Characteristics of strong shaking durationin Taiwan
Ya-Ting Lee, Kuo-Fong Ma, Yu-Ju Wang and Kuo-Liang Wen
Graduate Institute of Geophysics, National Central University, Jhongli, Taiwan 320, R.O.C
AbstractStrong shaking duration plays an important role to affect the yield damage caused by an earthquake. In this study, we analyzed the acceleration seismograms ofTaiwan Strong Motion Network to characterize the strong shaking duration with function of the earthquake magnitude and distance. We defined the duration to be thelength of interval across the dissipated energy within 5%~95% of the total energy during the time interval between the first and the last amplitude which equal to or
greater than a specified threshold value (here we gave the threshold value for 10gal). We calculated the strong shaking duration for 395 events with the magnitude rangedof ML=5.0~7.0 and the depth 50km during 1994 to 2010. We, thus, obtained an empirical equation of strong shaking duration with magnitude and distance as ME(τ,Δ) =2.3243 + 3.4171log(τ) + 0.0031Δ, where Δ is hypocenter distance (km), and τ is strong shaking duration time (sec). The equation can provide the characteristics of strong
shaking duration preliminarily for the Taiwan earthquakes. Also we considered the site condition. The four empirical equations of different site classes are established as:ME(τ) = 3.1947 + 2.8408 log(τ) + 0.0068Δ for B site (firm to hard rock), ME(τ) = 2.5859 + 3.3500 log(τ) + 0.0034Δ for C site (dense soil and soft rock), ME(τ) = 3.0225 +2.4587 log(τ) + 0.0044Δ for D site (stiff soil), and ME(τ) = 4.0424 + 1.6154 log(τ) + 0.0040Δ for E site (soft soil). The residual of the logarithm strong shaking duration isnormally distribution. This study also validated these equations using the earthquakes with the same criteria for the year of 2011 to 2012. The result indicated that theempirical duration equations can be applicable to estimate the strong shaking duration for the criteria earthquakes (ML5.0-7.0, depth< 50km) in Taiwan.
Definition of the Strong Shaking Duration

Strong Ground Motion Data and the Strong Shaking Duration(1) Bracketed duration: the time interval between the first and last amplitude greater than a level ofthreshold value. (Bolt, 1973)(2) Significant duration the time interval of the predetermined percentage of the total energy(Trifunac and Brady, 1975; Martin and Haresh, 1979).
(3) This study: the duration to be the length of interval across the dissipated energy within 5%~95%
of total energy during the time interval between the first and the last amplitude which equal to orgreater than 10gal (Fig. 1).
Figure 1 An example of theduration time of strong groundmotion record by the accelerationseismogram of HWA station. The
red dash lines show the timeinterval between the first and thelast amplitude which equal to orgreater than 10gal. The red lines
show the interval across thedissipated energy within 5%~95%of the total energy of the intervalof dash lines.

Mlog(τ ) = log(τ 0 ) + c' ∆ M (τ 0 ) = a + b(log τ 0 )
M (τ , ∆ ) = a + b(log τ ) − c∆

7.5

7.5

77

6.5

6.5

<Me>

Development of the Empirical Equations of Strong Shaking Duration

665.5

5.5

55

4.5
0Figure 3 Earthquakes distribution of theselected events from 1994 to 2010 (bluedots) with ML=5.0-7.0 and the depth<50km and the selected events from 2011 to2012 (red dots) for validation of thederived empirical equations

Figure 2 Distribution of strongmotion stations of Taiwan Strong
Motion Instrumentation Program(TSMIP). The colors denote the siteclassifications as defined by Kuo et al.
(2012).

0.51logτ 0

1.5

2Figure 6 The regressed
relationship between the strong
shaking duration at 0 km
distance(τ0) and magnitude(M).

4.5
4.55

5.5

6
<Mob>

6.577.5

Figure 7 The comparison of theestimated magnitudes <Me>and the observed magnitudes<Mob> for every 0.2 magnitudeinterval with c=-0.0009.

Figure 8 The probability
density of the residuals ofLogarithm duration time

Empirical Equation of Duration in Different Site Conditions

Validation of the Empirical Strong Shaking Duration Equations
(a)

(b)
(a)

7.5

7.5

77

6.5

6.5

66

5.5

5.5

55

4.5
0

0.5

1logτ0

1.5

4.5
02

0.5

Site D
7.5

7.5

77

6.5

6.5

6

5.5

55
0.5

1logτ01.521.5265.5

4.501logτ0Site EM

Figure 5 The probability densityof the residuals of Logarithm
duration time for 0.2 magnitudeinterval of M=5.0-7.0. The reds
display the normally distribution.

M

Figure 4 Logarithm of strong shaking duration
time decay with distance for 0.2 magnitudeinterval of M=5.0-7.0. The red lines show thebest regression of the data and red dash lines
show the ±RMS range (68% of data in this range).

Site CM

M

Site B

1.524.500.5

1logτ0Figure 9 The regression
relationship of strong shaking
duration at zero distance (τ0)
and magnitude(M) for different
site classes.

Figure 10 The comparison of
the average of the estimatedmagnitude <Me> to theobserved magnitudes <Mob>for
magnitude in 0.2 interval forsite classes B, C, D, and E.

Figure 11 The probability
density of the residuals ofLogarithm duration time forsite classes B, C, D, and E.

M E (τ) = 3.1947 + 2.8408 log(τ) + 0.0068Δ for site class B with σ=0.2324;
M E (τ) = 2.5859 + 3.3500 log(τ) + 0.0034Δ for site class C with σ=0.2239;
M E (τ) = 3.0225 + 2.4587 log(τ) + 0.0044Δ for site class D with σ=0.2396;
M E (τ) = 4.0424 + 1.6154 log(τ) + 0.0040Δ for site class E with σ=0.2497;
Figure 12 The comparison of the estimatedduration to the observed duration for theearthquakes within ML=5.0~7.0 from 2011 to2012. The dash lines show the range within thestandard deviation σ, 2σ, and 3σ of theestimated strong shaking duration (the 68% ofstrong shaking duration data within τe±σ sec,95% within τe±2σ sec, and 99.7% within
τe±3σ). The colors of the strong shaking
duration (circles) denote the site classes of therecording data. (a) for the earthquakes within
ML=5.0~7.0 from 2011 to 2012 (b) for Chi-Chiearhtquake(b)

Figure 13 Histogram of theresidual of the logarithm duration
for site classes B, C, D, and E.
The σ are standard deviation
values. (a) for the earthquakes
within ML=5.0~7.0 from 2011 to2012 (b) for Chi-Chi earhtquake

Couclusion
The major objective of this study is to establish the empirical strong shaking duration equations
for Taiwan earthquakes. This study made a new definition for the strong shaking duration which is inconsideration of the amplitude and energy factors. We analyzed the strong ground motion ofacceleration from TSMIP network and obtained the empirical equations for different site classes B, C,D, and E individually. We also validated the equations using the earthquakes with ML5.0-7.0 and thedepth < 50km for the years of 2011 to 2012. The validation result of the empirical equations showsthat most of the τe values are comparable with the τob values, that indicated the empirical duration
equations can be applicable to estimate the strong shaking duration for the criteria earthquakes(ML5.0-7.0, depth< 50km). These empirical equations could provide the characteristics of strong
shaking duration preliminarily for Taiwan earthquakes. We also found that some extreme data (τ >50seconds) are on soil alluvium sites (plains and basin areas) in site class D and E. The site effect could
efficiently cause longer strong shaking duration (Fig. 9).