geosciences

Article Ground Motion Model for Spectral Displacement of Intermediate-Depth Earthquakes Generated by Vrancea Seismic Source

Paul Olteanu * and Radu Vacareanu

Department of Reinforced Concrete Structures, Technical University of Civil Engineering Bucharest,

020396 Bucures, ti, Romania; [email protected] * Correspondence: [email protected]; Tel.: +40-723-160-367



Received: 23 May 2020; Accepted: 21 July 2020; Published: 23 July 2020


Abstract: In support of displacement-based design (DBD), an attenuation model for the prediction of the spectral displacement of intermediate-depth earthquakes generated by Vrancea source is proposed. DBD is an alternative to force-based design, the main benefits being a better and confident description of the structural response and the removal of some of the inconsistencies of force-based code design. The basic input for DBD is the displacement response spectrum (DRS). Vrancea intermediate-depth source is responsible for the seismic hazard for most of the Romanian territory. The source produces, on average, two or three earthquakes with MW > 7.0 per century, the prominent characteristics being the large displacement demand and large predominant periods ( 1.5 s) for sites located in ≈ the Romanian Plain. The model is applicable for sites positioned in front of the South-Eastern Carpathian Arc on type B and C soils. Equations predicting spectral displacement were developed by two-stage regression analysis, using a database containing national analog records of moderate-strong earthquakes and the available digital records, of smaller earthquakes. The model was extended for periods up to 8.0 s using national digital strong motion records and Japanese high-quality digital records of earthquakes triggered by a similar seismo-tectonic environment. The model successfully reproduced observed data, for both type B and C soils and the goodness of fit was tested using methods available in literature.

Keywords: displacement-based design; seismic design; GMPE; displacement response spectra; intermediate-depth earthquake; Vrancea

1. Introduction Romania is a country exposed to seismic hazard throughout its territory, a fact that is supported by historical evidence spanning more than ten centuries. There are 14 known seismic sources affecting the territory of the country, nine of them located inside the country’s borders. All except one produce shallow earthquakes, most of them with maximum credible magnitudes less than 7.0, being of local interest. On the other hand, the Vrancea subcrustal seismic source, located where the East European plate and the Intra-Alpine and Moesian sub plates converge, is by far the most aggressive source and affects the whole country. Two or three major earthquakes are generated per century, with hypocenters at depths of 70–110 or 130–160 km and epicenters localized inside a small rectangular region with dimensions of about 80 40 km. Vrancea subcrustal earthquakes are felt at large distances over an × extended area in South-East Europe. Intermediate-depth earthquakes usually occur in subduction zones where two tectonic plates are in contact, one slipping and sinking underneath the other. For the Vrancea seismic zone there is evidence that subduction ceased 10 million years ago [1]. Since the 1970s, the researchers hypothesized

Geosciences 2020, 10, 282; doi:10.3390/geosciences10080282 www.mdpi.com/journal/geosciences Geosciences 2020, 10, 282 2 of 23 that the intermediate-depth seismicity in the Vrancea area is related to the dipping of a portion of a tectonic plate into the mantle (asthenosphere). This would be the last stage of the subduction process. The nature of the plate (oceanic or continental) is, for the time being, a subject of debate among seismologists. The fact that there is a low seismic activity, located at depths of 40–70 km, has led to the idea that the plate fragment is already detached from the continental crust. Accordingly, the fragment, originally quasi-horizontal, has reached a nearly vertical position, and is colder and denser than the surrounding environment and descends under the action of gravity. The bottom of the descending fragment is located at a minimum depth of 350 km. Interaction between gravitational forces, buoyancy, viscous and friction forces produces shear forces large enough to trigger earthquakes in the descending body [2]. The focal mechanism for all MW > 7 earthquakes is reverse faulting with the fault plane oriented along the NE-SW direction [3]. At least one major event (4 March 1977, MW = 7.4) was a multi-shock source, with a foreshock and a subsequent three shocks generated within a 20-s time interval. This feature is in agreement with a large release of energy over the surface of the rupture with local asperities or stress field non-uniformities. As mentioned, the epicenters of the subcrustal Vrancea earthquakes are confined to a small rectangular region elongated along the NE-SW direction [4]. The alignment of the epicenters towards the NE-SW, as well as of the rupture plane for the major shocks, can partly explain the directional effects towards Bucharest (SW) or Moldova (NE). There is a tendency of increasing magnitude with increasing depth. This phenomenon was explained by the increase in resistance of the asperity cell along with the increase in the depth due to the lithostatic pressure. Regression relations that correlate with the magnitude of the earthquake with the length of the rupture surface, and the surface area of the rupture [5] can provide the maximum magnitude of the source. The maximum values for the surface rupture length are 150–200 km and, for the surface of the rupture area, 8000 km2. These values lead to a maximum credible earthquake magnitude of M 8.1 ≈ W ≈ and a probable focal depth estimated between 140 and 170 km [4]. This paper focuses on the main input for DBD procedure, the relative displacement spectrum, for earthquakes of intermediate-depth and sites located in front of the Carpathian Arc, corresponding to the historical regions of Moldova, Muntenia and Dobrogea.

2. Ground Motion Model Ground motion prediction equations (GMPE) quantitatively represent the way in which a parameter of the earthquake ground motion decreases with increasing source-site distance. The vast majority of prediction equations use the horizontal response spectral acceleration (SA) as a parameter that is representative of the seismic motion. In the 1990s, the concepts of performance-based design and displacement-based design were devised, to better control the structural behavior. These concepts have, as a starting point, the idea that is more meaningful to set and check specific performance levels (a certain earthquake intensity measure and a corresponding damage state), and the fact that the damage caused by earthquakes to building structures is better related to the peak relative displacements than to peak accelerations. Although GMPEs for peak ground displacement were available since 1974 [6,7], only in 1998 [8], then in 2004 [9], were significant efforts towards the development of GMPE for relative displacement response spectrum made. In recent years, the attenuation models for DRS began to receive researchers’ attention due to increasing DBD popularity, in the studies of Akkar and Bommer [10], Cauzzi et al. [11,12] and Faccioli et al. [11–13], followed more recently in [14,15]. Some of the aforementioned models provide the DRS with different values of damping, all of them are valid for shallow earthquakes (note that the GMPE in [15] uses a database which also includes Romanian strong motion records generated by shallow earthquakes). In Romania, the first studies on ground motion models were developed by Lungu 1994 [16] and Radu 1994 [17]. The models were azimuth-dependent and predicted the peak ground acceleration (PGA). Subsequent studies by Stamatovska and Petrovski [18] for PGA, Sokolov [19] for pseudo-spectral Geosciences 2020, 10, 282 3 of 23 acceleration, peak ground velocity and Medvedev-Sponheuer-Karnik (MSK) scale seismic intensity, followed the approach of azimuth-dependent coefficients. In 2000, Lungu [20] developed another model based on the same functional form as the one in 1994, with coefficients which are not azimuth-dependent. An attenuation model for peak ground acceleration of Vrancea subcrustal earthquakes was elaborated [21] and used in the Romanian seismic design code, P100-1/2013, in order to estimate the horizontal forces needed for design. More recently, Vacareanu et al. [22], developed a new model for spectral acceleration in 2015 [23], introducing a zonation of Romanian territory in Geosciences 2020, 10, x FOR PEER REVIEW 3 of 25 Fore-Arc and Back-Arc regions, accounting for the different attenuation and filtering, corresponding to the two regionsanother located model based on theon the sides same of functional the Carpathian form as the Arc. one in 1994, with coefficients which are not Theoretically,azimuth-dependent. DRS needed An attenuation for displacement-based model for peak ground design acceleration could of beVrancea determined subcrustal from the earthquakes was elaborated [21] and used in the Romanian seismic design code, P100-1/2013, in order pseudo-accelerationto estimate the spectra, horizontal provided forces needed that for the design spectral. More recently, ordinates Vacareanu at intermediate-long et al. [22], developed periods a are reliable. Responsenew model for spectra spectral derived acceleration from in 2015 analog [23], intr recordsoducing area zonation considered of Romanian valid territory up to in periodsFore- of 4 s. High-qualityArc digitaland Back-Arc records regions, provide accounting valid for spectral the differe ordinatesnt attenuation for and periods filtering, exceeding corresponding 10 s.to the The displacementtwo regions located spectra on the sides are of more the Carpathian dependent Arc. on moment magnitude than the acceleration Theoretically, DRS needed for displacement-based design could be determined from the pseudo- spectra, andacceleration the shape spectra, and provided ordinates that ofthe the spectral DRS ordinates are much at intermediate-long more sensitive periods to the are way reliable. acceleration processingResponse/correction spectra was derived performed from analog than therecords acceleration are considered spectrum valid up ordinates.to periods of A4 s. GMPE High-quality was developed for the relativedigital displacement records provide valid spectrum spectral applicable ordinates for inperiods Romania, exceeding using 10 s. a database of analog and digital records, by directThe processingdisplacement ofspectra DRS are of themore records. dependent on moment magnitude than the acceleration spectra, and the shape and ordinates of the DRS are much more sensitive to the way acceleration processing/correction was performed than the acceleration spectrum ordinates. A GMPE was 2.1. Strong Motion Database. Processing of Records. Ground Types developed for the relative displacement spectrum applicable in Romania, using a database of analog In orderand digital to develop records, by a direct GMPE, processing a database of DRS of containing the records. strong motion records was compiled.

The databank2.1. Strong used Motion for this Database. study Processing contains of Records. 272 ground Ground motionTypes records (544 horizontal components) from 15 intermediate-depth earthquakes. A number of nine earthquakes were produced by Vrancea In order to develop a GMPE, a database containing strong motion records was compiled. The subcrustaldatabank source (235used records),for this study while contains six 272 were ground recorded motion in records Japan. (544 The horizontal database components) contains from earthquakes with magnitudes15 intermediate-depth 5.2 M earthquakes.7.4, with focalA number depths of nine in theearthquakes range 65–160were produced km and bypartly Vrancea covers the ≤ W ≤ database consideredsubcrustal source by (235 Vacareanu records), while et al. six in were [23 ].reco Fromrded in the Japan. total The number database contains of records, earthquakes 169 were from with magnitudes 5.2≤ MW≤ 7.4, with focal depths in the range 65–160km and partly covers the stations located on type C ground (62%), the remainder being recorded on ground type B. Digital database considered by Vacareanu et al. in [23]. From the total number of records, 169 were from records add to 57% of the total number and are generated by earthquakes having 5.2 M 7.1. stations located on type C ground (62%), the remainder being recorded on ground type B. Digital≤ W ≤ Therefore,records most earthquakesadd to 57% of the in thetotal database, number an withd are generatedMW > 7.0, by wereearthquakes analogical having recorded5.2≤ MW≤ 7.1. in Romania. Figure1 showsTherefore, the databasemost earthquakes configuration; in the database, the size with of M theW >7.0, data were point analogical is correlated recorded within Romania. its magnitude. Figure 1 shows the database configuration; the size of the data point is correlated with its magnitude. w Magnitude, M

Figure 1. FigureOrigin, 1. Origin, ground ground type, type, magnitude magnitude and and epicentral distance distance distribution distribution of the records. of the records.

Geosciences 2020, 10, 282 4 of 23

Because of the small number of ground motion recorded on firm ground (rock or rock-like Geosciences 2020, 10, x FOR PEER REVIEW 4 of 25 formation including, at most, 5 m of weaker material at the surface and vs30 > 800 m/s, type A according to Eurocode 8) andBecause the of scarcitythe small ofnumber strong of ground ground motion motions recorded behind on firm the ground Carpathian (rock or rock-like Arc (Transylvania), these recordsformation were notincluding, selected at most, in 5 the m of database. weaker material at the surface and vs30 >800 m/s, type A according to Eurocode 8) and the scarcity of strong ground motions behind the Carpathian Arc (Transylvania), Figure2thesea,b records shows were the not main selected tectonic in the database. structures and the major recorded seismic events produced by the VranceaFigure intermediate-depth 2a,b shows the main source. tectonic structures and the major recorded seismic events produced by the Vrancea intermediate-depth source.

(a)

(b)

Figure 2. (a) Main tectonic structures in Romania, Google Earth 7.3.3.7699 45°23’37” N, 26°26’34” E, Figure 2. (a) Main tectonic structures in Romania, Google Earth 7.3.3.7699 45◦23037” N, 26◦26034” eye altitude 925 km, viewed 19 June 2020; (b) Localization of the major earthquakes recorded in E, eye altitudeRomania. 925 Google km, viewed Earth 7.3.3.7699 19 June 45°40’56” 2020; N, (26b)°39’33” Localization E, eye altitude of 124 the km, major viewed earthquakes 19 June 2020. recorded in Romania. Google Earth 7.3.3.7699 45 40 56” N, 26 39 33” E, eye altitude 124 km, viewed 19 June 2020. ◦ 0 ◦ 0

The decision to include non-Romanian records was taken as a result of the lack of high-quality (digital) national records for earthquakes with M 6.0. The recommendation in the literature is to W ≥ use records from other countries, when there are not enough local records available. Furthermore, it is desirable to extend the databases with "import" records to obtain GMPE, especially when local records do not cover the full range of magnitudes and distances for which the attenuation model is designed. The Japanese earthquakes [24] have focal depth in the range of 65–125 km and magnitudes 6.0 M 7.1. Unfortunately, the database of the two networks (KiK-net and K-NET) does not ≤ W ≤ Geosciences 2020, 10, 282 5 of 23

include records for seismic events with Mw > 7.1 for depths between 60 and 200 km. Table1 summarizes the main characteristics of the earthquakes selected in the database.

Table 1. Database structure.

Focal Number of Date Latitude Longitude Country Local Time Depth M Horizontal (year/month/day) ( N) ( E) w of Origin ◦ ◦ (km) Components 1977/03/04 19:21:54 45.77 26.76 94 7.4 4 RO 1986/08/30 21:28:37 45.52 26.49 131 7.1 70 RO 1990/05/30 10:40:06 45.83 26.89 91 6.9 92 RO 1990/05/31 00:17:48 45.85 26.91 87 6.4 66 RO 2004/10/27 20:34:36 45.84 26.63 105 6.0 92 RO 2005/05/14 01:53:21 45.64 26.53 149 5.5 14 RO 2005/06/18 15:16:42 45.72 26.66 154 5.2 14 RO 2009/04/25 17:18:48 45.68 26.62 110 5.4 10 RO 2013/10/06 01:37:21 45.67 26.58 135 5.2 108 RO 2001/12/02 22:02:00 39.40 141.26 122 6.4 6 JAP 2003/05/26 18:24:00 38.81 141.68 71 7.0 24 JAP 2005/07/23 16:35:00 36.58 140.14 73 6.0 6 JAP 2008/07/24 00:26:00 39.73 141.63 108 6.8 16 JAP 2011/04/07 23:32:00 38.20 141.92 66 7.1 18 JAP 2013/02/02 23:17:00 42.70 142.23 102 6.5 4 JAP

In [11,12], attention is drawn to the sensitivity of the displacement spectra to the quality of the recording (digital vs. analog) and the way the accelerograms are processed. Analog records obtained during seismic movements are affected by various types of errors (due to instrumentation and digitization, among others) that affect recording quality, especially at high (>20 Hz) and low (<0.5 Hz) frequencies. Low-frequency errors affect the history of velocities and displacements, while high frequency errors particularly affect the peak ground acceleration. To limit the effect of these errors, various corrections and filters are used. Filtering removes the errors, however, along with them, it eliminates the useful information present in the filtered frequency range [25]. The analog records were obtained in a form already processed; the waveforms were not further adjusted. The methodology used for filtering is described in [25]. The filtering procedure is not uniformly applied, the filter is of Ormsby type and the cutting thresholds are 0.15–0.25 Hz for low frequencies and 25–28 Hz for high frequencies. The digital records were processed by applying a fourth-order Butterworth filter with the lower threshold at 0.05 Hz while the higher is at 50 Hz. Although the Romanian seismic code in force evaluates soil conditions following the approach of Lungu, which is based on control periods [26], for important structures, the code recommends studies to characterize field conditions: the shear and compression wave velocity profile, vs and vp, down to the base rock or minimum for the first 30 m and the terrain stratification (thickness, density, type). Then, the weighted average value vs on the considered stratification is calculated and the soil is classified according to Eurocode 8. In this study, Eurocode 8 [27] terminology was used. vs,30 has the advantage that it is a proven method (used in countries like US, Japan), is recommended by national seismic design code and can be applied relatively easily. Within the BIGSEES project (a Romanian multidisciplinary study aimed at improving earthquake risk mitigation in a Eurocode 8 framework), a database containing stratifications and compression wave velocities was created. Most borehole measurements were conducted in the 1970s, and information on shear wave velocities is no longer available [28]. There is a small number of boreholes with depths between 13 and 150 m, located in Bucharest, for which there is a complete set of data. In the study of Allen and Wald [29], a methodology is proposed to obtain information on shear wave velocity using topographic slope data. Using a correlation between the topographic slope and the data recorded by vs,30 in several locations in the United States, Taiwan, Italy, Puerto Rico, New Zealand and Japan, the vs,30 data from the slope topography survey can be used to describe the soil conditions at a regional level. Following this methodology, a map was created [28], which allows the assessment of soil conditions for Romanian territory. Geosciences 2020, 10, 282 6 of 23

Studies by Neagu and Aldea, [28], using data from 19 bore holes in Bucharest showed a good correlation between values given by the Allen and Wald study [29] and field measurements. The differences between the two datasets are, on average, 12% (the slope method slightly underestimating the shear wave velocity), with a maximum difference of 28%. In spite of all these differences, ground type classification is the same for both methods for the surveyed sites. In this study, the values of the shear velocities for the first 30 m, for locations where the waveforms were recorded, are according to [29] and available on the United States Geological Survey website [30]. Japanese sites, are usually assigned vs,30 values [24]. However, some sites do not have boreholes extending to the depth of 30m, so the values for vs,30 were determined using the methodologies described in [31] and using the database files available in [32].

2.2. Ground Motion Prediction Equation The coefficients of the attenuation model for relative displacement response spectrum ordinates were determined using two-stage regression analysis, following the methodology given in Joyner and Boore [33,34]. Two-stage regression is used in order to uncouple magnitude scaling and distance scaling. The method is used extensively in determining the coefficients of attenuation laws, and is based on maximizing the likelihood of the set of observations. The first step of the two-stage regression algorithm consists of determining the coefficients which give the distance dependence, and an array of deviations (for each record). In the second step, coefficients expressing magnitude dependence are determined by maximizing the likelihood of the set of observations. The functional form of the GMPE, given in [33], is based on the random-effects model of Brillinger and Preisler [35] q q 2 2 2 2 lg(SD) = a + b(MW 6) lg D + h + c D + h + εr + εe (1) − − epi epi where SD (cm) is the spectral ordinate of relative displacement (as a geometrical mean of two perpendicular horizontal components) for 5% damping, MW is the moment magnitude of the earthquake, Depi (km) is the epicentral distance, a, b, c and h are coefficients which are determined through regression, εr is an independent random variable normal distributed, which takes values for every record, εe is an independent random variable normal distributed with values for every earthquake and lg denotes 2 base 10 logarithm. Random variable εr has the mean equal to 0 and variance σr , represents the variability between seismic stations (intra-event), while random variable εe has 0 mean and variance 2 σe , representing the variability between seismic events (inter-event). Total variance is

2 2 2 σ = σr + σe (2)

Original functional form [33] uses the Joyner-Boore distance (the shortest distance from the seismic station to the vertical projection of the ruptured surface) as a metric instead of Depi, which was used in this study. Because Joyner-Boore distance is not available for intermediate-depth earthquakes generated by the Vrancea source, epicentral distance was chosen as a predictor variable. The attenuation model used for peak ground acceleration in P100-1/2013 zonation uses as a distance metric the hypocentral (focal) distance, Rhypo. For this study, epicentral distance was proved to be similarly correlated with computed spectral displacements as the hypocentral distance. Moreover, formally, the significance of the epicentral distance is closer to the Joyner-Boore than the focal distance. Figures3 and4 presents, side by side, the correlation factors of spectral displacements (for earthquakes with M 6 recorded in Romania and Japan) with D and R for T = 1.0 s. ≥ epi hypo The records were arranged in three bins, according to their magnitude and soil type. One can notice, for soil type B and C, the epicentral distance correlates with the logarithm of spectral displacement as the focal distance does, with the exception of strong earthquakes and soft soil (type C). Geosciences 2020, 10, x FOR PEER REVIEW 7 of 25

was used in this study. Because Joyner-Boore distance is not available for intermediate-depth Geosciences 2020earthquakes, 10, 282 generated by the Vrancea source, epicentral distance was chosen as a predictor variable. 7 of 23 GeosciencesThe 2020attenuation, 10, x FOR PEERmodel REVIEW used for peak ground acceleration in P100-1/2013 zonation uses7 ofas 25 a distance metric the hypocentral (focal) distance, Rhypo. For this study, epicentral distance was proved was used in this study. Because Joyner-Boore distance is not available for intermediate-depth to be similarly correlated with computed spectral displacements as the hypocentral distance. The firstearthquakes two terms generated of the by GMPEthe Vrancea take source, into epicentral account distance the quasilinear was chosen as variation a predictorof variable. the logarithm of Moreover, formally, the significance of the epicentral distance is closer to the Joyner-Boore than the The attenuation model used for peak ground acceleration in P100-1/2013 zonation uses as a amplitudefocal with distance. magnitude, Figures 3 with and 4 thepresents, moment side by magnitude side, the correlation scale factors being of selected spectral displacements to express the size of distance metric the hypocentral (focal) distance, Rhypo. For this study, epicentral distance was proved the earthquakes(for earthquakes used in with the M database. ≥6 recorded Thein Romania third and term Japan) corresponds with Depi and toRhypo the forgeometric T = 1.0 s. attenuation of to be similarly correlated with computed spectral displacements as the hypocentral distance. 1.5 1.5 the seismicMoreover, waves, formally, which decreases the significance proportionally of the epicentral with distance the is inverse closer to ofthe the Joyner-Boore distance. than The thefourth term correspondsfocal to distance. the anelastic Figures 3 attenuation, and 4 presents, due side by to side, the mediathe correlation traversed factors by of spectral the seismic displacements waves. 1 1 (for earthquakes with M ≥6 recorded in Romania and Japan) with Depi and Rhypo for T = 1.0 s. 1.5 1.5

0.5 0.5

1 1 lg(Depi) lg(Rhypo) 0 0 1.21.622.4 1.8 2 2.2 2.4 2.6 0.5 0.5 Fit Mw>7 -0.5 -0.5 R2 = 0.285361 Fit Mw>7 Mw > 7 Mw > 7 2 lg(Depi) R = lg(R0.309514hypo) Fit 6.57 Fit 6.07 Fit 6.07 Fit 6.57 Mw > 7 Mw > 7 R2 = 0.309514 -1.5 Fit 6.57 (a) Fit 6.07 (b) Fit 6.0

Figure 3. FigureTheCorrelation records 3. Correlation were of thearranged of logarithmthe logarithm in three of ofbins, spectralspectral according di displacementsplacement to their withmagnitude withepicentral epicentral and and soil hypocentral type. and One hypocentral can notice,distance for soil for Ttype = 1.0 Bs, soiland type C, Bthe (a) Correlationepicentral withdistance the epicentral correlates distance; with (theb) Correlation logarithm with of thespectral distance forhypocentralT = 1.0 s,distance. soil type B (a) Correlation with the epicentral distance; (b) Correlation with the displacement as the focal distance does, with the exception of strong earthquakes and soft soil (type hypocentral distance. C). The records were arranged in three bins, according to their magnitude and soil type. One can 1.5 1.5 notice, for soil type B and C, the epicentral distance correlates with the logarithm of spectral displacement as the focal distance does, with the exception of strong earthquakes and soft soil (type C). 1 1 1.5 1.5

0.5 0.5

1 1 lg(Depi) lg(Rhypo) 0 0

lg(SD) 1.2 1.6 2 2.4 1.8 2 2.2 2.4 2.6 0.5 0.5

-0.5 -0.5 Fit Mw>7 Fit Mw>7 Mw > 7 Mw > 7 R2 = 0.463648 R2lg(D= 0.271404epi) lg(Rhypo) 0 6.5< Mw < 7 0 6.5< Mw < 7 Fit 6.5

lg(SD) 1.2 1.6 2 2.4 1.8 2 2.2 2.42 2.6 6.0< Mw <6.5 R2 = 0.522088 6.0< Mw <6.5 R = 0.543799 -1 -1 Fit Mw>7 Fit 6.07 Fit 6.07 Fit 6.07 Fit 6.0 7 Mw > 7 R2 = 0.463648 R2 = 0.271404 -1.5 6.5< Mw < 7 -1.5 6.5< Mw < 7 Fit 6.57 Fit 6.07 Fit 6.0

 2 no.rec 1 X lgY1j lgY2j σ2 = − (4) c no.rec 4 j=1

2 where σ1 isGeosciences the variance 2020, 10, x computedFOR PEER REVIEW in the first stage of regression, and indexes 1 and 2 are8 the of 25 horizontal perpendicular components of the record j. The original expression has natural logarithms instead of decimal logarithmsThe first at two the terms right of the side GMPE of the take equation, into accoun andt the thequasilinear GMPE variation was also of the expressed logarithm of in terms of amplitude with magnitude, with the moment magnitude scale being selected to express the size of 2 natural logarithms.the earthquakesσc usedis a in correction the database. applied The third through term corresponds variance to the in ordergeometric to attenuation take into of account the that a randomlyseismic oriented waves, horizontal which decreases component proportionally could be with larger the inverse than the of the computed distance. geometricThe fourth term mean. corresponds to the anelastic attenuation, due to the media traversed by the seismic waves. 1.2

0.9

0.6

0.3

MW 0 lg(SD) lg(SD) 6.4 6.6 6.8 7 7.2 7.4

-0.3

100>Depi>50 100>Depi>50 150>D >100 -0.6 epi R2 = 0.855229 200>D >150 epi 150>Depi>100 Fit 100>D >50 R2 = 0.52362 -0.9 epi 200>Depi>150 Fit 150>Depi>100 R2 = 0.815735 Fit 200>Depi>150 -1.2 (a) (b)

Figure 5. FigureSpectral 5. Spectral displacement displacement as aasfunction a function ofof momentmoment magnitude magnitude for T for= 1.0T s,= ground1.0 s, type ground C, type C, moderate-large national records 1977, 1986, 1990. (a) Linear dependence; (b) Quadratic dependence moderate-large national records 1977, 1986, 1990. (a) Linear dependence; (b) Quadratic dependence of of logarithm of spectral displacement with magnitude. logarithm of spectral displacement with magnitude. As expected, there is a strong correlation between the moment magnitude and logarithm of The coespectralfficients displacements, of the attenuation as shown in Figure model 5. For were the moderate-large determined national separately records for set, ground the records type B and ground typewere C, sorted due toin muchthree bins, smaller according ordinates to their and epic dientralfferent distance. spectral A slightly shapes better of displacementcorrelation is spectra observed for a quadratic expression of the lg(SD) variation, especially for the case of sites located at computed on ground type B. epicentral distances between 100 and 150 km. Considering a quadratic dependence of lg(SD) with Aimingmagnitude at a better would prediction require an ofadditional the response term in the for functional large earthquakes form. (MW > 7.1), the opportunity of adding a quadraticIn thisterm study, to the the relative basic displacement attenuation spectr modelum ordinates was explored, are expressed leading as the to geometric the following mean equation of two perpendicular horizontal components. It is preferred to perform the regression analysis based on this quantity for it is regarded as statistically representativeq for anyq random direction. Most 2 2 2 2 2 lg(SD) = a + b(MW 6) + d(MW 6) lg D + h + c D + h + εr + εe (5) attenuation models use the− geometric mean− instead− of the maximumepi value as theepi expected parameter. Variability between seismic stations (intra-event), expressed through variance σr2 can be which hascomputed, indeed led adapted to the after improvement [36,37], as in the predictions of the DRS for the earthquake recorded on σσσ222=+ 4th of March 1977 and has, to a certain degree, reducedrc1 the residual values. (3) Due to the fact that all the moderate and major earthquakes in Romania are analog-recorded, 2 no. rec ()− the calculated values of the displacement spectra1 canlg beYY12 consideredjj lg valid up to periods of maximum σ 2 = (4) c  4 s. Efforts have been made to predict spectralno.4 rec j values=1 up to 8 s. National records after 2004 are digital and of high2 quality, but were produced by earthquakes with M 6.0. This was one of the where σ1 is the variance computed in the first stage of regression, and indexesW ≤ 1 and 2 are the reasons whyhorizontal Japanese perpendicular intermediate-depth components of earthquakes, the record j. The with original magnitudes expression has close natural to thelogarithms major events in Romania, wereinstead added of decimal to the logarithms database. at the Recordings right side of the from equation, Japan and are the high-quality GMPE was also digital expressed records in that can 2 be consideredterms reliable of natural for logarithms. periods σ exceedingc is a correction 10 applied s. through variance in order to take into account that a randomly oriented horizontal component could be larger than the computed geometric mean. The coefficients of the attenuation model were determined separately for ground type B and 3. Resultsground and Discussion type C, due to much smaller ordinates and different spectral shapes of displacement spectra To investigatecomputed on the ground database type B. dependence of the attenuation model, the regression was performed on three sets of data, one of which contains national records of moderate-large earthquakes of 1977, 1986 and 1990; the second set of data was made up of digital records only (national, with 5.2 MW 6.0 ≤ ≤ and Japanese, from Kik-Net and K-NET networks, with 6.0 M 7.1) with coefficients calculated up ≤ W ≤ to periods of 8 s and, finally, a set which contains the entire database and coefficients calculated for periods in the range 0.1–4.0 s. Geosciences 2020, 10, 282 9 of 23

The GMPE is valid in the area in front of the Carpathian Arc: Moldova, Muntenia and Dobrogea on ground types B and C.

3.1. Moderate-Strong Set of Records

The first dataset includes records from 4th of March 1977 earthquake (MW =7.4), 31st of August 1986 (MW = 7.1), 30th and 31th of May 1990 (MW = 6.9 and MW = 6.4). The main features are the large displacement demands imposed on high rise structures (T >1.0 s) located on ground type C, this characteristic being common amongst historical earthquakes, such as the massive 1940 earthquake, which inflicted heavy damage on tall buildings in Bucharest, and the devastating earthquake of 1802, that caused the collapse of Coltei Tower and the majority of bell towers in Bucharest. Due to the fact that the set of accelerograms from these earthquakes had already been processed [25], no further adjustments were made. The records were then sorted by the ground type and then the computation of elastic displacement spectra for a 5% damping was performed. The software used for spectra calculation was Seismosignal [38] for a range of periods between 0.025 and 4.000 s, with 0.025 s increment. The geometrical mean of spectral displacement for every period and record in the set was then computed. Two examples are given in Figure6 to illustrate the di fference in DRS shape and a period ofGeosciences peak value 2020, 10 in, x FOR terms PEER of REVIEW soil type category and epicentral distance. 10 of 25

50 SD, cm 45

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10 INCERC77-Geomean INCERC77-EW INCERC77-NS 5 T, s 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 (a) (b)

Figure 6. Displacement spectra of 4th of March 1977 earthquake, MW = 7.4, for two stations (a) INCERC Figure 6. Displacement spectra of 4th of March 1977 earthquake, MW = 7.4, for two stations (a) INCERC Bucharest (Depi = 155 km), type C soil; (b) Chișinău (Depi=269 km), type B soil. Bucharest (Depi = 155 km), type C soil; (b) Chis, inău (Depi=269 km), type B soil. One can observe the large difference between the maximum displacement values (48.5 cm at OneINCERC can observe station (National the large Institute difference of Research between and Development the maximum in Constructions), displacement compared values to 3.3 (48.5 cm at INCERCcm station in Chisinau) (National and between Institute the spectral of Research forms, although and Development the maximum valu in Constructions),es of the displacements compared to 3.3 cm in Chisinau)are located within and between the same period the spectral interval: forms, 1.5–2.0 althoughs. the maximum values of the displacements As expected, the spectral maximum value scales with the magnitude, as can be seen in Table 2 are locatedfor within INCERC the recordings same period for the interval:earthquakes 1.5–2.0 in thiss. dataset (table includes also the peak ground As expected,acceleration the (PGA) spectral values). maximum value scales with the magnitude, as can be seen in Table2 for INCERC recordings for the earthquakes in this dataset (table includes also the peak ground acceleration Table 2. Magnitude scaling of displacement spectra, INCERC site (PGA) values). Event MW PGA, cm/s2 SDmax, cm (year/month/day)Table 2. MagnitudeEW scaling of displacementNS spectra,EW INCERC site NS 1977.03.04 7.4 188 207 32.4 48.4 1986.08.31 Event7.1 109 96 PGA, cm/s2 8.8SD , cm 12.4 M max 1990.05.30 (year/month6.9 /day) 99 W 66 9.3 3.4 EW NS EW NS Note that, for1977 an increase/03/04 in magnitude 7.4 from 7.1 to 7.4, 188 the PGA 207 increases 32.4 two-fold, 48.4 while the maximum spectral1986 displacement/08/31 increases four 7.1 times and, 109 for a magnitude 96 8.8 increase 12.4 from 6.9 to 7.1, PGA increases by 25%1990 and/05/ displacements30 double 6.9 (the geometric 99 mean 66 of the 9.3 two components). 3.4 The difference in magnitude affects the long period components of the ground motions while PGA is related to short period components. Note that, for an increase in magnitude from 7.1 to 7.4, the PGA increases two-fold, while the After calculating geometric mean and intra-event variance, the two-step regression was maximumperformed spectral following displacement the procedure increases described four in times[33,34], and,with the for coefficients a magnitude of the increaseattenuation from 6.9 to model determined by maximizing likelihood. Coefficients were determined for periods ranging from 0.10 to 4.00 s with an increment of 0.1 s and are presented in Appendix A. Figure 7 presents the outcome of predictions of recorded seismic ground motions found in the database against computed DRS, as a geometrical mean of the two horizontal components of the actual records. The top of the figure shows spectra reproduced on type B soils: at the left are Onesti station and 1990 earthquakes, while at the right are the results for Cahul and Valenii de Munte stations. The lower side of the figure presents DRS reproduced on type C soil for the 1986 and 1990 earthquakes for Ramnicu Sarat (left), respectively, Otopeni and Peris stations (right). The stations were selected so that the epicentral distance can be the same.

Geosciences 2020, 10, 282 10 of 23

7.1, PGA increases by 25% and displacements double (the geometric mean of the two components). The difference in magnitude affects the long period components of the ground motions while PGA is related to short period components. After calculating geometric mean and intra-event variance, the two-step regression was performed following the procedure described in [33,34], with the coefficients of the attenuation model determined by maximizing likelihood. Coefficients were determined for periods ranging from 0.10 to 4.00 s with an increment of 0.1 s and are presented in AppendixA. Figure7 presents the outcome of predictions of recorded seismic ground motions found in the database against computed DRS, as a geometrical mean of the two horizontal components of the actual records. The top of the figure shows spectra reproduced on type B soils: at the left are Onesti station and 1990 earthquakes, while at the right are the results for Cahul and Valenii de Munte stations. The lower side of the figure presents DRS reproduced on type C soil for the 1986 and 1990 earthquakes for Ramnicu Sarat (left), respectively, Otopeni and Peris stations (right). The stations were selected so that the epicentral distance can be the same. Geosciences 2020, 10, x FOR PEER REVIEW 11 of 25

(a) (b)

(c) (d)

Figure 7. FigurePredicted 7. Predicted vs. vs. computed computed displacement displacement spectra spectra for 1986, for1990-1 1986, (May 30) 1990-1 and 1990-2 (May (May 30) 31) and 1990-2 earthquakes (a) 1990 events, type B soil, 50 km; (b) 1986, 1990 events, type B soil, 100 km; (c) 1986, (May 31) earthquakes (a) 1990 events, type B soil, 50 km; (b) 1986, 1990 events, type B soil, 100 km; 1990 events, type C soil, 50 km; (d) 1986 event, type C soil, 100 km. (c) 1986, 1990 events, type C soil, 50 km; (d) 1986 event, type C soil, 100 km. The thin lines represent the geometric mean of the two horizontal components for each record. The thinThe linesthick representred line designates the geometric the median mean value ofof the predicted two horizontal spectrum, componentswhilst the grey forzone each record. The thick redencompasses line designates a zone ± 1σ from the medianthe median value values. of the predicted spectrum, whilst the grey zone Using the attenuation relationship, the change in displacement spectra with changing encompasses a zone 1σ from the median values. magnitude, ground± type and epicentral distance was analyzed. There is a narrowing of the area of Usinglarge theattenuation amplificationsrelationship, of the displacement the change spectrum in with displacement increasing magnitude spectra withof the changingearthquake, magnitude, ground typeespecially and epicentralfor soil type C. distance Smaller earthquakes was analyzed. tend to have There quasi-flat is aareas narrowing over an extended of the range area of large of periods, as confirmed by the displacement spectra calculated for the 1986 and 1990 earthquakes. There is a large difference between displacement demands of earthquakes separated by one degree of moment magnitude, particularly for type C soil, as shown in Figure 8.

Geosciences 2020, 10, 282 11 of 23 amplifications of the displacement spectrum with increasing magnitude of the earthquake, especially for soil type C. Smaller earthquakes tend to have quasi-flat areas over an extended range of periods, as confirmed by the displacement spectra calculated for the 1986 and 1990 earthquakes. There is a large difference between displacement demands of earthquakes separated by one degree of moment magnitude,Geosciences particularly 2020, 10, x FOR for PEER type REVIEW C soil, as shown in Figure8. 12 of 25

Geosciences 2020, 10, x FOR PEER REVIEW 12 of 25 SD(T) C /SD(T) B SD(T) C /SD(T) B

(a) (b)

Figure 8. Displacement demand, function of magnitude and soil conditions. (a) Spectral displacement Figure 8. Displacement demand, function of magnitude and soil conditions. (a) Spectral displacement

function of magnitude, Depi =epi100 km, type B soils represented with dashed lines, type C soils with function of magnitude,(a )D = 100 km, type B soils represented with dashed lines,(b) type C soils with continuouscontinuous lines; (b lines;) the (b ratio) the ratio between between displacement displacement on on grou groundnd type typeC and C displacement and displacement on ground on ground type B, SD(T)type B,/ SD(T)C/SD(T), D B, D=epi100 = 100 km. km. FigureC 8. DisplacementB epi demand, function of magnitude and soil conditions. (a) Spectral displacement functionRegarding of magnitude, the soil conditions, Depi = 100 km,there type are B very soils highrepresented values with of the dashed relative lines, amplification type C soils with between Regardingcontinuous the soil lines; conditions, (b) the ratio between there displacement are very high on grou valuesnd type ofC and the displacement relative amplificationon ground between the expected spectral values on soil C with respect to soil B. However, for moderate magnitudes (MW the expected≈ 7.0),type spectral these B, SD(T) are reduced valuesC/SD(T)B ,to D on epivalues = soil 100 km.found C with in the respect literature to [11]. soil These B. However, large values forof amplification moderate are magnitudes (M 7.0supported), these are by the reduced computed to valuesDRS for foundseismic stations in the literaturelocated at the [11 same]. These epicentral large distance, values for of 1986 amplification W Regarding the soil conditions, there are very high values of the relative amplification between ≈ and 1990 earthquakes. For smaller magnitudes, MW ≤6.5, there is only a small increase (15–30%) in are supportedthe expected by the spectral computed values on DRS soil forC with seismic respect stations to soil B. However, located atfor themoderate same magnitudes epicentral (M distance,W for displacement for sites located on ground type C relative to sites on ground type B. 1986 and 1990≈ 7.0), earthquakes.these are reduced For to values smaller found magnitudes, in the literatureM [11]. These6.5, there large isvalues only of aamplification small increase are (15–30%) The epicentral distance variation is analyzed in FigureW 9. For soil type C, the pronounced peak supported by the computed DRS for seismic stations located≤ at the same epicentral distance, for 1986 in displacementis near 2.30 for s sitesand has located a very limi onted ground tendency type to migrate C relative to longer to sites periods on with ground increasing type epicentral B. and 1990 earthquakes. For smaller magnitudes, MW ≤6.5, there is only a small increase (15–30%) in The epicentraldistance. Soil distance type B is characterized variation is by analyzed much lower in spectral Figure displacements,9. For soil type with C,a pronounced the pronounced peak peak is displacement for sites located on ground type C relative to sites on ground type B. at around 1.70 s followed by a relatively flat area. near 2.30 s andThe has epicentral a very distance limited variation tendency is analyzed to migrate in Figure to 9. longer For soil periodstype C, the with pronounced increasing peak epicentral distance.is Soil near type 2.30 s B and is characterizedhas a very limited by tendency much to lower migrate spectral to longer displacements, periods with increasing with aepicentral pronounced peak at arounddistance. 1.70 s followedSoil type B byis characterized a relatively by flatmuch area. lower spectral displacements, with a pronounced peak at around 1.70 s followed by a relatively flat area.

(a) (b)

Figure 9. Displacement spectra for an event with MW = 7.5 and 50, 100, 150, 200 km epicentral distances. (a) ground type B; (b) ground type C. (a) (b)

Figure 9. Displacement spectra for an event with MW = 7.5 and 50, 100, 150, 200 km epicentral Figure 9. Displacement spectra for an event with MW = 7.5 and 50, 100, 150, 200 km epicentral distances. distances. (a) ground type B; (b) ground type C. (a) ground type B; (b) ground type C.

Geosciences 2020, 10, 282 12 of 23

Geosciences 2020, 10, x FOR PEER REVIEW 13 of 25 For every 50 km increase in epicentral distance, the spectral displacement values drop by 1/3. For every 50 km increase in epicentral distance, the spectral displacement values drop by 1/3. The increaseGeosciences in epicentral 2020, 10, x FOR distance PEER REVIEW flattens the peaks and smoothens the spectra. 13 of 25 In orderThe increase to bring in epicentral the GMPE distance outcomes flattens the closer peaks to and the smoothens data collected the spectra. during strong earthquakes In order to bring the GMPE outcomes closer to the data collected during strong earthquakes (M 7.1), itFor was every attempted 50 km increase to introduce in epicentral a quadratic distance, the term spectral in the displacement attenuation values model. drop by Figure 1/3. 10 shows W (MW≥ 7.1), it was attempted to introduce a quadratic term in the attenuation model. Figure 10 shows ≥ The increase in epicentral distance flattens the peaks and smoothens the spectra. the reproducedthe reproduced and computed and computed DRS DRS spectra spectra for for Vrancea Vrancea largest largest recorded earthquakes earthquakes of 1977 of 1977and and 1986. In order to bring the GMPE outcomes closer to the data collected during strong earthquakes 1986. (MW≥ 7.1), it was attempted to introduce a quadratic term in the attenuation model. Figure 10 shows the reproduced and computed DRS spectra for Vrancea largest recorded earthquakes of 1977 and 1986.

(a) (b)

Figure 10.FigurePredicted 10. Predicted and computed and computed displacement displacement spectra spectra for fortwo twolarge large earthquakes earthquakes recorded recordedat the at the INCERC site, with quadratic(a) term (a) 4 March 1977; (b) 31 August 1986. (b) INCERC site, with quadratic term (a) 4 March 1977; (b) 31 August 1986. Figure 10. Predicted and computed displacement spectra for two large earthquakes recorded at the It is noted from Figure 10 that the median value ± 1σ envelopes the two components of each It is notedINCERC from site, Figure with quadratic 10 that term the (a) median4 March 1977; value (b) 31 August1σ envelopes 1986. the two components of each record for these two large earthquakes. Figure 11 presents± the predicted spectra using the GMPE with quadratic term for soil type C, a subcrustal seismic event with MW =7.5 and epicentral distances of 100 record for theseIt is two noted large from earthquakes. Figure 10 that the Figure median 11 valuepresents ± 1σ theenvelopes predicted the two spectra components using of the each GMPE with and 150 km. quadraticrecord term for these soil two type large C, aearthquakes. subcrustal Figure seismic 11 presents event the with predictedMW = spectra7.5 and using epicentral the GMPE distances with of 100 and 150 km.quadratic term for soil type C, a subcrustal seismic event with MW =7.5 and epicentral distances of 100 and 150 km.

(a) (b)

Figure 11. Predicted displacement spectra for a MW = 7.5 seismic event type C soil, with quadratic term (a) 100 km epicentral(a) distance; (b) 150 km epicentral distance. (b)

Figure 11. Predicted displacement spectra for a MW = 7.5 seismic event type C soil, with quadratic Figure 11.ThePredicted displacement displacement demand reaches spectra very for large a MW values,= 7.5 seismicfor both eventmedian type and Cmedian soil, with+ 1σ,quadratic for term (a) 100 km epicentral distance; (b) 150 km epicentral distance. term (spectrala) 100 kmperiods epicentral larger than distance; 2 s. The (b two) 150 predictions km epicentral highlight distance. peaks at 2.3–2.4 s for median and 2.6 s for median + 1σ, and a “sombrero” shape for the DRS. A recent study [39] on the design displacement The displacement demand reaches very large values, for both median and median + 1σ, for spectra, using stochastic finite-fault predictions, pointed to mean displacements in excess of 100 cm The displacementspectral periods demandlarger than reaches 2 s. The two very predictions large values, highlight for peaks both medianat 2.3–2.4 ands for median and+ 12.6σ, s for spectral periods largerfor median than + 1 2σ, s.and The a “sombrero” two predictions shape for the highlight DRS. A recent peaks study at [39] 2.3–2.4 on the design s for displacement median and 2.6 s for median +spectra,1σ, and using a “sombrero” stochastic finite-fault shape predictions, for the DRS. pointed A recentto mean study displacements [39] on in the excess design of 100 displacementcm spectra, using stochastic finite-fault predictions, pointed to mean displacements in excess of 100 cm (at 2.0–2.5 s) for sites located in the Bucharest area, for an event with MW = 7.5. Using the GMPE with a quadratic term, similar values for the median spectra were found. Due to the quadratic term, the attenuation model reaches an extremum point. Its numerical value, sat MW , is obtained by deriving the expression of the GMPE in relation to the magnitude, zeroing and solving the equation [23]. Geosciences 2020, 10, 282 13 of 23

For ground type B, an upper limit magnitude must be set for the whole range of periods. sat Unfortunately, MW is in the magnitude range of the dataset analyzed. Therefore, the quadratic term attenuation law for soil type B is q q 2 2 2 2 2 lg(SD) = a + b(MW 6) + d(MW 6) lg D + h + c D + h + εr + εe − − − epi epi (6) use Mw = 7.00 for Mw > 7.00, 0.0 T 4.0s ≤ ≤ For ground type C, for T 0.2 s, M sat is larger than 7.60. For T > 0.2 s, M sat is lower than 6.40. ≤ W W Therefore, the GMPE with quadratic term, for soil type C is q q 2 2 2 2 2 lg(SD) = a + b(MW 6) + d(MW 6) lg D + h + c D + h + εr + εe − − − epi epi use Mw = 7.60 for Mw > 7.60, T 0.20s (7) ≤ use Mw = 6.40 for Mw < 6.40, T > 0.20s

sat In fact, with the exception of spectral periods between 0.2 and 0.4 s, MW is larger than 7.9, so the attenuation model with quadratic term could be extended to this magnitude.

3.2. The Set of High-Quality Digital Records This set includes only digital records from earthquakes with magnitudes in the range 5.2 M 7.1, which occurred at depths between 66 and 135 km in Romania and Japan. After filtering ≤ W ≤ the records according to the procedure described above, the DRS were calculated for periods up to 8.0 s using Seismosignal [38] and ViewWave [40] software. The purpose for which the investigation was pushed to such large period values was to map the area of the spectrum beyond 4 s, where reliable information from the large and moderately analog recorded earthquakes is not available. There is information suggesting that spectral peaks have higher ordinates than those present in the relative displacement spectrum at 2.0 s for large earthquakes and locations in the Romanian Plain. Both seismological (Brune Model) and geotechnical considerations lead to the conclusion that such peaks would be around 5–6 s. Unfortunately, this study could only highlight this to a small extent. Up to 4.00 s, the increment was 0.10 s, then it was set to 0.20 s for periods between 4.0 and 6.0 s and finally, for periods up to 8.00 s, the regression coefficients were determined at a 0.40 s increment. Figure 12 presents the prediction of the DRS for two sites located on ground type B and C, for a MW = 6.0 earthquake.Geosciences The prediction2020, 10, x FOR PEER is compared REVIEW to the computed displacement spectra from the15 of records.25

(a) (b)

Figure 12. Predicted and computed displacement spectra for 27 October 2004 MW = 6.0 earthquake (a) Figure 12. Predicted and computed displacement spectra for 27 October 2004 MW = 6.0 earthquake Onesti station, type B soil; (b) Ramnicu Sarat station, type C soil. (a) Onesti station, type B soil; (b) Ramnicu Sarat station, type C soil. However, the model manages to reasonably predict the spectrum of a record that was not included in this regression dataset, EREN 1986, presented in Figure 13. The reproduced spectrum, according to the GMPE coefficients derived using this dataset, is steeper for this record and yields plateau values larger than those predicted using the GMPE derived using a moderate-strong national set, which was computed directly from the record. The steeper slope is distinctive for records of small magnitude earthquakes, for which this dataset is very rich, whilst the large values in the constant displacement region are due to Japanese records, with a higher displacement demand for the same earthquake magnitude.

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Figure 13. Prediction EREN site (type C soil, Depi = 121 km), 1986 earthquake (MW = 7.1), median values.

It is worth noting that, thanks to the abundance of reliable instrumental data collected from the earthquakes in this dataset, some anomalies were identified. There are significant differences between the spectral ordinates of the computed spectra for sites with a similar epicentral distance and the soil conditions located in Dobrogea versus sites located in Moldova or Romanian Plain. There were also important amplifications (by a factor of three to six) of the ground motion at large distances from the epicenter (Singureni station, 2013 event and Fulga de Sus, Petresti stations, 2004 earthquake).

Geosciences 2020, 10, x FOR PEER REVIEW 15 of 25

Geosciences 2020, 10, 282 14 of 23

After 4.00 s, which is the last period for which the analog records are considered reliable, there are no relevant peaks, just flat zones; probably, earthquakes in this database were not strong enough to excite the layers of sediment that have fundamental periods between 4.0 and 8.0 s. Some records (a) (b) have small peaks around 6–7 s. Spectral values are lower than those corresponding to the first peak, which is aroundFigure 12. 1.20 Predicted s for groundand computed type displaceme C (insteadnt ofspectra about for 2.00–2.3027 October 2004 s for M theW = 6.0 first earthquake set of records). (a) Onesti station, type B soil; (b) Ramnicu Sarat station, type C soil. However, the model manages to reasonably predict the spectrum of a record that was not included in this regressionHowever, dataset, the model EREN manages 1986, to presented reasonably in pred Figureict 13the. Thespectrum reproduced of a record spectrum, that was according not to theincluded GMPE in coe thisffi cientsregression derived dataset, using EREN this 1986, dataset, presented is steeper in Figure for 13. this The record reproduced and yieldsspectrum, plateau valuesaccording larger thanto the those GMPE predicted coefficients using derived the using GMPE this derived dataset,using is steeper a moderate-strong for this record and national yields set, whichplateau was computed values larger directly than those from predicted the record. using Thethe GMPE steeper derived slope using is distinctive a moderate-strong for records national of small magnitudeset, which earthquakes, was computed for directly which from this the dataset record. is Th verye steeper rich, slope whilst is thedistinct largeive valuesfor records inthe of small constant displacementmagnitude region earthquakes, are due for to which Japanese this dataset records, is withvery arich, higher whilst displacement the large values demand in the forconstant the same displacement region are due to Japanese records, with a higher displacement demand for the same earthquake magnitude. earthquake magnitude.

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T, s 0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

FigureFigure 13. Prediction 13. Prediction EREN EREN site site (type (type C C soil, soil,D Depiepi= = 121 km), km), 1986 1986 earthquake earthquake (M (WM =W 7.1),= 7.1), median median values. values.

It is worthIt is worth noting noting that, that, thanks thanks to to the the abundance abundance of reliable reliable instrumental instrumental data data collected collected from from the the earthquakesearthquakes in this in dataset,this dataset, some some anomalies anomalies were we identified.re identified. There There are significantare significant differences differences between the spectralbetween ordinates the spectral of theordinates computed of the spectra computed for spec sitestra with for asites similar with epicentrala similar epicentral distance distance and the soil conditionsand the located soil conditions in Dobrogea located versus in Dobrogea sites locatedversus sites in Moldovalocated in Moldova or Romanian or Romanian Plain. TherePlain. There were also importantwere also amplifications important amplifications (by a factor (by of a threefactor toof three six) ofto thesix) of ground the ground motion motion at largeat large distances distances from the epicenterfrom the epicenter (Singureni (Singureni station, statio 2013n, 2013 event event and and Fulga Fulga de de Sus,Sus, Pe Petrestitresti stations, stations, 2004 2004 earthquake). earthquake). These features were also observed for the 1986 earthquake, for Otopeni station. Possible causes may be local tectonics and the existence of unknown faults or adverse site effects. Locally, these could channel the seismic energy different than estimated through the attenuation model. Nevertheless, the anomalies occur for a rather small number of stations.

3.3. Analysis of the Complete Data Set The set includes all records in the database: 272 pairs of perpendicular horizontal components. With the increase in the number of records (especially those of small magnitude earthquakes, MW = 5.0–6.0), the variability increases. The recorded ground motions of the 4 March 1977 earthquake, which imposes the highest displacement demands, loses its share from the first set (containing only 116 pairs of components), which is reflected in the shape and spectral values generated by this model. Figure 14 shows a prediction of the median displacement spectra corresponding to a seismic event of MW = 7.5, located at an epicentral distance of 150 km; all three sets of regression coefficients for both C and B soils are analyzed. For ground type C, the similarity between the shapes and values of sets one and three (the complete set) to 2.00 s is observed, after which they evolve separately, both having Geosciences 2020, 10, x FOR PEER REVIEW 16 of 25

These features were also observed for the 1986 earthquake, for Otopeni station. Possible causes may be local tectonics and the existence of unknown faults or adverse site effects. Locally, these could channel the seismic energy different than estimated through the attenuation model. Nevertheless, the anomalies occur for a rather small number of stations.

3.3. Analysis of the Complete Data Set The set includes all records in the database: 272 pairs of perpendicular horizontal components. With the increase in the number of records (especially those of small magnitude earthquakes, MW = 5.0–6.0), the variability increases. The recorded ground motions of the 4 March 1977 earthquake, which imposes the highest displacement demands, loses its share from the first set (containing only 116 pairs of components), which is reflected in the shape and spectral values generated by this model. Geosciences 2020Figure, 10, 28214 shows a prediction of the median displacement spectra corresponding to a seismic 15 of 23 event of MW = 7.5, located at an epicentral distance of 150 km; all three sets of regression coefficients for both C and B soils are analyzed. For ground type C, the similarity between the shapes and values peaks atof approximatelysets one and three 2.30 (the s.complete The second set) to set,2.00 containings is observed, only after smallwhich andthey moderateevolve separately, earthquakes, both has a differenthaving spectral peaks shape, at approximately with peaks between2.30 s. The 1.20 second and 1.60set, s.containing only small and moderate earthquakes, has a different spectral shape, with peaks between 1.20 and 1.60 s.

(a) (b)

Figure 14. Prediction of a seismic event with MW = 7.50 and Depi = 150 km, median values, the three Figure 14. Prediction of a seismic event with MW = 7.50 and Depi = 150 km, median values, the three sets (a) soil type B (b) soil type C. sets (a) soil type B (b) soil type C. As pointed out before, the sets two and three, containing large amounts of records from smaller As pointed out before, the sets two and three, containing large amounts of records from smaller earthquakes, have steeper slopes. Dependence on database results is more evident in type B soil for earthquakes,sets one haveand three, steeper where, slopes. although Dependence spectral shapes on database are similar results and reach is more their maximum evident in between type B soil for sets one1.30 and and three, 1.50 s, where, the plateaus although which spectral occur after shapes the peak are are similar at completely and reach different their levels. maximum between 1.30 and 1.50 s,After the plateaus examining which the above occur figures, after the the following peak are conclusions at completely can be didrawn:fferent levels. After• examiningFor Type B soils, the abovethe coefficients figures, of the the following attenuation conclusions model corresponding can be drawn: to the complete set seem to be an appropriate trade-off with respect to the values for the other two groups of records; For• Type B soils, the coefficients of the attenuation model corresponding to the complete set seem • For prediction of DRS generated by very strong earthquakes, MW≥ 7.40, the GMPE with the to be ancoefficients appropriate resulting trade-o fromff thewith regression respect of to the the first values set is closer for the to the other observed two groups data for oftype records; C For predictionsoils. The GMPE of DRS with generated quadratic by term very matches strong both earthquakes, the spectral Mshapes 7.40,and the the maximum GMPE with the • W ≥ coefficientsdisplacement resulting reasonably from thewell regressionand leads to ofgreater the firstdisplacement set is closer demand to than the observedthe one shown data in for type Figure 14. A design spectrum should envelope all relevant shapes, considering the appropriate C soils. The GMPE with quadratic term matches both the spectral shapes and the maximum ordinates of the peaks and the variability, through an appropriate number of standard displacementdeviations. reasonably well and leads to greater displacement demand than the one shown in Figure 14. A design spectrum should envelope all relevant shapes, considering the appropriate ordinates of the peaks and the variability, through an appropriate number of standard deviations.

3.4. Model Testing Once the regression coefficients have been calculated, it is important to check that the data provided by the attenuation law are reliable and whether the attenuation model can generate useful information from a dataset other than that used for regression. An important role in model testing is played by residuals, with quantities resulting from the differences between the recorded values and the values predicted by the attenuation model. Positive values of residual indicate underestimation of the seismic motion amplitudes, with negative ones indicating overestimation. Normalized residuals (NRES) are traditionally defined as Yes µes ε = − (8) σ with ε being the normalized residual, Yes is the logarithm of the amplitude of ground motion recorded during the earthquake e at station s, µes is the logarithm of the median value provided by the GMPE, and σ is the standard deviation of the attenuation model. Figure 15 shows the distribution of normalized residuals for four periods. Geosciences 2020, 10, x FOR PEER REVIEW 17 of 25

3.4. Model Testing Once the regression coefficients have been calculated, it is important to check that the data provided by the attenuation law are reliable and whether the attenuation model can generate useful information from a dataset other than that used for regression. An important role in model testing is played by residuals, with quantities resulting from the differences between the recorded values and the values predicted by the attenuation model. Positive values of residual indicate underestimation of the seismic motion amplitudes, with negative ones indicating overestimation. Normalized residuals (NRES) are traditionally defined as − μ ε = Yes es σ (8)

with ε being the normalized residual, Yes is the logarithm of the amplitude of ground motion recorded Geosciences 2020during, 10, 282 the earthquake e at station s, μes is the logarithm of the median value provided by the GMPE, 16 of 23 and σ is the standard deviation of the attenuation model. Figure 15 shows the distribution of normalized residuals for four periods. Residuals, T0.5s

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(a) (b) Count Count

(c) (d)

Figure 15. DistributionFigure 15. Distribution of normalized of normalized residualsresiduals for fordifferent diff periods,erent periods,data set 3. (a data) T = 0.50 set s; 3.(b) T ( a= ) T = 0.50 s; 1.00 s; (c) T = 1.50 s; (d) T = 2.00 s. (b) T = 1.00 s; (c) T = 1.50 s; (d) T = 2.00 s. Figure 16 presents the distribution of normalized residuals compared to those produced by a Figure 16standard presents normal the distribution distribution using Q-Q of (quantile-quantile) normalized residuals plots. A Q-Q compared plot is a meaningful to those way produced to by a standard normalassess graphically distribution two probability using Q-Q distributions, (quantile-quantile) helping to check plots. that the A two Q-Q populations plot is have a meaningful the way to assess graphically two probability distributions, helping to check that the two populations have the same statisticalGeosciences 2020 distribution., 10, x FOR PEER REVIEW The more normalized the residuals are when approaching18 of 25 the line that passessame through statistical the distribution. origin, the The better more normalized the normal the distribution residuals are when describes approaching the residual the line that distribution. We see a distributionpasses through close the origin, to the the normalbetter the one, normal both distribution in histograms describes andthe residual in the distribution. alignment We of residuals with the line.see a distribution close to the normal one, both in histograms and in the alignment of residuals with the line.

y=x y=x Data Data

(a) (b)

FigureFigure 16. Q-Q 16. Q-Q plot, plot, dataset dataset 3.3. ( (aa) )TT = =0.500.50 s; (b s;) T ( b= )1.00T = s. 1.00 s.

The plots for 1.0, 1.5 and 2.0 s have most of the residuals between −1 and + 1, and they are close to the theoretical distribution. A small part deviates from the expected repartition, usually the ones that are larger than + 1.5. Therefore, there is a small tendency of the GMPE to underestimate the DRS ordinates for those periods, as shown in Figure 17. Keeping in mind that the numerical values of the residuals are reasonably small (smaller than + 2), the deviation could be accepted. Both positive and negative outliers are usually from earthquakes with a low magnitude (5.2, 5.5).

y=x y=x Data Data

(a) (b)

Figure 17. Q-Q plot, dataset 3. (a) T = 1.50 s; (b) T = 2.00 s.

Two quantities can be introduced: the inter-event and the intra-event residuals. Inter-event residuals are calculated [41] using the following equation

Geosciences 2020, 10, x FOR PEER REVIEW 18 of 25

same statistical distribution. The more normalized the residuals are when approaching the line that passes through the origin, the better the normal distribution describes the residual distribution. We see a distribution close to the normal one, both in histograms and in the alignment of residuals with the line.

y=x y=x Data Data

Geosciences 2020, 10, 282 17 of 23

(a) (b) The plots for 1.0, 1.5 and 2.0 s have most of the residuals between 1 and + 1, and they are close − to the theoretical distribution.Figure A small 16. Q-Q part plot, deviates dataset 3. (a) from T = 0.50 the s; (b) expected T = 1.00 s. repartition, usually the ones that are larger thanThe plots+ 1.5. for Therefore,1.0, 1.5 and 2.0 there s have is most a small of the residuals tendency between of the −1 GMPEand + 1, and to underestimatethey are close the DRS ordinates forto those the theoretical periods, distribution. as shown A small in Figure part deviates 17. Keeping from the expected in mind repartition, that the usually numerical the ones values of the that are larger than + 1.5. Therefore, there is a small tendency of the GMPE to underestimate the DRS residuals areordinates reasonably for those small periods, (smaller as shown than in Figure+ 2), 17. the Keeping deviation in mind couldthat the benumerical accepted. values Both of the positive and negative outliersresiduals are are usually reasonably from small earthquakes (smaller than + with2), the adeviation low magnitude could be accepted. (5.2, 5.5).Both positive and negative outliers are usually from earthquakes with a low magnitude (5.2, 5.5).

y=x y=x Data Data

(a) (b)

Figure 17.FigureQ-Q 17. plot,Q-Q plot, dataset dataset 3.3. ( aa) )TT = 1.50= 1.50 s; (b) s; T (=b 2.00) T s.= 2.00 s. Two quantities can be introduced: the inter-event and the intra-event residuals. Inter-event Two quantitiesresiduals are can calculated be introduced: [41] using the following the inter-event equation and the intra-event residuals. Inter-event residuals are calculated [41] using the following equation

N 1 XS Geosciences 2020, 10, x FOR PEER REVIEW δBe = (Yes µes) 19 of 25 (9) Ns − s=1

NS δ =−1 μ where Ns is the number of stations, and YesBYandeesesµesare() previously defined. Intra-event residuals(9) are N = given by s s 1 where Ns is the number of stations, and Yes and μes are previously defined. Intra-event residuals are δWes = Yes (µes + δBe) (10) given by − δμδ=−() + The evaluation of these parameters allowsWYes verification es es B of e the distribution of inter-event(10) residuals with the magnitude and distribution of intra-event residuals with distance. Figure 18 presents the The evaluation of these parameters allows verification of the distribution of inter-event residuals with distributionthe formagnitude two periods and distribution of 0.50 and of 1.00intra-event s, for re thesiduals third with set ofdistance. data andFigure soil 18type presents C. the distribution for two periods of 0.50 and 1.00 s, for the third set of data and soil type C. 0.6 0.8

0.6 0.4

0.4

0.2 0.2

MW MW 0 0 55.566.577.555.566.577.5 Residual Residual

-0.2 -0.2

-0.4

-0.4 -0.6 R2 = 0.000115245 R2 = 0.00223216 -0.6 -0.8 (a) (b)

Figure 18.FigureInter-event 18. Inter-event residuals residuals dependence dependence onon magnitude, magnitude, set 3. set (a) 3. T (=a 0.50) T s;= (0.50b) T =s; 1.00 (b )s. T = 1.00 s.

The correlation between the moment magnitude and the value of the inter-event residuals for both periods is small and can be neglected. This is due to the relatively small number of earthquakes in the set. The digital set has also a negligible correlation with regression lines with minor slopes. Considering the data presented in the literature, the results shown above can be considered satisfactory. Residual Residual

(a) (b)

Figure 19. Dependence with distance of intra-event residuals, set 3. (a) T = 0.50 s; (b) T = 1.00 s.

Geosciences 2020, 10, x FOR PEER REVIEW 19 of 25

NS δ =−1 μ BYeeses() (9) Ns s=1

where Ns is the number of stations, and Yes and μes are previously defined. Intra-event residuals are given by δμδ=−() + WYes es es B e (10) The evaluation of these parameters allows verification of the distribution of inter-event residuals with the magnitude and distribution of intra-event residuals with distance. Figure 18 presents the distribution for two periods of 0.50 and 1.00 s, for the third set of data and soil type C. 0.6 0.8

0.6 0.4

0.4

0.2 0.2

MW MW 0 0 55.566.577.555.566.577.5 Residual Residual

-0.2 -0.2

-0.4

-0.4 -0.6 R2 = 0.000115245 Geosciences 2020, 10, 282 R2 = 0.00223216 18 of 23 -0.6 -0.8 (a) (b) The correlation between the moment magnitude and the value of the inter-event residuals for both periodsFigure is small 18. andInter-event can be residuals neglected. dependence Thisis on due magnitude, to the relativelyset 3. (a) T = small0.50 s; ( numberb) T = 1.00 of s. earthquakes in the set.The The correlation digital set between has also the amoment negligible magnitude correlation and the with value regression of the inter-event lines with residuals minor for slopes. Consideringboth periods the data is small presented and canin be the neglected. literature, This the is due results to the shown relatively above small can number be considered of earthquakes satisfactory. Fromin the Figureset. The 19 digital, one canset has see thatalso a there negligible is no correlationcorrelation betweenwith regression residuals lines and with distance. minor slopes. The above figuresConsidering are representative the data ofpresented the entire in rangethe literature, of periods the covered results byshown the GMPE.above can be considered satisfactory. Residual Residual

(a) (b)

GeosciencesFigureFigure 2020 19., 10Dependence 19., x FORDependence PEER REVIEW with with distance distance of of intra-event intra-event residuals, set set 3. 3. (a () aT) =T 0.50= 0.50 s; (b s;) T (b =) 1.00T = s.1.00 20 of s. 25

WithFrom the valuesFigure 19, of theone residuals,can see that it isthere possible is no correlation to calculate between some statisticalresiduals and parameters distance. byThe which the qualityabove figures of the are attenuation representative relation of the canentire be range assessed. of periods Those covered were by proposed the GMPE. in [42], and they are median ofWith the the normalized values of the residuals residuals, (MEDNR), it is possible mean to calculate of the some normalized statistical residuals parameters (MEANNR) by which and standardthe quality deviation of the of attenuation the normalized relation residuals can be asse (STDNR).ssed. Those Depending were proposed on these in [42], indicators and they and are limit values,median the attenuation of the normalized models residu are groupedals (MEDNR), into fourmean categories of the normalized of confidence, residuals rated (MEANNR) from A (best) and to D standard deviation of the normalized residuals (STDNR). Depending on these indicators and limit (those not recommended to apply). The three statistical indicators are calculated for each period, for values, the attenuation models are grouped into four categories of confidence, rated from A (best) to eachD set (those of data, not recommended and point towards to apply). an A The rating three for statis alltical sets indicators and a large are majority calculated of for spectral each period, periods. forTables each A1set –ofA4 data, present and point the towards coefficients an A rating of the fo GMPEr all sets alongand a large with majority the MEANNR, of spectralMEDNR periods. and STDNR indexesTables A1–A4 for each present spectral the period.coefficients of the GMPE along with the MEANNR, MEDNR and STDNRFigure 20indexes presents for each the distributionspectral period. of the normalized residuals as a function of magnitude. For all periods, theFigure residuals 20 presents are uniformlythe distribution distributed of the normal for allized magnitudes, residuals as except a function for aof minor magnitude. concentration For for 5.2all earthquakesperiods, the forresiduals small periodsare uniformly (0.3–0.5 distri s), asbuted also shownfor all inmagnitudes, Figure 16a. except for a minor concentration for 5.2 earthquakes for small periods (0.3–0.5 s), as also shown in Figure 16a.

3

2

1

0 NRES NRES

-1

-2

MW -3 5.0 5.5 6.0 6.5 7.0 7.5 (a) (b) (c)

FigureFigure 20. 20.Distribution Distribution of of normalized normalized residuals with with magnitude, magnitude, set 3. set (a) 3. T (=a 0.30) T =s; 0.30(b) T s;= 1.00 (b) Ts; =(c)1.00 s; (c) TT= =1.50 1.50 s.

3

2

1

0 NRES NRES NRES

-1

-2

Depi -3 0 50 100 150 200 250 300 350 (a) (b) (c)

Figure 21. Distribution of normalized residuals with epicentral distance, set 3. (a) T = 0.30 s; (b) T = 1.00 s; (c) T = 1.50 s.

The distribution of NRES with respect to epicentral distance is shown in Figure 21. For all periods, the residuals are very uniformly distributed.

The normalized residual’s analysis, both in terms of magnitude and distance, showed that the GMPE provides non-biased estimates of the DRS of the records found in the database.

Geosciences 2020, 10, x FOR PEER REVIEW 20 of 25

From Figure 19, one can see that there is no correlation between residuals and distance. The above figures are representative of the entire range of periods covered by the GMPE. With the values of the residuals, it is possible to calculate some statistical parameters by which the quality of the attenuation relation can be assessed. Those were proposed in [42], and they are median of the normalized residuals (MEDNR), mean of the normalized residuals (MEANNR) and standard deviation of the normalized residuals (STDNR). Depending on these indicators and limit values, the attenuation models are grouped into four categories of confidence, rated from A (best) to D (those not recommended to apply). The three statistical indicators are calculated for each period, for each set of data, and point towards an A rating for all sets and a large majority of spectral periods. Tables A1–A4 present the coefficients of the GMPE along with the MEANNR, MEDNR and STDNR indexes for each spectral period. Figure 20 presents the distribution of the normalized residuals as a function of magnitude. For all periods, the residuals are uniformly distributed for all magnitudes, except for a minor concentration for 5.2 earthquakes for small periods (0.3–0.5 s), as also shown in Figure 16a.

3

2

1

0 NRES NRES

-1

-2

MW Geosciences 2020-3 , 10, 282 19 of 23 5.0 5.5 6.0 6.5 7.0 7.5 (a) (b) (c)

The distributionFigure 20. Distribution of NRES of with normalized respect residuals to epicentral with magnitude, distance set 3. is ( showna) T = 0.30 in s; Figure(b) T = 1.00 21 .s; For(c) all periods, the residualsT = are 1.50 verys. uniformly distributed.

3

2

1

0 NRES NRES NRES

-1

-2

Depi -3 0 50 100 150 200 250 300 350 (a) (b) (c)

FigureFigure 21. Distribution 21. Distribution of of normalizednormalized residuals residuals with with epicentral epicentral distance, distance, set 3. (a) T set = 0.30 3. s; ( a(b)) TT = 0.30 s; 1.00 s; (c) T = 1.50 s. (b) T = 1.00 s; (c) T = 1.50 s. The distribution of NRES with respect to epicentral distance is shown in Figure 21. For all Theperiods, normalized the residuals residual’s are very analysis, uniformly both distributed. in terms of magnitude and distance, showed that the GMPE provides non-biased estimates of the DRS of the records found in the database. FiguresThe 22 normalized and 23 show residual’s the attenuation analysis, both of in the terms model of magnitude with the distance,and distance, along showed with that a comparison the with twoGMPE other provides GMPE non-biased for spectral estimates displacement. of the DRS Unfortunately, of the records found the in two the models database. are calibrated against data from shallow earthquakes. The reference models are Cauzzi and Faccioli [11], presented with an orange dotted line, and Hassani et al. [14], drawn with a blue dashed line. Measured data are shown with blue dots, and are from a M = 6.9 earthquake in Figure 22 and two M = 7.1 earthquakes in Figure 23. The thick red line is the median of the proposed GMPE, the shaded band delimitates a region 1σ. Figure 22 shows the attenuation on type B soil, while Figure 23 displays the model ± on type C soil. For soil class B, the proposed model shows a similar attenuation with GMPE by Hassani et al., especially for periods of 1.0 and 1.5 s, while the Cauzzi and Faccioli model attenuates at a higher rate. For soil class C, the attenuation of the proposed model is higher than for type B soil for epicentral distances larger than 100 km, and almost inexistent for distances less than 100 km for all three studied periods. This is consistent with the attenuation provided by the model of Vacareanu et al. [23], which showed limited or no reduction in spectral acceleration for epicentral distances up to 100 km. It is significantly different than the one corresponding to the other two models. The Cauzzi and Faccioli model is increasingly attenuating with the distance, while Hassani et al. has a rather constant attenuation. The model fits well the measured data for type B soil. For soil type C, for 0.3 and 1.0 s, there is a group of records with virtually the same distance, located in Bucharest, for which the GMPE overestimates the displacement. Bearing in mind the fact that the outlying measured data are very localizedGeosciences and the 2020 whole, 10, x FOR dataset PEER REVIEW is from two earthquakes only, this situation might not be21 of relevant. 25

10 SD, cm

1

0.1 SD-1sigma SD-median SD+1sigma Cauzzi & Faccioli 2008 Hassani et al 2017 Measured

Depi, km 0.01 10 100 (a) (b) (c)

FigureFigure 22. Attenuation 22. Attenuation of the of the model model with with distance distance and co comparisonmparison with with other other models, models, type B type soil, Bset soil, set 3. 3. (a) T = 0.30 s; (b) T = 1.00 s; (c) T = 1.50 s. (a) T = 0.30 s; (b) T = 1.00 s; (c) T = 1.50 s. Figures 22 and 23 show the attenuation of the model with the distance, along with a comparison with two other GMPE for spectral displacement. Unfortunately, the two models are calibrated against data from shallow earthquakes. The reference models are Cauzzi and Faccioli [11], presented with an orange dotted line, and Hassani et al. [14], drawn with a blue dashed line. Measured data are shown with blue dots, and are from a M = 6.9 earthquake in Figure 22 and two M = 7.1 earthquakes in Figure 23. The thick red line is the median of the proposed GMPE, the shaded band delimitates a region ± 1σ. Figure 22 shows the attenuation on type B soil, while Figure 23 displays the model on type C soil. For soil class B, the proposed model shows a similar attenuation with GMPE by Hassani et al., especially for periods of 1.0 and 1.5 s, while the Cauzzi and Faccioli model attenuates at a higher rate. For soil class C, the attenuation of the proposed model is higher than for type B soil for epicentral distances larger than 100 km, and almost inexistent for distances less than 100 km for all three studied periods. This is consistent with the attenuation provided by the model of Vacareanu et al. [23], which showed limited or no reduction in spectral acceleration for epicentral distances up to 100 km. It is significantly different than the one corresponding to the other two models. The Cauzzi and Faccioli model is increasingly attenuating with the distance, while Hassani et al. has a rather constant attenuation. The model fits well the measured data for type B soil. For soil type C, for 0.3 and 1.0 s, there is a group of records with virtually the same distance, located in Bucharest, for which the GMPE overestimates the displacement. Bearing in mind the fact that the outlying measured data are very localized and the whole dataset is from two earthquakes only, this situation might not be relevant.

10 100 SD, cm SD, cm

1 10

0.1 1 SD-1sigma SD-1sigma SD-median SD-median SD+1sigma SD+1sigma Cauzzi & Faccioli 2008 Cauzzi & Faccioli 2008 Hassani et al 2017 Hassani et al 2017

Measured Depi, km Measured Depi, km 0.01 0.1 10 100 10 100 (a) (b) (c)

Figure 23. Attenuation of the model with distance and comparison with other models, type C soil, set 3. (a) T = 0.30 s; (b) T = 1.00 s; (c) T = 1.50 s.

The median values for the total standard deviation are in the range 0.30–0.35 (log10 units) for type B soil, and usually smaller for type C soil. These values are smaller than the ones reported in the literature [11,23], due to the limited number and region-specificity of the records.

Geosciences 2020, 10, x FOR PEER REVIEW 21 of 25

10 SD, cm

1

0.1 SD-1sigma SD-median SD+1sigma Cauzzi & Faccioli 2008 Hassani et al 2017 Measured

Depi, km 0.01 10 100 (a) (b) (c)

Figure 22. Attenuation of the model with distance and comparison with other models, type B soil, set 3. (a) T = 0.30 s; (b) T = 1.00 s; (c) T = 1.50 s.

Figures 22 and 23 show the attenuation of the model with the distance, along with a comparison with two other GMPE for spectral displacement. Unfortunately, the two models are calibrated against data from shallow earthquakes. The reference models are Cauzzi and Faccioli [11], presented with an orange dotted line, and Hassani et al. [14], drawn with a blue dashed line. Measured data are shown with blue dots, and are from a M = 6.9 earthquake in Figure 22 and two M = 7.1 earthquakes in Figure 23. The thick red line is the median of the proposed GMPE, the shaded band delimitates a region ± 1σ. Figure 22 shows the attenuation on type B soil, while Figure 23 displays the model on type C soil. For soil class B, the proposed model shows a similar attenuation with GMPE by Hassani et al., especially for periods of 1.0 and 1.5 s, while the Cauzzi and Faccioli model attenuates at a higher rate. For soil class C, the attenuation of the proposed model is higher than for type B soil for epicentral distances larger than 100 km, and almost inexistent for distances less than 100 km for all three studied periods. This is consistent with the attenuation provided by the model of Vacareanu et al. [23], which showed limited or no reduction in spectral acceleration for epicentral distances up to 100 km. It is significantly different than the one corresponding to the other two models. The Cauzzi and Faccioli model is increasingly attenuating with the distance, while Hassani et al. has a rather constant attenuation. The model fits well the measured data for type B soil. For soil type C, for 0.3 and 1.0 s, there is a group of records with virtually the same distance, located in Bucharest, for which the GMPE Geosciencesoverestimates2020, 10, 282 the displacement. Bearing in mind the fact that the outlying measured data are very20 of 23 localized and the whole dataset is from two earthquakes only, this situation might not be relevant.

10 100 SD, cm SD, cm

1 10

0.1 1 SD-1sigma SD-1sigma SD-median SD-median SD+1sigma SD+1sigma Cauzzi & Faccioli 2008 Cauzzi & Faccioli 2008 Hassani et al 2017 Hassani et al 2017

Measured Depi, km Measured Depi, km 0.01 0.1 10 100 10 100 (a) (b) (c)

FigureFigure 23. Attenuation23. Attenuation of of the the model model with with distance distance and comparison with with other other models, models, type type C soil, C soil, set set 3. (a) T3.= (0.30a) T = s; 0.30 (b) s;T (=b) 1.00T = 1.00 s; ( cs;) T(c)= T 1.50= 1.50 s. s.

TheThe median median values values for for the the total total standardstandard deviation are are in inthe the range range 0.30–0.35 0.30–0.35 (log10 (log10 units) units) for for typetype B soil, B soil, and and usually usually smaller smaller for for type type CC soil.soil. Thes Thesee values values are are smaller smaller than than the theones ones reported reported in the in the literature [11,23], due to the limited number and region-specificity of the records. literature [11,23], due to the limited number and region-specificity of the records.

4. Conclusions Using a database of strong motion records of intermediate depth earthquakes from Romania and Japan, an attenuation model for spectral displacement is developed. The main variables are earthquake magnitude, epicentral distance and soil type. The coefficients of the GMPE are determined for ground types B and C (classified according to Eurocode 8), for periods between 0.10 and 4.00 s with an increment of 0.10 s, and it is applicable for sites located in front of the Carpathian Arc, at epicentral distances between 30 to 300 km. The coefficients were determined through two-stage regression. Using a set of digital strong motion records, a GMPE with coefficients determined up to 8.0 s was created. In order to predict the DRS of very strong earthquakes, a quadratic term was added to the original equation, which significantly improved the prediction of such strong seismic events. As our investigation shows, magnitude and soil type have the largest impact, while the epicentral distance has a smaller influence. Increasing the magnitude or diminishing the epicentral distance leads to a shrinking of the zone with high amplifications. Especially for moderate–strong seismic events, large amplifications were found to occur on type C sites. The models were tested with good results by appraising inter-event and intra-event residuals, according to the relevant scientific literature. Although the present work aims at providing input data for DBD, it is also useful for assessing the displacement demand for seismic design, for a specific earthquake scenario, described by simple parameters, such as ground type, moment magnitude and epicentral distance.

Author Contributions: Conceptualization, P.O. and R.V.; methodology, R.V.; validation, P.O. and R.V.; formal analysis, P.O.; investigation, P.O. and R.V.; resources, P.O. and R.V.; data curation, R.V.; writing—original draft preparation, P.O.; writing—review and editing, P.O.; visualization, P.O.; supervision, R.V.; All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to thank National Research Institute for Earth Science and Disaster Resilience (NIED, http://www.kyoshin.bosai.go.jp/for providing access to K-NET and Kik-net ground motion record databases. The support from Cristian Neagu for vs30—classification of soil types in Romania is deeply acknowledged. The authors would like to express their gratitude for the constructive comments received from three anonymous reviewers who helped us to improve considerably the quality of this article. Conflicts of Interest: The authors declare no conflict of interest. Geosciences 2020, 10, 282 21 of 23

Appendix A

Table A1. Coefficients of the GMPE for set 1, Equation (1), ground type B

2 2 2 T (s) a b c h σr σe σ Meannr Mednr Stdnr 0.20 0.9743 0.4724 5.39 10 4 85.2 5.78 10 2 1.37 10 2 7.15 10 2 0.0304 0.0943 0.9110 × − × − × − × − 0.40 2.3198 0.5288 2.20 10 3 198.2 6.71 10 2 6.64 10 3 7.38 10 2 0.0414 0.0750 0.9411 − × − × − × − × − 0.60 1.9598 0.5393 8.33 10 4 105.8 1.12 10 1 2.48 10 3 1.14 10 1 0.0123 0.0605 0.9680 − × − × − × − × − 0.80 1.9577 0.5734 4.98 10 4 102.1 1.06 10 1 1.99 10 3 1.08 10 1 0.0089 0.0544 0.9637 − × − × − × − × − 1.00 1.8047 0.5086 5.82 10 4 59.6 1.04 10 1 1.13 10 2 1.15 10 1 0.0404 0.0896 0.9163 × − × − × − × − 1.50 1.9139 0.5507 3.91 10 4 52.8 8.72 10 2 6.62 10 3 9.38 10 2 0.0264 0.0738 0.9369 × − × − × − × − 2.00 2.0080 0.4867 3.40 10 4 54.8 7.55 10 2 1.70 10 2 9.26 10 2 0.0709 0.2011 0.8895 × − × − × − × − 2.50 2.1979 0.3974 1.02 10 4 64.1 6.25 10 2 2.33 10 2 8.59 10 2 0.0994 0.1528 0.8700 − × − × − × − × − 3.00 2.2554 0.3990 3.15 10 4 70.2 5.48 10 2 2.61 10 2 8.10 10 2 0.1131 0.1188 0.8616 − × − × − × − × − 4.00 2.4494 0.3673 6.72 10 4 103.0 7.30 10 2 1.46 10 2 8.76 10 2 0.0691 0.0614 0.9025 − × − × − × − × −

Table A2. Coefficients of the GMPE for set 1, Equation (1), ground type C.

2 2 2 T (s) a b c h σr σe σ Meannr Mednr Stdnr 0.20 1.0593 0.5428 3.93 10 4 102.9 4.08 10 2 1.60 10 2 5.67 10 2 0.0534 0.0326 0.9321 − × − × − × − × − 0.40 1.6011 0.7340 7.56 10 4 112.7 4.29 10 2 3.19 10 3 4.61 10 2 0.0211 0.0292 0.9278 − × − × − × − × − 0.60 2.2368 0.8472 2.93 10 3 137.3 4.15 10 2 1.91 10 2 6.07 10 2 0.0502 0.1198 0.8650 − × − × − × − × − 0.80 2.1411 1.0527 2.79 10 3 126.3 4.20 10 2 1.09 10 2 5.29 10 2 0.0039 0.0290 0.8338 − × − × − × − × − 1.00 1.7332 1.1249 1.18 10 3 62.5 3.42 10 2 3.75 10 2 7.17 10 2 0.0722 0.1226 0.8098 − × − × − × − × − 1.50 2.5936 1.1916 3.63 10 3 155.6 4.96 10 2 1.27 10 2 6.23 10 2 0.0606 0.0235 0.7777 − × − × − × − × − 2.00 2.2520 1.2897 2.83 10 3 103.4 4.90 10 2 3.84 10 2 8.74 10 2 0.1454 0.1444 0.7392 − × − × − × − × − 2.50 2.1502 1.2317 2.00 10 3 81.7 4.52 10 2 6.80 10 2 1.13 10 1 0.2015 0.1721 0.7079 − × − × − × − × − 3.00 2.2834 1.0479 1.70 10 3 88.9 5.57 10 2 6.86 10 2 1.24 10 1 0.1907 0.1798 0.7256 − × − × − × − × − 4.00 2.3475 0.8141 1.30 10 3 90.7 6.84 10 2 4.72 10 2 1.16 10 1 0.1346 0.2371 0.7931 − × − × − × − × −

Table A3. Coefficients of the GMPE for set 3, Equation (1), ground type B.

2 2 2 T (s) a b c h σr σe σ Meannr Mednr Stdnr 0.20 1.0841 0.5578 2.23 10 4 88.3 8.15 10 2 3.76 10 2 1.19 10 1 0.0336 0.0661 0.8095 − × − × − × − × − 0.40 1.5353 0.6640 4.13 10 4 90.0 1.03 10 1 3.47 10 2 1.38 10 1 0.0484 0.0169 0.8504 − × − × − × − × − 0.60 1.7131 0.6964 5.89 10 4 80.9 1.19 10 1 2.52 10 2 1.44 10 1 0.0323 0.0618 0.8826 − × − × − × − × − 0.80 1.7831 0.7259 3.70 10 4 78.4 1.12 10 1 4.62 10 2 1.58 10 1 0.0221 0.0008 0.8135 − × − × − × − × − 1.00 1.6559 0.7388 3.97 10 4 49.1 1.08 10 1 4.19 10 2 1.50 10 1 0.0205 0.0369 0.8197 × − × − × − × − 1.50 1.7453 0.8348 5.91 10 6 51.2 8.64 10 2 3.68 10 3 9.00 10 2 0.0107 0.1041 0.9654 − × − × − × − × − 2.00 1.7491 0.8445 5.95 10 5 52.0 8.04 10 2 3.63 10 2 1.17 10 1 0.0733 0.2136 0.8254 − × − × − × − × − 2.50 1.8158 0.8383 3.87 10 4 62.6 6.95 10 2 5.32 10 2 1.23 10 1 0.1175 0.1905 0.7903 − × − × − × − × − 3.00 1.8308 0.8688 5.16 10 4 68.4 6.50 10 2 5.79 10 2 1.23 10 1 0.1359 0.2026 0.7784 − × − × − × − × − 4.00 1.8552 0.8807 5.74 10 4 80.9 7.61 10 2 6.92 10 2 1.45 10 1 0.1532 0.2343 0.7880 − × − × − × − × −

Table A4. Coefficients of the GMPE for set 3, Equation (1), ground type C

2 2 2 T (s) a b c h σr σe σ Meannr Mednr Stdnr 0.20 3.0994 0.6661 5.70 10 3 278.0 4.47 10 2 3.08 10 2 7.55 10 2 0.0610 0.2030 0.9760 − × − × − × − × − 0.40 6.9703 0.8816 1.00 10 2 483.3 4.16 10 2 5.17 10 2 9.34 10 2 0.1374 0.3661 0.9482 − × − × − × − × − 0.60 9.1643 0.9443 1.26 10 2 534.6 3.82 10 2 7.56 10 2 1.14 10 1 0.0743 0.1374 0.8699 − × − × − × − × − 0.80 3.5193 1.0032 5.55 10 3 239.0 4.33 10 2 8.46 10 2 1.28 10 1 0.0086 0.0062 0.8242 − × − × − × − × − 1.00 2.8424 1.0528 4.04 10 3 169.3 3.99 10 2 9.75 10 2 1.37 10 1 0.0835 0.0959 0.8115 − × − × − × − × − 1.50 3.3158 1.1715 5.05 10 3 205.3 4.37 10 2 7.10 10 2 1.15 10 1 0.0748 0.1774 0.8594 − × − × − × − × − 2.00 3.0047 1.2101 4.54 10 3 177.3 4.15 10 2 5.09 10 2 9.24 10 2 0.0080 0.1074 0.9204 − × − × − × − × − 2.50 2.8699 1.2264 4.20 10 3 167.4 4.10 10 2 5.52 10 2 9.63 10 2 0.0166 0.1358 0.9195 − × − × − × − × − 3.00 2.7517 1.2277 3.79 10 3 165.2 4.73 10 2 5.38 10 2 1.01 10 1 0.0133 0.0967 0.9319 − × − × − × − × − 4.00 2.9025 1.2132 4.11 10 3 187.1 5.49 10 2 5.50 10 2 1.10 10 1 0.0208 0.0342 0.9336 − × − × − × − × − Geosciences 2020, 10, 282 22 of 23

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