Journal of JSCE, Vol., -, (Originally published in Journal of Japan Society of Civil Engineers, Ser. A, Vol. 9, No., -, in Japanese) A METHOD OF EXPRESSING SEISMIC INTENSITY FOR A WIDER PERIOD RANGE Akira SAKAI Member of JSCE, Associate Professor, Dept. of Civil Eng. and Architecture, Saga University (Honjo, Saga 8-8, Japan) E-mail: sakaia@cc.saga-u.ac.jp The instrumental seismic intensity of Japan Meteorological Agency (JMA) uses three types of filters which consist of high-cut, low-cut and period functions. An extended function of the low-cut filter is used to evaluate the effect of long-period range on seismic intensity in the paper. An asymptotic filter processing of acceleration in the extended function is proposed to express seismic intensities corresponding to velocity and displacement. The seismic intensity level using the running r.m.s. method is applied to clarify the effects of various frequency-weighted accelerations on seismic intensity. The seismic intensity levels corresponding to velocity and displacement are also discussed and compared with intensities of spectral characteristics. Key Words : seismic intensity, instrumental seismic intensity, velocity, displacement, seismic intensity level, long-period strong ground motion. INTRODUCTION The instrumentation of seismic intensity in Japan Meteorological Agency (JMA) has advanced parallel to conventional seismic intensity observation since 988 ). From April 99, after experiencing the Hyogoken Nambu Earthquake on January, 99, only the automatic measurement by the instrumental seismic intensity meter has been carried out thereby abolishing the conventional manner of observation based on human perception and behavior of the surroundings. The JMA scale determined by the instrumental seismic intensity, which is consistent with the conventional seismic intensity scale, can be released immediately thus allowing prompt reporting. The original instrumental seismic intensity was proposed on the basis of the Kawasumi formula ) denoted by an acceleration. Moreover, the instrumental seismic intensity specifically uses filtered accelerations to which both high-cut and a low-cut filters, as well as a filter corresponding to the effect of the seismic period are considered. The present instrumental seismic intensity improved in 99 fundamentally accords with the approach of the original scale. The following revisions are pointed out ). :) The three time histories of acceleration in three directions, which added the vertical to the two horizontal directions are used. ) The acceleration of the long-period region is evaluated somewhat higher than that of the original seismic intensity. ) The evaluation method considering the duration of the acceleration is introduced. The present JMA scale ) is also changed to ten degrees (,,,,, lower, upper, lower, upper, and ), with lower and upper degrees added to the extent of the phenomenon, compared to only and of the conventional seismic intensity. The instrumental seismic intensity, however, is considered as mainly corresponding to the short-period band up to about one second, in order to cut the long-period wave through the low-cut filter. It is well known that the seismic intensity does not correspond to the damage of various structures with a wide range of frequency characteristics ). As methods of expressing seismic intensity that consider the effect of medium or long period over one second, as well as the combined seismic intensities obtained from a velocity waveform and a displacement waveform ), ), a method using each periodic band of velocity response spectrum 8) and a method based on the velocity response of a single-degree-of-freedom system 9) are proposed. The effective evaluation methods of the long period seismic motion are also discussed ). The treatment of the periodical band for the calculation of seismic intensity is an important matter concerning the evaluation of damage for various
structures with wide-range frequency domains, and gives a significantly different evaluation by using a basic physical value. Acceleration, velocity, displacement and the response spectrum are used as basic physical values for various proposed seismic intensities ), ), 8), 9). The seismic intensity with various filters based on acceleration is compared with the instrumental seismic intensity. The seismic intensities corresponding to velocity and displacement, are also proposed in the paper. The existing methods of expressing the time histories of seismic intensity are as follows: ) Instantaneous instrumental seismic intensity (IISI) for arbitrary duration of the time window ), ) Real-time seismic intensity (I r ) defined by using an approximating filter in the time domain instead of the original filter in the frequency domain ), and ) Seismic intensity level (L Fs ) using the running r.m.s. method ). The maximum value of the seismic intensity level (L Fs ) max, proposed by the author ) has a good coincidence with the instrumental seismic intensity, without using a threshold value of the vector acceleration for which the total time is.second. The time histories of the seismic intensity levels corresponding to velocity and displacement are also discussed in the paper.. FILTER CHARACTERISTICS OF, AND PROBLEMS WITH THE INSTRU- MENTAL SEISMIC INTENSITY () Filtering of previous and present instrumental seismic intensity The previous instrumental seismic intensity, I, was expressed by the formula (I = log(a) +. + log (kt), a: acceleration (gal), T: period, k: cofficient (.)), which considered the effect of the period to conform with the conventional manner of measuring seismic intensity through human perception on the basis of the Kawasumi formula (I = log(a) +.) ). The time histories in only two horizontal components were processed by filters. The calculation method for the present instrumental seismic intensity had three main areas of improvement in 99 ), ) as follows: ) Three components, which added the vertical component, are used as the time histories of acceleration. ) The period region affecting the seismic intensity expands, to some extent, to the long period. ) The amplitude of a vector acceleration used in the instrumental seismic intensity is determined using not a maximum value but a value corresponding to the duration time of. second. The filtered acceleration for the previous and present instrumental seismic intensities is obtained by using three filter functions on the frequency, f, in the following equations. Weighting factor. I=log(a)+.9 f =.Hz... Fig. Weighting factor for the instrumental seismic intensity. ) Filter on the period effect: F a (f) / F a ( f ) k / f () where the values of k are. and., respectively, for the previous and present instrumental seismic intensities, applying the Kawasumi formula as the expression method. The present instrumental seismic intensity, however, is changed to the following equation on the basis of the period of one second. / F a ( f ) / f () ) High-cut filter: F a (f) ( f ) F a Low cut High cut Period effect ((/f) / ) in Total (λ a (f)) Instrumental seismic intensity /.9 X.X. X 8.9.. X X X X = f / f c ( f c = H z ) () ) Low-cut filter: F a (f) F / a ( f ) exp( ( f / f ) ) () where f is the lower limit of frequency used for the calculation of seismic intensity. The value of f for the present instrumental seismic intensity is.hz, which is smaller than.hz for the previous intensity and expanded to the long-period region. These three filters and the weighting factor λ a (f) (in total), which multiplied these filters in the present instrumental seismic intensity, are shown in Fig.. a ( f ) Fa( f ) Fa ( f ) Fa ( f ) () First, the calculation of the present instrumental seismic intensity carries out the Fourier spectrum of acceleration in three directions, then the Fourier spectrum is revised by using the weighting factor λ a (f). Next, the three time histories of the filtered acceleration obtained by the inverse Fourier spectrum are synthesized as a vector acceleration. Finally, a value in which the accumulated time for acceleration larger than a is. second in the time history is calculated. The present instrumental seismic intensity is given by the following equation using the
Weighting factor Weighting factor. Low cut High cut Period effect in Total (λ a(f)) (a) α=-. α=-. α=. α=. α=. F a(f)f a (f), f =.... (b). Low cut High cut Period effect in Total (λ a(f)) f =. f =. f =. Low cut filter (-exp(-(f/f ) )) α, α=.... Fig. Influence of α and ƒ on the weighting factor. (a) Acceleration(cm/sec ) (f =.) JMA Seismic Intensity(α=.) λ a(f) (α=.) λ a(f) (α=.) λ a(f) (α=-.) λ a(f) (α=-.) Seismic Intensity Scale Upper Lower Upper Lower... (b) JMA Seismic Intensity(f =.) λ a(f) (f =.) λ a(f) (f =.)... Fig. Relationship between period and acceleration in each seismic intensity scale. Acceleration(cm/sec ) (α=.) Seismic Intensity Scale Upper Lower Upper Lower value of a. I log a. log. log a.9 () () A revision of the low-cut filter The filter characteristic of the present instrumental seismic intensity shows a decreasing tendency in the period side longer than. seconds by the low-cut filter, F a (f). Therefore, the seismic intensity will have a low value in the period side longer than. seconds. A revised low-cut filter, which introduced a new parameter α, will be used to change the effect of the low-cut filter arbitrarily on the filtered acceleration for the longer period region. F ( ) exp( ( / ) ) a f f f () The parameters α, ƒ show a decreasing rate of the filter for the period. However, the filter F a(f) changes in increasing function for the period, when the value of parameter α becomes negative. Moreover, even if the value of α is positive, the curve, which multiplied the three filters of Eq.(), Eq.(), and Eq.(), shows an increasing tendency for the period within the range of α smaller than.. In the paper, the ninth Butterworth filter (cutoff frequency.hz) is used to decrease the effect of the long-period region longer than about seconds. F n / f / a ( f ) / f c (n=9, f c =.Hz) (8) Therefore, the weighting factor tends to decrease rapidly in the period longer than 9 seconds. The weighting factor λ a (f) from which only the low-cut filter differs is given in the following equation unlike the weighting factor λ a (f) (Eq.()) of the present instrumental seismic intensity. a ( f ) Fa ( f ) Fa ( f ) Fa ( f ) (.) (9a) a ( f ) Fa ( f ) Fa ( f ) Fa ( f ) Fa ( f ) (.) (9b) The values used for both α and ƒ in the low-cut filter of the present instrumental seismic intensity was.. To clarify the effect of parameters α and ƒ on the weighting factor λ a (f), Figs.(a)(b) show the comparison between λ a (f) used in the filter F a(f) and the various values of α and ƒ (α=.,., -., -., ƒ =.,.) smaller than. to better evaluate the medium- and long-period regions. The weighting factor λ a (f) (solid line) multiplied all filters using the same filter on the period effect (two-dot chain line) and high-cut filter (dashed line) as the present instrumental seismic intensity, but differs only in the low-cut filter (broken line). Although the peak of the weighting factor is. (period. seconds) in the present instrumental seismic intensity (α=.), the value of the peak changes to. (period. seconds) for α=. and a constant value of. (period longer than 8. seconds) for α=. as shown in Fig.(a) (ƒ =.). The weighting factor in the value
Instrumental seismic intensity... a max =gal a max =8gal a max =gal a max =gal a max =gal (f =.) Instrumental seismic intensity ( α=.). λ a(f) ( α=.) Acceleration of λ a(f) ( α=-.) sine wave (sec) non-filter.. Fig. Relationship between period and the instrumental seismic intensity to various acceleration amplitudes. of α smaller than. uses the ninth Butterworth filter to avoid an increasing tendency in the long period, and shows the peak value of. (α=-.) and.8 (α=-.), respectively, in 9. seconds. On the other hand, the effect of f on the peak of λ a (f) in Fig.(b) (α=.) shows an increasing tendency along the line of the filter on the period effect F a (f), so that the values of the peak are. (period. seconds) for f =., and.8 (period. seconds) for f =.. Figs.(a)(b) show the relation between the period and the acceleration in each seismic intensity scale with the various values of α and ƒ, to clarify the influence of these parameters on the acceleration in the medium- and long-period regions. The acceleration in each seismic intensity scale as shown in Fig.(a) becomes a smaller value in the period region, which is longer than the period of. seconds, as the value of α decreases. The acceleration in the seismic intensity scale, however, shows a rapid increase in the region longer than nine seconds in which the influence of the low-cut filter F a (f) appears within the range of α<.. On the other hand, Fig.(b) shows that the increasing rate of the acceleration in each seismic intensity scale is the same as that of the present intensity scale in the region with a longer seismic period, which shows a minimal acceleration, though the period becomes longer with the decreasing value of f. () Influence of the period on velocity and displacement The present instrumental seismic intensity will be evaluated as smaller in a region longer than the period of. seconds, because of the use of the Velocity (cm/sec) (a) gal a max=8gal gal gal Acceleration of sine wave (sec) a max =gal (f =.) Instrumental seismic intensity ( α=.) λ a(f) ( α=.) λ a(f) ( α=-.) non-filter.... Instrumental seismic intensity gal Acceleration of sine wave Displacement (cm) (b) (sec) gal gal8gal (f =.) Instrumental seismic intensity ( α=.) λ a(f) ( α=.) λ a(f) ( α=-.) non-filter a max =gal.... Instrumental seismic intensity Fig. Relationship between period and velocity and displacement in various acceleration amplitudes. weighting factor λ a (f) as shown in Fig.. However, a damage is considered to have a different aspect from the past damage situation, when velocity and displacement increase with a longer period even if the seismic acceleration is the same. To understand the relation between acceleration, velocity, and displacement in the instrumental seismic intensity, the accelerogram of the sinusoidal wave of seconds was used. Fig. shows the relation between the period and the instrumental seismic intensity relative to various acceleration amplitudes (a max =~gal). The instrumental seismic intensity relative to the maximum acceleration in a region shorter than. second is evaluated to be smaller as the period becomes shorter. The seismic intensity in the periodic region longer than second, however, is evaluated to be greater until it peaks at. seconds, though it becomes a lower value again after the period. The relations used the value. (broken line) and -. (two-dot chain line) as the parameter α of the lowcut filter are also shown in Fig.. The seismic intensity in the medium- and long-period regions will be evaluated as a larger value as the value of α becomes smaller.
The maximum velocity v max and the maximum displacement u max relative to the acceleration of the sine wave (maximum acceleration amplitude, a max, and period, T) are given by the following equations: v a T / (a) max max max amax ( T / ) u (b) The values of v max and u max depend on the period of the acceleration, in proportion to period and period squared, respectively. Therefore, the velocity and the displacement corresponding to the instrumental seismic intensity will be affected by not only the weighting factor of acceleration, but also by the period expressed in Eq.(). Figs.(a)(b) show the relationship between the maximum velocity or the maximum displacement and the instrumental seismic intensity to each acceleration amplitude within the period range of. to seconds. The instrumental seismic intensity has not evaluated the tendency of the velocity and the displacement to increase in the medium- and long-period regions, since the weighting factor of acceleration is smaller than the period longer than. seconds. On the other hand, the instrumental seismic intensity to the parameter α of the low-cut filter in the medium- and long-period regions can be evaluated as a larger value from which the increase of velocity and displacement is more largely taken into consideration by using a small value of α.. VARIOUS FILTERINGS AND EX- PRESSION OF SEISMIC INTENSITY CORRESPONDING TO VELOCITY AND DISPLACEMENT () Seismic intensity level using the running r.m.s. method The various seismic intensities using the velocity and displacement waveforms or the velocity response spectrum ), ), 8), which can take the mediumand long-period zones into consideration besides the instrumental seismic intensity and also the time history expression of seismic intensity ), ), ), are proposed. The seismic intensity level obtained with the application of the running r.m.s. method to the same frequency-weighted acceleration as the instrumental seismic intensity is proposed by the author ), without using the duration time of. seconds, which becomes more than the absolute acceleration value of a necessary to calculate the instrumental seismic intensity. The seismic intensity level can express the time history of the seismic intensity, and the time domain of integration used for the running r.m.s. method can be set as an arbitrary value. The outline of the seismic intensity level follows. Vector acceleration of components (cm/sec ) (b) Tsukidate (MYG) Seismic intensity acceleration level Instantaneous instrumental Seismic intensity level seismic intensity, IISI the running r.m.s. IISI (non-filter) method (τ= sec) the total time (τ= sec) Time (sec) Fig. Time history of the seismic intensity level L Fs. Seismic intensity acceleration level, L is, Seismic intensity level, L Fs In general, the running r.m.s. method is applied to the evaluation of an intermittent impulse and a transitional vibration. The seismic intensity level proposed by applying the running r.m.s. method uses the weighted r.m.s. acceleration A Fcom (t ) of the following equation, using the vector acceleration a Fcom that added the filtered accelerations in NS, EW, and UD directions obtained by the same filtering as the instrumental seismic intensity. A (a) The off the Pacific coast / t Fcom ( t ) afcom ( t) dt t Acceleration Filtered acceleration () where τ: integral time of the running average, t: time, and t : observation time (instantaneous time). Also, the r.m.s. acceleration A com (t ) without frequency filtering is given by using the non-filtered vector acceleration a com as well as Eq.(). The seismic intensity acceleration level L is and the seismic intensity level L Fs are defined respectively so that they may be expressed with the same form as the instrumental seismic intensity by using A com (t ) and A Fcom (t ) instead of the acceleration, a, in the following equations: Lis ( t ) log Acom ( t ) cs () Fs ( t ) log AFcom ( t ) cs () L where c s is a constant and used. that is a value when the correlation with the (L Fs ) max in the integral time τ of seconds and the instrumental seismic intensity is the highest. Figs.(a)(b) show an example of the result obtained by the above-mentioned calculation method of the seismic intensity level (Tsukidate (MYG), K-NET: the off the Pacific coast of Tohoku Earthquake). The maximum value of filtered vector acceleration (a Fcom ) is gal, and is remarkably small at about percent compared with the maxi-
Maximum seismic intensity level, (L Fs ) max The Mid Niigata Prefecture Earthquake in (a) The off the Pacific coast (b) Fig. Relationship between the instrumental seismic intensity I and the seismic intensity level (L Fs ) max. mum value of non-filtered vector acceleration (a com ) of 9 gal. The filtered acceleration has become small by the weighting factor of the instrumental seismic intensity, from which the predominant period of acceleration is. second in the short side. The time history of seismic intensity level L Fs is also smaller than that of the seismic intensity acceleration level L is, which is about, and the value of (L Fs ) max is. compared to. of (L is ) max. The instantaneous instrumental seismic intensity (IISI) with -second time windows, which is another expression of the time history, has a good agreement with the seismic intensity level as shown in Fig.(b). The relationship between the instrumental seismic intensity I and the maximum seismic intensity level (L Fs ) max (the integral time τ of seconds) is shown in Figs.(a)(b), for seismic waves ) observed in the ground level on the Mid Niigata Prefecture Earthquake in (K-NET, KiK-net: points) and the off the Pacific coast (K-NET, KiK-net: points). The correlation of I and (L Fs ) max is high within the difference of ±. for both earthquakes. () Filtering of accelerogram corresponding to velocity and displacement The present instrumental seismic intensity evaluates the seismic intensity low in the medium- and long-period regions as already pointed out, though the filter on the period effect in Eq.() with the inclination of. in the logarithm of the period is used and has an intermediate characteristic of the velocity and the displacement. The filtering that evaluates the influence of velocity and displacement is not enough considering the use of low-cut filter in Eq.(). For this reason, the seismic intensity calculated by the weighting factor λ a (f) of Eq.(9b) using the filter F a(f) instead of F a (f) is first discussed as the reassessment of the medium- and long-period regions in the paper. The instrumental seismic intensity, I f,α, used the weighting factor λ a (f) and not λ a (f) of the present intensity. It is expressed by using the frequency-weighted acceleration, a, corresponding to (τ=sec) (τ=sec) r =.998 r =.988 Instrumental seismic intensity, I the duration of. second. I f, log a.9 () The seismic intensity level L Fs using the weighting factor λ a (f) is given as follows: L Fs log AFcom csa log AFcom. () where A Fcom is the weighted r.m.s. acceleration using λ a (f). The parameter α (<.) of F a(f) in Eq.() has an important relation to the weighting factor λ a (f) from the relationship between the period T and y(t) (=F a (f)f a(f)). The gradient m T to the period in the logarithm can be obtained by differentiating log y(t) of log T. log y( T ) log( F ( f ) F ( f )) log( a a T exp( ( f / f.logt log exp T / T Here, the gradient m at T is given by the following relation as a function of α. m lim m. () T T ) ) ) () The weighting factors of acceleration corresponding to velocity and displacement will correspond to the value of gradient m of for velocity and for displacement from Eq.(). The values of α are -. (m =) and -. (m =) from Eq.(), respectively. Thus, a new filter on the period effect will be introduced by using the asymptotic line, F fa (f), which has the arbitrary gradient m to the filter of F a (f)f a(f) (=y(t)). The new filter F fa (f) is given by the following equation, assuming that F fa (f) coincides with y(t) at the long period T (=T b ), and that the period is denoted by T a when the value of F fa (f) is equal to one. m F fa ( f ) ( T / T a ) (m > ) (8) where T a is obtained by using α, T (=/f ), m and T b. b m α b m Ta T exp T / T (9) A weighting factor λ fa (f) of acceleration that used the filter F fa (f) on the period effect y(t) with an arbitrary gradient m is expressed in contrast with λ a (f) in Eq.(9b). f ) F ( f ) F ( f ) F ( ) () fa ( fa a a f where both the high-cut filter F a (f) and the low-cut filter F a (f) are assumed to be the same filters as that of λ a (f). The seismic intensity level L fa using λ fa (f) as the weighting factor of acceleration instead of λ a (f) is given as follows: L log. () fa A Fcom where (A Fcom ) fa is the weighted r.m.s. acceleration using the weighting factor λ fa (f). The weighting factors, λ av (f) and λ ad (f), using the filter F fa (f) corresponding to the velocity (m=) and fa
Weighting factor of acceleration Weighting factor of acceleration Weighting factor of acceleration.... (Instrumental seismic intensity) λ a (f)=f a (f)f a (f)f a (f) λ a(f) (α=-.) λ a(f) (α=-.) λ a(f)=f a (f)f a(f)f a (f)f a (f) f =. Hz (Instrumental seismic intensity) λ a (f)=f a (f)f a (f)f a (f) λ a(f) (α=-.) λ a(f) (α=-.) λ a(f)=f a (f)f a(f)f a (f)f a (f) f =. Hz.. λ. av (f) λ ad (f) T av =.8sec, T ad =.sec.. Fig.8 Influence of ƒ and α on the weighting factor of acceleration. the displacement (m=) are given by using the value, T av and T ad, of the period in case F fa (f) with m= and are equal to one. f ) T / T F ( f ) F ( () av a a f ) T / T F ( f ) F ( f ) av ( ad ( f ) ad a a () The seismic intensity level, L Fav and L Fad, using these factors are expressed, respectively, as follows: L log A. () Fav λ av (f) (Eq.()) corresponding to velocity λ ad (f) (Eq.()) corresponding to displacement T av =.8sec, T ad =.sec T av =.sec, T ad =.8sec Fvcom λ av (f) λ ad (f) (Instrumental seismic intensity) λ a (f)=f a (f)f a (f)f a (f) λ a(f) (α=-.) λ a(f) (α=-.) λ a(f)=f a (f)f a(f)f a (f)f a (f) f =. Hz L Fad log AFdcom. () where A Fvcom and A Fdcom are the weighted r.m.s. acceleration using the weighting factors, λ av (f) and λ ad (f). Figs.8(a)(b)(c) show the effects of f and α on the weighting factor considering the velocity and the displacement. The weighting factor λ a(f) shown with (a) (b) (c) (a) Acceleration (cm/sec ) Seismic Intensity Scale Upper Lower Upper Lower Instrumental seismic intensity,i (λ av (f)) corresponding to velocity... (b) Acceleration (cm/sec ) Seismic Intensity Scale Upper Lower Upper Lower Instrumental seismic intensity,i (λ ad (f)) corresponding to displacement... Fig.9 Relationship between period and acceleration corresponding velocity and displacement. a broken line is a curve that has an asymptotic line in the weighting factors, λ av (f) and λ ad (f) corresponding to velocity and displacement. Here, the corresponding values of parameter α of the filter F a(f) are -. and -., respectively. The value of T b uses seconds as a sufficiently long period. Also, the parameter f uses not only.hz (Fig.8(b)) of the present instrumental seismic intensity but also.hz (Fig.8(a)) and.hz (Fig.8(c)). The weighting factor becomes large and moves to the left side with the increasing value of f in the domain longer than the period T (=/f ). In addition, the weighting factor λ fa (f) with arbitrary gradient m in the logarithm is shown to be turning on the point at the period T of.,., and. seconds, and increases in T>T or decreases in T<T with the increasing m value. Figs.9(a)(b) compare the relation between the period and the acceleration for each seismic intensity scale when both λ a (f) of the instrumental seismic intensity and λ av (f), λ ad (f) corresponding to the velocity and the displacement are used as the weighting factors. The acceleration values that used the weighting factors λ av (f) and λ ad (f) in each seismic intensity scale are evaluated to be larger than those of the instrumental seismic intensity in periods longer than. and.8 seconds, respectively. 8
() Seismic intensity level using the weighting factors of velocity and displacement The expression of the seismic intensity described so far is based on acceleration. The expression method of seismic intensity using the waveforms of velocity and displacement will be discussed here. The weighting factors λ v (f) and λ d (f), which multiplied the high-cut filter F a (f) and the low-cut filter F a (f) similar to that of the instrumental intensity, will be used as the filter of velocity waveform and displacement waveform as follows: Velocity: v ( f ) Fv ( f ) Fv ( f ) Fa ( f ) Fa ( f ) () Displacement: d ( f ) Fd ( f ) Fd ( f ) Fa ( f ) Fa ( f ) () The seismic intensity level L fv in velocity for the sinusoidal wave can be expressed by using the weighted r.m.s. velocity v which is relevant to the weighted r.m.s. acceleration a v that used λ av (f) corresponding to velocity. The equation is as follows: L log a. fv v logav( f ) amax /. T log Fa ( f ) Fa ( f ) amax /. Tav amax T log Fa ( f ) Fa ( f ). (8) Tav logv. Tav logv log. Tav The seismic intensity level L fv for the velocity wave, as well as that for the sinusoidal wave, in an earthquake is assumed to be expressed by the following equation. Lfv logv log. (9) Tav The seismic intensity level L fd for the displacement wave is also similarly given by using the weighted r.m.s. displacement d and the period T ad. L log log fd d. () Tad Here, the obtained values of T av and T ad are. seconds and.8 seconds, respectively as shown in Eq.(9) when the value of f (=/T ) uses.hz as the same value in the low-cut filter of the instrumental seismic intensity. Therefore, the following equations expressed with a function of only the weighted r.m.s. velocity v and the weighted r.m.s. displacement d are obtained as the seismic intensity levels L fv and L fd. L fv L fd logv logv logd logd log... log.8.. () (). COMPARISONS OF THE MAXIMUM VALUE AND THE TIME HISTORY OF SEISMIC INTENSITY LEVEL WITH VARIOUS WEIGHTING FACTORS () Influence of the weighting factor on the instrumental seismic intensity and the maximum seismic intensity level The paper divides the weighting factors for acceleration into three types: ) λ a (f) (Eq.()) for the instrumental seismic intensity, ) λ a (f) (Eq.(9)) extended only to the low-cut filter, and ) λ av (f) (Eq.()) and λ ad (f) (Eq.()) corresponding to velocity and displacement, respectively. The values of parameter α and f of a low-cut filter will have a large influence on the weighting factor λ a (f) in the medium- and long-period regions, as shown in Fig.. Especially, the value of α makes the weighting factor λ a (f) in a region longer than the period of. seconds increases rapidly (Fig.(a)), and enlarges the seismic intensity relative to the acceleration (Fig.(a)), so as to become smaller than the α value of.. To clarify the influence of α on the instrumental seismic intensity in the medium- and longperiod regions, the relationship between the instrumental seismic intensity I f,α (Eq.(), f =.Hz) used λ a (f) and the present instrumental seismic intensity I for each earthquake is shown in Figs.(a)~(d). The seismic waves ), ) recorded on the ground surface are used for the four earthquakes, namely, the Tokachi-oki Earthquake in (K-NET: points), the Iwate-Miyagi Nairiku Earthquake in 8 (K-NET, KiK-net: points), the Mid Niigata Prefecture Earthquake in, and the off the Pacific coast previously shown. The instrumental seismic intensity I f,α is almost in agreement with the present instrumental seismic intensity I (α=.) with the value of α from. to. for the four earthquakes. Here, the weighting factor λ a (f) for α=. is a constant value of. in the period longer than 8. seconds. The value of I f,α in comparison with I shows a slightly increasing tendency in α=, which has the same gradient m of. of the filter on the period effect in I and a large increase in the α value of -. corre- 9
I f,α I f,α I f,α I f,α Maximum seismic intensity level, (L Fs) max (f =.Hz) (b) (f =.Hz) The off the Pacific coast of α= α= α= α= Tohoku.. -. -. Earthquake Instrumental seismic intensity, I (c) (c) (c) (c) (f =.Hz) Instrumental seismic intensity, I Fig. Relationship between period and acceleration corresponding to velocity and displacement. (a) (b) (a) α=. f =. Hz α=-. f =. Hz α=-. (a) (a) α= α= α=. -. -. Instrumental seismic intensity, I (b) (b) (b) r =.998 The Mid Niigata Prefecture Earthquake in r =.99 The off the Pacific coast (a) (a) f =. Hz α=-. r =.99 The Mid Niigata Prefecture Earthquake in (b) f =. Hz α=-. Mid Niigata Prefecture Earthquake in Tokachi-oki α= α= α= α= Earthquake.. -. -. in Instrumental seismic intensity, I (d) (d) (d) (d) (f =.Hz) α=. α=. α= -. Iwate-Miyagi Nairiku α= Earthquake -. in 8 r =.9 The off the Pacific coast Instrumental seismic intensity, I f,α Fig. Relationship between the instrumental seismic intensity I f,α and the maximum seismic intensity level (L Fs) max. Maximum seismic intensity level, (L Fs) max Maximum seismic intensity level, (L Fs) max (a) The Mid Niigata Prefecture Earthquake in : m= (L Fs) max : f =. Hz, α=-. (b) The off the Pacific coast (c) (d) : m= (L Fs) max : f =. Hz, α=-. The Tokachi-oki Earthquake in : m= (L Fs) max : f =. Hz, α=-. The Iwate-Miyagi Nairiku Earthquake in 8 : m= (L Fs) max : f =. Hz, α=-. (a) The Mid Niigata Prefecture Earthquake in (b) The off the Pacific coast (c) (d) : m= (L Fs) max : f =. Hz, α=-. : m= (L Fs) max : f =. Hz, α=-. The Tokachi-oki Earthquake in : m= (L Fs) max : f =. Hz, α=-. The Iwate-Miyagi Nairiku Earthquake in 8 : m= (L Fs) max : f =. Hz, α=-. Maximum seismic intensity Maximum seismic intensity level, level, Fig. Comparison between the maximum seismic intensity level (L Fs) max and that,. sponding to displacement. In particular the increasing rate of the seismic intensity in α< is large in both the off the Pacific coast and the Tokachi-oki Earthquake in, because it is thought that the observation points recorded the seismic wave containing the longer period component more than they did for the other earthquakes. Figs.(a)~(b) show the relationship between the instrumental seismic intensity I f,α and the maximum seismic intensity level (L Fs) max using the same weighting factor λ a (f) for α=-., -. and f =.Hz. A high correlation is seen between I f,α and (L Fs) max, as well as between I and (L Fs ) max, as shown in Fig.. Hence, the influence of the weighting factor on the seismic intensity will be discussed by using the seismic intensity level instead
Maximum seismic intensity level, (L Fav) max, Maximum seismic intensity level, (L Fav) max, (a) The Mid Niigata Prefecture Earthquake in f =. Hz : m= (b) The off the Pacific coast (c) f =. Hz : m= The Tokachi-oki Earthquake in f =. Hz : m= (d) The Iwate-Miyagi Nairiku Earthquake in 8 f =. Hz : m= (a) The Mid Niigata Prefecture Earthquake in (b) The off the Pacific coast (c) The Tokachi-oki Earthquake in f =. Hz : m= f =. Hz : m= f =. Hz (L Fa d ) max : m= (d) The Iwate-Miyagi Nairiku Earthquake in 8 f =. Hz (L Fa d ) max : m= Maximum seismic intensity level, (L Fs ) max Fig. Comparison between the maximum seismic intensity level (L Fs ) max and that,. of the instrumental seismic intensity. The weighting factor λ a (f) used for L Fs has a large value in the period less than approximately two seconds as compared with the weighting factors, λ av (f) and λ ad (f), used for L Fav and L Fad, as shown in Fig.8. The comparison between the maximum seismic intensity level (L Fs) max and, with the parameter α=-., -. and f =.Hz is shown in Figs.(a)~(d) for the four earthquakes. Properly, it means that the contribution of the period component less than about two seconds on the seismic intensity level becomes higher so that the difference between (L Fs) max and, increases. Moreover, in comparison with the maximum seismic intensity levels corresponding to velocity (Figs.(a)~(d)) and displacement (Figs.(a)~ Maximum seismic intensity, (L fv ) max (a) The off the Pacific coast (L fv ) max f =. Hz : m= Maximum seismic intensity, Maximum seismic intensity, (L fd ) max (a) Fig. Comparison between the maximum seismic intensity level, and (L fv ) max, (L fd ) max. (d)), the difference between (L Fs) max and is larger than the difference between (L Fs) max and in the seismic wave having a lot of shorter period components and conversely smaller than that of longer period components. This is due to the gradient m of λ ad (f) (m=) in the logarithm of period being larger than that of λ av (f) (m=). These features are observed more remarkably in the off the Pacific coast and the Tokachi-oki Earthquake in. Figs.(a)~(d) show the relationship between the maximum seismic intensity level (L Fs ) max using the same weighting factor λ a (f) as the instrumental seismic intensity and, corresponding to velocity and displacement (f =.Hz, m=, ). The weighting factors used in these seismic intensity are λ a (f) (solid line) and λ av (f) (dashed line) or λ ad (f) (two-dot chain line) as shown in Fig.8(b), and the periods T i in the intersection of both factors are. seconds and.8 seconds, respectively. It means that the contribution of the periodic component over T i to the seismic intensity is more than that below T i when or is larger than (L Fs ) max. The value of for the four earthquakes in Figs.(a)~(d) shows a value smaller than (L Fs ) max in most observation points. The value of in Figs.(a)~(d), however, is larger than that of (L Fs ) max in the half point or more. Thus, the relationship between (L Fs ) max and or would show a different aspect in each observation point due to the difference in the frequency characteristics of the seismic wave. It is known that the maximum seismic intensity levels, (L fv ) max and (L fd ) max, using the velocity wave and the displacement wave are almost the same as those for levels and, using the weighted acceleration corresponding to velocity and displacement, respectively, as shown in Fig.. This is due to the use of the same high-cut and low-cut filters as that for acceleration. Also, Figs.(b)(c) show the relationship between the maximum seismic intensity level ((L fv ) max, (L fd ) max ) and the maximum value (v max, d max ) of velocity and displacement with The off the Pacific coast (L fd ) max f =. Hz : m= Maximum seismic intensity,
Maximum seismic intensity level, (L Fs ) max Maximum seismic intensity level, (L fv ) max Maximum seismic intensity level, (L fd ) max (a) Maximum acceleration, α max (gal) (b) Weighting factor,λ v (f) Weighting factou,λ a (f) The off the Pacific coast The Mid Niigata Prefecture Earthquake in Maximum velocity, v max (cm/s) (c) Weighting factor,λ d (f) The off the Pacific coast The Mid Niigata Prefecture Earthquake in The off the Pacific coast The Mid Niigata Prefecture Earthquake in Maximum displacement, d max (cm) Fig. Relationship between the maximum seismic intensity and a max, v max, d max. the same high-cut and low-cut filters, in the off the Pacific coast and the Mid Niigata Prefecture Earthquake in. The relation between (L Fs ) max and the maximum value a max of the acceleration is added in Fig.(a). The maximum seismic intensity level is distributed on the line, which has an approximate gradient for a max, v max, d max on a semi-logarithm, and these dispersions show the extent of about.. These tendencies were similarly recognized in two other earthquakes. The combined seismic intensity proposed by Kiyono et al. ), ) (It is called Kiyono index in the paper) uses the time history of velocity and displacement. Since the maximum seismic intensity levels and are obtained from the weighting factors λ av (f) and λ ad (f) corresponding to the velocity and displacement, these seismic intensity levels are compared with the Kiyono index which is expressed by I m (=.9 log(v )+.) for medium period and I l (=.9 log(d )+.) for long period, as shown in Figs.(a)~(d). The maximum seismic intensity levels and become small in the Kiyono index, I m and I l, as the value of seismic intensity decreases. These tendencies are deemed to have originated from the following two factors: ) The Kiyono indices, I m and I l, are a little larger than and, from which the gradients.9 Maximum seismic intensity level,, Maximum seismic intensity level,, (a) The Mid Niigata Prefecture Earthquake in f =. Hz : m= (b) The off the Pacific coast (c) f =. Hz : m= The Tokachi-oki Earthquake in f =. Hz : m= (d) The Iwate-Miyagi Nairiku Earthquake in 8 f =. Hz : m= (a) The Mid Niigata Prefecture Earthquake in f =. Hz : m= (b) The off the Pacific coast f =. Hz : m= (c) The Tokachi-oki Earthquake in f =. Hz : m= (d) The Iwate-Miyagi Nairiku Earthquake in 8 f =. Hz : m= Seismic intensity by Kiyono et al., Seismic intensity by Kiyono et al., I m (midium period) I l (long period) Fig. Comparison between the Kiyono index and the maximum seismic intensity level,. and.9 in the logarithms for velocity (v ) and displacement (d ), respectively, are smaller than. ) The periodic region of the Chebyshev filter uses the Kiyono index (pass band and interception of high-cut (Hz, Hz) and low-cut (.Hz,.Hz)) has designated the range, which is wider than that of filters F a (f) and F a (f) for both short- and long-period sides. () Comparison of the time histories of seismic intensity level In the seismic intensity level using the running r.m.s. method, the time history of the seismic intensity can be expressed. Here, the time histories for three kinds of seismic intensity levels L Fs, L Fav, and L Fad are compared. Fig. is a comparison of three
Seismic intensity level, L Fs, L Fav, L Fad Fourier spectrum of acceleration (cm/sec) The off the Pacific coast Tsukidate(MYG) Seismic intensity level L Fs L Fav (corresponding to velocity) L Fad (corresponding to displacement) Time (sec) Fig. The time history of seismic intensity level. (a) Tsukidate Non-filtered acc. (MYG) Filtered acc. (λ a ) (b) Filtered acc. Filtered acc. (c) The off the Pacific coast Filtered acc. (λ a ) (f =.,α=-.) Filtered acc. (λ av ) (m=) (λ a ) (f =.,α=-.) (λ ad ) (m=).. Fig.8 Comparison of the Fourier spectrum of acceleration with various filters. kinds of seismic intensity levels with the same Tsukidate (MYG; K-NET) as the observation point in Fig. in the off the Pacific coast of Tohoku Earthquake. The maximum seismic intensity levels, and, corresponding to velocity and displacement have appeared at the same time as (L Fs ) max, though the values of.9 and.8 are smaller than the value of. for (L Fs ) max. The relative relation of these three seismic intensity levels L Fs, L Fav and L Fad can be associated with the Fourier spectrum of the weighted acceleration. Figs.8(a)(b)(c) compare the Fourier spectrum of the frequency-weighted acceleration used to calculate these seismic intensity levels. The weighting factors used in each figure are as follows: (a) Non-filtered and the weighting factor λ a (f) of acceleration for the instrumental seismic intensity, (b) The weighting factor λ a(f) (α=-.) of acceleration used F a (f)f a (f) instead of the low-cut filter of the instrumental seismic intensity and the weighting factor λ av (f) (m=) of acceleration corresponding to velocity, (c) The weighting factor λ a(f) (α=-.) and the weighting factor λ ad (f) (m=) of Seismic intensity level, L Fs, L Fav, L Fad Seismic intensity level, L Fs, L Fav, L Fad (a) The off the Pacific coast Misawa (AOM) L Fs L Fav L Fad (b) The Earthquake of northern coast in Iwate Prefecture 8 Misawa (AOM) L Fs L Fav L Fad Time (sec) Fig.9 Comparison of the time histories of seismic intensity levels for two earthquakes (Misawa, K-NET). acceleration corresponding to displacement. The filtered acceleration used λ a (f) in Fig.8(a) shows the largest spectrum at the short period of. second as well as the predominant period of. second for the observation seismic wave. The peak of spectrum of the filtered acceleration used λ a(f) in the short period of. second (α= -., -.) indicates the comparatively large value of almost the same or half that of the peak value in a long period, respectively in Figs.8(b)(c). That is, the seismic intensity levels L Fav, L Fad corresponding to velocity and displacement become smaller than L Fs, from which the ratio of the peak value in both the short period and the long period of the Fourier spectrum does not become large in the case of the seismic wave having a predominant period remarkable in the short period. The relative relation of the seismic intensity levels L Fs, L Fav, and L Fad will change with the frequency characteristics of input seismic waves even if in the same observation point. Figs.9(a)(b) show an example of these relative relations in two earthquake waves ((a) the off the Pacific coast of Tohoku Earthquake, (b) the Earthquake of northern coast in Iwate Prefecture 8) in the observation point, Misawa, (AOM: K-NET). The seismic intensity level in Fig.9(a) shows a large value in the order of L Fs, L Fav, and L Fad, though the time in the peak value of both L Fav and L Fad is about seconds late compared to that of L Fs. On the other hand, the reverse order is seen in the seismic intensity level including a peak value until about seconds in Fig.9(b). The difference in such seismic intensity level can be de-
Fourier spectrum of acceleration (cm/sec) Fourier spectrum of acceleration (cm/sec) (a) (b) (c) The off the Pacific coast Filtered acc.(λ a ) (f =.,α=-.) Filtered acc. (λ av ) (m=) Filtered acc. (λ a ) (f =.,α=-.) Filtered acc. (λ ad ) (m=) Non-filtered acc. Filtered acc. (λ a ) Misawa (AOM).. (a) The Earthquake of northern coast in Iwate Prefecture 8 Non-filtered acc. Filtered acc. (λ a ) Misawa (AOM) (b) Filtered acc. (λ a ) (f =.,α=-.) Filtered acc. (λ av ) (m=) (c) Filtered acc. (λ a ) (f =.,α=-.) Filtered acc. (λ ad ) (m=).. Fig. Comparison of Fourier spectrum of acceleration with various filters for two earthquakes. termined from the Fourier spectrum of the filtered acceleration shown in Figs.(a)~(c) and Figs. (a)~(c), as well as in Fig.8. The spectrum of the acceleration has almost the same peak value at the period of. and. seconds in the observation wave, but has the largest peak value at the period of around. seconds in the seismic wave using the weighting factor λ a (f) of the instrumental seismic intensity as shown in Fig.(a). Therefore, the proportion of the short period component for λ a(f) (α= -., -.) in Figs.(b)(c) is extremely small, and the large amplification is shown only in the longperiod side. Alternatively, since the spectrum of the observation wave in Fig.(a) has the largest peak value at the short period of. second, the influence of the long-period component in λ a(f) in Figs. (b)(c) on velocity and displacement would become small. Accordingly, the remarkable amplification in the long period region is not recognized as well as the case of Tsukidate as shown in Fig.8.. CONCLUSIONS The various weighting factors for acceleration are proposed to express the seismic intensity in consideration of velocity and displacement. Also, the time history indications of various seismic intensity levels are performed by using the running r.m.s. method. The main results are as follows: ) The extension of the function of the low-cut filter used for the instrumental seismic intensity is an effective method to evaluate the influence of the medium and long period on the seismic intensity. The weighting factor of acceleration for the seismic intensity will be given by the filter using the asymptote with arbitrary gradient m, in which the values of and correspond to the filter of velocity and displacement, respectively. From the characteristics of these weighting factors, the relation between the instrumental seismic intensity and the seismic intensity corresponding to velocity and displacement can be clarified. ) The influence of the weighting factor on the seismic intensity was clarified by comparison with the instrumental seismic intensity, the Kiyono index, and the maximum seismic intensity level using the various weighting factors, in particular corresponding to velocity and displacement. Moreover, the seismic intensity level for velocity waveform and displacement waveform using the same high-cut and low-cut filters for acceleration is mostly in agreement with the seismic intensity level using the weighting factor of acceleration corresponding to velocity and displacement. ) The seismic intensity levels corresponding to not only the instrumental seismic intensity but also to velocity and displacement are expressed in the time histories. The relative relation of these seismic intensity levels can be pointed out by the difference in the Fourier spectrum of the various filtered accelerations. This paper is a basic research on the expression of the seismic intensity considering the influence of the medium and long periods, and pointed out the possibility of various seismic intensity expressions. However, it will have future problems on the detailed relation between the seismic intensity and the damage of structures having a predominant medium or long period. Likewise, studies on the integral time of the running average on the running r.m.s. method, the value of c s in Eq.() and the seismic intensity using the weighting factor with various values of f and α are required.
NOTATIONS F a (f), F a (f), F a (f) : filter on the period effect, highcut filter and low-cut filter, respectively, which were used for instrumental seismic intensity λ a (f) : weighting factor of acceleration for instrumental seismic intensity F a (f) : low-cut filter with parameters α, f F a (f) : the ninth Butterworth filter (cutoff frequency.hz) λ a(f) : weighting factor of acceleration used F a (f) (α >.) or F a (f) F a (f) (α <.) instead of low-cut filter for instrumental seismic intensity L is : seismic intensity acceleration level L Fs : seismic intensity level I : instrumental seismic intensity (weighting factor, λ a (f)) I f,α : instrumental seismic intensity used weighting factor, λ a(f) L Fs : seismic intensity level used weighting factor, λ a(f) F fa (f) : filter with the gradient m for period in logarithm λ fa (f) : weighting factor of acceleration given by F fa (f)f a (f)f a (f) L fa : seismic intensity level used weighting factor, λ fa (f) λ av (f) : weighting factor of acceleration corresponding to velocity λ ad (f) : weighting factor of acceleration corresponding to displacement L Fav : seismic intensity level used weighting factor, λ av (f), corresponding to velocity L Fad : seismic intensity level used weighting factor, λ ad (f), corresponding to displacement λ v (f) : weighting factor of velocity λ d (f) : weighting factor of displacement L fv : seismic intensity level of velocity L fd : seismic intensity level of displacement REFERENCES ) Seismic Intensity Observation Advisory Committee : The report of seismic intensity observation advisory committee, 988.. (in Japanese) ) Kawasumi, H. : Seismic intensity and seismic intensity scale, Journal of the Seismological Society of Japan, Vol., pp. -, 9. (in Japanese) ) Japan Meteorological Agency : Calculation method of instrumental seismic intensity, http://www.seisvol.kishou.go.jp/eq/kyoshin/kaisetsu/calc_ sindo.htm (in Japanese) ) Seismic Intensity Problem Study Committee : The final report of seismic intensity problem study committee, 99.. (in Japanese) ) Japan Meteorological Agency and Fire and Disaster Management Agency : The report of study committee concerning the seismic intensity, 9.. (in Japanese) ) Kiyono, J., Fujie, K. and Ohta, Y. : A combined instrumental seismic intensity -concept, formulation and application-, Doboku Gakkai Ronbunshuu, No. /I-, pp. -, 999. (in Japanese) ) Kiyono, J., Toki, K., Usuda, T. and Ohta, Y. : Engineering characterization of instrumental seismic intensity and importance of introducing multi-valued seismic intensity, Doboku Gakkai Ronbunshuu, No. 8/I-, pp. -8,.. (in Japanese) 8) Sakai, Y., Kanno, T. and Koketsu, K. : Proposal of instrumental seismic intensity scale from response spectra in various period ranges, Journal of Structural and Construction Engineering (Transactions of AIJ), No. 8, pp. -,.. (in Japanese) 9) Shino, I. : Seismic intensity based on velocity response of single-degree-of-freedom system, Doboku Gakkai Ronbunshuu A, Vol., No., pp. 8-8,.. (in Japanese) ) Japan Meteorological Agency (Seismological and Volcanological Department) : The report of the treatment of information on the long-period ground motion,.. (in Japanese) ) Kuwata, Y. and Takada, S. : Instantaneous instrumental seismic intensity and evacuation, Journal of Natural Disaster Science, Vol., No., pp. -,. ) Kunugi, T., Aoi, S., Nakamura, H., Fujiwara, H. and Morikawa, N. : A real-time processing of seismic intensity, Earthquake, Vol., pp. -, 8. (in Japanese) ) Sakai, A. : A proposal of seismic intensity level using the running r.m.s. method, Doboku Gakkai Ronbunshuu A, Vol. 8, No., pp. -8,. (in Japanese) ) National Research Institute for Earth Science and Disaster Prevention (NIED), Strong-motion seismograph networks (K-NET, KiK-net) http://www.kyoshin.bosai.go.jp/ ) Japan Meteorological Agency : Strong-motion observation results - Strong-motion observation data of the main earthquake. http://www.seisvol.kishou.go.jp/eq/kyoshin/jishin/index.ht ml (Received June, )