Journal of JSCE, Vol. 3, 160-173, 2015 (Originally published in Journal of Society of Civil Engineers, Ser. A1, Vol. 70, No. 3, 346-358, 2014 in Japanese)

AN EXPRESSION OF THE SEISMIC INTENSITY LEVEL FOR LONG-PERIOD GROUND MOTION

Akira SAKAI1

1Member of JSCE, Associate Professor, Dept. of Civil Eng. and Architecture, Saga University (Honjo 1, Saga 840-8502, Japan) E-mail: [email protected]

The long-period ground motion scale of the Japan Meteorological Agency (JMA), which is divided into four classes depending on the maximum velocity response spectrum, is tried for long-period ground mo- tion, although the seismic intensity scale with ten classes based on the instrumental seismic intensity is used. The present study proposes the long-period ground motion scale by using a long-period seismic in- tensity level with the intermediate characteristics of velocity and displacement. The long-period seismic intensity level based on the seismic intensity level is obtained for the maximum value to have a correlation between the long-period ground motion scale of the JMA. Not only the design of the long-period ground motion waveform, but also the observed seismic waves are used for comparison with the long-period seismic intensity level and various seismic intensity levels, as well as the maximum velocity response spectrum.

Key Words : seismic intensity, velocity, displacement, long-period seismic intensity level, long-period strong ground motion

1. INTRODUCTION 1996 fundamentally accords with the approach of the original scale. The following revisions are pointed Most of the seismic intensity scales for expressing out: 1) the three time histories of acceleration in three the degree of shaking at each ground surface during directions, which add the vertical to the two hori- are classified into twelve classes of in- zontal directions, are used; 2) the acceleration of the tensity, such as the Modified Mercalli scale (MM in long-period region is evaluated somewhat higher the United States and Korea), Medvedev-Sponheuer- than that of the original seismic intensity; and 3) the Karnik scale (MSK in CIS countries, Russia, East evaluation method considering the duration of the European countries, , , etc.) and European acceleration is introduced. The instrumental seismic Macroseismic scale (EMS in European countries). intensity, however, is considered as mainly corre- For these seismic scales, the Japan Meteorological sponding to the short-period band up to about one Agency (JMA) defines ten classes of seismic inten- second, in order to cut the long-period wave through sity1). From April 1996 in Japan, only the automatic the low-cut filter. It is well known that the seismic measurement by the instrumental seismic intensity intensity does not correspond to the damage of var- meter has been carried out, thereby abolishing the ious structures with a wide range of frequency conventional manner of observation based on human characteristics5). To express seismic intensity that perception and behavior of the surroundings. The considers the effect of medium or long period over original instrumental seismic intensity was proposed one second, as well as the combined seismic intensi- on the basis of the Kawasumi formula2) denoted by an ties obtained from a velocity waveform and a dis- acceleration. Moreover, the instrumental seismic placement waveform6), 7), a method using each peri- intensity specifically uses filtered accelerations to odic band of velocity response spectrum8) and a which both high-cut and low-cut filters, as well as a method based on the velocity response of a sin- filter corresponding to the effect of the seismic pe- gle-degree-of-freedom system9) are proposed. The riod, which has the intermediate characteristics of effective evaluation methods of the long-period acceleration and velocity, are considered. The pre- seismic motion are also discussed10). Furthermore, sent instrumental seismic intensity3), 4) improved in the existing methods of expressing the time histories of seismic intensity are as follows: 1) instantaneous

160 instrumental seismic intensity (IISI) for arbitrary Low cut (F (f))(α=0.5) 11) a3 Instrumental seismic duration of the time window , and 2) real-time 10 High cut (Fa2(f)) intensity seismic intensity (Ir) defined by using an approxi- Period effect (F a1(f)) λ mating filter in the time domain instead of the orig- in Total ( a(f)) 12) λa(f)=Fa1(f)Fa2(f)Fa3(f) inal filter in the frequency domain . 1 The seismic intensity level (LFs) using the running f0 =0.5Hz r.m.s. method that can express the time histories of seismic intensity is proposed by the author13). The (a) 0.1 maximum value of the seismic intensity level 0.01 0.1 1 10 (LFs)max, has a good coincidence with the instrumen- # tal seismic intensity. The seismic intensity levels F a3(f)*Fa4(f) α=-0.5 10 # 3 α corresponding to velocity and displacement are also F a3(f)={1-exp(-(f/f0) )} α=-0.17 # suggested and clarify the concern with filter proper- in Total (λ a(f)) # # λ a(f)=Fa1(f)Fa2(f)F a3(f)Fa4(f) ties of the instrumental seismic intensity based on Weighting factor of acceleration 1 acceleration14). f0 =0.5Hz In recent years, the long-period ground motion, α=0.17 which has large influence on the shaking of tall (b) buildings and tanks, has attracted attention, and a 0.1 0.01 0.1 1 10 presentation of the degree of shaking is required. The Period (s) JMA has presented four classes of long-period ground motion using the maximum value of the ab- Fig.1 Weighting factor of acceleration. solute-velocity response spectrum, and the present trial is carried out15). The paper will clarify the rela- tion between the maximum absolute-velocity re- sponse spectrum and the seismic intensity level cor- period; and 3) the amplitude of a vector acceleration responding to velocity proposed by the author14). used in the instrumental seismic intensity was de- Futhermore, a new long-period seismic intensity termined using not a maximum value but a value level that uses the seismic intensity level having the corresponding to the duration time of 0.3 second. The middle quality of velocity and displacement is also filtered acceleration for the instrumental seismic proposed to present the long-period ground motion, intensities was obtained by using three filter func- and compared with the long-period ground motion tions on the frequency, f, in the following equations. scale of the JMA. The long-period ground motion 1) Filter on the period effect: Fa1(f) acceleration waveform of "Tentative measures of 1/ 2 Fa1 ( f )  1/ f (1) long-period ground motion in high-rise buildings, 2) High-cut filter: Fa2(f) etc." (Ministry of Land, Infrastructure, Transport and 16) Tourism) was used to investigate the long-period Fa2 ( f )  1/ 2 seismic intensity level in the paper. 1 0.694X 2  0.241X 4  0.0557 X 6      8 10 12  0.009664 X  0.00134 X  0.000155 X  2. EXPRESSION OF THE SEISMIC IN- X = f / fc ( fc = 10Hz) (2) TENSITY FOR A WIDER PERIOD 3) Low-cut filter: Fa3(f) 14) 3 1/ 2 RANGE Fa 3 ( f )  1  exp( ( f / f 0 ) )  (3) where f0 is the lower limit of frequency used for the (1) Filtering of the instrumental seismic intensity calculation of seismic intensity. The value of f0 for and the revision of the low-cut filter the present instrumental seismic intensity is 0.5Hz. The instrumental seismic intensity on the basis of The weighting factor λa (f) (in total), which multi- the Kawasumi formula2) uses filtered acceleration, plied these three filters in the instrumental seismic which consider the effect of the period to conform intensity, is given as follows: with the conventional manner of measuring seismic a ( f )  Fa1( f )Fa2 ( f )Fa3 ( f ) (4) intensity through human perception. The calculation First, the calculation of the present instrumental method for the instrumental seismic intensity had seismic intensity carries out the Fourier transform of 3), 4) three main areas of improvement in 1996 as fol- acceleration in three directions, then the Fourier lows: 1) three components, which added the vertical spectrum is revised by using the weighting factor λa component, were used as the time histories of accel- (f). Next, the three time histories of the filtered ac- eration; 2) the period region affecting the seismic celeration obtained by the inverse Fourier transform intensity was expanded, to some extent, to the long

161 are synthesized as a vector acceleration. Finally, a and displacement waveforms or the velocity re- value in which the accumulated time for acceleration sponse spectrum6), 7), 8), 9), which consider the medi- larger than a0 is 0.3 second in the time history is um- and long-period zones besides the instrumental calculated. The instrumental seismic intensity, I, is seismic intensity and also the time history expression 11), 12), 13) given by the following equation using the value of a0. of seismic intensity , are proposed. The

I  2loga0  0.94 (5) seismic intensity level obtained with the application The filter characteristic of the instrumental seismic of the running r.m.s. method to the same frequen- intensity shows a decreasing tendency in the period cy-weighted acceleration as the instrumental seismic 13) side longer than 1.6 seconds by the low-cut filter, intensity is proposed by the author . The seismic intensity level can express the time history of the Fa3(f), as shown in Fig.1(a). Therefore, the seismic intensity will have a low value in the period side seismic intensity, and the time domain of integration longer than 1.6 seconds. used for the running r.m.s. method can be set as an A revised low-cut filter, which introduced a new arbitrary value. The outline of the seismic intensity parameter, α, was suggested by the author to change level follows. the effect of the low-cut filter arbitrarily on the fil- In general, the running r.m.s. method is applied to tered acceleration for the longer period region14). the evaluation of an intermittent impulse and a tran- F # ( f )  1 exp(( f / f )3 )  (6) sitional vibration. The seismic intensity level pro- a3 0 posed by applying the running r.m.s. method uses the The parameters α, ƒ show a decreasing rate of the 0 weighted r.m.s. acceleration A (t ) of the follow- filter for the period. However, the curve, which Fcom 0 ing equation, using the vector acceleration a that multiplied the three filters of Eq.(1), Eq.(2), and Fcom adds the filtered accelerations in NS, EW, and UD Eq.(6), has an increasing tendency for the period directions obtained by the same filtering as the in- within the range of α smaller than 0.17, as shown in strumental seismic intensity. Fig.1(b). The primary natural period of most 1/ 2 t long-period structures such as a very tall building and  1 0 2  AFcom (t0 )   a Fcom (t)dt  (9) t  the sloshing of an oil storage tank is considered to   0  last about 10 seconds, although the extremely long where τ: integral time of the running average; t: time; period of about 20 seconds is assumed in a long-span and t0: observation time (instantaneous time). Also, bridge. In the paper, the ninth Butterworth filter the r.m.s. acceleration Acom(t0) without frequency (cutoff frequency 0.1Hz) is used to decrease the ef- filtering is given by using the non-filtered vector fect of the long-period region longer than about 10 acceleration acom, as well as Eq.(9). The seismic in- seconds. tensity acceleration level Lis and the seismic intensity 1/ 2 2n level LFs are defined respectively so that they may be F ( f )  1/ 1 f / f (n=9, fc1=0.1Hz) (7) a4 c1 expressed with the same form as the instrumental Therefore, the weighting factor tends to decrease seismic intensity by using A (t ) and A (t ) in- rapidly in the period longer than 9 seconds. The com 0 Fcom 0 # stead of the acceleration, a0, in the following equa- weighting factor λ a (f) from which only the low-cut tions: filter differs is given in the following equation unlike Lis (t0 )  2log10 Acom (t0 )  1.25 (10) the weighting factor λa (f) (Eq.(4)) of the present in- strumental seismic intensity. LFs (t0 )  2log10 AFcom (t0 )  1.25 (11) # ( f )  F ( f )F ( f )F # ( f )F ( f ) (8) where the value of 1.25 is a value when the correla- a a1 a2 a3 a4 tion with the (L ) in the integral time τ of 2 sec- where F (f) is used in the range of α smaller than Fs max a4 onds and the instrumental seismic intensity is the 0.17. Although the peak of the weighting factor is highest. 1.17 (period 1.6 seconds) in the instrumental seismic The instrumental seismic intensity evaluates the intensity (α=0.5), the value of the peak changes to a seismic intensity low in the medium- and long-period constant value of 1.41 (period longer than 8.0 sec- regions as already pointed out, though the filter on onds) for α=0.17 as shown in Fig.1(b) (ƒ =0.5). The 0 the period effect in Eq.(1) with the inclination of 0.5 weighting factor in the value of α smaller than 0.17 in the logarithm of the period is used and has the uses the ninth Butterworth filter to avoid an in- intermediate characteristic of acceleration and ve- creasing tendency in the long period, and shows the locity. The filtering that evaluates the influence of peak value of 6.03 (α=-0.17) and 26.8 (α=-0.50), velocity and displacement is not enough considering respectively, in 9.0 seconds. the use of low-cut filter in Eq.(3). For this reason, the

seismic intensity calculated by the weighting factor (2) Seismic intensity levels with various weighting λ# (f) of Eq.(8) using the filter F# (f) instead of F (f) factors of acceleration a a3 a3 was examined by the author14) as the reassessment of The various seismic intensities using the velocity the medium- and long-period regions. The parameter

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α (<0.17) of F # (f) in Eq.(6) has an important rela- a3 λ (f), m=1.0, Tav =1.40 s # av tion to the weighting factor λ (f) from the gradient m λ (f), m=2.0, Tad =1.68 s a 10 ad of the period T and the filter on the period effect, y(T) λap(f), m=1.5, Tap =1.65 s # (=Fa1(f)F a3(f)), in the logarithm. Here, the gradient Instrumental seismic m at T→∞ is given by the following relation as a intensity, λa(f) 1 function of α. f0 = 0.5 Hz m  0.5  3 (12) The weighting factors of acceleration corresponding 0.1 to velocity and displacement will correspond to the value of gradient m of 1 for velocity and 2 for dis- placement. The values of α are -0.17 (m =1) and -0.5 0.01 (m =2), respectively. Thus, a new filter on the period Weighting factor of acceleration 0.1 1 10 effect will be introduced by using the asymptotic line, Period (s) Fig.2 Influence of the gradient m on the weighting factor of Ffa (f), which has the arbitrary gradient m to the filter acceleration. of y(T). The new filter Ffa (f) is given by the following equation, assuming that F (f) coincides with y(T) at fa the long period T (=Tb ), and that the period is de- noted by Ta when the value of Ffa(f) is equal to one. Figure 2 shows the effects of the gradient m on the m weighting factor of acceleration. The weighting F fa ( f )  (T / Ta ) (m > 0) (13) factors, λ (f) and λ (f), corresponding to the velocity where T is obtained by using α, T (=1/f ), m and T . av ad a 0 0 b (m=1) and the displacement (m=2) are given by  1   1  3 m Eqs.(17) and (18) with the periods, Tav of 1.40 and Tad Ta  Tb 2m  1 exp T0 /Tb (14) of 1.68 seconds, respectively. In addition, the A weighting factor λfa (f) of acceleration that uses the weighting factor λap(f), using the period Tap of 1.65 filter Ffa (f) on the period effect y(T) with an arbitrary # seconds in case Ffa(f) with m=1.5 is equal to one, can gradient m is expressed in contrast with λ a (f) in Eq.(8). be interpreted as having the intermediate character- istics of velocity and displacement. The weighting  fa ( f )  F fa ( f )Fa2 ( f )Fa4 ( f ) (15) factor λfa(f) with arbitrary gradient m in the logarithm where both the high-cut filter F (f) and the low-cut a2 is shown to be turning on the point at the period T0 filter F (f) are assumed to be the same filters as that a4 (=1/f0) as described in the following. The value of of λ# (f). a Ffa(f) in the frequency f0 (=1/T0) of Eq.(13) is given The seismic intensity level Lfa using λfa (f) as the by the following equation without depending on the weighting factor of acceleration instead of λ (f) is a value of m, when Ta in Eq.(14) disregards the high given as follows: 2 terms more than (T0/Tb) using Maclaurin’s theorem. m L fa  2logAFcom fa 1.25 (16) F fa ( f 0 )  (T0 / Ta ) where (AFcom)fa is the weighted r.m.s. acceleration m   1    using the weighting factor λfa (f).  1       2m  3 m  The weighting factors, λ (f) and λ (f), using the  T0 / Tb T0 /Tb  T0 av ad    filter Ffa (f) corresponding to the velocity (m=1) and    the displacement (m=2) are given by using the value, (21) Tav and Tad, of the period in case Ffa(f) with m=1 and 2 The rotation point of the weighting factor λfa (f) is are equal to one. (2.0, 1.41) at the frequency f0 of 0.5Hz, and moves to av ( f )  T /Tav Fa2 ( f )Fa4 ( f ) (17) the right side with the decreasing value of f0. The  ( f )  T /T 2 F ( f )F ( f ) (18) value of f0 in the paper uses the same value of 0.5Hz ad ad a 2 a 4 as the instrumental seismic intensity, though the The seismic intensity level, L and L , using these Fav Fad seismic intensity levels corresponding to velocity factors are expressed, respectively, as follows: and displacement show small values so as to lower LFav  2log AFvcom 1.25 (19) the value of f0. L  2log A 1.25 (20) Fad Fdcom In addition, the seismic intensity levels Lfv and Lfd where AFvcom and AFdcom are the weighted r.m.s. ac- for the waveforms of velocity and displacement can * celeration using the weighting factors, λav(f) and be expressed by the weighted r.m.s. velocity v and * λad(f). However, it has been noted that a long-period the weighted r.m.s. displacement d using the component will be overestimated by increasing the high-cut filter Fa2(f) similar to that of the instru- value of gradient m, when the noise on the mental seismic intensity and the low-cut filter Fa4(f). long-period region is contained in a comparatively The equations are as follows14): small-scale observation .

163 7 7 The 2011 off the Pacific coast The Mid Niigata Prefecture (a) Funehiki (FKS008) (K-NET) of Tohoku Earthquake in 2004 6 The 2011 off the Pacific coast 6 (a1) (a2) Fad of Tohoku Earthquake LFs

,L 5 5 LFav max Fav LFad ) Fs 4 ,L 4 Fs 3 3 K-NET K-NET (500 points) (211 points) 2 2 3 4 5 6 7 2 3 4 5 6 7

2 Maximum seismicintensity level, (L 0 50 100 150 200 Instrumental seismic intensity, I Instrumental seismic intensity, I 7 7 Naruko (MYG005) The 2011 off the Pacific coast The 2011 off the Pacific coast The Mid Niigata Prefecture (b) of Tohoku Earthquake Earthquake in 2004 (K-NET) of Tohoku Earthquake 6 6 (b1) (b2) max ) 5 5 Fad ,(L 4 4 max K-NET K-NET ) (500 points) (211 points) Seismic intensity level, intensity Seismic L L Fav Fs 3 3 LFav (LFav ) max (LFav ) max (LFad ) max (LFad ) max LFad 2 2 2 3 4 5 6 7 2 3 4 5 6 7 0 50 100 150 200 Maximum seismic intensity level, (L Maximum seismic intensity level, Maximum seismic intensity level, Time (s) (LFs)max (LFs)max Fig.3 The time history of seismic intensity level, LFs, LFav, LFad. Fig.5 Comparison between the instrumental seismic intensity and the maximum seismic intensity levels.

1000 (a) Funehiki Non-filtered acc. (FKS008) Filtered acc.( λa) the other hand, the values of (LFav)max and (LFad)max at 500 The 2011 off the Pacific coast (cm/s) of Tohoku Earthquake the Naruko observation point in Fig.3(b), are oppo- sitely larger than the value of (LFs)max. The relative 0 relation of these three seismic intensity levels LFs, 1000 (b) Naruko (MYG005) LFav, and LFad can be associated with the Fourier spectrum of the weighted acceleration. Figures 4(a) Non-filtered acc. 500 Filtered acc.( λa) and 4(b) compare the Fourier spectrum of the fre- quency-weighted acceleration used to calculate these 0 seismic intensity levels. The filtered acceleration

Fourier spectrum of acceleration of spectrum Fourier 0.1 0.5 1 5 10 used λa (f) at Funehiki in Fig.4(a) shows the largest Period (s) spectrum at the short period of 0.3 second, and the Fig.4 Comparison of the Fourier spectrum of acceleration. large spectrum has not appeared in the medium- or long-period region. That is, the seismic intensity * levels LFav and LFad corresponding to velocity and L fv  2logv  2.55 (22) displacement at Funehiki are smaller than LFs, from * (23) L fd  2logd  3.54 which the values of LFav, LFad indicate small value in

It is confirmed that the seismic intensity levels, Lfv the case of the seismic wave having a predominant and Lfd, indicate almost the same value as the seismic period in the short period. On the contrary, there is intensity levels LFav and LFad using the weighting the predominant period at Naruko in Fig.4(b) near factors of acceleration corresponding to velocity and 2.0 and 3.5 seconds, and the seismic intensity level displacement. shows a large value in the order of LFs, LFav, and LFad Figures 3(a) and 3(b) show an example of three as shown in Fig.3(b). kinds of seismic intensity levels, LFs, LFav, and LFad, The relationship between the instrumental seismic obtained by the above-mentioned calculation method intensity I and the maximum seismic intensity level (Funehiki (FKS008), Naruko (MYG005), K-NET: (LFs)max is shown in Figs.5(a1) and 5(a2), for seismic the 2011 off the Pacific Coast of Tohoku Earth- waves17) observed in the ground surface on the 2011 quake)17). The maximum seismic intensity levels, off the Pacific Coast of Tohoku Earthquake (K-NET: (LFav)max and (LFad)max, corresponding to velocity and 500 points) and the Mid-Niigata Prefecture Earth- displacement, at the Funehiki observation point in quake in 2004 (K-NET: 211 points). The correlation Fig.3(a), show the values of 5.0 and 4.7, which are of I and (LFs)max is very high for both earthquakes. smaller than the value of 5.6 for (LFs)max as almost the Figures 5(b1) and 5(b2) show the relationship be- same value of the instrumental seismic intensity. On tween the maximum seismic intensity levels,

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(LFav)max, (LFad)max, and (LFs)max. The maximum seis- Table 1 Long-period ground motion scale based on the maxi- mic intensity level (LFav)max has a smaller value than mum absolute velocity response spectrum, (Sva)max, that of (LFs)max in most observation points in the (JMA). Mid-Niigata Prefecture Earthquake. On the other Long-period ground Absolute velocity response spectrum, S (h=5%) hand, the maximum seismic intensity levels, (LFav)max va motion scale (Period, T: 1.5s

3. PROPOSAL OF A SEISMIC INTEN- Table 2 List of eleven points used as an object of long-period SITY LEVEL FOR LONG-PERIOD ground motion. GROUND MOTION Location Calculated seismic waves Reference Tonan Linkage Miyagi Representative Tokai (1) Long-period ground motion scale of the Region Area point & -kai (Tonan -oki point in the area Latit ude Longitude Earth- notation Earth- -kai→ Earth- Japan Meteorological Agency (JMA) quake quake Tokai) quake Shinjuku ward office The long-period ground motion scale of the Japan KGIN 35.6939 139.6922 ○○ ○ ○ (Tokyo) 15) Area 1 Meteorological Agency is divided into four stages TKY007 Shinjuku (Tokyo) 35.7107 139.6859 ○○ ○ ○ as long-period indices, from the behavioral difficul- Chiyoda ward office E4E 35.6897 139.7550 ○○ ○ ○ Kanto (Tokyo) Area 2 ties of a person to the damage caused by migration region TKY027 Mizue (Tokyo) 35.6926 139.8912 ○○ ○ ○ and fall such as fixtures and furnitures, etc., in Area 3 E56 Yokohama city hall 35.4397 139.6533 ○○ ○ ○ high-rise buildings during a natural period from al- Area 4 E62 Chiba city hall 35.6031 140.1050 ○○ ○ ○ most 1.5 to 8 seconds. The value for the scale divi- Midori ward office Area 5 AIC004 35.0635 136.9737 ○○ ○ - (Nagoya city) sion uses the maximum absolute velocity response Tokai Area 6 NAG Nagoya city hall 35.1647 136.9681 - region ○○ ○ spectrum (Sva)max (h=5%) in the period of 1.6 to 7.8 Area 7 AIC003 Tushima city hall 35.1732 136.7404 ○○ ○ - seconds, which is obtained from the observation data Sakai ward office Area 8 OSK006 34.5894 135.4711 ○○ ○ - kansai (Sakai city) of the seismograph installed on the ground. The region Konohana ward office Area 9 OSKH02 34.6627 135.3897 ○○ ○ - (Osaka) boundary values of (Sva)max in each class are 5cm/s, 15cm/s, 50cm/s, and 100cm/s as shown in Table 1.

The index, which used the maximum velocity re- sponse spectrum in a long-period ground motion, is three subduction-zone earthquakes (Tokai Earth- an effective method for evaluating the shaking of quake (Mw8.0), Tonankai Earthquake (Mw8.1), and high-rise buildings, etc., in noting the maximum Miyagi-oki Earthquake (Mw7.6)) are dealt with as response value of the structure with various natural object earthquakes. The time history waveform of the periods. In the paper, however, the maximum seismic long-period earthquake ground motion for design is intensity level corresponding to the velocity is dis- calculated on the basis of both acceleration response cussed as a new expression of the seismic intensity spectrum at engineering bedrock in each observation for a long-period ground motion through the clarifi- point and the average and standard deviation of cation of the relation of the (Sva)ma with the average group delay time. For more detailed content, the value of the velocity response spectrum for the wider reference to the above-mentioned tentative measures period of 1.5 to 8 seconds. will be recommended. The long-period ground mo- tion waveform used for the present study is obtained (2) A new seismic intensity level for long-period by using “ARTEQ-LP,” the software for the ground motion long-period ground motion seismic wave evaluation 18) The acceleration waveform of the long-period of Kozo Keikaku Engineering Inc. . Table 2 shows ground motion used for the present study is calcu- eleven reference points as the target of long-period lated based on “Tentative measures of long-period ground motion for this study in the three regions of ground motion in high-rise buildings, etc.” of the Kanto, Tokai, and Kansai divided into nine areas. As Ministry of Land, Infrastructure, Transport and the object earthquake, not only Tokai Earthquake, Tourism16). In the tentative measures, the procedure Tonankai Earthquake, and Miyagi-oki Earthquake of calculating an acceleration waveform including but also linkage-type earthquake (Tonankai Earth- the wider period of 0.1 to 10 seconds is summarized quake-Tokai Earthquake, delay time 65.4 seconds) for aseismatic design of high-rise buildings, and are used. The acceleration waveform for these

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100 (a) Tokai Earthquake 100 (a) Tonankai Earthquake 0 0 -100 E56 -100 NAG tion (gal) tion Accelera- tion (gal) tion 20 Accelera- 20 10 (b) 10 (b) 0 0 -10 -10 (cm/s) (cm/s)

Velocity -20 Velocity -20 10 (c) 10 (c) 0 0 -10 -10 -20 -20 Displace- Displace- ment (cm) 0 100 200 300 ment(cm) 0 100 200 300 Time (s) Time (s) 7 7 (LFs ) Tokai Earthquake (d) (LFs ) Tonankai Earthquake (d) E56 (L ) 6 (LFav ) 6 Fav NAG

Fad (L ) Fad (LFad ) Fad , L , L 5 5 Fav Fav , L , L 4 4 Fs Fs L L 3 3 Seismic intensity level, Seismic intensity level, 2 2 0 100 200 300 0 100 200 300 Time (s) Time (s) Fig.6 The time history of acceleration, velocity, displacement Fig.7 The time history of acceleration, velocity, displacement and seismic intensity level in area-3 (E56, Tokai Earth- and seismic intensity level in area-6 (NAG, Tonankai quake). Earthquake). earthquakes is calculated about 1300 seconds at in- 150 tervals of 0.02 second. As for the analysis time, the h=5% NAG E4E waveform for 600 seconds in the first half of the (Tonankai) (Tokai) acceleration waveform is used. (cm/s) E56 (Tokai) Figures 6(a), 6(b), 6(c) and Figs.7(a), 7(b) and 100 7(c) show the time histories of acceleration, velocity, and displacement in area-3 (E56) in Tokai Earth- quake and area-6 (NAG) in Tonankai Earthquake for 50 300 seconds, respectively. The time histories of these waveforms in E56 show a remarkably long-period aspect, and the maximum value of velocity and di- aplacement appears at 195 seconds later than 75 Velocity response spectrum 0 0 2 4 6 8 10 seconds at the time of the maximum acceleration of Period (s) 78 gal. On the other hand, the time history of the velocity in NAG shows the maximum value of Fig.8 Comparison the velocity response spectrum in each point. 23cm/s at the time of only about 10 seconds late to the maximum acceleration of 155 gal at 70 seconds. The large amplification of velocity and displacement LFad that used the weighting factor λad(f) corre- near 200 seconds in E56 is not caused in NAG. The sponding to the displacement shows a relatively large difference of both points can be distinguished also value due to the inclusion of the long-period com- with the seismic intensity levels of LFs, LFav, and LFad, ponent in the small acceleration value close to 60 which correspond to the instantaneous instrumental seconds. On the other hand, the value of LFs in NAG seismic intensity, velocity, and displacement, re- of the Tokai region shown in Fig.7(d) has a peak spectively, shown in Fig.6(d) and Fig.7(d). The value in 80 seconds, and is larger than the value of maximum value of the seismic intensity level LFs in LFav and LFad at that time. The values of LFav and LFad Fig.6(d) (E56) appears at 120 seconds indicating the gradually increase until about 200 seconds because second peak of the acceleration, and the difference of the long-period tendency to some extent. The between the values of LFav and LFad at that time is not maximum value of LFav corresponding to velocity recognized so much. The values of LFav and LFad, has not exceeded the value of (LFs)max. The effect of however, increase by forming after 120 seconds into the long-period component on the seismic intensity a long period, and indicate the peak value around 200 level can be guessed also from the velocity response seconds, although the value of LFs shows a decreas- spectrum (h=5%) in each point shown in Fig.8. The ing tendency. In addition, the seismic intensity level bold lines in the figure show the velocity response

166

7 7 m (a) (b) (a) E4E max 6 ) 6 100 E56 Fad NAG NAG max )

5 ,(L 5 Fs

max 50 ) (L 4 4 Fav

3 3 (LFav)max max

(LFad)max ) va va 2 Maximum seismic intensity level, (L 2 Maximum seismic intensity level, 2 3 4 5 6 7 2 3 4 5 6 7 (S Instrumental seismic intensity, Maximum seismic intensity level, (LFs ) max I (L ) Fs max 10 (LFav ) max Fig.9 Comparison between the instrumental seismic intensity and (LFad ) max the maximum seismic intensity levels. (LFap ) max 5 2 3 4 5 6 7 Maximum velocity response spectru response velocity Maximum (cm/s) Maximum seismic intensity level, spectrum in E56 (solid line), E4E (dashed line) and (LFs)max ,(LFav)max ,(LFad)max ,(LFap)max max NAG (broken line). The period in these peak values )

E4E Fav greatly differs, and shows the value longer than six (b) L 100 E56 6 ( seconds in E56 and E4E. In contrast, the maximum NAG peak value in NAG appears one second shorter than 50 E56 level, six seconds, and the second peak value in the period 5 y of 2.7 seconds is almost the same as the peak value in E4E

E56. In the case of ground motion waveform, which max NAG )

has a peak value of the velocity response spectrum va 4 near the period of one second such as the point of (S 10 NAG, it is suggested that the value of (LFs)max may (Sva ) max not necessarily become smaller than that of (L ) (LFav ) max Fav max 5 3 and (LFad)max. Figures 9(a) and 9(b) show the rela- 5 10 50 100 tionship between the maximum seismic intensity Maximum velocity response spectrum, (cm/s) SI* (cm/s) Maximum seismic intensit level and the instrumental seismic intensity in each , 1.5

max (L ) -(L ) E56 max Fad max Fav max E4E ) point. The maximum seismic intensity level (LFs)max ) (LFap)max-(LFav)max Fav Fav 1 shows good coincidence with the instrumental seis- (c) -(L mic intensity as well as in the case of the observed -(L NAG

max 0.5 max ) earthquake shown in Figs.5(a1) and 5(a2). Moreover, ) Fap the values of (LFav)max and (LFad)max are larger than the Fad 0 (L (L 0 1 2 3 4 5 6 7 8 value of (LFs)max except for the case of NAG men- Period in (S ) (s) tioned above, and the tendency is more remarkable so va max as to contain a lot of long-period component. Fig.10 Relationship between the maximum seismic intensity This present study proposes a seismic intensity level and the maximum velocity response spectrum. level for long-period ground motion through the comparison of the relationship between various seismic intensity levels and the maximum velocity velocity response spectrum (Sva)max and the maxi- response spectrum used for the long-period ground mum seismic intensity level (LFav)max corresponding motion scale of the Japan Meteorogical Agency. to velocity is given by exponential approximation as Figure 10(a) shows the relationship between the follows, although the dispersion is seen somewhat: various maximum seismic intensity levels (LFs)max, lnSva max  1.12 1.07 LFav max (24) (LFav)max, (LFad)max, (LFap)max and the maximum ve- The point such as E4E, however, where the value of locity response spectrum (Sva)max (h=5%) uses the (Sva)max is larger than that in other points, exists even long-period ground motion seismic wave for the in the case of the same value of (LFav)max. The dif- design of the eleven points shown in Table 2. Here, ference in the value of (Sva)max may be caused by not the maximum seismic intensity level (LFap)max is ob- reflecting the extent of the distribution of Sva for the tained by using the weighting factor λap(f) with the period. Here, the following equation for the integral value of gradient m of 1.5, which indicates the in- value of the velocity response spectrum from the termediate characteristic of velocity and displace- period of 1.6 to 7.8 seconds was defined as SI* value, ment as shown in Fig.2. Three reference points in as well as the integral value from the period of 0.1 to E4E, E56, and NAG in the figure are the same as the 2.5 seconds used for the spectrum intensity value (SI points in Fig.8. The relationship of the maximum value).

167

7.8 * 1 5 15 50 100 SI (h)  S (h,T )dT (25) max va ) 5 6.2 1.6 Lv (LLv)max 1.8 Figure 10(b) shows the relationship between (Sva)max, (L =0.168 (ln(S va)max+1.12) (L ) and SI* value (h=5%). The correlation with 4 Fav max E56 SI* value for the larger (S ) region is good for the va max E4E value of (L ) compared with (S ) so that the 3 Fav max va max NAG point in E4E where SI* value is smaller than that in other points for the same value of (Sva)max. The rela- 2 tionship between (LFav)max and SI* value is given in the following equation by exponential approxima- 1 tion. Long-period seismic intensity scale (JMA) L  0.93ln(SI * ) 1.44 (26) 1 2 3 4 Fav max 0 5 10 15 50 100

When the above equation (26) is substituted for the intensity seismic long-period Maximum velocity, to corresponding level Maximum velocity response spectrum, approximation (24) of (Sva)max and (LFav)max, the fol- (Sva)max (cm/s) lowing equation is obtained as a relational expression of (Sva)max and SI*. Fig.11 Relationship between the maximum velocity response * spectrum (Sva)max and the maximum long-period seismic Sva max  1.52 SI (27) intensity level corresponding to velocity, (LLv)max. The solid line in Fig.10(b) shows Eq.(26) and Eq.(27), respectively. The difference among maxi- Table 3 Long-period ground motion scale based on the maximum mum seismic intensity levels (LFav)max, (LFad)max, and long-period seismic intensity level, (LLp)max. (LFap)max for the same value of (Sva)max has a tendency to decrease for the period of 5 or less seconds in Long-period ground Maximum long-period seismic intensity (Sva)max as shown in Fig.10(c). In the present study, motion scale level, (L ) the maximum seismic intensity level in the period Lp max more than 5 seconds will be used as the evaluation 1 1 ≤(LLp)max< 2 criterion for the long-period ground motion, and the 2 2 ≤(LLp)max< 3 relation of these levels is expressed in Figs.10(a) and 3 3 ≤(LLp)max< 4

10(c) as follows: 4 4 ≤(LLp)max

LFad max  LFav max  1.0 (28)

LFap   LFav max  0.5 (29) max obtained from Eq.(31a). The solid line in the figure is In order to correspond to the long-period ground the relational expression of (Sva)max and (LLv)max in motion scale of the JMA using (Sva)max (Table 1), a Eq.(31b), and shows a good agreement for the maximum long-period seismic intensity level (LLv)max boundary value of the long-period ground motion corresponding to velocity using the maximum seis- scale of the JMA. The value of (LLv)max in each point mic intensity level (LFav)max is first defined by the is almost correspondent to the long-period ground power function of the following equation. motion scale. The point lower than the scale of the L  c L  d Lv max Fav max (30) JMA, however, will exist when the value of (Sva)max is  cln(S )  1.12 /1.07 d larger than the value of (LFav)max by Eq.(24) or SI* va max value by Eq.(27) such as the point of E4E. Thus, the where the coefficients of c and d can be obtained by maximum long-period seismic intensity level (L ) the least squares method using the value of (5,1), Lv max corresponding to velocity tends to show a value (15,2), (50,3), and (100,4) corresponding to the value lower than the long-period ground motion scale using of ((S ) , (L ) ) in the long-period ground mo- va max Lv max (S ) , when the extent of the distribution of the tion scale of the JMA as shown in Table 1. The co- va max velocity response spectrum in the long period nar- efficients of c and d are 0.19 and 1.8, respectively, rows. and the correlation coefficient is 0.997. Therefore, The long-period seismic intensity level L corre- the maximum long-period seismic intensity level Lv sponding to velocity may be given using the seismic (L ) is given by the following equation using Lv max intensity level L as well as (L ) of Eq.(31a) in (L ) or (S ) . Fav Lv max Fav max va max the following equation. 1.8 LLv max  0.19* LFav max (31a) 1.8 LLv  0.19 * LFav  (32) 1.8 LLv max  0.168*ln Sva max 1.12 (31b) In addition, the long-period seismic intensity level The plotting points shown in Fig.11 are the maxi- LLd corresponding to displacement shall be in accord mum long-period seismic intensity levels (LLv)max with the value of LLv on the average in a long-period

168 region. Then, the long-period seismic intensity level 5 LLd, which uses the seismic intensity level LFad cor- (a) Tokai Earthquake LLp 4 L responding to displacement is given as follows: Lp Lv

L E56 1.8 LLd LLd  0.19 * LFad 1.0 (33) 3 The effect of the long-period ground motion on the 2 evacuation behavior, the uneasy feelings of humans and the overturning/slipping of furniture, etc. in 1 high-rise buildings may be dependent on the re- 0 sponse to not only the velocity but also the dis- 0 100 200 300 5 placement. Therefore, the seismic intensity level LFap having the intermediate characteristics of velocity (b) Tonankai Earthquake LLp 4 LLv NAG and displacement is used for the long-period seismic LLd intensity level LLp in this study as follows: 3 L  0.19* L 0.5 1.8 (34) Lp Fap Long-period seismic intensity level, 2 (corresponding to velocity and displacement) and velocity to (corresponding

Table 3 shows the long-period ground motion scale Ld

, L 1

using the value of maximum long-period seismic Lv L intensity level (LLp)max. 0 0 100 200 300 Time (s)

4. LONG-PERIOD SEISMIC INTENSITY Fig.12 The time history of the long-period seismic intensity level in the long-period ground motion waveform for LEVEL FOR VARIOUS SEISMIC design. WAVEFORMS 5 (1) Long-period seismic intensity level for the (LFs )max (L ) long-period ground motion waveform 4 Fav max (LFad )max The long-period seismic intensity level LLp is max (L )

) Fap max

calculated for the long-period ground motion wave- Lp 3 form of the reference point in Table 2, and is com- pared with the long-period seismic intensity level LLv, 2 LLd corresponding to velocity and displacement. Figures 12(a) and 12(b) show the time histories of 1 the long-period seismic intensity level, LLp, LLv, and (LLp)max =0.19* ((L ) - 0.5) 1.8 L calculated for area-3(E56) in Tokai Earthquake seismic long-period Maximum (L level, intensity Fap max Ld 0 and area-6(NAG) in Tonankai Earthquake at the 0 1 2 3 4 5 6 7 same point shown in Fig.6 and Fig.7, respectively. Maximum seismic intensity level The differentiation between the long-period seismic (LFs)max ,(LFav)max ,(LFad)max ,(LFap)max intensity level LLp and LLv, LLd in Fig.12(a) is very Fig.13 Relationship between the maximum seismic intensity small because of the waveform having a long-period levels and the maximum long-period seismic intensity characteristic. However, the long-period seismic level (LLp)max. intensity level LLp, which is smaller than LLv corre- sponding to velocity for 100 to 150 seconds, is in- ferred to be greatly affected by the medium-period velocity and displacement may also change greatly in component rather than by the long-period of the the time histories of these levels. The evaluation of waveform. On the other hand, the long-period seis- the long-period ground motion in such a case has mic intensity level LLp before 200 seconds in NAG of suggested that there is a need to consider the char- Fig.12(b) is smaller than the value of LLv corre- acteristic of the time history change, and should be sponding to velocity because the seismic intensity dealt with as a future problem. Figure 13 shows the level LFav is larger than LFad as already pointed out in relationship between the various maximum seismic Fig.7, though the remarkable difference between LLp intensity levels and the maximum long-period seis- and LLv is not recognized after 200 seconds. Espe- mic intensity level (LLp)max. The solid line in the fig- cially, the value of LLv in 80 seconds is one class ure is a curve of the maximum long-period seismic larger than that of LLp, and shows a larger value than intensity level (LLp)max by Eq.(34) using the maxi- the maximum value of LLp overall for 200 seconds. mum seismic intensity level (LFap)max. The various Thus, the large/small relation of the long-period maximum seismic intensity levels with the same seismic intensity level LLv and LLd corresponding to value of (LLp)max are not intersected and become large

169

5 15 50 100 5 5 Funehiki (FKS008) (a) (a) LLp

(L ) , , 4 Lp max 4 E56 Lp The 2011 off the Pacific coast LLv L max (L ) of Tohoku Earthquake ) 4 Lv max L 3 Ld

Lp (L ) 3 Ld max

(L E4E 3 2 NAG 2 1

2 Long-period seismic scale (proposed) intensity 0 1 0 50 100 150 200 1 5 The 2011 off the Pacific coast Long-period seismic intensity scale (JMA (b) Naruko (MYG005) of Tohoku Earthquake 4 0 1 2 3 4 5 10 15 50 100 3 Maximum velocity response spectrum, (Sva)max (cm/s)

Long-period seismic intensitylevel, 2

5 and displacement) velocity to (corresponding (b) Ld 1 LLv , L LLp L Lv Ld

L 0

(corresponding to velocity and displacement) 4 E56 0 50 100 150 200

max Time (s) ) E4E Ld 3 Fig.15 The time history of the long-period seismic intensity Maximum long-period seismic intensity level, intensity seismic long-period Maximum

, (L level L (the 2011 off the Pacific Coast of Tohoku NAG Lp

max Earthquake). )

Lv 2 Period at

(L (LLv)max (LLd)max (Sva )max > 5 s < 5 s 1 that in other points, however, tends to be smaller than 1 2 3 4 5 the value of (LLv)max corresponding to velocity. The Maximum long-period seismic comparison of differences between the maximum intensity level, (LLp)max seismic intensity level (L ) and (L ) , (L ) 0.4 Lp max Lv max Ld max , (L ) -(L ) to the period for (S ) is shown in Figs.14(b) and 0.2 Ld max Lv max va max max max (LLp)max-(LLv)max E56 ) ) 14(c). The difference in the value of (LLp)max and Lv Lv 0 (LLd)max corresponding to displacement is very small.

(L (c) - -(L -0.2 However, the value of (LLp)max in contrast with that of max max E4E ) ) -0.4 (LLv)max corresponding to velocity tends to become Ld

Lp NAG -0.6

(L small in order to decrease the effect of the dis- (L 0 1 2 3 4 5 6 7 8 placement in the period of five seconds or less for Period at (S ) (s) va max (Sva)max, although that is almost the same in the period Fig.14 Relationship between the maximum long-period seismic of five seconds or more.

intensity level (LLp)max and (LLv)max, (LLd)max. (2) Long-period seismic intensity level for the observed seismic waves at almost the same ratio in the order of (LFs)max, The seismic waves observed on the ground surface (LFav)max, (LFap)max, (LFad)max except for the point of on the 2011 off the Pacific Coast of Tohoku Earth- NAG. quake (K-NET: 500 points) and the Mid-Niigata The maximum velocity response spectrum (Sva)max Prefecture Earthquake in 2004 (K-NET: 211 points) used as the long-period ground motion scale of the mentioned above are used for calculating the JMA is compared with the maximum long-period long-period seismic intensity level. Figures 15(a) seismic intensity level (LLp)max and (LLv)max, (LLd)max and 15(b) show an example of the time history of the corresponding to velocity and displacement, as long-period seismic intensity level in two observa- shown in Fig.14(a). The long-period ground motion tion points (Funehiki (FKS008), Naruko (MYG005), scale using the maximum seismic intensity level K-NET: the 2011 off the Pacific Coast of Tohoku (LLp)max is almost the same as the scale of the JMA as Earthquake). As already pointed out in Fig.3 that well as (LLv)max corresponding to velocity, except for shows the time histories of the seismic intensity lev- the point of E4E having one class lower than that of els LFs, LFav, and LFad in these two points, the value of the JMA scale. The value of (LLp)max in the case of the LFav and LFad corresponding to velocity and dis- shorter period for (Sva)max in the point of NAG than placement in Funehiki where the predominant period

170

5 5 (a) (a) T he 2011 off the Pacific (LFs )max coast of Tohoku , 4 (LFav )max Earthquake

4 (L ) max 4 K-NET

Fad max )

(L ) Lp max Fap max ) 3 (L Lp 3 3 (L 2

2 2 scale (proposed) (LLp)max Long-period seismic intensity seismic Long-period K-NET 1 (LLv)max 1 The 2011 off the 1 (LLd)max

intensity level, intensity Pacific coast of Maximum long-period seismic Tohoku Earthquake Long-period seismic intensity scale (JMA) 0 1 2 3 4 1 2 3 4 5 6 7 0 5 10 15 50 100 500 Maximu m s eis mic in ten s ity level Maximum velocity response spectrum (LFs)max ,(LFav)max ,(LFad)max ,(LFap)max (Sva)max (cm/s) 5 (b) 5 (LFs )max (b) T he Mid Niigata Prefecture (LFav )max 4 Earthquake in 2004 4 (LFad )max 4 K-NET

(L ) displacement) and velocity to (corresponding max Fap max )

max 3 Lp 3 ) (L Ld 3 Maximum long-period seismic intensity level, intensity seismic long-period Maximum 2 , (L 2 scale (proposed) max

) 2 (L ) K-NET Lp max Lv

Long-period seismic intensity seismic Long-period (L ) The Mid Niigata 1 Lv max 1 (L Prefecture (LLd)max Earthquake 1 intensity level, intensity Maximum long-periodseismic in 2004 (JMA) 0 Long-period seismic intensity scale 1 2 3 4 5 6 7 1 2 3 4 0 Maximu m s eis mic in ten s ity level 5 10 15 50 100 500 (LFs)max ,(LFav)max ,(LFad)max ,(LFap)max Maximum velocity response spectrum (Sva)max (cm/s) Fig.16 Relationship between the maximum seismic intensity level and the maximum long-period seismic intensity Fig.17 Relationship between the maximum long-period seismic level for observation seismic waves. intensity level and the maximum velocity response spectrum for observation seismic waves. in the short period of 0.3 seconds is smaller than that in Naruko, although the maximum seismic intensity having the intermediate characteristics of LFav and level (LFs)max in Funehiki shows a conversely larger LFad corresponding to velocity and displacement, value of 5.6 compared to 5.0 in Naruko. Then, the tends to become small for (LFs)max and (LFav)max so long-period seismic intensity level LLp in Funehiki that the predominant period appears to be short. That shown in Fig.15(a) is considerably smaller than LLv is, the values of (LFs)max and (LFav)max for (LLp)max in corresponding to velocity, and the difference of one Fig.16 will shift to the right side than to the line of or more has appeared near the peak value in these (LFap)max thus increasing the short-period component. levels. The long-period seismic intensity level LLp in These tendencies were generally recognized in all Naruko having a predominant period of 2.0 seconds seismic intensity regions in the Mid-Niigata Prefec- shown in Fig.15(b) has a small difference with LLv ture Earthquake in 2004, but were observed only in corresponding to velocity about 0.5, and the maxi- the larger seismic intensity region in the 2011 off the mum value of LLp is larger than that in Funehiki in Pacific Coast of Tohoku Earthquake. The maximum contrast to the case of the seismic intensity level. long-period seismic intensity level (LLp)max is com- Figures 16(a) and 16(b) compare the relationship pared between not only the maximum seismic inten- between the various maximum seismic intensity sity levels but also in the maximum velocity response levels and the maximum long-period seismic inten- spectrum using the long-period ground motion scale sity level (LLp)max in each observation point in both of the JMA. Figures 17(a) and 17(b) show the rela- the 2011 off the Pacific Coast of Tohoku Earthquake tionship between the maximum velocity response and the Mid-Niigata Prefecture Earthquake in 2004. spectrum (Sva)max and the maximum long-period The maximum long-period seismic intensity level seismic intensity levels (LLp)max, (LLv)max, and (LLd)max (LLp)max, which uses the seismic intensity level LFap in both earthquakes. The maximum long-period

171 seismic intensity level (LLv)max corresponding to ve- long-period seismic intensity level is also able to locity shows almost the same class of the JMA, indicate the effect of the seismic waveform, in- though the observation points showing the smaller or cluding the long-period component on velocity larger class near the boundary of the long-period and displacement in the time history. ground motion scale exist to some extent. In contrast to (LLv)max, the maximum long-period seismic inten- sity level (LLd)max corresponding to displacement NOTATIONS shows a value lower than that of the class of the JMA in many observation points. Especially, the lowering Fa1 (f), Fa2 (f), Fa3 (f) : filter on the period effect, high- of two classes is found in the maximum velocity cut filter and low-cut filter, respectively, response spectrum (Sva)max of 50 cm/s or more. The which were used for instrumental seismic long-period ground motion scale used in the intensity long-period seismic intensity level (LLp)max in the λa (f) : weighting factor of acceleration for instru- paper indicates an intermediate value of (LLv)max and mental seismic intensity # (LLd)max corresponding to velocity and displacement, F a3 (f) : low-cut filter with parameters α, f0 and is one class smaller than that of the JMA scale for Fa4 (f) : the ninth Butterworth filter (cutoff frequency the larger (Sva)max region in many observation points. 0.1Hz) # # λ a(f) : weighting factor of acceleration used F a3 (f) # (α > 0.17) or F a3 (f) Fa4 (f) (α < 0.17) instead 5. CONCLUSIONS of low-cut filter for instrumental seismic in- tensity The long-period seismic intensity level using a Lis : seismic intensity acceleration level seismic intensity level with the intermediate char- LFs : seismic intensity level acteristics of velocity and displacement is proposed I : instrumental seismic intensity (weighting factor, as an expression of seismic intensity for the λa (f)) long-period ground motion through a comparison Ffa (f) : filter with the gradient m for period in loga- with the long-period ground motion scale of the JMA. rithm The main results are as follows: λfa (f) : weighting factor of acceleration given by 1) The maximum seismic intensity level corre- Ffa (f)Fa2 (f)Fa4 (f) sponding to velocity for the long-period ground Lfa : seismic intensity level using the weighting motion waveform has high correlation between factor, λ fa (f) the integral value, compared to the maximum λav (f) : weighting factor of acceleration correspond- value of the velocity response spectrum in the ing to velocity integral interval from 1.6 to 7.8 seconds in the λad (f) : weighting factor of acceleration correspond- long-period region. ing to displacement 2) The long-period ground motion scale of the Japan λap(f) : weighting factor of acceleration having the Meteorological Agency has been divided by the intermediate characteristics of velocity and maximum value of the velocity response spec- displacement trum. The long-period seismic intensity level LFav : seismic intensity level using the weighting proposed in the paper is a seismic intensity based factor, λav (f), corresponding to velocity on the seismic intensity level corresponding to LFad : seismic intensity level using the weighting velocity, which has a good correlation with the factor, λad (f), corresponding to displacement average value of the velocity response spectrum LFap : seismic intensity level using the weighting in the long-period region. Also, the proposed level factor, λap (f), with the intermediate character- is an index for the long-period ground motion istics of velocity and displacement given by the seismic intensity level using the LLv : long-period seismic intensity level correspond- weighting factor of acceleration with the gradient ing to velocity m of 1.5 to the period which has the intermediate LLd : long-period seismic intensity level correspond- characteristics of velocity and displacement. ing to displacement 3) The long-period ground motion scale using the LLp : long-period seismic intensity level maximum long-period seismic intensity level for the observation seismic wave has some observa- REFERENCES tion points that are lower than those of the JMA. 1) Seismic Intensity Observation Advisory Committee : The Especially, the lowering of one class is recog- report of seismic intensity observation advisory committee, 1988.2. (in Japanese) nized in the larger maximum velocity response 2) Kawasumi, H. : Seismic intensity and seismic intensity spectrum region in many observation points. The scale, Journal of the Seismological Society of Japan, Vol.

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