13th World Conference on Earthquake Engineering
Vancouver, B.C., Canada
August 1-6, 2004
Paper No. 910

ON A RATIONAL STRONG MOTION INDEX COMPARED WITH
OTHER VARIOUS INDICESYutaka NAKAMURA1SUMMARY
Ijma, instrumental seismic intensity of Japan Meteorological Agency, is just an artificial index without
physical meaning and can not be calculated in realtime. On the other hand, DI [1] is defined by thelogarithm of the absolute value of the inner product of an acceleration vector and a velocity vector withregards to the power of an earthquake motion, and can be calculated in realtime. The realtime seismic
intensity RI was proposed derived from the DI. The differences of RI value, maximum RI, and Ijma werean average of 0.05 and standard deviation 0.132 for strong motion records at totally 910 sites with Ijma 1
to 7 of M4-M8 Earthquakes. Furthermore, a calculation method for the instrumental MMI, Modified
Mercalli Intensity, based on DI value, maximum DI, was also proposed and the validity was verified.
Based on this technique, a new palm-top digital alarm seismometer AcCo, Acceleration Collector, thatgives a real-time display of the RI value or the instrumental MMI and the maximum acceleration by turns
was developed.
INTRODUCTION
In Japan considering about standardization of seismic intensity, it is impossible to avoid thinking about
Ijma, instrumental seismic intensity defined by JMA, Japan Meteorological Agency, although Ijma whichis artificial index without physical meaning is expedient and has a difficulty that cannot calculate inrealtime. In this paper, new index DI is proposed from Kg value, proposed to evaluate the vulnerability ofground, has a relationship with the damage of small buildings on the ground. DI is defined as a logarithmof an inner product of acceleration and velocity vectors. It has a physical meaning as a power ofearthquake motion, and is easy to speculate maximum DI relating with damage, also can calculate inrealtime, and DI and instrumental seismic intensity has almost the same property. Here some indicesderived from DI are proposed and they are compared with ordinary indices as maximum acceleration, Ijmaand SI value, maximum spectrum intensity originally defined by Housner [2]. By comparing DI value withmaximum acceleration, Ijma and SI value, RI, Realtime Intensity derived from DI, which can calculateand indicate real time and instrumental MMI, Modified Mercalli seismic Intensity, based on DI value, will
be proposed. Furthermore development of palm top digital alarm seismometer which gives a realtime
display of the RI value or the instrumental MMI and the maximum acceleration will be reported.

1Dr., System and Data Research Co., Ltd., Tokyo, Japan. Email: yutaka@sdr.co.jp

DI VALUE AND THE OTHER STRONG MOTION INDICESHere the strong motion indices such as DI value will be viewed.
Kg value [3], index of vulnerability of surface ground using micro tremors, is found to have a relationshipnot only with the liquefaction of ground but also with the damage of surroundings. Research on DI wasstarted at this point and the concept of DI was proposed in 1998 [4]. P wave alarm system based on the PI
value, the maximum DI of P-wave part, was at work for Tohoku Shinkansen in the same year.
Defined formula of Kg value, Kg=A2/F, can be thought as follow. Inner product of an response
acceleration vector a and an response velocity vector v can be considered to product of the amplification
factor and a square of basement ground acceleration as the input by response of surface ground. Then Kg
value correspond to the amplification factor. Thus sites which shows large Kg value has strong motion
and cause extensive damage to structures. Therefore calculating the power in direct was thought by using
acceleration record. Avoiding the value to be large, DI was defined by taking logarithm of power as
below.
DI = log (|Σ(a .v)|)(1)

By analyzing DI changing by time and maximum DI, DI value, DI increases when seismic wave arrives
and shows good relation between DI value and Ijma with shift. The amount of shift is 0.6 when DI value
is calculated with the earthquake motion of acceleration in Gal (cm/s/s) and velocity in 0.001cm/s withinfrequency range of between 0.1Hz and 5Hz.
The influence of vertical motion to calculate DI value was considered with data set of 314 sites including
the 2003 Miyagiken-Oki Earthquake, the 2003 Miyagiken-Hokubu Earthquakes, and the 2003 TokachiOki Earthquake. Between DI value calculated from three component, and omitting vertical motion
component, they have only differs average of 0.013 and standard deviation of 0.035. Therefore DI value
will be calculated by two horizontal components, in this paper. However DI value is calculated, fromcm/s/s about acceleration and cm/s about velocity, and also change the definition of “DI” from “DamageIndex” [5] to “Destructive Intensity”.
Nowadays maximum acceleration observed at ground surface is publicized from many organizations,though frequency range is not definite. Maximum acceleration increases for wide frequency range.
According to recent improvement of observation technique, observed frequency range is spreading. So theobserved large maximum acceleration doesn’t cause damage expected from past experience. Contrary
with this JR has already restrained the frequency range between 0.1 Hz and 5Hz for acceleration to alarm.
In this paper, records of several earthquakes observed by K-NET, KiK-net and also by Taiwan
Meteorological Agency are adopted. The range of data set for Magnitude and Ijma are M3.8~8.0 and0.6~6.6, respectively. Main samples of earthquakes are the 1995 Hyogoken-Nanbu Earthquake (M7.2),
the 2000 Tottori Earthquake (M7.3), the 2001 Geiyo Earthquake (M6.7), the 2003 Miyagiken-Oki
Earthquake (M7.0), the 2003 Miyagiken-Hokubu Earthquakes (M5.4-M6.2), the 2003 Tokachi-Oki
Earthquake (M8.0), and the 1999 Chi-Chi Earthquake of Taiwan(M7.6). Maximum acceleration (PGA)
publicized based on these data are calculated by two horizontal component or three component waveform
without filtering and including up to 30Hz. To distinguish PGA from maximum acceleration with JRalarm characteristic, “5HzPGA” will be used.
Ijma is calculated by each organization based on the definition of JMA. SI value has several variations,but here the definition of Tokyo Gas Company, acknowledged as SI sensor is adopted. This SI value isslightly smaller than the SI value defined by Incorporated Administrative Agency Public Works ResearchInstitute (PWRI).

SI value cm/s (Tokyo GAS method)

1000
5H zP G A cm /s/s

100

101100100.101234561701234567Ijma

Ijma

Figure 1 The relationship Ijma and SI value.

Figure 2 The relationship Ijma and 5HzPGA.

P G A in cm /s/s

1000

100

10

101234567Ijma
Figure 3 The relationship between Ijma and PGA.

RELATIONSHIP BETWEEN IJMA, SI VALUE AND 5HZPGAIn this section, 3 types of practical major indices, Ijma, SI value and 5HzPGA will be mutually compared.
Figures 1 and 2 show relationships between Ijma and 5HzPGA, and between Ijma and SI value,respectively. According to these figures, range of dispersion corresponding with Ijma, SI value shows
almost same as 5HzPGA. Figure 3 shows wide dispersion on the relationship Ijma and PGA. Thesefigures show that acceleration generally does not have good relations with damage, but 5HzPGA omittinghigh frequency component shows conformity with SI value which shows good relation with damage.
Here, to discuss on same frequency range are proposed because maximum acceleration depends on it.
PROPOSAL OF RI VALUE AND RELATIONSHIP WITH IJMA
RI value corresponded to Ijma will be defined as below.
RI = DI + 2.4(2)765Ijma432
1001234567RI value

Difference ofIjma and RI value

Figure 4 The relationship between RI value, maximum RI, and Ijma

1.0

差

0.5
0.0
-0.5
3

45

6M agnitude

789Figure 5 The relationship between magnitude and difference of Ijma and RI value

Figure 4 shows the relationship between RI value, maximum RI, and Ijma. Data set used here hasmagnitude range of M3.8 to M8.0 and Ijma range of 0.6 to 6.6. Number of strong motion data is 910,
difference between Ijma and RI value is average 0.050, standard deviation 0.134. Thus both RI value andIjma can be seen same practically. Figure 5 shows relationship between magnitude and difference of RI
value and Ijma. It tends that RI value is a little smaller than Ijma when M<7, a little larger than Ijma whenM>7. Since predominant frequency becomes smaller as magnitude becomes larger, RI value becomes
smaller than Ijma when predominant frequency is high, and when predominant frequency becomes lower
it becomes larger than Ijma. From a trend of recent relations between damage of earthquake andearthquake motion, this characteristic of RI value seems more proper for index of strong motion.

PROPOSAL OF INSTRUMENTAL MMI
In former section RI value related to Ijma was defined based on DI. In this section instrumental MMI will
be proposed. Scales of Ijma and MMI are 0 to 7 and 1 to 12, respectively. First RI value corresponding toIjma will be uniformly enlarged to MMI, then verified the validity comparing with maximum accelerationand maximum velocity. Proposed formula is below,
MMI=(11/7)*RI + 0.50=(11/7)*DI + 4.27(3)Figure 6 shows comparison between MMI calculated by formula (3) and PGA. In this figure relationship

P G A in cm /s/s

1000

100

10

Modified Mercalli Intensity
by C.F.Richter(1958)
revised by B.A.Bolt(1993)
by David J. Wald (1999)

112

3456789 10 11 12M M I by A cC o (sim ulation)

Figure 6 The comparison between MMI and PGA.

between MMI and PGA proposed by Richter [6], Bolt [7] and Wald [8] are shown. By this after thedefinition of Richter, PGA corresponding to MMI increases and relationship between instrumental MMI
and PGA is including the relationship between PGA and MMI defined by Richter, Bolt and Wald.
Figure 7 shows relationship between instrumental MMI and 5HzPGA and this relationship well matcheswith relationship Richter’s first definition. These figures can be interpreted as follows; the maximum
acceleration is able to measure for high frequency range recently, since high frequency does not contribute
well to damage, PGA including high frequency range deviated from seismic intensity. Generally strong
motion of higher than 5Hz is not effective to damage. In past, the observation range was about lower than5Hz, so the relationship between the instrumental MMI and 5HzPGA is expected to be similar to therelationship between MMI and PGA in original.
Figure 8 shows that the relationship between instrumental MMI and maximum velocity PGV almostagrees with the relationship by Bolt [9]. Therefore, validity of calculating MMI with formula (3) inrealtime is verified.

5H zPG A in cm /s/s

1000

100

10Modified Mercalli Intensity
by C.F.Richter(1958)
revised by B.A.Bolt(1993)
by David J. Wald (1999)

112

3456789 10 11 12M M I by A cC o (sim ulation)
Figure 7 The relationship between instrumental MMI and 5HzPGAP G V in cm /s

100

101
proposed by B. A. Bolt (1993)

0.1
123456789 10 11 12M M I by A cC o (sim ulation)

Figure 8 The relationship between instrumental MMI and maximum velocity PGVDEVELOPMENT OF PALM-TOP DIGITAL ALARM SEISMOMETER
Maximum acceleration is important to estimate the seismic force. DI, basis of RI value and instrumental
MMI, relates power of earthquake motion, which is important to estimate destructive energy of earthquake
motion. Based on this technique, digital alarm seismometer AcCo, Acceleration Collector, is developed.
Figure 9 shows the exterior view of AcCo. Table 1 is main specifications for AcCo. AcCo gives realtime
display of 5HzPGA and instrumental seismic intensity RI or MMI. Applying that accurate DI value can becalculated without using vertical component, it made saving in cost. AcCo has palm-top body weighs
below 1kg. AcCo has RS232C port to output digital waveform. Also it can record the waveforms for two
events, maximum and next, with pre-event-memory.

GalMMIGal and MMI, or RI, will be displayed withalternation every 0.5 seconds
Figure 9 Photo of AcCo and illustration its display manner

Dimension
WeightPower Supply
Operating temperature
Operating humidity
Sensor typeMeasurement range
Noise levelResolution
Sampling rate
Frequency range
Event Memory (option)
Frequency range
Contents of a display
Display type
Frequency range
Alarm conditions
Output method
Contents of an output
Output method

Table 1 The main specifications for AcCoPHYSICAL SPECIFICATIONS
17cm(w) x 12cm(h) x 6.5cm(d) (not including projections)
0.8 kg (not including a battery)
AC100V-240V, 50/60Hz, and 4VA (AC adapter attached, battery back up (*1)
0-50°CLess than 80% (not dew)
Measurement
Acceleration 2 direction
Each direction up to 2g (2 x 980Gal)
Less than 1Gal-rms
Approximately 1/6Gal
1/100 seconds
DC-10Hz
Record length 108 sec within pre-event memory 30 sec for max and next
events
Display
0.1-5HzThe maximum acceleration, RI or MMI(option)
4 characters of high luminosity 7 segment Light Emitting Diode
Alarm output
0.1-5Hz
Exceeding preset level (*2)
Red LED luminescence, buzzer and output via RS-232C
OutputWaveform and other information
The original protocol using RS-232C (D-SUB 9 pin socket). (Separately
optional software and optional cable are required to communication with PC.)

* The characteristics above-mentioned changes not with a guaranteed value but with observation conditions.

(*1) 006P(9V) battery are required for back up.
(*2) selectable from 12 stages of 10, 15, 20, 25, 30, 40, 50, 80,100,120,150 and 200Gal.

CONCLUDING REMARKSThis paper considered of rational index value of earthquake motion and proposed new index; RI value,Realtime seismic Intensity, that becomes almost the same with Ijma. Also proposed concrete method tomeasure MMI, which is standard seismic intensity among the world and verified its validity. Furthermore
palm top digital alarm seismometer which can display seismic intensity and acceleration in realtime wasdeveloped.
It is expected that this inexpensive digital alarm seismometer contributes to develop rational vulnerable
design and also leads the change of earthquake disaster prevention, with making strong motion index
common sense to public or making record strong motion easier for various structures.

ACKNOLEDGEMENTS
In this paper, the waveform data was mainly provided by K-KET and KIK-net of NIED, National ResearchInstitute for Earth Science and Disaster Prevention, and the Meteorological Agency of Taiwan. Dr. K. T.
Shabestari, former researcher of Earthquake Disaster Mitigation Research Center, calculated Ijma and SI
value of the 1995 Hyogoken-Nanbu Earthquake, the 2000 Tottori Earthquake and the 2001 Geiyo
Earthquake.
Midorikawa
laboratoryofTokyo
Instituteof
Technology,
http://www.enveng.titech.ac.jp/midorikawa/, calculated Ijma of the 1999 Chi-Chi Earthquake. Ijma of
Otherearthquakes
calculatedby
CUE,
Conference
onUsageof
Earthquakes,
http://www.sdr.co.jp/cue/cuemainjn.html, are used. I would like to sincerely express my highest
appreciation and gratitude to people and organizations above mentioned.

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