International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Stochastic gound motion simulation for crustal earthquakes in Japan Itoi, Tatsuya Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  1 Stochastic Ground Motion Simulation for Crustal Earthquakes in Japan Tatsuya Itoi Associate Professor, Graduate School of Engineering, the University of Tokyo, Tokyo, Japan  ABSTRACT: In this study, an empirical simulation model of stochastic ground motion for crustal earthquakes in Japan is proposed based on the ground motion records observed by K-NET in Japan from 1997 to 2011. The proposed model is developed based on that by Rezaeian & Der Kiureghian (2010). The characteristics of ground motion depends on various parameters such as magnitude, distance from source to site and local site conditions (shallow soil as well as deep subsurface structure), which is included in the parameters in the proposed model. The proposed model is considered useful when conducting probabilistic risk analysis of structures such as base-isolated or vibration-controlled buildings.  1. INTRODUCTION For probabilistic seismic risk analysis of structure such as base-isolated or vibration-controlled structures, time history analysis is employed. Ground motion time history is needed for the analysis. For conventional seismic risk analysis, artificially-generated ground motion time history where amplitude is adjusted so that it fits ground motion intensity with some exceedance probability is used. Exceedance probability of the ground motion intensity measure for amplitude adjustment is obtained based on probabilistic seismic hazard analysis for the intensity measure. The ground motion parameter such as its duration, however, is conservatively assumed frequently, which prevents realistic estimate by overestimating or underestimating the risk of the structure. On the other hand, ground motion simulation considering the fault rupture process such as the empirical Green’s function method is widely used. It is, however, not appropriate to be utilized in probabilistic seismic hazard analysis. This is because it requires much time and resource as well as because there is no established method for variability in simulated ground motion.   Therefore, in this study, an empirical simulation model for ground motion time history is developed based on that proposed by Rezaeian & Der Kiureghian (2008, 2010), and an empirical attenuation relation of ground motion time history is proposed, based on the observed records by K-NET in Japan.  2. MODELLING OF GROUND MOTION  2.1. Overview In this study, a model for velocity time history of ground motion is developed based on Rezaeian & Der Kiureghian (2008, 2010). Velocity time history 𝑣(𝑑) is assumed as follows:  𝑣(𝑑) ∝ π‘ž(𝑑, 𝜢)𝑒0(𝑑) (1) where, π‘ž(𝑑, 𝜢) is a time modulating function and 𝑒0(𝑑) is the stochastic process where variance is constant in time. The gamma distribution is employed for the time modulating function π‘ž(𝑑, 𝜢) as follows: π‘ž(𝑑, 𝜢) ∝ 𝑑𝛼1exp(βˆ’π›Ό2𝑑) (2) where, 𝛼1  and 𝛼2  are the constants. These constants are determined by determining 𝑑𝑝, the time where the amplitude of envelope reaches maximum, and 𝑑𝑑, the time where the amplitude 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  2 of envelope becomes 0.1 times the maximum amplitude. The amplitude of velocity time history 𝑣(𝑑) is defined by integrated squared velocity 𝐼𝑉  as follows: 𝐼𝑉 = ∫ 𝑣2(𝑑)π‘‘π‘‘βˆž0 (3) The stochastic process 𝑒0(𝑑) in Equation (1) is modelled by the weighted average of two stochastic processes, 𝑒1(𝑑) and 𝑒2(𝑑), as follows: 𝑒0(𝑑) = βˆšπ‘Ÿ(𝑑)𝑒1(𝑑) + √(1 βˆ’ π‘Ÿ(𝑑))𝑒2(𝑑) (4) where, the direct S waves are modeled using  𝑒1(𝑑), while the later phases are modeled using 𝑒2(𝑑). The stochastic process, 𝑒1(𝑑) and 𝑒2(𝑑), respectively are modeled as the response of 1 DOF system with different natural frequency π‘“π‘˜ and damping coefficient πœπ‘˜  which is excited by Gaussian process π‘€π‘˜(𝜏) as follows: π‘’π‘˜(𝑑) ∝ ∫ β„Žπ‘˜(𝑑 βˆ’ 𝜏|π‘“π‘˜, πœπ‘˜)π‘€π‘˜(𝜏)π‘‘πœπ‘‘βˆ’βˆž (5) The weight π‘Ÿ(𝑑) in Equation (4) is assumed proportional to time t as follows: π‘Ÿ(𝑑) = {1 βˆ’π‘‘π‘‘π‘  (0 < 𝑑 ≀ 𝑑𝑐)0                (𝑑 > 𝑑𝑐) (6) The model proposed here needs eight parameters, πΌπ‘‰οΌŒπ‘“1οΌŒπ‘“2,𝜁1,𝜁2οΌŒπ‘‘cοΌŒπ‘‘π‘οΌŒπ‘‘π‘‘ , to simulate velocity time history of ground motion. 2.2. Ground motion parameters Ground motion parameters, πΌπ‘‰οΌŒπ‘“1οΌŒπ‘“2,𝜁1,𝜁2οΌŒπ‘‘cοΌŒπ‘‘π‘οΌŒπ‘‘π‘‘, are estimated for each recorded ground motion time history. The procedure for parameter estimation is almost same as that in Rezaeian & Der Kiureghian (2008, 2010).  3. GROUND MOTION DATABASE  Database for ground motion time histories recorded at K-NET stations at fault distances less than 100 km is compiled from crustal earthquakes of moment magnitude (Mw) larger than 5, which occurred from 1997 to 2011. Figure 1 shows the location of earthquake hypocenter, while the relation between magnitude and fault distance for each record is shown in Figure 2. The range of site condition for recorded motions is 200m/s ≀𝑉𝑆30 ≀ 700m/s and 𝑍1500 ≀ 2000m. Ground motion parameters, πΌπ‘‰οΌŒπ‘“1οΌŒπ‘“2,𝜁1,𝜁2 , 𝑑c , 𝑑𝑝 , 𝑑𝑑 , are estimated for each component record.  e Figure 1: Location of earthquake hypocenter   Figure 2: Relation between magnitude and fault distance for ground motion database  4. PREDICTION EQUATION  4.1. Transformation of probability distribution for ground motion parameters First, statistics for each ground motion parameters are analyzed. Table 1 shows the probability 0 20 40 60 80 10055.566.57Fault distance (km)MW  Strike-slipNormalReverseReverse(oblique)12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  3 distribution and its parameters for each ground motion parameter. Table 1 shows the parameters for probability distribution for each ground motion parameter estimated by the maximum likelihood method.  Table 1: Parameter values.   Then, each ground motion parameter is transformed so that it fits the standard normal distribution as follows: 𝑣𝑖 = π›·βˆ’1 (𝐹𝛩𝑖(πœƒπ‘–)) (7) where, π›·βˆ’1( )  is the inverse of the standard normal distribution. The probability density function for the gamma distribution is as follows: 𝑓𝑋(π‘₯) =1𝛽𝛼𝛀(𝛼)π‘₯π›Όβˆ’1π‘’βˆ’π‘₯𝛽 (8) where, the 𝛼  and 𝛽  are distribution parameters, and 𝛀( ) is the gamma function. The probability density function for the beta distribution is as follows: 𝑓𝑋(π‘₯) =1𝐡(π‘ž, π‘Ÿ)π‘₯π‘žβˆ’1(1 βˆ’ π‘₯)π‘Ÿβˆ’1 (9) where, and π‘ž  and π‘Ÿ  are the distribution parameters, and 𝐡( ) is the beta function. The probability density function for the lognormal distribution is as follows: 𝑓𝑋(π‘₯) =1π‘₯𝜎lnπ‘‹βˆš2πœ‹π‘’π‘₯𝑝 {βˆ’(lnπ‘₯ βˆ’ πœ‡ln𝑋)22𝜎ln𝑋2} (10) where, πœ‡ln𝑋  and 𝜎ln𝑋  are the distribution parameters. Mean ground motion parameters 𝑣AM𝑖 , which are the average of those for each component, 𝑣NS𝑖 and 𝑣EW𝑖 , is calculated as follows: 𝑣AM𝑖 =12(𝑣NS𝑖 + 𝑣EW𝑖) (11) Standard deviation of 𝑣NS𝑖 βˆ’ 𝑣AM𝑖  is estimated as follows: 𝜎comp𝑖 = √Var(𝑣NS𝑖 βˆ’ 𝑣AM𝑖) (12) Table 2 shows the estimated standard deviation for each ground motion parameter.  Table 2: Standard deviation of  𝑣NS𝑖 βˆ’ 𝑣AM𝑖   4.2. Prediction equation In this section, a prediction equation for each ground motion parameter is obtained. The explanatory variables for the equation are those for source, propagation path and site amplification characteristics as follows: 𝑣AMπ‘–π‘—π‘˜ = 𝑔(π‘€π‘Šπ‘—, 𝐷𝑗, π‘…π‘—π‘˜ , 𝑉𝑆30π‘˜, 𝑍1500π‘˜)+ πœ€π‘—π‘˜ (13) where, π‘€π‘Šπ‘— , 𝐷𝑗 , π‘…π‘—π‘˜ , 𝑉𝑆30π‘˜  and 𝑍1500π‘˜  are moment magnitude, hypocenter depth, shortest fault distance, 30 meter average shear wave velocity and depth to the layer with shear wave velocity of 1500m/s.  The regression equation for each ground motion parameter is as follows: 𝑣AM1= π‘Ž10 + π‘Ž11π‘€π‘Š6.0+ π‘Ž12𝐷10km+ π‘Ž13log10 (𝑅 + π‘Ž1610π‘Ž17π‘€π‘Š40km)+ π‘Ž14log10 (𝑉𝑆30400m/s)+ π‘Ž15min(𝑍1500, π‘Žπ‘–9)100m+ πœ€1 (14)  𝑣AM𝑖= π‘Žπ‘–0 + π‘Žπ‘–1π‘€π‘Š6.0+ π‘Žπ‘–2𝐷10km+ π‘Žπ‘–3𝑅40km+ π‘Žπ‘–4log10 (min(𝑉𝑆30, π‘Žπ‘–8)400m/s)+ π‘Žπ‘–5log10 (𝑍1500100m) + πœ€π‘– (𝑖 = 2,3) (15)  (unit) Distibution BoundI V (v 1) (m2/s) Lognorm l (0, ∞) mlnEv -8.308 slnEv 2.777f 1 (v 2) (Hz) Gamma (0, ∞) af1 4.549 bf1 0.8055f 2 (v 3) (Hz) Gamma (0, ∞) af2 1.597 bf2 1.328z 1 (v 4) - Beta (0, 1) qz1 1.0147 rz1 5.484z 2 (v 5) - Beta (0, 1) qz2 0.8117 rz2 2.553t c (v 6) (s) Gamma (0, ∞) atc 3.707 btc 5.143t p (v 7) (s) Gamma (0, ∞) atp 1.415 btp 3.226t d - t p (v 8) (s) Lognormal (0, ∞) mln(td-tp) 3.488 sln(td-tp) 0.8019Distribution parametersParamet rv 1 v 2 v 3 v 4 v 5 v 6 v 7 v 80.083 0.385 0.194 0.569 0.389 0.627 0.311 0.23312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  4 𝑣AM𝑖 = π‘Žπ‘–0 + π‘Žπ‘–1π‘€π‘Š6.0+ π‘Žπ‘–2𝐷10km+ π‘Žπ‘–3𝑅40km+ π‘Žπ‘–4log10 (𝑉𝑆30400m/s)+ π‘Žπ‘–5𝑍1500100m+ πœ€π‘–  (𝑖 = 4,5,7) (16)  𝑣AM𝑖 = π‘Žπ‘–0 + π‘Žπ‘–1π‘€π‘Š6.0+ π‘Žπ‘–2𝐷10km+ π‘Žπ‘–3min(𝑅, π‘Žπ‘–6)40km+ π‘Žπ‘–4log10 (𝑉𝑆30400m/s)+ π‘Žπ‘–5min(𝑍1500, π‘Žπ‘–9)100m+ πœ€π‘–(𝑖 = 6,8) (17) The regression results and the standard deviation of residuals are shown in Table 3, while the correlation coefficients between residuals are shown in Table 4.  4.3. Simulation of ground motion by proposed equations Ground motion time history of north-south component is simulated using the proposed equations. Figure 3 shows some samples for velocity and acceleration time histories for simulated ground motions. Ground motions are simulated for the source with π‘€π‘ŠοΌ6.5, 𝐷=15km and the site for 𝑅 =10km, 𝑍1500 =1000m, 𝑉𝑆30=500m/s. Figure 3 shows the comparison with respect to acceleration response spectra between the simulated ground motions and existing attenuation equations. Simulated acceleration response spectra are higher in the short period range. Effects of deep subsurface structure are simulated by the proposed model, while existing attenuation equations do not. Figure 4 shows the amplification of response spectrum (T=2s) due to deep subsurface structure, which is harmonic with the existing empirical relationship proposed by Itoi & Takada (2012).   Table 3: Regression coefficients and standard deviation of prediction error for Equations (14) – (18)   Table 4: Correlation coefficients between prediction errors for Equations (14) – (18).  i 0ai 1ai 2ai 3ai 4ai 5ai 6ai 7ai 8ai 9seiIVvGM1-8.046 8.400 0.254 -2.193 -1.498 0.099 31.65 0.394 - 444.1 0.386f1vGM23.022 -3.248 0.163 0.207 0.914 -0.330 - - 393.9 - 0.863f2vGM33.558 -3.212 0.301 -0.121 2.371 -0.673 - - 253.6 - 0.718z1 GM4-1.460 2.015 -0.133 -0.161 1.499 -0.009 - - - - 0.851z2vGM5-0.640 0.807 -0.144 0.096 2.099 -0.021 - - - - 0.803tcvGM6-3.726 2.215 -0.054 0.730 -0.712 0.118 65.77 - - 664.0 0.934tpvGM7-4.885 4.706 -0.315 0.303 -0.527 0.051 - - - - 0.690td-tpvGM8-3.865 2.116 -0.263 1.432 -0.648 0.185 48.81 - - 640.0 0.723GMPvGM1vGM2vGM3vGM4vGM5vGM6vGM7vGM8vGM11 -0.229 .061 - .075 -0.311 -0.162 0.008 -0.203vGM21 0.332 -0.338 0.287 -0.027 -0.006 -0.072vGM31 -0.134 -0.221 -0.176 -0.227 -0.537vGM41 0.157 -0.181 0.068 0.103vGM51 0.010 -0.139 -0.039vGM6sym. 1 0.109 0.444vGM71 0.330vGM8112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  5  Figure 3: Samples of simulated ground motions (north-south component) (π‘€π‘ŠοΌ6.5, 𝐷=15km and the site for 𝑅=10km, 𝑍1500=1000m, 𝑉𝑆30=500m/s)   5. CONCLUSIONS In this study, an attenuation relation for velocity ground motion time history is proposed for crustal earthquake in Japan. The proposed model is harmonic with existing attenuation relation for acceleration response spectra. The proposed relation can be applied to crustal earthquake with 5.1 ≀ π‘€π‘Š ≀ 6.9, and at the site for the shortest distance 𝑅 ≀ 100km  and the soil condition 200m/s ≀ 𝑉𝑆30 ≀ 700m/s and 𝑍1500 ≀ 2000m. The proposed model, however, is not applicable to the near-field ground motion at a soft soil site, because the non-linearity of soil amplification is not included in the proposed model, which will be discussed in the future study.  6. ACKNOWLEDGEMENT Ground motion data are provided by NIED (K-NET).   (a) 𝑅=10km 𝑍1500=20m  (b) 𝑅=10km 𝑍1500=1000m Figure 4: Comparison between simulated ground motions and conventional attenuation relation for response spectra  (π‘€π‘ŠοΌ6.5, 𝐷=15km, 𝑉𝑆30=500m/s)   Figure 5: Amplification for Sa(T=2s) due to deep subsurface structure (π‘€π‘ŠοΌ6.5, 𝐷=15km, 𝑉𝑆30=500m/s)  0 20 40-200002000cm/s20 20 40-1000100cm/s0 20 40-200002000cm/s20 20 40-1000100cm/s0 20 40-200002000cm/s20 20 40-1000100cm/s0 20 40-200002000cm/s20 20 40-1000100cm/s0 20 40-200002000cm/s2time(s)0 20 40-1000100cm/stime(s)10-110010-1100101102103Period(s)Pseudo velocity(h=0.05)(cm/s)  Kanno et al.Uchiyama & MidorikawaSatohSimulated (median)Simulated (+-sigma)10-110010-1100101102103Period(s)Pseudo velocity(h=0.05)(cm/s)  Kanno et al.Uchiyama & MidorikawaSatohSimulated (median)Simulated (+-sigma)0 500 1000 1500 200011.522.5Z1500(m)Amplification due to deep subsurface structure  Simulated (median)Itoi & Takada (2012)12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  6 7. REFERENCES Itoi, T. & Takada, T. (2012). β€œEmpirical correction of ground motion prediction equations of response spectra at rock sites for near-field earthquakes considering amplification effect with deep subsurface structure”, Journal of Japan Association for Earthquake Engineering, 12(1), 1_43-1_61. (in Japanese) Kanno, T. et al. (2006). β€œA New Attenuation Relation for Strong Ground Motion in Japan Based on Recorded Data” Bulletin of the Seismological Society of America, 96(3), 879–897. Rezaeian & Der Kiureghian (2008). β€œA stochastic ground motion model with separable temporal and spectral nonstationarities”, Earthquake Engineering and Structural Dynamics, 37(13), 1565-1584.                                  Rezaeian & Der Kiureghian (2010). β€œSimulation of synthetic ground motions for specified earthquake and site characteristics”, Earthquake Engineering and Structural Dynamics, 39(10), 1155-1180. Satoh, T. (2008). β€œAttenuation relations of horizontal and vertical ground motions for P wave, S wave, and all duration of crustal earthquakes” Journal of structural and construction engineering 73(632), 1745-1754 . (in Japanese) Uchiyama, Y. & Midorikawa, S. (2006). β€œAttenuation relationship for response spectra on engineering bedrock considering effects of focal depth” Journal of structural and construction engineering (606), 81-88. (in Japanese)  

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