depends on reservoir porosity taken from a static reservoir model constrained by petrophysical well logs. The total reservoir pore volume was constrained to match the volume of gas initially in place obtained from analysis of pressure depletion versus gas production data. However, uncertainty remains in the distribution of porosity, particularly away from well control. The relationship between reservoir porosity and uniaxial compressibility was based on laboratory measurements of plug, and core samples recovered from the reservoir. Some uncertainty remains BOURNE ET AL The Authors. 9001

12 Figure 7. The time sequence of geodetic network geometries used for monitoring subsidence above the Groningen field using optical leveling (H) and interferometric synthetic aperture radar (InSAR) (D) observations. Each dot denotes the location of a leveling benchmark or a persistent InSAR scatterer. in the relationship between these measurements and the uniaxial compressibility of the bulk reservoir due to limited sampling and differences in length scale. This was represented as a single field-wide scalar parameter which was constrained by minimizing the misfit between the computed surface subsidence and all the available subsidence measurements obtained by leveling and InSAR surveys. BOURNE ET AL The Authors. 9002

13 Figure 8. (a) Time series of surface subsidence measurements relative to the first survey in April (b) Surface subsidence measurements in relation to mean reservoir pressure depletion. The resulting linear poroelastic compaction model (Figure 9) yields a reasonable fit to these geodetic data [Hejmanowski, 1995, 2000]. However, there are alternative reservoir compaction models that also fit these data, such as higher-order models for the relationship between reservoir pressure depletion and compaction. One depends on the time history of local pressure depletion [Mossop, 2012]. Another depends on the instantaneous local rate and state of pressure depletion [Nederlandse Aardolie Maatschappij (NAM), 2013]. Also, there remains uncertainty about the mechanical properties of the subsurface surrounding the reservoir measured from petrophysical logs and core materials. These properties influence the relationship between reservoir compaction and surface subsidence, and so allow another set of alternative compaction models. Further studies are ongoing to reduce these uncertainties through improved model calibration and to assess the influence of these uncertainties by establishing a comprehensive range of acceptable compaction models given the available field and laboratory data. This paper will focus on application of the seismological model to the simple linear poroelastic compaction model. S. J. Bourne et al. (under review, 2014) describe the influence of these epistemic uncertainties in the compaction model on the assessment of seismic hazard. Figure 9. The distribution of pressure depletion, reservoir compressibility, net reservoir thickness, and reservoir compaction according to the linear poroelastic compaction model from 1960 to Local map coordinates are given as kilometers. BOURNE ET AL The Authors. 9003

14 3.5. Earthquake History The Royal Netherlands Meteorological Institute (KNMI) has monitored seismicity in the Netherlands since at least 1986, the first earthquake recorded in the north of the Netherlands was in December Current seismicity observed in this area is generally considered to be induced by production from the northern gas fields Groningen and others. A local monitoring network in the NE of the Netherlands was installed in This array originally consisted of eight stations at which three-component geophones were deployed at four depth levels in shallow (200 to 300 m deep) boreholes. In 2010, a major upgrade of this array was carried out. This comprised extension of the network by deploying six additional stations (in 120 m deep boreholes), implementation of real-time continuous data transmission to the data center, and an automatic detection and location capability. Complementing the geophone array, a number of accelerometer stations were added to the network for surface strong Figure 10. Earthquake epicenters for ML 1.5 from 1995 to 2012 in relation to the model of reservoir compaction from 1960 to The motion measurement which can also be grey polygon denotes the outline of the Groningen field. The 14 level used as an additional input to the event discrete color bar denotes the compaction intervals used to measure location calculations. Dost et al. [2012] the distribution of earthquakes with respect to compaction. describe the composition of the monitoring network and its evolution over time. Figure 3 shows the stations comprising the network in the vicinity of the Groningen field. For the Groningen field earthquake catalog, the magnitude of completeness for located events is taken to be ML = 1.5, starting in April 1995, with an event detection threshold of ML = 1.0 [see Dost et al., 2012]. Dost et al. [2012] reported that the catalog for the north of the Netherlands contained 640 events. Here we restrict our analyses to the 187 events with ML 1.5 recorded within the Groningen field between 1 April 1995 and 30 October Figure 10 shows earthquake epicenters in relation to reservoir compaction within the Groningen field, note the concentration of events within the region of greatest compaction. Epicenters of events in the catalog are determined to within about m but, because of the sparseness of the monitoring array, depths can only be estimated for a handful of fortuitously located events. For other events a depth of 3000 m approximate reservoir depth has been assumed. In our analysis it is assumed that moment magnitude and local magnitude are the same in this area over the observed magnitude range [see van Eck et al., 2006]. The full earthquake catalog is publicly available and may be downloaded from the KNMI website. The compaction model gives reservoir compaction maps as a function of time. By spatial and temporal interpolation reservoir compaction values can be assigned to each earthquake in the catalog. Figure 11 suggests a strong bias in the origin time and location of ML 1.5 events toward larger reservoir compaction: for example, 90% of these events occurred at a time and place when the reservoir compaction was at least 0.18 m. This is very unlikely to be a chance process given 50% of the reservoir by area experienced less than 0.18 m of reservoir compaction over this period (Figure 11). Rather, it implies that the occurrence of earthquakes, in space and time, is strongly influenced by the reservoir compaction. The location of the first observed ML 1.5 event in 1991 is within the region of greatest compaction. Over the following 20 years, the areal footprint of earthquake locations spreads mostly toward the south-east and approximately tracks a reservoir compaction contour as it extends away from the center of the field. The time series of ML 1.5 BOURNE ET AL The Authors. 9004

15 Figure 11. The areal extent of M 1.5 earthquake locations through time remains for the most part (80%) within the 0.18 m reservoir compaction contour (red line) according to the linear poroelastic reservoir compaction model. events magnitudes, labeled according to the reservoir compaction at the time and location of each event (Figure 12), suggests there is no single threshold in compaction above which induced seismicity occurs but rather a much more continuous process where the likelihood of an event occurring increases according to the local reservoir compaction. A key characteristic of the earthquake catalog is the slope of the Gutenberg-Richter frequency-magnitude plot, known as the b value. A standard method for determining the b value is the maximum likelihood method originally formulated by Aki [1965] and Utsu [1966]. Marzocchi and Sandri [2003], among others, have updated the Aki and Utsu expression by including a term which corrects for the finite width of the magnitude bins used to catalog these data. Applying this binning-corrected version of the maximum likelihood method to the Groningen field data yields b = The usual expression for the standard deviation of the maximum-likelihood b value is σ = b n, where n is the number of events. Using this expression gives the 95% (2σ) confidence interval for the estimated b value as 0.90 to Figure 13 shows the fit of this model to the observed frequency magnitude distribution. The Poisson counting errors associated with finite sample sizes within each magnitude bin indicate b = 1 is a sufficient description of these data. Although a truncated frequency-magnitude distribution with a maximum magnitude of M max = 3.9 also fits these data (Figure 13), there is no upper bound to the 95% confidence interval on the estimate of M max because the b = 1 model without any truncation is sufficient to describe these data given their counting errors. Estimates of the b value appear to depend on reservoir compaction. Each event was labeled according to the reservoir compaction at the event s origin time and epicenter. Based on these labels, subsets of events were selected within a range of compaction values. To avoid the possibility of bias from variable sample sizes, the range of compaction was adjusted to ensure each subset contained exactly 50 events. The resulting maximum likelihood b-value estimates and their 67% confidence intervals (Figure 14) indicate a Figure 12. Time series of M L 1.5 earthquake magnitudes versus reservoir compaction at the origin time and map location of each event. BOURNE ET AL The Authors. 9005

16 Figure 13. The frequency magnitude distribution of M L 1.5 events within the Groningen field between 1995 and 2012 has a maximum likelihood estimate for the b value of 1. Due to the small number of events, stochastic variability for the larger magnitude, lower frequency events is appreciable as indicated by the grey region that denotes the 95% confidence interval on the Poisson counting error. This means there is no statistically significant evidence for an upper bound to the frequency-magnitude distribution despite previous reports of M max 3.9 [de Crook et al., 1995, 1998; van Eck et al., 2006; Dost et al., 2012]. statistically significant decrease in b value with increasing compaction. This suggests the central area of the reservoir not only experienced the most compaction and the greatest density of events but also the greatest proportion of larger magnitude events. Due to the small sample size, we recognize the possibility that the confidence intervals might be underestimated to the point that this apparent trend in b value with compaction is not statistically significant. The fraction of induced strain accommodated by seismogenic fault slip within the Groningen field is central to assessing future seismicity on the basis of future gas production and reservoir compaction. The total seismic moment observed in the catalog of M L 1.5 events from 1995 to 2012 is about Nm. However, given the change in reservoir compaction over the same period, the total seismic moment expected if all this strain had been accommodated by seismogenic slip on faults, i.e., α = 1, is about Nm. Clearly, most of the strain so far has not been accommodated by earthquakes, and the observed partition fraction is extremely small at α = The 95% confidence interval for this estimate, calculated by consideration of the confidence bounds of a Pareto sum distribution [Zaliapin et al., 2005] for the total seismic moment of 188 M L 1.5 independent events with β = 2 3, is to Over this period of observation, the upper bound of this confidence interval is still significantly less than 1. Uncertainties in the reservoir compaction model are far too small to allow for the possibility that α = 1:over the monitoring period less than 0.1% of the induced strain has been accommodated by earthquakes. This discrepancy might indicate that nonseismogenic deformation mechanisms, such as fault creep and ductile Figure 14. Maximum likelihood b-value estimates for subsets of the M 1.5 between 1995 and 2012 binned according to reservoir compaction. Bin sizes were selected to ensure every bin contains 50 events. Vertical black bars denote the 67% confidence interval for the maximum likelihood estimate, and horizontal grey lines denote the bin sizes. flow, are dominant. However, it is also possible that most induced strain is elastic and so remains available to be released by future earthquakes. Figure 15 shows the evolution of the partition factor with ongoing production it appears that the partition factor has increased with production over the monitoring period by a factor of 5, from an initial value of about A notable feature of the Pareto sum distribution for the total seismic moment is the skew of the confidence bounds around the median, for example, the 95% confidence interval shown in Figure 15 extends from just below the median to a factor of 100 above. Consequently, the apparent trend of increasing total seismic moment per unit gas production is not yet statistically significant as a strain model with constant partitioning BOURNE ET AL The Authors. 9006

17 Figure 15. The trend of total seismic moment with total gas production since April 1995 suggests that the fraction of induced strain accommodated by induced seismicity is small (α 10 3 ) but might be increasing with gas production. (α = ) does not fall outside the 95% confidence interval. However, if the current apparent trend continues, it represents an increase in the expected total seismic moment released per unit gas production. Strain partitioning that increases with gas production may, in principle, be explained by a population of faults with variable fault strengths. As pressure depletion increases, more-or-less uniformly throughout the gas reservoir (Figure 10), the most vulnerable faults will destabilize first and those within the region of greatest reservoir compaction will then most likely incur most slip. Further, pressure depletion will then destabilize yet more faults throughout the field, and again with most fault slip preferentially located within the region of greatest compaction. As pressure depletion increases, the fraction of unstable faults increases and so does the fraction of strain accommodated by fault slip. Because strain partitioning follows reservoir compaction rather than reservoir pressure depletion, there seems to be a role for slipping faults to transfer stress to nearby stable faults in a manner that tends to destabilize them. Such mechanical interactions between faults may lead to failure avalanche effects [e.g., Dahmen et al., 2011] that emerge as nonlinear increases in strain partitioning with increasing reservoir compaction Strain Partitioning Results The map of reservoir compaction between 1957 and 2012 was divided into discrete independent compaction intervals c i ± δc 2 where c i =[0.01,, 0.33] m and δc = 0.02 m. Within each interval, the total bulk reservoir volume change was computed according to the compaction model and the total number of M 1.5 events and their total seismic moment computed according to the earthquake catalog (Figure 10). Event numbers are subject to a counting uncertainty that follows a Poisson distribution which has a standard uncertainty interval of approximately N ± N. If the activity rate, measured as the number of events per unit reservoir volume change, is independent of reservoir compaction, then event numbers should be randomly distributed with respect to reservoir volume changes. This is not the case (Figure 16a). Instead, the number of events per unit volume change increases substantially with reservoir compaction in a markedly log linear fashion (Figure 16b). These results indicate that doubling the reservoir compaction from 0.15 m to 0.3 m increased the number of M 1.5 events per unit volume change by a factor of 10. Total seismic moments are subject to stochastic variability that follows a Pareto sum distribution. If the fraction of reservoir volume changes accommodated by earthquakes is independent of reservoir compaction, then there would be no significant bias in the distribution of total seismic moments with respect to compaction. Instead, we observe total seismic moments to be underrepresented relative to volume changes for smaller values of reservoir compaction, and vice versa (Figure 16c). The strain partitioning fraction, estimated according to (32), increases strongly with increasing compaction in an approximate log linear fashion (Figure 16d). Doubling the reservoir compaction from 0.15 m to 0.3 m increased this fraction by a factor of about 100. Clearly, both the number of events and the total seismic moment per unit reservoir volume change have increased substantially with increasing reservoir compaction. We suggest this is the mechanism responsible for the observed escalation in the activity rate and seismic moment release rate with production. At lower levels of reservoir compaction, more of the induced strain may be accommodated by elastic deformation; however, as compaction increases more and more of the rock volume exceeds its elastic limit and so an increasingly large fraction must be accommodate as slip on faults. BOURNE ET AL The Authors. 9007

18 Figure 16. (a) Reservoir volume change within discrete intervals of reservoir compaction according to the reservoir compaction model from 1960 to 2012 and the number of M 1.5 earthquakes observed over the period 1995 to 2012 within these same compaction intervals. (b) The number of M 1.5 events per unit reservoir volume change within each interval of reservoir compaction exhibits a log linear trend. Vertical black bars in Figures 16a and 16b denote counting errors as a 67% confidence interval for a Poisson distribution with a median value equal to the observed value. (c) The distribution of total reservoir moment and total seismic moment within the same compaction intervals. (d) The total seismic moment per unit total reservoir moment exhibits a log linear trend with reservoir compaction. Vertical black bars in Figures 16c and 16d denote stochastic variability as a 67% confidence interval for the Pareto sum distribution with a median value equal to the observed value. Figure 17. The solution space found for the exponential trend strain partitioning model is contiguous and bounded although there is a strong negative correlation between the f and g values. Solutions were sought by a random search within the indicated polygon. A single dot denotes each solution found, and its color represents the total seismic moment computed over the earthquake catalog interval from 1995 to The observed total seismic moment over this interval is Nm. Figure 17 shows the distribution of acceptable strain partitioning model parameters obtained according to the method described in section 2.3. This indicates a wide spread of parameter values that reflects scatter in the limited number of strain partitioning estimates and the effect of stochastic variability according to the Pareto sum distribution. There is also a strong negative correlation between f and g values due to a trade-off between the parameters; that is, a larger intercept value (f value) may, in part, be compensated by a smaller slope value (g value) due to the limited range of observed compaction values. The total seismic moment computed by the model over the earthquake catalog interval from 1995 to 2012 also exhibits considerable BOURNE ET AL The Authors. 9008

19 Figure 18. (a) The distribution of strain partitioning models consistent with the observed strain partitioning values. (b) The probability of exceeding a giventotal seismic moment computed according to the reservoir compaction and the strain partitioning models. (c) The frequency distribution of residuals between the set of acceptable strain partitioning models and the set of resampled strain partitioning observations. (d) The distribution of residuals with respect to the observed strain partitioning values exhibit no evidence for any significant scale bias. variability relative to the observed total seismic moment of Nm. This is also due to the allowance for stochastic variability in the observed total seismic moment as described by the Pareto sum distribution. The resulting confidence intervals on the exponential trend partitioning model (Figure 18a) are consistent with the scatter and uncertainty associated with the data points. Uncertainty associated with extrapolating this model to the larger values of compaction expected in the future is quantified and appears as wider confidence intervals for compaction values increasing above the largest observed compaction bin of 0.35 m. The frequency distribution of residuals between each acceptable realization of the model and the observed strain partitioning follows a zero-mean normal distribution supporting the use of least squares optimization (Figure 18c). Moreover, there is no evidence for any significant scale bias in this distribution of residuals (Figure 18d). Figure 18b shows the computed probability distribution of total seismic moment for the earthquake catalog interval from 1995 to 2012 and the 2 year, 5 year, and 10 year intervals starting in Model Validation The strain partitioning model was calibrated using the areal distribution of all observed events (1995 to 2012) relative to the areal distribution of reservoir compaction at the end of this period (2012). The temporal development of seismicity and reservoir compaction was not used to calibrate the seismological model. Consequently, the computed and observed time series of total seismic moment should agree even though the model has not been calibrated to ensure agreement. Figure 19 shows the results of this comparison. To account for the absence of earthquake monitoring with completeness for M L 1.5 prior to 1995, the observed time series starts with the median value computed for the model in The computed increase in the median total seismic moment is clearly a good fit to the observed values (Figure 19a). Likewise, the slope of the log linear trend of observed total seismic moment with cumulative gas production (Figure 15) is reproduced by the seismological model (Figure 19b). BOURNE ET AL The Authors. 9009

20 Figure 19. Model of median total seismic moment with (a) time and (b) cumulative gas production compared to the history of observed total seismic moment. Dashed lines denote the 95% confidence interval around the median model of total seismic moment. This is contingent on past and future seismicity following the same trend as the observed seismicity. The grey line denotes the maximum magnitude if all the previously accumulated reservoir moment were to be released in a single event Time-Dependent Seismicity The computed seismic moment release rate depends on two competing effects. First, the seismic moment released per unit gas production increases with reservoir compaction. Second, the rate of gas production eventually decreases due to reservoir pressure depletion. Over the next 20 years or so, the first effect is expected to dominate and so the annual seismic moment is expected to tend to increase year-on-year. Thereafter, the second effect will likely dominate as the annual gas production naturally declines to levels well-below current production rates. Figure 20 shows predicted initial escalation and then the long decline in annual seismic moment release according to the seismological model. This includes a wide range of uncertainty between the expected value and the upper bound of the 95% confidence interval, but the same clear temporal trend with a maximum sometime between 2025 and 2035 based on the current production plan. Although the historic seismicity is clearly consistent with the seismological model between 1995 and 2013, there is clearly significant uncertainty about future changes in seismicity as indicated by the modeled confidence interval. Such time dependence is intrinsic to induced seismicity that necessarily has a beginning and an end. This however raises questions about how to assess time-dependent seismic hazards in relation to standards that were designed with time-independent natural seismicity in mind [e.g., Comité Européen de Normalisation, 2004]. Figure 20. The median annual total seismic moment release based on the seismological model for the Groningen field. This calculation was obtained using the 2013 gas production plan and the linear poroelastic reservoir compaction model. The upper and lower bounds denote the 95% confidence interval of the seismological model. Dots denote the observed annual seismic moment between 1995 and Earthquake Probabilities Stochastic simulations of earthquake catalogs for a 3, 5, and 10 year interval from 2013 onward according to the procedure described in section 2.6 yielded estimates for the magnitude with a given chance of exceedance (Table 1). These calculations are based on a linear poroelastic model of reservoir compaction, a constant b value of b = 1, and the 2013 gas production plan. The reliability of these probability estimates are contingent on the future seismicity following the trend of increasing fault strain partitioning observed in the historic seismicity; although this needs not be the case. BOURNE ET AL The Authors. 9010

21 Table 1. Estimated Magnitudes With a 50%, 10%, and 2% Chance of Exceedance Over a 3, 5, and 10 Year Period From 2013 Onwarda Period P50 P10 P a These estimates are based on the seismological model for the linear poroelastic compaction model and the 2013 gas production plan. The validity of this model is contingent on future-induced seismicity following the same trend of increasing fault strain partitioning observed within the historic earthquake catalog and a stationary b value of 1. Figure 21 shows the number of events expected per square kilometer according to the seismological model for the entire period of induced seismicity since the start of gas production up to 2013, 2016, 2018, and These maps illustrate the increasing localization of epicenters with time within the region of greatest compaction. Notice that event density increases within the central part of the reservoir from about 5 km 2 to about 10 km 2, whereas toward the flanks of the reservoir these increases are considerably smaller. Figure 21. Event density maps for induced seismicity since the start of gas production up to 2013, 2016, 2018, and 2023 based on the seismological model of the Groningen field according to the linear poroelastic compaction model and the 2013 gas production plan. BOURNE ET AL The Authors. 9011