update,comparison,andinterpretationoftheground...

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Update, Comparison, and Interpretation of the Ground-Motion Prediction

Equation for “The Geysers” Geothermal Area in the Light of New Data

by Nitin Sharma and Vincenzo Convertito

Abstract The reliability and accuracy of the ground-motion prediction equations(GMPEs) are of prime interest while evaluating seismic hazard for any region. Theregular updates and minimization of the uncertainties associated with the coefficientsof the GMPEs are important for improving ground-motion predictions and consequentperformance of seismic hazard maps.

Thus, in the present study, we propose an update of the GMPEs estimated bySharma et al. (2013) in The Geysers geothermal area. The update is done usingthe huge dataset available and by extending the magnitude range as well as distancerange. The previous dataset used by Sharma et al. (2013) was composed of 212 earth-quakes recorded at 29 stations with the magnitude range between 1:3 ≤ Mw ≤ 3:3 anddistance range between 0:6 ≤ Rhypo ≤ 20 km. The new dataset encloses 10,974induced earthquakes recorded at 29 stations with the magnitude range between0:7 ≤ Mw ≤ 3:3 and distance range between 0:1 ≤ Rhypo ≤ 73 km. We computeupdated GMPEs for peak ground velocity (PGV), peak ground acceleration (PGA),and 5% damped spectral acceleration (SA) (T) at T 0.05, 0.1, 0.2, 0.5, and 1.0 s.

The mean ground-motion predictions of the updated model proposed in thepresent study and the associated uncertainties are compared with the previous modelproposed by Sharma et al. (2013) and with other models specifically developed forsmall-magnitude earthquakes. The GMPEs are derived using a nonlinear mixed-effectregression technique that accounts for both interevent and intraevent dependencies inthe data. We also demonstrate the dependency of aleatory (random) uncertainties andepistemic (informative) uncertainties on source, medium, and site properties. We alsoconcluded that the medium is behaving homogeneously in terms of peak ground-motion attenuation by analyzing uncertainties associated with different ground-motion periods.

Electronic Supplement: Table showing the site correction parameter and/or siteterm obtained and figures showing distributions of residuals for peak ground velocity(PGV), peak ground acceleration (PGA), and spectral accelerations (SAs).

Introduction

Enhanced geothermal systems (EGSs) provide a signifi-cant contribution to clean power generation on a global stage.But the EGSs are associated with induced earthquakes, andmany studies have shown that induced seismicity increaseswith field operations. There are several studies emphasizingthe impact of industrial activities in geothermal areas, suchas Basel (Häring et al., 2008), Hengill (Jousset and François2006) and The Geysers (Majer andMcEvilly, 1979; Majer andPeterson, 2005, 2007; Eberhart-Phillips and Oppenheimer,1984; Enedy et al., 1992; Stark, 1992, 2003; Foulger et al.,1997; Ross et al., 1999; Smith et al., 2000). Though the in-duced earthquakes are small-to-moderate in size (Mw < 4),

their shallow depth and high frequency of occurrence can in-crease seismic hazard in nearby regions. To evaluate seismichazard, ground-motion prediction equations (GMPEs) are thefundamental tool for predicting ground-motion intensitiesbased on predictor variables such as the magnitude of earth-quakes, source-to-site distance, and local site conditions.

It is worth noticing that existing ground-motion modelsmay provide inconsistent predictions for small-magnitudeearthquakes occurring at shallow depths and, in particular,those caused by anthropogenic activity. The review studydone by Douglas (2011) does not list any ground-motionmodel based on induced seismicity records and derived by

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Bulletin of the Seismological Society of America, Vol. 108, No. 6, pp. 3645–3655, December 2018, doi: 10.1785/0120170350

Downloaded from https://pubs.geoscienceworld.org/ssa/bssa/article-pdf/108/6/3645/4562749/bssa-2017350.1.pdfby University College of London useron 15 May 2019

a regression technique. By recognizing this fact, Douglaset al. (2013) developed GMPEs by combining data fromsix geothermal areas in Europe. However, that study cannotbe considered exhaustive, and the need for region-specificGMPEs still exists. This is because, for small-magnitudeearthquakes, stress drop (e.g., Chiou et al., 2012; Gülerceet al., 2016) and local site conditions (e.g., Harmsen,2011) are region specific.

These facts motivated Sharma et al. (2013) to focus onthe world’s largest geothermal area, The Geysers, which is avapor-dominated geothermal field located about 120 kmnorth of San Francisco, California. They presented the firstGMPEs for induced earthquakes in The Geysers geothermalarea. Moreover, Convertito et al. (2012) have shown thatobserved peak ground acceleration (PGA) in The Geysersgeothermal area actually exceeds 1:2 m=s2 (12% of g; gbeing the acceleration of gravity), which corresponds tolight-to-moderate shaking, resulting in a significant increasein seismic hazard. It is thus of prime importance to timelyupdate and improve the existing GMPEs, in particular forthose areas where anthropogenic operations may affect thepropagation medium and the stress field.

In the present work, we reestimated the GMPEsproposed by Sharma et al. (2013; hereinafter, SH13). Weextended the applicability range of the GMPEs in term ofmagnitude, distance, and ground-motion parameters. TheSH13 model was estimated from 212 earthquakes recordedat 29 stations for peak ground velocity (PGV), PGA, and 5%damped spectral accelerations (SAs, at T � 0:2, 0.5, and1.0 s). In the present work, we reestimate the GMPEs using10,947 earthquakes recorded at 29 stations in terms of the

same peak-ground-motion parameters and add two structuralperiods, that is, T � 0:05 and 0.1 s.

Although the data for SH13 range between 1:3 ≤ Mw ≤3:3 and distances range between 0:6 ≤ Rhypo ≤ 20 km, thenew dataset includes earthquakes with magnitudes rangingbetween 0:7 ≤ Mw ≤ 3:3 and hypocentral distances rangingbetween 0:1 ≤ Rhypo ≤ 73 km. The distribution of the pre-vious and new dataset is shown in Figure 1, from which it isclear that the new dataset has a significant spread over a widermagnitude, depth, and hypocentral distance ranges. Thus, be-fore advancing further, it is important to emphasize that theupdated model is valid for hypocentral distances up to 73 kmand magnitude ranges between 0:7 ≤ Mw ≤ 3:3.

We used the nonlinear mixed-effect regression techniqueto update the GMPEs (Lindstrom and Bates, 1990; Abra-hamson and Youngs, 1992). We consider the GMPE as amixed model in which the total uncertainty is split intointerevent and the intraevent uncertainties that are assumedto be independent, normally distributed variables with theirown variances. The interevent and intraevent components ofthe total uncertainty represent the earthquake-to-earthquakevariability and the variability among observations within asingle event, respectively (see Abrahamson and Silva, 1997;Atik et al., 2010; Baltay et al., 2017).

Computation of GMPEs requires three major types ofinformation, such as source, medium, and site. The sourceinformation is derived from magnitude; the medium proper-ties and propagation effect are included through source-to-site distance; and the local site information is generally avail-able as VS30 (averaged shear-wave velocity). However, in thepresent case, the VS30 values for The Geysers geothermal

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Figure 1. Distribution and comparison of new data (gray circles) with old data (black cross), (a) magnitude versus hypocentral distanceand (b) magnitude versus depth.

3646 N. Sharma and V. Convertito


area were not available. Hence, the GMPEs are inferredthrough a two-step method (for details, see Emolo et al.,2011, 2015; Sharma et al., 2013). In the first step, a referencemodel is obtained that does not explicitly account for pos-sible station (or site) effects. In the second step, a first-ordercorrection is introduced for station effects based on theanalysis of the total residuals’ distribution at each stationwith respect to the reference model. The purpose of introduc-ing this methodology is to overcome the problems associatedwith the lack of local-site geological information. Thegroundwork is discussed in detail in the Estimation ofNew GMPEs section.

Data Processing

In The Geysers geothermal area, induced seismicity hasbeen monitored regularly since the 1960s. The inducedseismicity is monitored by the dense Lawrence BerkeleyNational Laboratory, Geysers/Calpine (BG) surface seismicnetwork, with some nearby stations of the Northern Califor-nia Seismic Network. The BG network consists of 32 three-component stations, 29 of which were used for the presentstudy (gray triangles in Fig. 2). The BG stations are distrib-uted in an area of about 20 × 10 km2, covering the entire

geothermal field. The details of the instruments have alreadybeen discussed in a previous work by Sharma et al. (2013),and for sake of brevity, details are not mentioned here. Weretrieved waveforms for the period 24 July 2007 through 18November 2010 and associated the traces with the eventsfrom the Northern California Earthquake Data Center(NCEDC) catalog. The hypocentral distances range from 0.1up to 73 km, and the magnitude range is 0:7 ≤ Mw ≤ 3:3.The hypocentral parameters (event latitude, longitude, mag-nitude, epicenter distance, and depth) were available from theNCEDC catalog. For the largest portion of earthquakes an-alyzed in this study, the NCEDC catalog provides a durationmagnitude MD as the magnitude measure. However, toobtain results compatible with other studies and suitablefor seismic hazard analysis purposes, we converted MD intomoment magnitude, Mw, using a linear relationship (equa-tion 1) retrieved using theMw data provided by Douglas et al.(2013):

EQ-TARGET;temp:intralink-;df1;313;131Mw � 0:473��0:035� � 0:900��0:017�MD: �1�We selected waveforms with a signal-to-noise ratio of morethan 10 in the whole analyzed frequency range, which is0.5–35 Hz. This selection ensures the analysis of high-

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Figure 2. Distribution of earthquakes and seismic stations used for the analysis done in the present work. Gray circles indicate eventlocation, whereas black triangles are the seismic stations. LBNL, Lawrence Berkeley National Laboratory. (Inset) The location of the Geysersgeothermal area which is approximately 116 km north of San Fransisco, California. The color version of this figure is available only in theelectronic edition.

Update, Comparison, and Interpretation of the GMPE for “The Geysers” Geothermal Area 3647


quality data. We applied an instrument correction to thewaveforms within the same frequency band. The meanand the trend were also removed. Then, a zero-phase shiftand four-pole Butterworth filter in the frequency band be-tween 0.7 and 35 Hz were applied. Further, to measurethe correct values of the selected ground-motion parameters,we cut the waveforms in a specific time window, starting atthe origin time and ending at the time corresponding to 98%of the total energy contained in the waveform only (to restrictcoda waves that are not required for analysis). The signal isfinally tapered with a 0.1% cosine-taper function. Afterprocessing, we obtained 523,422 waveforms (horizontalcomponents only) corresponding to 10,974 earthquakes(light gray dots in Fig. 2) with a focal depth not exceeding5 km. This depth has been selected considering that the earth-quakes occurring at depths less than 5 km are likely inducedearthquakes (e.g., Eberhart-Phillips and Oppenheimer, 1984;Grigoli et al., 2017). Once the time window is selected, PGVis measured as the largest value among the peak values ofamplitude of the two as-recorded orthogonal horizontal com-ponents (Baker and Cornell, 2006) because they are equiv-alent to the actual ground vibration experience at the site.The waveforms are then differentiated and filtered in a fre-quency band ranging between 0.7 and 35 Hz (to avoid thehigh-frequency noise added while differentiating) to measurePGA and the 5% damped spectral ordinates SA�T� atT � 0:05, 0.1, 0.2, 0.5, and 1.0 s (Mendez and Pacor, 1984).

Estimation of New GMPEs

To estimate the GMPE coefficients and uncertainties, weuse the nonlinear mixed-effects regression following themethods of Lindstrom and Bates (1990) and Abrahamsonand Youngs (1992). The mixed-effect technique has the ad-vantage of statistically splitting total uncertainties into bothinterevent and intraevent components, and, furthermore, italso can account for random and fixed-effect dependencieson the data (e.g., Abrahamson and Silva, 1997).

In the present application, we assume that earthquakemagnitude (Mw) and hypocentral distance

(Rhypo ��R2

epi � depth2�q

) represent the predictor varia-

bles that account for source and propagation effects, suchas geometrical and inelastic attenuation, whereas PGV,

PGA, and SA at periods T � 0:05, 0.1, 0.2, 0.5, and1.0 s are considered as response variables. We first definethe reference model and then apply a station and site-effectcorrection. The reference model is formulated as follows:

EQ-TARGET;temp:intralink-;df2;313;540 logYi;j � a� bMi � c log��R2hypoi;j � h2

q� � ηi � ∈i;j;

�2�in which Yi;j is the ground-motion parameter of interest, thatis, PGV (in m=s), PGA (in m=s2), and SA at the selected peri-ods (in m=s2) observed for the ith event at the jth station,M ismoment magnitude (Mw), and the hypocentral distance Rhypo

is measured in km. Though we use hypocentral distance, ourGMPEs predict too-large values at small distances (Joyner andBoore, 1981); thus we include the mathematical parameter hto suppress the unrealistic large value at small distances. It isalso worth noting that the values of the parameter h retrievedduring regression are small because we are dealing with small-magnitude-induced earthquakes. In this respect, Abrahamsonet al. (2014) have shown that the fictitious depth (here, the hparameter) was reduced to 1 km for the earthquakes whilecomputing GMPEs for small-magnitude earthquakes. Hencethis result provides a significant contribution to the discussionabout the magnitude dependence of the h parameter. It is alsonoted that we did not include a square dependence on the mag-nitude in equation (2), because it is effective at large-magnitude values (e.g., Bommer et al., 2007). In addition,other studies, such as that proposed by Baltay and Hanks(2014), quantitatively confirmed that a quadratic term M2

is not required for magnitude Mw < 3:5.The terms ηi and Єij are the interevent and intraevent

uncertainties, respectively. The corresponding standard devia-tions are represented by τ and Φ, respectively. σ representstotal standard deviation, such that σ �

��τ2 � Φ2

p. The regres-

sion coefficients (a, b, c, and h), together with their relativeuncertainties and standard deviations, are reported in Table 1.

Site/Station Correction to Retrieve The Final Model

In the second step, the final model is obtained by analyz-ing the total residuals (logYobs − logYpred) at each station (seeSharma et al., 2013). We mentioned that the correction isintended in a broader sense with respect to the standard site

Table 1Regression Coefficients and Associated Uncertainty for the Reference Model of Equation (2)

Parameter a� σa b� σb c� σc h� σh τ (Interevent) Φ (Intraevent) σ Total R2

PGV (m=s) −4.801 ± 0.015 1.249 ± 0.006 −1.817 ± 0.010 1.658 ± 0.041 0.236 0.350 0.422 0.606PGA (m=s2) −2.806 ± 0.012 1.171 ± 0.005 −2.010 ± 0.009 1.565 ± 0.036 0.174 0.342 0.384 0.664SA at 0.05 s (m=s2) −2.205 ± 0.012 1.095 ± 0.005 −2.160 ± 0.010 1.654 ± 0.034 0.172 0.337 0.378 0.677SA at 0.1 s (m=s2) −2.547 ± 0.015 1.206 ± 0.005 −1.915 ± 0.012 2.000 ± 0.044 0.187 0.3739 0.418 0.606SA at 0.2 s (m=s2) −3.428 ± 0.016 1.341 ± 0.008 −1.563 ± 0.011 1.671 ± 0.051 0.279 0.366 0.460 0.565SA at 0.5 s (m=s2) −4.598 ± 0.015 1.406 ± 0.007 −1.409 ± 0.009 1.471 ± 0.047 0.274 0.314 0.416 0.619SA at 1.0 s (m=s2) −5.002 ± 0.014 1.363 ± 0.007 −1.597 ± 0.008 1.563 ± 0.041 0.265 0.327 0.421 0.615

PGV, peak ground velocity; PGA, peak ground acceleration; SA, spectral acceleration.



effect because it is not based on the VS30 values, which are notavailable for the stations used in the present study. To this end,we analyze the residuals’ distribution at each station obtainedusing the reference model. As explained in the Introduction,we tested the null hypothesis of a Gaussian zero-mean distri-bution at the 95% confidence level by a Z-test. We assume thata deviation from the expected zero-mean value can be reason-ably ascribed to a site/station effect that can be corrected usinga dummy correction factor. Indeed, because of the assumeddefinition of the residual (logYobs − logYpred), a positivedeviation from the zero-mean value indicates the underestima-tion of the model prediction with respect to the observations(on average Yobs > Ypred), whereas a negative deviation indi-cates an overestimation of the model prediction (on averageYobs < Ypred), and a zero deviation indicates equivalence(on average Yobs � Ypred). Thus, using the outcome of theZ-test in terms of both value and sign, at each station we as-signed a dummy variable swith a value of−1, 0, or 1, depend-ing on the mean residual value (negative, zero, or positive) thatallows us to recover the observed residual deviation from theexpected zero-mean value. We did not use the Z-test score as acontinuous variable similar to the VS30 values and did not in-troduce it directly into the model. This is because we believethat, contrary to the well-established effect of the VS30 values,the proposed approach cannot provide the actual amplificationvalue but can only test if there is or is not site effect, that is, abinary variable. The retrieved sj parameter for each station,along with a new coefficient e, is then used to set up the finalmodel, that is, the corrected model, which is expressed asEQ-TARGET;temp:intralink-;df3;55;385

logYi;j � a� bMi � c log��R2hypoi;j � h2

q�

� esj � ηi � ∈i;j: �3�The inferred coefficients and their uncertainties are listed inTable 2. It can be noted that, after considering the site/stationeffect, the total standard deviation is reduced, and the residuals’distribution is improved because they are centered at zero (seeFig. 3a). The station-wise residuals’ distribution before andafter station/site correction is also shown in Figure 3b. For sakeof brevity, we are showing the result for PGA only. It is alsoworth noting that there is a considerable improvement inresidual distribution at each station with their maxima alignednear zero. A clear reduction in the intraevent component of theuncertainty is observed. Because intraevent uncertainty ac-counts for the effect of medium properties, site effects, etc.,on the ground-motion variability, a significant reduction of thiscomponent seems to confirm that our assumption of associat-ing the s parameter with the site/station effect is correct (Atiket al., 2010). The increase in the R2 value again confirms theimprovement of the fit of the corrected (final) model.

Comparison of Final Model with Previous SH13 andOther GMPEs

The fit of the final model and its comparison with ourprevious model (SH13) is shown in Figure 4. It can be noted

that the SH13 model is overestimating the predictions (seeFig. 4) for both PGV and PGA, and the difference increasessignificantly with distance. This difference can be attributedto the fact that the present model has been developed using alarger dataset that is reliable for distances up to 73 km andmagnitudes ranging between 0:7 ≤ Mw ≤ 3:3, whereas theprevious model (SH13) was applicable for distances up to20 km and magnitudes ranging between 1:3 ≤ Mw ≤ 3:3.

The updated model proposed in the present study is alsocompared with models obtained from other studies as well,that is, Atkinson (2015; hereafter, AK15) and Douglas et al.(2013; hereafter, D13). The comparisons of both D13 andAK15 are shown in Figure 4, and for the sake of brevity,we have shown results for PGA and PGVonly. We observedthat the predictions of model D13 are satisfactory, especiallyfor earthquakes with Mw ≤ 2:0. This can be ascribed to thefact that the D13 model has been developed using mixed datafrom six different geothermal areas in Europe and America.On the other hand, the AK15 model has been developedusing small-to-moderate size earthquakes from the NextGeneration Attenuation-West2 (NGA-West2) database andwas tuned for induced seismic scenarios. The model AK15is overestimating the predictions; this might be due to the factthat the GMPEs are developed for other regions and are notsuitable for The Geysers geothermal region. The aforemen-tioned comparison between our model and models developedfor other regions confirms that it is certainly indispensable todevelop the region and tectonic environment-specificGMPEs for the accurate performance of the models and con-sequently seismic hazard maps.

The residuals’ distribution for PGA and PGV is showninⒺ Figure S1 (available in the electronic supplement to thisarticle). The comparisons between the final updated modeland SH13 for other ground-motion periods (SA atT � 0:2, 0.5, and 1.0 s) are also shown in Ⓔ Figure S2.

Residuals and Uncertainties Analysis

To verify the reliability of the final model (i.e., equa-tion 3) to fit the data, the residuals are analyzed as the func-tion of the magnitude and hypocentral distance. The totalresiduals obtained for the final model are shown in Figure 3.The residuals are centered about zero, and no significant cor-relation with distance and magnitude is observed. The binnedaverage value of the residuals (binned at 0.1 km bin width) isalso centered around zero.

According to the study made by Atik et al. (2010), theinterevent residuals account for the influence of source fea-tures (averaged over all azimuths) that are not properly cap-tured by the considered predictor variables (essentially,magnitude and depth in the present study). Though the depthis not an explicit predictor variable, nevertheless, it is usefulfor analyzing the residual distribution to express various fea-tures, for example, the stress drop or the variation of slip inspace and time. It would be thus interesting to analyze thedependency of the interevent residuals as a function of depth



and magnitude. For the earthquakes analyzed in the presentstudy, we found a slight positive correlation with depth forhigh-frequency ground-motion data. This result could indi-cate that there is an increase in stress drop with depth (e.g.,McGarr, 1984; see Fig. 5a) and confirms that correlation be-tween high-frequency ground motion and the stress drop also

exists for small-magnitude-induced earthquakes. On theother hand, interevent residuals as a function of magnitudedo not show any significant correlation (see Fig. 5b).

We also analyzed the total standard deviation and itscomponents (interevent and intraevent) for the final model(see Fig. 6a). The interevent component (accounting for

Figure 3. (a) Distribution of residuals (logYobs − logYpred) obtained from the final model after station/site correction as a function of the(left) hypocentral distance and (right) magnitude of events, respectively. The binned average value of residuals is represented by gray circles.(b) The distribution of residuals at each station (upper) before and (lower) after the site/station correction. It can be clearly observed that, afterthe correction, the maxima of residuals at each station shifted toward zero. (Continued)



source effect) varies significantly with the period of groundmotion, and the overall trend is positive. Conversely, the in-traevent component (accounting for medium and site effects)does not show significant variations with different periods

(Table 2). This observation can be interpreted as the fact that,after site/station correction, the models properly account forthe average propagation medium properties at the consideredperiods and frequencies. This can be due to the fact that con-

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sidering a huge number of events in a relatively small volumecan produce an averaging response of the medium that makesit appear as homogeneous. Thus, this observation suggeststhat, being mostly vapor-dominated and hot, the mediumheterogeneities are obscured, and the region is showing

the same effect as that of a homogeneousmedium in terms of peak-ground-motionattenuation.

We also noticed that the contributionof the interevent uncertainties to the totalstandard error dominates with respect tothe intraevent component. In Figure 6band Table 3, we compare the uncertaintiesof the updated model retrieved in thepresent study with the SH13 model. Wealso observe that the interevent uncertain-ties are large when a large dataset (10,974events) is used, as compared to the inter-event uncertainties of SH13 obtained with212 events. This is because the aleatory(random) component in interevent uncer-tainties depends on the location-basedvariability of the events (see Baltay et al.,2017) and tends to increase with the in-creasing number of events.

Concerning the epistemic (informa-tive) component in intraevent uncertain-ties, it is reduced when a large dataset(10,974 events) is used as compared tothe SH13 model. The site term is repeat-able, and the information-based uncertain-ties depend on the multiple recordings ateach station. Thus, more recordings in-crease information and reduce the episte-mic component of intraevent uncertainties.

Conclusions

In the present work, we used datafrom 10,974 earthquakes to update ourprevious GMPEs at The Geysers geother-mal field (Sharma et al., 2013) and showedthat these new GMPEs are applicable with

a magnitude range from 0:7 ≤ Mw ≤ 3:3 and distance rangebetween 0:1 ≤ Rhypo ≤ 73 km. The purpose of the presentstudy is not only to update and compare our own previousGMPEs (SH13) with an updated model obtained by a largerdataset but also to understand many other aspects of GMPEs,

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Figure 4. Comparison of new ground-motion prediction equations (GMPEs; solidline) with old GMPEs, the Sharma et al. (2013; hereafter, SH13; dashed line), the Doug-las et al. (2013; hereafter, D13), and the Atkinson (2015; hereafter, AK15) models for(a) peak ground velocity (PGV) and (b) peak ground acceleration (PGA). The correctionfactor is assumed as s � 0 (see equation 3). The figure is showing a fitting for magni-tudes of Mw � 3:0, 2.0, and 1.0.

Table 2Regression Coefficients and Associated Uncertainty for the Final Model of Equation (3)

Parameter a� σa b� σb c� σc h� σh e� σe

τ(Interevent)

Φ(Intraevent) σ Total R2

PGV (m=s) −4.976 ± 0.013 1.281 ± 0.006 −1.660 ± 0.008 1.485 ± 0.036 0.161 ± 0.001 0.237 0.283 0.370 0.702PGA (m=s2) −2.954 ± 0.011 1.206 ± 0.005 −1.897 ± 0.007 1.507 ± 0.028 0.227 ± 0.001 0.188 0.254 0.316 0.798

SA at 0.05 s (m=s2) −2.367 ± 0.011 1.139 ± 0.005 −2.066 ± 0.006 1.432 ± 0.024 0.233 ± 0.001 0.194 0.239 0.307 0.832SA at 0.1 s (m=s2) −2.669 ± 0.013 1.237 ± 0.005 −1.775 ± 0.009 2.106 ± 0.036 0.255 ± 0.001 0.195 0.275 0.337 0.755SA at 0.2 s (m=s2) −3.519 ± 0.016 1.350 ± 0.007 −1.418 ± 0.009 1.947 ± 0.047 0.220 ± 0.001 0.278 0.294 0.405 0.658SA at 0.5 s (m=s2) −4.632 ± 0.014 1.420 ± 0.007 −1.431 ± 0.008 1.607 ± 0.040 0.170 ± 0.001 0.268 0.264 0.376 0.681SA at 1.0 s (m=s2) −5.137 ± 0.014 1.379 ± 0.007 −1.466 ± 0.008 1.393 ± 0.041 0.161 ± 0.001 0.262 0.284 0.386 0.669



in terms of residuals with their compo-nents. We followed the two-step method toestimate GMPEs. In the first step, a refer-ence model is considered that does notaccount for station/site effects. Then, inthe second step to obtain the final model,residuals at each station are analyzed and,based on a Z-test on the residuals, adummy parameter is introduced for eachstation that accounts for the station/site ef-fects. This technique is promising for theregions where no site information in formof VS30 is available.

We took advantage of the nonlinearmixed-effect regression technique and splitthe total standard error into its two maincomponents, interevent and intraevent, forboth the reference and the final model.

The main findings can be summarizedas follows:

• the total residuals show no correlationwith hypocentral distances and mag-nitude;

• the interevent residuals do not show anysignificant correlation with magnitudebut show a slight positive correlationwith depth for high-frequency data. Thisresult indicates an increase in the stressdrop with depth and suggests that high-frequency ground motion is directlyproportional to the stress drop for small-magnitude-induced earthquakes;

• the intraevent component does not showsignificant variations with respect todifferent periods of SA (Table 2). Thisobservation can be interpreted as the factthat, after site/station correction, themodels properly account for the averagepropagation medium properties at theconsidered periods/frequencies. It canbe due to the fact that considering a hugenumber of events in a relatively smallvolume produces an averaging responseof the medium that makes it homo-geneous. This suggests that, beingmostly vapor-dominated and hot, the re-gion is showing the same effect as that ofa homogeneous medium by obscuringthe heterogeneities. In contrast, the inter-event deviations vary significantly withthe period of ground motion, and theoverall trend is positive;

• the value of fictitious depth (here, hparameter) retrieved from the regressionis small for small-magnitude earth-

−2−1

012

0 1 2 3 4 5

Depth (km)

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012

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012

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−2−1

012

Inte

reve

ntIn

tere

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reve

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SA(T = 0.5 s) (m/s2)

SA(T = 0.2 s) (m/s2)

SA(T = 0.1 s) (m/s2)

SA(T = 0.05 s) (m/s2)

PGA (m/s2)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Magnitude (Mw)

PGV (m/s)

(a) (b)

Figure 5. Interevent residual (in common log) distribution obtained after using thefinal model (a) as function of depth and (b) as a function of magnitude. The distributionof interevent residuals with respect to depth shows a positive trend, especially for highfrequencies (PGA, spectral acceleration �SA��T � 0:05 s�, SA�T � 0:1 s�), whereas in-terevent residuals as a function of magnitude do not show any significant trend.

0.15

0.20

0.25

0.30

0.35

0.40(a) (b)

Sta

ndar

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ror

PeriodsPGA PGV 0.05 s 0.1 s 0.2 s 0.5 s 1.0 s

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0.35

0.40

PGA PGV 0.2 s 0.5 s 1.0 s

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Intraevent

Interevent

NewOld

Figure 6. (a) Total standard error and its components (interevent and intraevent)obtained after the final model. Overall, the trend of the interevent uncertainties increaseswith the period, and its dominating effect also reflects on the shape and values of thetotal standard error. The intraevent components do not show large variations. (b) Stan-dard errors obtained from new GMPEs are compared with those of the SH13 model. Itcan be observed that the interevent uncertainties increase and the intraevent uncertaintiesdecrease with the addition of new data (solid line) as compared to the uncertainties ob-tained from SH13, that is, a small number of events (dashed lines).



quakes. This result further confirms that the h parameter ismagnitude dependent, as already shown by other studies(e.g., Abrahamson et al., 2014);

• when a large dataset (10,974 events) is used, interevent un-certainties tend to increase as compared to the intereventuncertainties of the SH13 model, whereas the epistemic(informative) component in intraevent uncertainties tendsto decrease. This is because whereas the aleatory (random)component in interevent uncertainty depends on the loca-tion-based variability of the events (see Baltay et al.,2017), that tend to increase with an increase in the numberof events, the information-based uncertainty, that dependson the multiple recordings at each station, decreases. Thus,it means that the number of recordings increase the infor-mation of the propagating medium and the site/station ef-fects and reduce the epistemic component of intraeventuncertainty;

• the contribution of the interevent uncertainties to the totalstandard error dominate with respect to the intraeventcomponent;

• the comparisons with the previous model SH13 and otherGMPEs suggest that region-specific ground-motion mod-els are a must for appropriate seismic hazard analysis;

• in conclusion, we think that the results of the present studyprovide an additional contribution to previous studiesabout ground-motion prediction in The Geysers geother-mal field and in the interpretation of uncertainties obtainedfrom ground-motion regression.

Data and Resources

The data of the Lawrence Berkeley National LaboratoryGeysers/Calpine seismic network have been retrieved fromthe Northern California Earthquake Data Center (NCEDC;network code BG; http://www.ncedc.org, last accessed Janu-ary 2012). Figures have been generated with the GenericMapping Tools (GMT; Wessel and Smith, 1991). The infor-mation about VS30 has been retrieved from https://earthquake.usgs.gov/data/vs30/ (last accessed June 2018).

Acknowledgments

The authors wish to thank all those people who supported this workdirectly or indirectly. The authors are thankful to Editor-in-Chief Thomas

Pratt and Associate Editor John Douglas, Annemarie Baltay, and two anony-mous reviewers for their constructive comments. The work has been sup-ported within the 7th Research Program of the European Union throughthe project GEISER “Geothermal Engineering Integration Mitigation of In-duced Seismicity in Reservoirs” and within the framework of the S4CE (Sci-ence for Clean Energy) project that received funding from the EuropeanUnion’s Horizon 2020 research and innovation action, under Grant Agree-ment Number 764810. N. S. is thankful for receiving research support andthe grant from project CLAIMS (Coupled Lithosphere-Atmosphere-Iono-sphere-Magnetosphere Systems) of the Indian Institute of Geomagnetismfunded by the Department of Science and Technology, India.

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PGV (m=s) 0.164 0.289 0.332 0.237 0.283 0.370PGA (m=s2) 0.151 0.276 0.315 0.188 0.254 0.316SA at 0.2 s (m=s2) 0.169 0.294 0.339 0.278 0.294 0.405SA at 0.5 s (m=s2) 0.175 0.290 0.339 0.268 0.264 0.376SA at 1.0 s (m=s2) 0.168 0.299 0.342 0.262 0.284 0.386



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Shillong Geophysical Research CentreIndian Institute of Geomagnetism3-1/2 Miles, Wilton Hall EstateUpper ShillongShillong 793005, Meghalaya, [email protected]

(N.S.)

Istituto Nazionale di Geofisica e Vulcanologia sezione di NapoliOsservatorio Vesuvianovia Diocleziano 32880124 Naples, Italy

(V.C.)

Manuscript received 23 November 2017;Published Online 9 October 2018



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