grant agreement no. 764810 science for clean...

This Project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 764810

Grant agreement No. 764810

Science for Clean Energy

H2020-LCE-2017-RES-CCS-RIA Competitive low-carbon energy

D5.6 Data-driven updating of empirical ground motion to

monitor induced seismicity and reservoir status

WP 5 – Data Gathering and Model Implementation

Due date of deliverable Month 30 - February 2020 Actual submission date 27/02/2020 Start date of project September 1, 2017 Duration 36 months Lead beneficiary UNISA Last editor Paolo Capuano Contributors Vincenzo Convertito, Raffaella De Matteis (UNISA) Dissemination level Public (PU)

Deliverable D5.6

PU of 28 Version 4.5

History of the changes

Version Date Released by Comments

1.0 19-01-20 Vincenzo Convertito First draft

2.0 24-01-20 Vincenzo Convertito Updated draft

3.0 04-02-20 Paolo Capuano Review and updated draft

3.1 08-02-20 Vincenzo Convertito Implementation of figure changes

3.2 11-02-20 Raffaella De Matteis Review and updated draft

4.0 12-02-20 Paolo Capuano Final draft

4.1

4.2

4.3

13-02-20

18-02-20

19-02-20

Camille Voirin

Alberto Striolo

Paolo Capuano

Formatting

Minor edits

Revised final draft

4.4 21-02-20 Thomas Bloch Review and minor edits

4.5 21-02-20 Paolo Capuano Last updates

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Table of Figures Figure 1: Sketch of the hypothesized fluid injection experiment ............................................. 8 Figure 2: Peak-ground velocities as function of the hypocentral distance measured on the waveforms simulated by using the homogeneous crustal model ........................................... 11 Figure 3: Result of the test aimed at comparing the constant Q models (squares) with Q frequency dependent models (circles) computed at 1 Hz (Q=10, 20 and 70) ........................ 12 Figure 4: Results of the test aimed at comparing the constant Q models (left panels) with Q frequency dependent models (right panels) computed at 1 Hz (Q=10, 20 and 70)................ 13 Figure 5: Peak-ground velocities as function of the hypocentral distance measured on the waveforms simulated by using the three layered models listed in Table 1.. .......................... 14 Figure 6: Residuals as function of distance and magnitude. (a) and (b) refer to MOD1 and to the regression of the GMPE coefficients assuming that only the parameter c is set to the reference value ........................................................................................................................ 16 Figure 7: Results of the sensitivity test of the coefficients of the GMPE as function of the magnitude for the three investigated models listed in Table 1. ............................................. 17 Figure 8: Plan view of the analysed earthquakes at St.Gallen geothermal site in the year 2013. Symbols sizes are proportional to the magnitude and colour coded according to the depth. The beachballs indicate two available focal mechanism solutions for the MLcor 3.5 event. Seismic network layout is indicated in right bottom frame. The blue line indicates the surface projection of the GT-1 well trajectory. ....................................................................... 18 Figure 9: The upper panel shows the three main phases of the geothermal project St.Gallen reported by Moeck et al. (2015) together with the well head pressure, and the injection rate at GT-1. The lower panel depicts the temporal evolution of seismicity from 2013-07-14 to 2013-10-22. Earthquakes are colour coded according to the depth.. .................................... 18 Figure 10: PGVs (on log scale) as function of the magnitude MLcor (purple crosses). ........... 19 Figure 11: Residuals distribution at the stations used to measure PGVs in the area around St.Gallen GT-1 well.. ................................................................................................................. 20 Figure 12: PGVs distribution at St. Gallen site as function of the hypocentral distance and colour coded according to the depth. The dashed lines correspond to the best fit model reported in eq. (12). ................................................................................................................. 21 Figure 13: Blu lines correspond to the results obtained by analyzing the whole selected catalogues (St.Gallen site) whose duration is indicated on the top of the upper panel. The dots correspond to the values of the parameter together with the uncertainty obtained from the analysis of each single earthquake. The red lines correspond to the moving average of the dots. ............................................................................................................................... 22 Figure 14 The upper panel is the same as in Figure 13 and is shown here to help the comparison with the VP/VS as function of time shown in the lower panel. The empty dots in the lower panel indicate the mean value of the VP/VS obtained for each analysed event (St.Gallen site). The red line corresponds to the moving average. ......................................... 23 Figure 15 The upper panel is the same as in Figure 13 and is shown here to help the comparison with the Qs as function of time shown in the lower panel. The dots in the lower panel indicate the mean value of the Qs obtained for each analysed event (St.Gallen site). The red line corresponds to the moving average ........................................................................... 24

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Table of contents

History of the changes ............................................................................................................... 2

Table of Figures .......................................................................................................................... 3

Key word list ............................................................................................................................... 5

Definitions and acronyms .......................................................................................................... 5

1 Introduction .......................................................................................................................... 6

1.1 General context............................................................................................................ 6

1.2 Deliverable objectives ................................................................................................ 6

2 Methodological Approach ..................................................................................................... 6

3 Feasibility study ..................................................................................................................... 6

3.1 The layered model ..................................................................................................... 8

3.2 Inferring the GMPE coefficients ................................................................................. 9

4 Analysis of One Real Dataset .............................................................................................. 17

4.1 Inferring the reference GMPE ................................................................................... 19

4.2 Temporal analysis of the GMPE coefficients and results validation ........................ 21

5 Conclusions ........................................................................................................................... 24

6 Bibliographical references ................................................................................................... 25

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Key word list Induced seismicity; Ground motion predictive equations; anelastic attenuation; spectral analysis; geo-energy exploitation

Definitions and acronyms Acronyms Definitions

S4CE Science for clean energy

GMPE Ground motion prediction equation

PGV Peak-ground velocity

VP P-wave velocity

VS S-wave velocity

M Earthquake Magnitude

ML Local magnitude

Mw Moment magnitude

Q Quality factor

Density

QP P-wave quality factor

QS S-wave quality factor

R Hypocentral distance

o Low-frequency spectral level

fc Corner frequency

T Travel time of the selected seismic phase

γ Spectral decay

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1 Introduction

1.1 General context

Enhanced Geothermal Systems (EGSs) may contribute to clean power generation at local and global stage. However, several studies do exist emphasizing the impact of industrial activities in geothermal areas like Basel, Switzerland (Häring et al., 2008), Hengill, Iceland (Jousset and Francios 2006), The Geysers, USA (Foulger et al., 1997; Enedy et al., 1992; Majer et al., 1979; Eberhart-Phillips and Oppenheimer, 1984; Ross et al.,1999; Stark, 1992, 2003; Smith et al., 2000; Majer et al., 2005; Majer et al., 2007) and Pohang, South Korea (Grigoli et al., 2018; Kim et al., 2018; Ellsworth et al., 2019). Induced earthquakes, though generally of small to light size (M<4), due to their shallow depth and high frequency of occurrence represent a primary source of seismic hazard in nearby regions. A few events, potentially connected with anthropogenic activities, have however occurred with significant magnitude and important consequences (Porter et al., 2019). In addition to induced events sub surface operations such as gas storage, fluid reinjection or hydraulic fracking may modify the physical properties of the rocks, in particular the seismic velocity and the anelastic attenuation.

1.2 Deliverable objectives

Within the scopes of the S4CE consortium, the objective of the present D5.6 deliverable “Data-driven updating of empirical ground motion to monitor induced seismicity and reservoir status” is to test if ground motion prediction equations (GMPE), which are generally used as a fundamental tool to compute seismic hazard, can be used for monitoring the physical properties of the rocks and, in particular, the quality factor and its variations during technological activities in geo-energy exploitation sites.

2 Methodological Approach

We propose a method to infer the quality factor, which controls the anelastic attenuation during waves propagation from the source to the station, by analysing the peak-ground motion parameters. In what follows, we first report the results of a feasibility study and then the application of the proposed method to a real dataset of a geothermal drill site.

3 Feasibility study We perform a synthetic test (Convertito et al., 2020) that reproduces the expected seismic activity (seismicity rate, minimum and maximum magnitude, etc.) induced by a fluid injection experiment and recorded at a local seismic network. To simulate the variation of the propagation medium properties during the field operations, for each earthquake the waveforms are computed by modifying physical parameters of the propagation medium and in particular the velocity and the quality factor Q. In the most general case the quality factor does depend on the frequency and this dependence is modelled by the functional

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Q(f)=Qo(f/fo)n, where fo is a reference frequency generally assumed to be 1Hz (e.g., Morozov, 2008) and Qo is the quality factor Q value at fo. For the technique proposed in this project, the first step consists in verifying the effect of using a constant Q and a frequency dependent Q model. In the second step, we use a layered crustal model to test the approach. For both tests, we selected a seismic network configuration and a distribution of earthquakes’ depth that reproduce a real case observed during a reservoir stimulation where medium properties variation is limited to a relatively small volume surrounding an injection well (e.g., Soultz-Sous-Forêts, (Alsace, France); Calò and Dorbath, 2013). Specifically, we selected 16 stations deployed on an area of 4x4 km2 (Figure 1), for 5 hypocentral depths (1.0, 1.5, 2.0, 2.5 and 3.0 km), which provide a range of hypocentral distances ranging between 1 and 6 km. Moreover, full-waveforms simulation is performed by computing the Green’s functions using the code AXITRA (Cotton and Coutant, 1997), based on the discrete wavenumber method. A triangle source-time function is used to represent the earthquake source whose duration is selected according to the Brune’s source model (Brune, 1970). For each selected magnitude value, the static stress-drop value is assigned by using an empirical relationship based on the results obtained by Lengliné et al. (2014) for Soultz-Sous-Forêts. The following analyses consider the peak-ground velocity (PGV) as ground-motion parameter of interest. In particular as PGVs we selected the maximum velocity measured on the vector composition of the three component seismograms. For testing the difference between a constant Q and a frequency-dependent Q, we compute synthetic three-component waveforms for a range of magnitude (0.0÷3.0) and a

homogeneous crustal model (VP = 4500 m/s, VS= 2300 m/s, density =2400 kg/m3). The number of events is assumed constant Nevents=50, while individual magnitude values are randomly selected from the Gutenberg-Richter relation assuming b=1.0. To further increase data heterogeneity, focal mechanisms are selected in the range: strike (140°, 180°), dip (40°, 70°) and rake (-100°, -80°) in accordance with an assumed regional stress-field. In particular, we refer to the state of stress at Soultz-Sous-Forêts (Valley and Evans, 2007). For three different decreasing constant Q values (Q =160, 80 and 50) the final PGV corresponds to the maximum velocity measured on the vector composition of the three component seismograms. These values are compatible with Q quality factors observed in sedimentary rock reservoirs (Abercrombie, 1998; Ripperger et al., 2009; Bethman et al., 2012; Hutchings et al., 2019 and references therein), and with laboratory measurements (e.g., Toksoz et al. 1979; Johnston et al., 1979).

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Figure 1: Sketch of the hypothesized fluid injection experiment. Grey triangles identify the seismic stations, dots represent the location of the earthquakes. Location and extension of the wells are also indicated together with the depth of the layers.

The Q-constant values are then compared with those obtained for three frequency dependent Q models. For the latter, we use the model Q(f) = (β/32)f 0.57 = Q0f 0.57 presented by Satoh (2004). To introduce a frequency-dependent anelastic attenuation, we convolved the Fourier amplitude spectra of the waveforms obtained by using the previous crustal model

(VP = 4500 m/s, VS= 2300 m/s, density =2400 kg/m3) without anelastic attenuation, with the A(R,f)=Aoe-πfR/βQ(f) function, where β coincides with VS. We select three different models, Q(f)=70f 0.57, Q(f)=50f 0.57 and Q(f)=20f 0.57. Note that, hypothesizing that the peak ground velocity is measured at about 8-10 Hz, the previous frequency dependent Q models provide values of Q very similar to the adopted constant values. Moreover, since PGVs are measured on S-waves, assuming that QP = QS for each model would not affect the final results.

3.1 The layered model

Given the same network geometry used in the analysis discussed in Figure 1, we compute synthetic waveforms and relative PGV values for the three crustal models listed in Table 1, that mimic the effects of increasing field operations. As for the selection of the layers thickness, velocity and density values we refer to the model proposed by Cuenot et al. (2008) and Valley and Evans (2007) for Soultz-sout-Forêts. We assume that the field operations affect

N

0.8 km

1.6 km

2.6 km

3.6 km

4.6 km

5.6 km

6.6 km

7.6 km

4 km4 km

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all the layers but that the highest attenuation is attained in the first two layers that could represent the sedimentary sequence.

Table 1: Structural models used to simulate waveforms and the relative PGVs shown in Figure 1. VP and VS refers to P- and S-wave velocity, ρ is the density and QP and QS the P and S quality factors. The last three columns report the three investigated anelastic models: MOD1, MOD2 and MOD3.

Z(m) VP(m/s) VS(m/s) ρ(kg/m3) QP, QS QP, QS QP, QS

0.0 1850 860 2000 50 20 10

800 2870 1340 2870 100 50 25

1600 5800 3310 2600 500 100 50

2600 5820 3320 2600 500 100 50

3600 5850 3340 2600 500 100 50

4600 5870 3350 2600 500 100 50

5600 5900 3370 2600 500 100 50

6600 5920 3380 2650 500 100 50

7600 5950 3400 2650 500 100 50

In order to mimic real data acquisition as much as possible, for each model, we generate a new earthquake catalogue assuming a specific b-value. Indeed, it is expected that the b-value changes in space and time during fluid injection operations, deviating from the usually observed b=1 value (Henderson et al., 1999; Cuenot et al., 2008; Convertito et al., 2012; Bachmann et al., 2012), although the variation is not strictly correlated with the injection rate and distance from the well (e.g., Cuenot et al., 2008; Bachmann et al., 2012). For the analysis of the layered crustal models, we assume that the b-value increases as function of the injection rate and moves from a starting value 1 to 1.2 and 1.5 in the last stage of the operations as observed during the hydraulic stimulation at Soultz-sout-Forêts (Cuenot et al., 2008) or during gas depletion in the Netherlands (Van Wees et al., 2014).

3.2 Inferring the GMPE coefficients

As a first task for a homogeneous, isotropic medium with no anelastic attenuation, we select a GMPE that corresponds to the reference model. For the analyses presented in this study, we select a GMPE with a formulation as simple as possible:

𝑙𝑜𝑔𝑌 = 𝑎 + 𝑏𝑀 + 𝑐𝑙𝑜𝑔𝑅 (1)

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where Y is the PGV, R is the hypocentral distance and M is the earthquake magnitude. In eq. (1), the coefficients a and b account for the effect of the earthquake size on Y, while c accounts for the geometrical spreading. The model is also associated with an error σlogY describing uncertainty in the value of Y given the predictive relationship. Equation (1) represents a simple model when compared to many formulations with higher degree of complexity (e.g., Douglas, 2003; Douglas et al., 2013) which could better account for the physical processes affecting the recorded ground motion parameter. However, additional terms accounting for non-linearity in magnitude scaling and magnitude-dependent geometrical spreading are effective and could be resolved for distances and magnitudes larger than those considered in this study. Such possible extension is discussed in the section “Simulation set-up” (Bommer et al., 2007; Cotton et al., 2008; Baltay and Hanks, 2014). To test if GMPEs can be used to monitor anelastic attenuation variations that can be correlated to the field operations, we have to introduce in the empirical model a coefficient that accounts for loss of energy by intrinsic anelastic attenuation (e.g., Knopoff, 1964; Del Pezzo and Bianco, 2013). The intrinsic anelastic attenuation is inversely related to the quality factor Q (Knopoff, 1964) and can be modelled as a filter of the form A(R,f)=Aoe-πfR/βQ , which is thus convolved with the source spectrum (Babaie Mahani and Atkinson, 2012). In the previous equation, Ao is the amplitude at the source, f is the frequency, R is the hypocentral distance, β is the shear-wave velocity. Thus, moving to the logarithm, the effect of A(R, f) on Y results in a linear function of the distance R with a constant coefficient d. The new model is thus formulated as follows:

𝑙𝑜𝑔𝑌 = 𝑎 + 𝑏𝑀 + 𝑐𝑙𝑜𝑔𝑅 + 𝑑𝑅 (2)

We notice that, as reported by Cotton et al. (2008), the interpretation of the term dR as the anelastic attenuation in this equation is only strictly correct when considering Fourier amplitudes for a particular frequency. However, given the limited magnitude range considered in the present study, we can assume that the PGVs are relative to a narrow frequency band. In the most general formulation of the anelastic attenuation model, Q is frequency dependent and should be written as Q(f)=Qo(f/fo)n where fo is a reference frequency generally assumed to be 1Hz (e.g., Morozov, 2008) and Qo is the quality factor Q value at fo. In what follows, we show that the assumption of a Q constant model does not substantially modifies the main results obtained, probably because the frequency dependence of Q does not have a significant effect on short near-source paths as those considered in this study. The approach proposed in this study is to use the earthquakes recorded during the field operations to infer and/or update the coefficients a, b, c and d (De Matteis and Convertito, 2015) and test which of them have to be analysed to monitor the status of the reservoir. In particular, we test two cases. In the first case, data of synthetic earthquakes are individually used to infer the new coefficients. A similar approach has been used by Chiou and Youngs (2008) to study the dependence of the anelastic attenuation term on the magnitude. In the second case all the earthquakes recorded during a fixed period are used to infer the new coefficients. Following Bommer et al. (2006), we select as reference GMPE the following equation:

𝑙𝑜𝑔𝑃𝐺𝑉 = 𝑎 + 𝑏𝑀 + 𝑐𝑙𝑜𝑔𝑅 (3)

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where PGV is in cm/s, the hypocentral distance R is in km and the logarithmic standard deviation is 0.297. The coefficients of Eq. (3) will be indicated as pref where p = a, b, and c whose values are a = -0.527, b = 0.521 and c = -1.058, as provided by Bommer et al. (2006). Although this model does not explicitly contain the anelastic attenuation term, it does not eliminate the physical process that, as a consequence, can be described implicitly via in the c coefficient. However, the aim of the present study is to verify if the additional d coefficient in the eq. (2) significantly varies from a statistical point of view when Q varies. We notice that the original equation by Bommer et al. (2006) uses ML, thus, we are assuming that it coincides with moment magnitude (MW) used for data simulations. The initial analysis is devoted to study the effect of considering Q constant quality factors vs Q frequency dependent quality factors. To this aim, we compute the coefficients of Eq. (2) starting from those relative to eq. (3) using PGVs simulated for models with Q =160, 80 and 50 that are compared with Q(f)=72f0.57, 20f0.57 and 10f0.57, respectively. The corresponding PGVs are shown in Figure 2. In particular, we test two cases: i) c=cref and inverting a, b and d; ii) b=bref, c=cref and inverting a and d for all the events together, and for individual events. In both cases, we assume that field operations do not affect the geometrical spreading of the S-waves travelling from the source to the receivers. In case ii) fixing b=bref, we hypothesize that the field operations only partially affect the earthquakes stress-drop.

Figure 2: Peak-ground velocities as function of the hypocentral distance measured on the waveforms simulated by using the homogeneous crustal model. The three upper panels refer to the three constant Q value: Q=160 (left panel), Q=80 (central panel) and Q=50 (right panel). The three lower panels refer to the three frequency dependent models: Q(f)=72f 0.57 (left panel), Q(f)=20f 0.57 (central panel) and Q(f)=10f 0.57 (right panel).

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For inferring the coefficients of the GMPE we used the Levenberg-Marquardt least squares algorithm (Marquardt, 1963) for curve fitting. The results obtained inverting all the earthquakes are depicted in Figure 3. We note that the d coefficient is sensitive to the variations of Q regardless of using a frequency dependent or a constant attenuation model. Concerning the other coefficients there is a kind of statistical balancing. In particular, when only c is set to the reference value, there is a variation of both a and b, likely due to the stress drop variations, with a reduction of the total standard error, whereas when both b and c are set to the reference values the total logarithmic standard deviation remains approximately unchanged.

Figure 3: Results of the test aimed at comparing the constant Q models (squares) with Q frequency-dependent models (circles) computed at 1 Hz (Q=10, 20 and 70). Lefts panels refer to the case in which all the events are used for the inference in which c is set to is set to the reference value, whereas right panels refer to the case in which both b and c are set to the reference values. The dashed horizontal lines correspond to the reference value of the parameter.

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As for the case in which data of individual events are used, the variation of the coefficient d is evident, in particular, when data from low magnitude events are inverted (Figure 4).

Figure 4: Results of the test aimed at comparing the constant Q models (left panels) with Q frequency dependent models (right panels) computed at 1 Hz (Q=10, 20 and 70), for the case in which data from each event are inverted separately and c and b are fixed to the reference values. The squares in the left and panels and the circles in the right panel are colour coded according to the magnitude of the events. The dashed horizontal lines correspond to the reference values of the parameters.

This can be explained by considering that the observed velocity spectrum can be modelled as

the product of two terms S(f) and A(R,f). The term S(f) = 2fo/(1+(f/fc)2) is the source

spectrum, where o is the low-frequency spectral level from which seismic moment can be computed and fc is the corner frequency. The term A(R,f)=Aoe-πfR/βQ is the attenuation spectrum model. If one assumes that PGV is measured at the maximum of the amplitude spectrum it can be shown that, at a given distance from the source, the effect of the anelastic attenuation is larger for smaller magnitude events that have higher corner frequencies compared to larger magnitude events. The same test shows that in order to obtain stable results both b and c must be set to the reference values in the inversion process of single events. Next, to simulate a more realistic propagation medium with respect to a homogeneous medium, we analyse PGVs data (Figure 5) simulated by using the three-layered models reported in Table1 (MOD1, MOD2 and MOD3). Incidentally, we notice that the Q value in the

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first layer in MOD3 is a value generally measured in the first 100 m (Abercrombie, 1998) that we arbitrarily extrapolated up to 800 m only to test an extreme case.

Figure 5: Peak-ground velocities as functions of the hypocentral distance measured on the waveforms simulated by using the three layered models listed in Table 1. PGVs in the left panel refer to MOD1, those in the central panel refer to MOD2 and those in the right panel to MOD3. The continuous black lines in the left panel correspond to the reference GMPE model computed for four magnitude values M 0.0, 1.0, 2.0 and 3.0. Dotted-dashed lines represent the GMPEs obtained by inverting all the data together and only the c coefficient is set to the value of the reference model. Dotted lines refer to the case in which both b and c are set to the values of the reference model. Dotted-dashed and dotted lines refer to the same magnitude values as the reference model.

As for MOD1, inverting for all the earthquakes, the GMPE updating provides the following coefficients when b and c are set to the values of the reference model (Eq. 3):

𝑙𝑜𝑔𝑃𝐺𝑉 = −3.29(±0.02) + 0.521M − 1.058logR − 0.046(±0.005)R (4) where PGV is in cm/s, R is in km and the logarithmic standard deviation is σ =0.272. Moreover, when only c is set to the reference value, the updated GMPE is:

𝑙𝑜𝑔𝑃𝐺𝑉 = −3.29(±0.01) + 0.900(±0.007)M − 1.058logR− 0.053(±0.003)R (5) with σ =0.180. As for MOD2, the updated GMPE when b and c are set to the values of the reference model is:

𝑙𝑜𝑔𝑃𝐺𝑉 = −3.12(±0.02) + 0.521M − 1.058logR − 0.107(±0.004)R (6) with σ =0.257 and:

𝑙𝑜𝑔𝑃𝐺𝑉 = −3.33(±0.01) + 0.997(±0.009)M − 1.058logR − 0.099(±0.002)R (7)

with σ =0.174, when only c is set to the reference value. Similarly, for MOD3 the updated GMPE for case i) is:

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𝑙𝑜𝑔𝑃𝐺𝑉 = −3.202(±0.01) + 0.521M − 1.058logR − 0.149(±0.003)R (8)

with σ =0.169 and for case ii) it is:

𝑙𝑜𝑔𝑃𝐺𝑉 = −3.41(±0.01) + 1.183(±0.009)M − 1.058logR − 0.149(±0.002)R (9) with σ =0.169. Note that for both the i) and ii) cases, the inferred d coefficient decreases with the decreasing of the quality factor, that is, when the attenuation is higher. The decrease of the standard deviation from MOD1 to MOD3 is likely due to the increase of the b-value of the Gutenberg-Richter relation used in our simulations. In particular, higher b-values correspond to a higher percentage of smaller magnitude events, which are similarly affected by the anelastic attenuation compared to the case in which a wider range of magnitude (i.e., lower b-value) is considered. In order to analyse the differences between the inferred d coefficients we use a Student’s t-test at 95% level of significance. The results indicate that the difference between the d values is statistically significant (see Table 2).

Table 2: Observed values of the statistic t to compare with the critical values tc = 1.96 and the corresponding computed P-value. Each row refers to the comparison between two inferred d values. The subscript indicates the corresponding GMPE model as reported in Equations 4 to 9.

MODELS tobs P-value

d4 - d6 466 <0.0001

d4 - d8 865 <0.0001

d6 - d8 411 <0.0001

d5 - d7 625 <0.0001

d5 - d9 1304 <0.0001

d7 - d9 866 <0.0001

In addition, for each investigated model we report in Figure 6 the distribution of residuals (logPGVobs − logPGVpred) as function of distance and magnitude. A regression analysis indicates that for all the considered GMPEs there is no trend in the residuals as function of distance. This means that all the models properly account for the geometrical and anelastic attenuation. On the other hand, when both b and c are set to the reference values (Eqs. 4, 6 and 8) there is a linear trend as function of the magnitude.

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Figure 6: Residuals as function of distance and magnitude. (a) and (b) refer to MOD1 and to the regression of the GMPE coefficients assuming that only the parameter c is set to the reference value. (c) and (d) refer to MOD1 and to the regression of the GMPE coefficients assuming that both b and c are set to the reference value. (e) and (f) same as (a) and (b), but for MOD2. (g) and (h) same as (c) and (d), but for MOD2. (i) and (l) same as (a) and

(b), but for MOD3. (m) and (n) same as (c) and (d), but for MOD3. The coefficients m and reported in each panel refer to the slope of the best-fit line (gray dashed line) and the linear correlation coefficient, respectively.

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The results obtained when the data for each earthquake are separately inverted are shown in Figure 7.

Figure 7: Results of the sensitivity test of the coefficients of the GMPE as function of the magnitude for the three investigated models listed in Table 1. Data used to infer the coefficients are those reported in Figure 5. Black squares identify the mean value of the corresponding parameter while the dashed horizontal lines correspond to the reference value of the parameter.

Also in this case, the d coefficient is sensitive, particularly for smaller events, to the variations of the anelastic attenuation, and the logarithmic standard deviation decreases with respect to the reference value. These features are better highlighted when we look at the mean values of a, d and σ, computed for 0.1 magnitude bin width (Figure 7). Similarly to the case of the homogeneous media, in order to obtain stable results it is necessary to set both b and c to

the reference values. This finding still holds when a random noise (in the range 40% of PGV at each station) is added to the simulated PGVs.

4 Analysis of One Real Dataset In order to assess the proposed approach on real data, we apply the developed procedure to the St. Gallen (Switzerland) test site, which is available to the S4CE consortium. The St. Gallen site hosted a deep geothermal project, and it is located in the Swiss Molasse Basin between Lake Constance and the Alps. The site is being run by St.Galler Stadtwerke, the local energy supplier and 100% owned by the city of St. Gallen, Switzerland. In this Section, we analysed data collected by Swiss Seismological Service in 2013 while realizing well control measures after drilling and acidizing the “St.Gallen GT-1” (GT-1) well, and consist of 346 earthquakes with magnitude (MLcor) between -1.2 and 3.5, recorded at 17 stations. Similarly to the synthetic test discussed above, PGVs correspond to the maximum

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velocity measured on the vector composition of the three component seismograms. All the waveforms have been corrected by recording instrument response, tapered at 5%, and filtered in the frequency range 0.2-80 Hz. Double-difference locations, P-picks, S-picks and P-polarities correspond to those used by Diehl et al. (2017).

Figure 8: Plan view of the analysed earthquakes at St.Gallen geothermal site in the year 2013. Symbols sizes are proportional to the magnitude and colour coded according to the depth. The beachballs indicate two available focal mechanism solutions for the MLcor 3.5 event. Seismic network layout is indicated in right bottom frame. The blue line indicates the surface projection of the GT-1 well trajectory.

Figure 9: The upper panel shows the three main phases of the geothermal project St.Gallen reported by Moeck et al. (2015) together with the well head pressure and the injection rate at GT-1. The lower panel depicts the temporal evolution of seismicity from 2013-07-14 to 2013-10-22. Earthquakes are colour coded according to the depth.

Deliverable D5.6


4.1 Inferring the reference GMPE

For the area under study there is no specific GMPE. Thus, the first task is to infer a reference GMPE by using the available dataset. To this aim we selected the model reported in Eq. (10)

𝑙𝑜𝑔𝑃𝐺𝑉 = a+bM+eM2+clogR+dR+st (10)

where, as for the previous cases M is the magnitude, R is the hypocentral distance, d is the coefficient that accounts for the anelastic attenuation, and s is a coefficient that accounts for site/station correction, which is accounted for by the parameter t.

Figure 10: PGVs (on log scale) as function of the magnitude MLcor (purple crosses). The green line corresponds to the best fit model of the linear function whereas the light-blue to the quadratic model (see text for the details).

With respect to the models used during the synthetic tests we investigated the square dependence of the PGVs on the magnitude. To test this hypothesis, we compared two models. The first one is logPGV=a+bM and the second is logPGV=a+bM+cM2 and used the Akaike Information Criterion AIC=N[Ln(MSE)]+2k to assess the actual statistical difference between

the two models. For the linear model we obtained a = -5.890.01, b= 0.840.02 and

misfit=0.529607. For the quadratic model we obtained a= -5.920.01, b= 0.790.02, c =

0.070.01 and misfit= 0.527803. Since we obtained AIC = -2261.35 for the linear model and AIC = -2271.51 for the Quadratic model, we can conclude that the quadratic model should be is favored. As next step we introduced the site/station correction. To this aim we followed the approach first proposed by Emolo et al. (2011) and then used by Sharma et al. (2013) and Sharma and Convertito (2018), which is based on a two-step analysis. In the first step a reference model without anelastic attenuation coefficient is inferred. The obtained reference model is then used to compute the residuals distribution at all the stations. The modal value of each distribution is used as the coefficient t in the model indicated in Eq. (10).

Deliverable D5.6


As for the reference model, we obtained:

𝑙𝑜𝑔𝑃𝐺𝑉 = -2.740.05+0.770.01M+0.0770.009M2-3.39 0.05logR (11) with σ = 0.359. Using the inferred model, we obtained the residual distributions shown in Figure 11.

Figure 11: Residuals distribution at the stations used to measure PGVs in the area around St.Gallen GT-1 well.

Finally, the best fit for the Eq.(10) yields the following coefficients:

𝑙𝑜𝑔𝑃𝐺𝑉 =-3.830.19 +0.7930.01M+0.0690.007M2-1.2060.388logR-

0.1000.019R+0.6870.021t (12) with σ = 0.298. The best model together with the used PGVs dataset as function of the hypocentral distance is shown in Figure 12.

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Figure 12: PGVs distribution at St. Gallen site as function of the hypocentral distance and colour coded according to the depth. The dashed lines correspond to the best fit model reported in eq. (12).

4.2 Temporal analysis of the GMPE coefficients and results validation

Based on the analysis of field operations (Figure 9) and the evolution of the seismicity observed at the field site St.Gallen, we divided the whole dataset in 5 sub-catalogues. Similarly to the procedure followed during the synthetic tests we performed a single earthquake analysis and the analysis of all the events recorded during a specific period. Using the results of the synthetic tests for the analysis of the real data we set b, c and s to their reference value, while invert for a and b. The results of the analysis are shown in Figure 13. We discarded from the results all the events for which the uncertainty on d is larger then 40% of the d value and all the events for which the inferred d was positive. The results of both the two approaches, that is, the one based on the whole catalogue and the one based on the analysis of single earthquakes indicate that the d coefficient is sensitive to the field operations, which seem to produce relevant variation in the anelastic properties of the propagation medium.

M=-1.0

M=3.0

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In order to validate the obtained results and for a proper interpretation we compared them with two standard analysis. The first one is based on the Wadati diagram analysis to estimate VP/VS from the P and S wave arrival times. The results are shown in Figure 14 and indicate a clear anti-correlation between d and VP/VS as expected. Indeed, when the presence of fluids increases, we observe a decrease in the anelastic attenuation and an increase in VP/VS, being this latter due to a decrease in the VS values.

T1

T2

T3

T4

T5

Figure 13: Blu lines correspond to the results obtained by analyzing the whole selected catalogues (St. Gallen site) whose duration is indicated on the top of the upper panel. The dots correspond to the values of the parameter together with the uncertainty obtained from the analysis of each single earthquake. The red lines correspond to the moving average of the dots.

Deliverable D5.6


The second interpretation is instead based on the spectral analysis. In particular, assuming that the source spectrum and the attenuation filter can be expressed as:

𝑆(𝑓) =Ω𝑜

1+(𝑓

𝑓𝑐)

𝛾 𝑒

−𝜋𝑇𝑓

𝑄 (12)

Where T is the Travel time of the selected seismic phase corresponding to the S-wave in the present study, γ defines the spectral decay, fc is the corner frequency and Q is the quality factor. For f<<fc the previous equation reduces to

𝑙𝑛𝑆(𝑓) = 𝑘 −𝜋𝑇𝑓

𝑄 (13)

From eq. (13), it can be easily seen that a linear fit provides Q.

Figure 14: The upper panel is the same as in Figure 13 and is shown here to help the comparison with the VP/VS as function of time shown in the lower panel. The empty dots in the lower panel indicate the mean value of the VP/VS obtained for each analysed event (St.Gallen site). The red line corresponds to the moving average.

Deliverable D5.6


The results of the analysis are shown in Figure 15 where a comparison with the d coefficient clearly demonstrates that Q and d provide the same information about the variation of the anelastic property of medium during the St Gallen project.

5 Conclusions

Within the consortium S4CE, Task 5.6 has, among its objectives, to test if GMPE, which are generally used as a fundamental tool to compute seismic hazard, can be used for monitoring the physical properties of the rocks and, in particular, the quality factor and its variations during technological activities in sub-surface geo-energy exploitation sites. Should this be the case, GMPEs could be used for monitoring and potentially prevent

Figure 15: The upper panel is the same as in Figure 13 and is shown here to help the comparison with the Qs as function of time shown in the lower panel. The dots in the lower panel indicate the mean value of the Qs obtained for each analysed event (St.Gallen site). The red line corresponds to the moving average.

Deliverable D5.6


induced seismicity and reservoir status of sites that are currently under development. To achieve this goal, Deliverable D5.6 reports a feasibility study on a model approach proposed by S4CE partner UniSA, as well as its application on a realistic dataset obtained from the S4CE field site St. Gallen. The results of the feasibility study have shown that the GMPEs can be used to monitor the variations of Q during field operations. In particular, we have shown that the coefficient d is sensitive to the anelastic attenuation variations and that this effect is more evident when the small magnitude events are analysed. The same tests also indicate that the variation of d due to anelastic attenuation dominates the variations possibly due to focal mechanisms. The same conclusion can be drawn from the analysis of the dataset from the St. Gallen field site. This conclusion has been also corroborated by the comparison with two additional conventional seismological analyses, i.e., the Wadati diagram analysis and spectral analysis.

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