Earthquakes and Structures, Vol. 6, No. 2 (2014) 141-161 DOI: http://dx.doi.Org/10.12989/eas.2014.6.2.141 141 Empirical ground motion model for Vrancea intermediate-depth seismic source Radu Vacareanu*\ Sorin Demetriu^, Dan Lungu\ Florin PaveP, Cristian Arion\ Mihail lancovici^, Alexandru Aldea^ and Cristian Neagu^ ^Department of Reinforced Concrete Structures, Technical University of Civil Engineering Bucharest, Bd. Lacul Teino. 122-124, Sector 2, 020396, Bucharest, Romania ^Department of Structural Mechanics, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei no. 122-124, Sector 2, 020396, Bucharest, Romania (ReceivedAugust 1, 2013, Revised October 12, 2013, Accepted October 22, 2013) Abstract. This article presents a new generation of empirical ground motion models for the prediction of response spectral accelerations in soil conditions, specifically developed for the Vrancea intermediate-depth seismic source. The strong ground motion database from which the ground motion prediction model is derived consists of over 800 horizontal components of acceleration recorded from nine Vrancea intermediate-depth seismic events as well as from other seventeen intermediate-depth earthquakes produced in other seismically active regions in the world. Among the main features of the new ground motion model are the prediction of spectral ordinates values (besides the prediction of the peak ground acceleration), the extension of the magnitudes range applicability, the use of consistent metiics (epicentral distance) for this type of seismic source, the extension of the distance range applicabihty to 300 km, the partition of total standard deviation in infra- and inter-event standard deviations and the use of a national strong ground motion database more than two times larger than in the previous studies. The results suggest that this model is an improvement of the previous generation of ground motion prediction models and can be properly employed in the analysis ofthe seismic hazard of Romania. Keywords: ground motion prediction equation; sfrong ground motion database; seismic hazard; acceleration response specfra; peak ground acceleration 1. Introduction A comprehensive description regarding the characteristics (focal depth range, area of seismic source, magnitude range, etc.) ofthe Vrancea subcrustal seismic source can be found in the papers of (Lungu et al. 2000), (Mamiureanu et al. 2010) and (Ismail-Zadeh et al. 2012). A more complex shape of this seismic source was defined by the National Institute for Earth Physics for the SHARE project (Vacareanu et al. 2013a). On average, this seismic source produeed 3 to 5 earthquakes oí Mw> 6.5 each century (Ismail-Zadeh et al. 2012). In the 20* century earthquakes with magnitudes Mw > 6.7, occurred in October 1908 {Mffr= 7.1, h = 125 km), November 1940 {Mw=l.l, h = 150 km), March 1977 {Mw= 7.4, h = 94 km), August 1986 (Miv= 7.1, h=Ul km) 'Corresponding author, Professor, E-mail: radu.vacareanu@utcb.ro Copyright © 2014 Techno-Press, Ltd. http://www.teclino-press.org/?journal=eas&subpage=7 ISSN: 2092-7614 (Print), 2092-7622 (Online) Radu Vacareanu et al. 142 and May 1990 {Mw= 6.9, h = 91 km), respectively. Several possible geodynamic models for the Vrancea subcmstal seismic source are presented in Radulian et al. (2000), Spemer et al. (2001), Milsom (2005), Mocanu (2010), Müller et al. (2010) or Ismail-Zadeh et al. (2012). The first studies regarding ground motion models for the prediction of the peak ground acceleration of intermediate-depth Vrancea subcmstal seismic events were performed by Lungu et al. (1994) and Radu et al. (1994). The functional form of the azimuth-dependent attenuation model is the following: \nPGA = (1) where: PGA is peak ground acceleration at the site, M- magnitude (surface- wave magnitude or moment magnitude), R - hypocentral distance to the site, h - focal depth, co, Cj, C2, C3, C4 - data dependent regression coefficients and s - random variable with zero mean and standard deviation o'e = CinPGA- The Same ñinctional form was also used by Lungu et al. (2000) for the development of a ground motion prediction equation that is not azimuth-dependent (using all available recorded data, regardless of their geographic location). Some additional (azimuth-dependent) ground motion prediction equations for the Vrancea subcmstal seismic source and for PGA were also developed in the papers of Stamatovska and Petrovski (1996) and Musson (1999). In the work of Sokolov et al (2008) a set of azimuth-dependent ground motion prediction equations specifically derived for the Vrancea subcmstal seismic for peak ground acceleration {PGA), peak ground velocity {PGV), pseudo-spectral acceleration (PSA) and MSK scale seismic intensity is given. Considering the fact that the parameters of this ground motion prediction model (Sokolov et al. 2008) are not readily available, this GMPE is not considered in the analysis. The characteristics of the four above-mentioned GMPEs developed for the Vrancea subcmstal seismic source are given in Table 1 using also data from the work of Douglas (2012). Table 1 Characteristics of the datasets for the considered ground motion prediction models GMPE Database No. of horizontal components No. of earthquakes Magnitude range Source-tosite distance range Focal depth range No. of soil classes Lungu et al. (1994) Stamatovska and Petrovski (1996) Musson (1999) Sokolov et al. (2008) Vrancea 160 3 6.9-7.4 10-310 91-131 1 Vrancea 190 4 6.4-7.4 10-310 87-131 1 3 6.9-7.4 10-310 91-131 1 4 6.4-7.4 10-310 87-131 1 Vrancea Vrancea 178 The main focus of this article is the development of a new ground motion prediction equation GMPE for Vrancea subcmstal seismic source. The perfomiance of this new model, which is based on an increased strong ground motion database is evaluated using several goodness-of-fit measures presented in the work of Scherbaum et al. (2004, 2009) and Delavaud et al. (2012). The analysis of the inter-event and intra-event residuals (Stafford et al. 2008, Scassera et al. 2009, Shoja-Taheri et al. 2010) is also perfonned for the available dataset of strong ground motions. Other GMPEs are 143 Empirical ground motion model for Vrancea intermediate-depth seismic source recommended for the Vrancea intermediate-depth seismic source in the paper of Delavaud et al (2012) which deals with attenuation models for the probabilistic seismic hazard assessment in Europe. The four recommended ground motion prediction equations for Vrancea are: Youngs et al. (1997), Zhao et al. (2006), Atkinson and Boore (2003) and Lin and Lee (2008). An evaluation of some of these models is shown in the papers of Vacareanu et al. (2013b, 2013c). In the final part of this paper the impact of the use of the new proposed GMPE on the seismic hazard levels for several cities in Romania is also assessed. 2. Strong ground motion database for regression anaiysis The proposed ground motion model for the prediction of spectral accelerations is derived from a national database (strong ground motion records from Vrancea subcrustal earthquakes) and an international database consisting altogether of 431 strong ground motions (861 horizontal components) recorded from 26 intermediate-depth seismic events with moment magnitudes in the range 5.2 < Mw < 7.8. The strong ground motions from Vrancea earthquakes were recorded in Romania, Republic of Moldova, Bulgaria and Serbia. The international strong ground motions were recorded in intermediate-depth earthquakes in Japan (K-net and Kik-net data). New Zealand, Mexico, Chile and India. The range of the focal depth of all earthquakes is in between 69 km to 173 km. This depth range is typical for seismic events produced in the Vrancea region, which are the main focus of this attenuation model. The main characteristics ofthe database used for the derivation ofthe ground motion prediction model are given in Table 2. All the analyzed strong ground motions were collected for the BIGSEES national research project from the seismic networks of INFP (National Institute for Earth Physics), INCERC (Building Research Institute), GEOTEC (Institute for Geotechnical and Geophysical Studies) and NCSRR (National Centre for Seismic Risk Reduction). For each seismic event, the date of occurrence, the magnitude, the position ofthe epicentre, the focal depth and the number of strong ground motions are presented in Table 3. Table 2 Characteristics ofthe database of strong ground motions ^,„„ GMPE T>. ^ u Database Proposed model y'a"C'ja+ International No. of u • ^1 horizontal components ,, No. of , , earthquakes ,. .^ , Magnitude ,r range, Mw Epicentral j.^ distance , range, km „ , , ,, Focal depth , ranee, km ° 465+395 9+17 5.2-7.8 2-647 69-173 The distribution of the soil conditions for the seismic stations which have recorded the strong ground motions in the database with respect to the earthquake magnitude is shown in Fig. 1. The soil conditions are defined according to Eurocode 8 (EN 1998-1) and are assigned according to Trendafilovski et al. (2009). The vast majority ofthe strong ground motions were recorded in soil conditions (classes B, C or D), the exception being some strong ground motions from Vrancea earthquakes recorded in the epicentral region in soil class A. These strong ground motions were also kept in the database due to the lack of strong ground motions recorded in soil conditions from the epicentral region of Vrancea intermediate-depth earthquakes. Although the proposed ground 144 Radu Vacareanu et al. motion prediction model is derived only for soil conditions, it is the authors' opinion that the use of the strong ground motions recorded on harder soil conditions (only in the epicentral region) does not affect the results for larger epicentral distances. In the case of some seismic station the exact soil classification could not be retrieved from the existing database. Nevertheless, the conditions for these stations were assigned as soil, so these data were also used in the regressions (these stations are deñned as not classified hereinafter). Table 3 Characteristics of the considered seismic events Event no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Country Romania Japan Mexico New IndiaMyanmar Chile Date Lat. Long. 04.03.1977 30.08.1986 30.05.1990 31.05.1990 28.04.1999 27.10.2004 14.05.2005 18.06.2005 25.04.2009 2.12.2001 26.05.2003 21.09.2005 12.06.2006 24.07.2008 2.02.2013 28.08.1973 24.10.1980 21.10.1995 15.06.1999 5.01.1973 8.09.1991 22.03.1995 6.08.1988 9.01.1990 45.34 45.52 45.83 45.85 45.49 45.84 45.64 45.72 45.68 39.40 38.81 43.71 33.13 39.73 42.70 18.29 18.03 16.92 18.18 -39.04 -40.24 -41.05 25.15 24.75 26.30 26.49 26.89 26.91 26.27 26.63 26.53 26.66 26.62 141.26 141.68 146.40 131.41 141.63 143.30 -96.45 -98.29 -93.62 -00.51 175.26 157.17 174.18 95.13 95.24 7.4 7.1 6.9 6.4 5.3 6.0 5.5 5.2 5.4 6.4 7.0 6.0 6.2 6.8 6.4 7.0 7.0 7.2 7.0 6.6 5.6 5.8 6.8 6.1 94 131 91 87 151 105 149 154 110 122 71 103 146 108 120 84 70 98 69 173 94 90 90 119 6.05.1995 13.06.2005 24.99 -20.01 95.29 -69.24 6.4 7.8 117 108 /z(km) No. of strong ground motions 3 38 46 25 11 50 15 18 27 6 26 8 7 21 20 4 8 5 15 7 8 12 17 10 5 19 The histograms in Fig. 1 and Fig. 2 reveal a concentration of the strong ground motions recorded at epicentral distances in the range 100 - 200 km. The distribution of the earthquake magnitude versus the focal depth for the 26 analyzed seismic Empirical ground motion model for Vrancea intermediate-depth seismic source 145 events is shown in Fig. 3. In Fig. 4 and Fig. 5 the distributions of the peak ground acceleration (defined as the geometric mean of the two horizontal components) with respect to the earthquake moment magnitude and epicentral distance of the recording seismic station are given. 160 -, 100 -1 Soil class A Soil class B Soil class C 80 - 120 - Soil class B Soil class C 1 Soil class D I Not classified [ ' I 60 ~ 40 40 20 - •T-'T^T"! If > ! 10 100 Epicentral distance, km 1 10 (a) (a) ,.J Romania Soil dass Eurocode 8 (2004) G A .A B 0 c ; i f M,l, ,, ...I... i lJ..J..f i,„,t„„l,„l„i„ international A-4A c O A© 7 - O ..Q: O <3mcm c i, Soil class Eurocode 8 (2004) O C!«i:GO 7 - 1000 100 Epicentral distance, km o o # o OOOSHBEffi) -*CO CD 6 - D O O ex» 6€3C o O CD o Go DD ...M. îMSSaE M CDßBQ m m o€SM 10 100 Epicentral distance, km 1000 (b) Fig. 1 Distribution of the earthquake magnitude Mw with the epieentral distance for Vrancea, Romanian strong ground motions 10 100 Epicentral distance, km 1000 (b) Fig. 2 Distribution of the earthquake magnitude Mw with the epicentral distance for international strong ground motions Radu Vacareanu et al. 146 D O Romania International D 7 - O g 6 - D -T 40 r 80 D D 120 Focal depth, km 160 200 Fig. 3 Distribution ofthe earthquake magnitude Afjf^with the event focal depth h 1000 1000 - o o [ Romania O 100 - 100 - i a. 10 - 5 6 ' B 1 10 100 Epicentrai distance ^w ,-,..„...,,. f.., , , . • rig. 4 Distribution oi the peak ground acceleration .., ., .f , -^ Ji li I with the earthquake magnitude Mw 1000 Fig. 5 Distribution of the peak ground acceleration ° ,T^^ .^ • , , . ... ^ , (P'^A) with the epicentral distance oí the ,. . . ^ . recording seismic station 3. Functional form and regression model In the present study the following functional form ofthe GMPE is selected: ^,¿ - 6) f (2) where / is the earthquake index,/ is the recording station's index, jy is the geometrical mean ofthe Empirical ground motion model for Vrancea intermediate-depth seismic source 147 two horizontal components of either PGA (in cm/s^) or 5% damped response spectral acceleration (in cm/s^) for a spectral period T, M^ is the moment magnitude (use M^ = 7.6 for events of M« > 7.6 for spectral periods up to 1.0 s and use M« = 8.0 for events of Mv > 8.0 for spectral periods in excess of 1.0 s), R is the source to site (hypocentral) distance in kilometers, h is the focal depth in kilometers and Q (A: = 1 to 6) are coefficients determined from the data set by regression analysis at each spectral period. The independent normally distributed variâtes ij^ and s\¡ are the inter-event residuals (error that represents earthquake to earthquake variability of ground motions) with zero mean and a standard deviation of T and respectively, the intra-event residuals (error that represents within earthquake variability of ground motions) with zero mean and a standard deviation of a. Both intra- and inter-event standard deviations a and r are period dependent, but are assumed independent of magnitude. The total standard deviation of the model's prediction is defined by: a^ = (3) V(T2 4 - T 2 The regression coefficients and the residual terms are obtained with the maximum likelihood method (Joyner and Boore 1993, 1994). The magnitude effect on the predicted values of ground motion parameters is considered through Ci to c^ coefficients. The influences of the geometrical spreading and of the anelastic attenuation are accounted for in relation (2) through C4 and C5 coefficients. The depth effect is given by the coefficient C(,. The coefficients ci to c^ as well as the standard deviations are shown in Tahle 4. One can notice from Table 4 the range of the total standard deviation from 0.71 to 0.92 and the rather balanced contribution of intra- and inter-event standard deviations to the total variability of the model. Table 4 Regression coefficients and standard deviations of the proposed GMPE T,s 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 8.5851 9.1790 9.5719 9.4383 9.2379 9.0571 8.9340 8.7733 8.6120 8.4383 8.3839 8.1855 7.8850 7.7061 7.5257 7.4295 7.0493 6.6822 6.4087 6.1352 c? C3 C4 1.4863 1.2914 1.5016 1.7468 1.9355 2.0346 2.0695 2.1370 2.1907 2.2422 2.2537 2.3182 2.3958 2.4470 2.4958 2.5124 2.6036 2.6306 2.6152 2.6116 -0.4758 -0.3798 -0.5250 -0.6167 -0.6987 -0.7008 -0.6845 -0.7029 -0.6726 -0.6653 -0.6684 -0.6193 -0.5977 -0.5812 -0.5865 -0.5638 -0.5870 -0.6053 -0.6290 -0.6607 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 c« -0.00138 -0.00095 -0.00193 -0.00267 -0.00269 -0.00289 -0.00276 -0.00271 -0.00275 -0.00271 -0.00247 -0.00287 -0.00312 -0.00329 -0.00329 -0.00324 -0.00312 -0.00275 -0.00236 -0.00198 0.00484 0.00447 0.00474 0.00571 0.00561 0.00518 0.00381 0.00308 0.00273 0.00242 0.00097 0.00036 0.00073 0.00039 -0.00002 -0.00115 -0.00175 -0.00218 -0.00290 -0.00313 0.738 0.923 0.874 0.818 0.823 0.790 0.793 0.773 0.755 0.729 0.729 0.719 0.711 0.728 0.732 0.730 0.735 0.750 0.751 0.752 T a 0.550 0.692 0.658 0.617 0.592 0.513 0.502 0.488 0.461 0.414 0.414 0.377 0.366 0.401 0.410 0.410 0.402 0.433 0.436 0.463 0.491 0.611 0.575 0.536 0.572 0.601 0.614 0.599 0.597 0.600 0.600 0.612 0.610 0.608 0.607 0.605 0.615 0.613 0.612 0.593 Radu Vacareanu et al 148 4. Evaluation of proposed GMPE The evaluation and validation of the proposed GMPE is performed in several steps. The first step consists of several comparisons of the proposed ground motion model with the observed data from the most instrumented seismic events produced by the Vrancea subcrustal seismic source. In Figure 6 the proposed model is compared with the spectral accelerations at 7 = 0.0 s, 0.3 s and 1.0 s obtained from the data recorded during the Vrancea earthquakes of August 1986 (Mfv = 7.1), May 1990 (M^= 6.9) and October 2004 (M^^= 6.0). 1000 -J~ Í '• I Vrancea 1986 earthquake I Vrancea 1986 10 iM'^'^.yi-.I 100 Epicentral distance, km Epicenifal distance, km EptcentraS distance, km Vrancea 1 9 ^ earthquake M^. = 6.9,ft= 91 km I Vrancea 1990 earthquake i Vrancea 1990 eartftquaî<e Mtt-=6.9.ft= 91 km T i 1 — I — 1 ^ 1 ^ ÎÛÛ Epicenlrai distance, km Epicentraî distance, km Epicentrai distance, km 7 = 0.3 s 1O00 -i a 100 5 I J Vrancea 2ûùA earthquake M^= 6,Q, h~ 1Û5 km 1 10 Epicentra! distance, km I Vrancsa 2004 earthquake . ^ w - 6 - 0 . ^ ^ 105 km Epicentraî distance, km Vrancea 2004 earîiiquake Epicentral distance, km Fig. 6 Comparison of observed and predicted spectral accelerations using the proposed GMPE for three spectral periods {T= 0.0 s, T= 0.3 s and T= 1.0 s) and for three suberustal Vrancea seismic events. Red circles correspond to observed values, solid lines correspond to predicted median values and shaded areas correspond to the region between the 16* and 84* percentile predicted values Empirical ground motion model for Vrancea intermediate-depth seismic source 149 It is noticeable from Fig. 6 that most of the observed data for all three periods are distributed between the median plus/minus one standard deviation. Fig. 7 shows the distribution of the normalized residuals NRES (Scherbaum et al. 2004) versus earthquake magnitude, focal depth and epicentral distance. In the second and third rows of plots the earthquakes are separated into three bins according to their magnitude: events with 5.2 < Mw< 6.0; events with 6.0 < Mw< 7.0 and events with 7.0 < Mw< 7.8. .25 0 tSO 600 300 s, km ?äO J-. ISO r 300 450 600 Epicentral dlstanc», km 2.5 750 150 300 K& 600 Epicenlra! distance, km 750 Fig. 7 Distribution of normalized residuals NRES with the magnitude of the seismic event, focal depth and epicentral distance of the recording station for three spectral periods (7= 0.0s, T= 0.3s and T= 1.0s) Radu Vaeareanu et al. 150 No significant bias in the distribution of the residuals can be observed from Fig. 7. However, the plots reveal a large amount of variability in the dataset. The histogram of normalized residuals NRES and of the likelihoods L/i (Scherbaum et al. 2004) for all the spectral periods is given in Fig. 8. It is visible that the distribution of the normalized residuals fits closely the standard normal probability distribution, while the LH distribution closely matches the uniform probability distribution. Fig. 9 displays the histograms of inter-event and intra-event normalised residuals (Stafford et al 2008), (Scassera et al. 2009), (Shoja-Taheri et al. 2010) computed for all the spectral periods. One can easily notice that the distribution of the normalised residuals follows the standard normal distribution. 0.12 n 0.4 NRES 0.6 0.8 LH Fig. 8 Histograms of normalized residuals NRES {left) and likelihoods LH {right) for all the spectral periods. The standard normal probability distribution is superimposed on the histogram of normalized residuals on the left 0.6 -i 0.5 - rO.4 - !0.3- ! 0.2 - 0.1 - - 2 - 1 0 1 2 Normalized inter-event residuals - 2 - 1 0 1 2 Normalized intra-event residuals Fig. 9 Histograms of normalized inter-event residuals {left) and normalized intra-event residuals {right). The standard normal probability distribution is superimposed on the histograms of normalized residuals Empirical ground motion model for Vrancea intermediate-depth seismic source 151 The use of magnitude independent standard deviations is confirmed in Fig. 10 in which the distribution of the inter-event residuals for four spectral periods is displayed. One can notice from Fig. 10 that the distribution of the residuals has no trend nor bias, being thus magnitude independent. D m n o ;.> Q « o c O -- D Fig. 10 Distribution ofthe inter-event residuals with the earthquake magnitude for four selected spectral periods (r= 0.0 s, 7=0.3 s, 7= 1.0 s and 7=2.0 s) The mean, median and standard deviation of the normalised residuals calculated for the subset of Vrancea sfrong ground motions are, respectively MEANNRES = -0.06, MEDNRES = -0.03 and STDNRES = 0.82. The sampling errors (Wu 1986) ofthe previously mentioned indicators are less than 1%. If one considers only the ground motions recorded in Vrancea intermediate depth earthquakes, the total standard deviation ofthe model's prediction decreases overall with 18%. Moreover, the bias introduced by the reduced sampling is very low, thus providing a high degree of confidence in using the proposed GMPE for Vrancea intermediate depth seismic events. 5. Comparison with other GMPEs The proposed ground motion prediction model is compared for three reference earthquakes with other GMPEs from literature in Fig. 11. The reference earthquakes used for comparison have magnitudes Mw = 6.5, Mw = 7.0 and Mw = 7.5 and are produced at a depth of 100 km. The comparisons are performed for three spectral periods T = 0.0 s, 0.2 s and 1.0 s. Our model is assessed against the Lungu et al. (2000) model (LEAOO) and the four GMPEs proposed within the SHARE project (Delavaud et al. 2012): Youngs et al. (1997) for soil conditions - YEA97, Atkinson and Boore (2003) for soil class D - AB03, Zhao et al. (2006) for soil class III - ZEA06 and Lin and Lee for soil conditions (2008) - LL08. The comparisons with the LEAOO model are perfonned only for T = 0.0 s. The first obvious conclusion which can be drawn from Fig. 11 is the relatively large scatter in Radu Vacareanu et al. 152 the median predictions. Moreover, one can notice the low attenuation with the epicentral distance of the LEAOO GMPE. The proposed model gives higher ground motion amplitudes for T = 0.2 s and r = 1.0 s for earthquakes with Mw<7.0. It is also worth mentioning the fact that in most of the analyzed cases, the proposed GMPE has similar median predictions as the Youngs et al (1997) model denoted as YEA97. One can notice from Fig. 11 the very similar predictions of the median amplitudes of spectral acceleration at the natural period 7 = 1.0 s given by both the YEA97 and proposed GMPEs. The previous remark shows that the spectral response is less sensitive to local conditions and, consequently better 1000 - 100 Epicentrat distance, km = 7.5.ft= 100 km soo Ep!cen!/aí öislajice, km îOO Epiœnfraî distance, i(fn 1O0 Epicentral distance, km Fig. U Median amplitudes for three spectral periods {T = 0.0 s,T= 0.2 s and T = 1.0 s) and for seismic events characterized by three magnitudes {Mw = 6.5, Mw = 7.0 and Mw = 7.5) with a focal depth of 100 km. The curves correspond to the proposed model and to 5 additional models: LEAOO, YEA97, AB03, ZEA06 and LL08 Empirical ground motion model for Vrancea intermediate-depth seismic source 153 constrained at higher natural periods. The attenuation rate with the epicentral distance of the proposed GMPE is smaller than that ofthe models developed for subduction earthquakes (YEA97, AB03, ZEA06, LL08) and larger than that of the model developed using only strong ground motions from Vrancea intermediate-depth earthquakes (LEAOO). In Fig. 12 the total standard deviation ofthe proposed GMPE is compared with the standard deviations of four other GMPEs: Youngs et al. (1997) - YEA97, Atkinson and Boore (2003) AB03, Zhao et al. (2006) ZEA06 and Lin and Lee (2008) - LL08. The standard deviation in the case ofthe YEA97 model is computed for a MpK= 7.0 earthquake. One can notice from Fig. 12 that the total standard deviation ofthe proposed model is the largest in the period range up to 7 = 0.7 s. However, for spectral periods in excess of 0.7 s the total standard deviation of the proposed model is smaller than that of the other considered ground motion prediction models, except the AB03 model. Proposed relation LL08 soil AB03 class D YEA97 soil M, - 7,0 ZEA06 class 111 0,5 Fig. 12 Comparison of total standard deviation for the analyzed GMPEs 6. Discussion Previous GMPEs developed for Vrancea subcrustal source by Lungu et al. (1994), Radu et al. (1994), Stamatovska and Petrovski (1996) or Musson (1999) are azimuth-dependent. Since the new GMPE proposed in this paper is based on a much larger database with both domestic and international earthquakes, the further need for azimuth dependency is investigated. In this respect, the normalised residuals between the observed and the predicted ground motion parameters is obtained for each of the 233 values in the subset of the seismic records generated by Vrancea intermediate-depth source and the pattern distribution of the residuals is investigated. The normalized residuals in each seismic station and for all Vrancea earthquake are represented on the map and the spatial distribution of the residuals is investigated. After careful investigation of the maps one can conclude that there is no need for further modification of GMPE in order to make it azimuth-dependent. In Fig. 13 the absolute values of maximum normalised residuals at spectral periods T = 0 s, T = 0.3 s and T = 1.0 s for the proposed GMPE are represented and one Radu Vacareanu et al. 154 Slauor> Soil Ciass A • c % Norms^ized Residuals 3--i . :„ - - C , , ^ - ^ ir M. 7 1 -BC • Wr S1 - 6 0 61-70 ' • • * 4k • • • \ ÄbsöiütB mBKiftiijm of notti'istiSQd tcsiduals at T - 0 s for proposea GMPB Station Soil Class Normalized Residuals -2--1 -t - 0 0-1 • m • 51-80 6 1*70 71-80 SSSES is- lesidimls af 7 = 03 s for proposed GMP£\ c,,»,»«, Continued Empirical ground motion model for Vrancea intermediate-depth seismic source 155 station Soil Class • c Normalized Residuals -1 »0 0*1 • • I*. 51 - 5 0 6.1-70 7.1 »BO Absolute W3í<ímum of normalised residuals at T - 1 s for proposed GMPE Fig. 13 Distribution of absolute values of maximum normalised residuals at 7= 0 s (top), r = 0.3 s (middle) and r = 1.0 s (bottom) for the proposed GMPE can notice that there is no significant azimuth dependency of the residuals. Nevertheless, there is a pattern of the spatial distribution of the values of the nonnalized residuals: there is a slight underestimation of the observed values in the regions in the front of the Carpathians Mountains (fore-arc region), an overestimation of the observed values in the regions in the back of the Caipathians Mountains (back-arc region) and a transition region in between fore-arc and back-arc. We are currently investigating this pattern in an ongoing research project and a GMPE valid for both fore-arc and back-arc regions is under development. Also, in Fig. 13 the soil conditions at the seismic stations are represented as soil classes defined in EN 1998-1 (2004). Fig. 13 reveals the rather uniform spatial distribution of the residuals and the apparent lack of correlation between the soil conditions and the residuals' values. Another issue to be discussed is the behaviour of the proposed GMPE for values of moment magnitude Mfi^ at the higher end of the scale. For example, in Fig. 14 the observed values of PGA in a distance range of 85 km to 115 km along with the predicted median values for an earthquake with a focal depth of 100 km and an epicentral distance of 100 km are represented. One can notice a saturation of the values of PGA along with a trend of predicted values to slightly decrease for M^ > 7.6. The decrease of the predicted values occurs irrespective of the epicentral distance and is produced by the quadratic term in magnitude; the same decrease is reported in the paper of Atkinson and Boore (2003). From Fig. 14, one can notice that the GMPE requires the capping of the maximum magnitude at Mw^cap - 7.6 for prediction of PGA values. Thus estimates of PGA values for seismic events of Mw > 7.6 should be made using My^^cap = 7.6. This saturation effect Radu Vacareanu et al. 156 does not imply that a maximum moment magnitude of 7.6 should be assigned in the probabilistic seismic hazard analysis. Rather, the PGA values for seismic events of Mw > 7.6 should be calculated using the value of Mwcap = 7.6 in the GMPE. More generally, a capping magnitude can be derived for any spectral period by differentiating relation (2) with respect to Mw and equating the result with zero. The analysis reveals that the capping magnitude is Mw.cap = 7.6 for spectral periods up to 1.0 s and Mw,cap = 8.0 for spectral periods in excess of 1.0 s. Nevertheless, from our analyses, the differences that arise in a probabilistic seismic hazard analysis performed with and without magnitude capping amounts 2% at the most for ground motion amplitudes with mean return periods larger than 1000 years in the case of Mw,cap = 7.6 and vanish for Mw,cap = 8.0. Actually, the capping moment magnitude Mw.cap = 8-0 corresponds to the higher end ofthe scale considered to provide reliable results in using the proposed GMPE. The decrease ofthe predicted values can be avoided if the quadratic source terms in the GMPE are refit to a linear form, i.e. Ci'+C2'(M«^6). For example, at 7 = 0 s, Ci'=8.2996, C2'=1.0105 and the predicted median values are presented in Fig. 14. Nevertheless, the need for such a recalibration is not necessary since the quadratic source terms provide a better fit than the linear magnitude scaling, especially at short epicentral distances, and the maximum value of moment magnitude Mw, cap is imposed. 1000 - 100 - o 10 - Fig. 14 Scaling oí PGA with moment magnitude in the distance range from 85 to 115 km; assumed event depth is 100 km The last issue to be discussed is the impact of the proposed GMPE on the results of probabilistic seismic hazard analysis, PSHA and the comparison of the PSHA results obtained using other GMPEs as well. In this section, the proposed GMPE, applicable to intermediate depth Vrancea earthquakes, is used to perform probabilistic seismic hazard analyses for some Romanian cities. The analyses are perfonned using the proposed GMPE and two other GMPEs applicable for Vrancea intermediate-depth earthquakes, namely (i) LEAOO (Lungu et al. 2000) - used for the peak ground acceleration and (ii) YEA97 (Youngs et al. 1997) for soil conditions - used for the peak ground acceleration and response spectral acceleration values as well. Empirical ground motion model for Vrancea intermediate-depth seismic source 157 The input data on seismicity of Vrancea intermediate-depth source are given in (Vacareanu et al. 2013a). Considering the seismic events of the 20* century with the lower-bound magnitude Mw.mm'^ 5.0 and the upper bound magnitude Mw,max= 8.1, the seismicity parameters are a = 10.3164 and ß = 1.9589. The Vrancea intermediate-depth seismic source is covered with a grid of uniformly distributed points at 0.1 degrees of latitude and longitude, respectively. The computations are perfomied based on the PSHA methodology given in (Kramer 1996) and (McGuire 1999, 2004) using developed MATLAB-based routines. The computations are performed using -3 < e < 3, where s is the number of logarithmic standard deviations by which the logarithm of the ground motion amplitude deviates from the mean value of the logarithm of the ground motion amplitude (McGuire 1999). 10" - Jj=0.3s — : 10' -; : 200 300 SA. cm.'s2 400 500 600 200 300 SA, cm/s2 400 500 600 j Craiova r : r — 1 i • [ : -* : — 1 10' -; 10' - - — yEA97 sod 10200 300 PGA. cmls^ 400 500 ßOO 100 200 :iOO SA, cm/s2 400 5Ö0 Ö00 Fig. 15 Hazard curves obtained with the proposed GMPE and LEAOO & YEA97 GMPEs for Focsani (top), Bucharest (middle) and Craiova (bottom) 15 8 Radu Vacareanu et al. The results of the PSHA, given in terms of hazard curves for peak ground accelerations and pseudo-spectral accelerations at spectral periods of r = 0.3 s and T= 1.0 s are presented in Figure 15 for 3 selected cities in Romania, namely Bucharest, Focsani, and Craiova. The shortest mean epicentral distance is for Focsani (60 km) and the longest one is for Craiova (260 km). For Bucharest the mean epicentral distance is 160 km. One can notice from Figure 15 that at short (in Focsani) and medium (in Bucharest) epicentral distances LEAOO provides the lowest hazard values for PGA, while YEA97 for soil conditions provides the highest values, the proposed GMPE lying in between. At long epicentral distances the three GMPEs provides very close results, the proposed relation pointing to lower hazard values at very large mean return periods (> 10000 years). For mean return periods of 500 to 1000 years and at large epicentral distances the PGA values obtained with all three GMPEs are almost the same. Regarding the values of the response spectral accelerations at periods of T = 0.3 s and T = 1.0 s, one can notice from Fig. 15 that YEA97 provides lower hazard values at r = 0.3 s and higher hazard values at 7 = 1.0 s. This trend is not noticed for short epicentral distances at r = 0.3 s (where the two GMPEs produce almost the same hazard values) and is very intense for large epicentral distances at T = 1.0 s where YEA97 provides hazard values much larger than the proposed GMPE for mean return periods in excess of 100 years. 7. Conclusions A new ground motion prediction model for Vrancea intermediate-depth seismic source is developed in this study. The database used in the regression analysis is by far the largest used for Vrancea. The extension of the database consists in including all the instrumented Vrancea earthquakes with moment magnitudes larger than 5.0 and an additional seventeen foreign intermediate-depth earthquakes. The use of international earthquake data is a temporary solution for filling the gaps in the national database. Nevertheless, as more strong ground motions recorded in Vrancea intermediate-depth earthquakes become available, we will revisit this analysis. The current extension ofthe database increased both the ranges of magnitudes and ofthe source-to-site distances. We consider that the proposed ground motion prediction model provides reliable results for a magnitude range Mw = 5.0 ^ 8.0, an epicentral distance range from 10 km to 300 km and a focal depth range from 60 km to 200 km. We acknowledge that there is some uncertainty related to the upper bound of the moment magnitude scale, which is poorly constrained by the data (extending to M^ = 7.8). The epicentral distance and the focal depth ranges may be extrapolated beyond the previously mentioned limits with some caution. We believe that this new GMPE might supersede the previous GMPEs derived for Vrancea intermediate-depth seismic source and address the limits identified in those models. In addition, the proposed GMPE covers peak ground accelerations and response spectral accelerations and a much broader range of earthquake magnitudes and source-to-site distances. The regression coefficients ofthe GMPE and the residual terms are obtained with the maximum likelihood method (Joyner and Boore, 1993, 1994). Both intra- and inter-event standard deviations a and r are period dependent but are independent of magnitude. The total, inter- and intra-event normalized residuals closely fit a standard normal distribution of probability. After carefril investigation of the residuals one can conclude that there is no need for frirther modification of GMPE in order to make it azimuth-dependent. The spatial distribution of the normalized residuals reveals that there is a slight underestimation of the observed values in the Empirical ground motion model for Vrancea intermediate-depth seismic source regions in the front of the Carpathians Mountains (fore-arc region), an overestimation of the observed values in the regions in the back of the Carpathians Mountains (back-arc region) and a transition region in between. A GMPE valid for both fore-arc and back-arc regions is under development in an ongoing research project. Also, the spatial distribution of the normalized residuals shows an apparent lack of correlation between the soil conditions and the residuals' values. The predicted values of ground motion parameters are applicable for average soil conditions (soil classes B and C in EN 1998-1). The estimates of ground motion parameters for seismic events with M^ > Mw,cap should be made using the impose capping magnitude, implying that the ground motion parameters' amplitudes for seismic events of Mw > Mw,cap should be calculated using the value oíM^xap in the proposed GMPE. Regarding the results of PSHA, for mean return periods of 500 to 1000 years (of interest for the design of regular buildings and structures) the PGA values obtained with the proposed GMPE and YEA97 at moderate and large epicentral distances are almost similar. As for the values of the pseudo-spectral accelerations at natural vibration periods of T = 0.3 s and 7" = 1.0 s, the YEA97 GMPE provides lower hazard values atT= 0.3 s and higher hazard values at r = 1.0 s as compared to the proposed ground motion model. The last remark is in line with one of the conclusions of Youngs et al. (1997) that "the attenuation relationship for SA ... may be somewhat conservative at longer periods". 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