6:15 PM - 7:30 PM
[SSS25-P07] Relations between seismic intensity by linear and nonlinear site responses using empirical transfer functions
In order to estimate broadband source models or predict strong motions to agree with intensity scale of historical earthquakes such as the 1923 Great Kanto earthquake and Nankai Trough earthquakes, intensity scale or seismic intensity should be calculated considering into nonlinear site responses. However, strong motions calculated by the stochastic Green’s function method using empirical site responses derived from weak motions or the empirical Green’s function method are not considered into nonlinear site responses. The site responses estimated by nonlinear seismic response analyses depend on subsurface structure models and the dynamic property models as well as the methods. In this study we develop an empirical relation between seismic intensity by linear and nonlinear site responses using many KiK-net records.
Firstly, we select strong motion records with peak ground accelerations greater than 300 cm/s2 of 68 earthquakes observed at 124 KiK-net stations and the weak motion records of 520 earthquakes there. Then we remove some records affected by rocking or uplifting vibrations of seismometers, basements or structures from the selected records. The record most strongly affected by such vibration was the strong motion records observed at KiK-net Haga with equivalent intensity scale of 7 during the 2011 Tohoku earthquake.
Then we calculate empirical transfer functions which are defined by spectral ratios of ground motions at a surface to vertical motions at a borehole for weak motions to those for strong motions. The strong motions by linear site responses are estimated from strong motion records multiplied by the empirical transfer functions, which are complex Fourier spectra, in the frequency domain. The strong motions in the time domain are calculated by the Fourier inverse method. This idea means that we use empirical transfer functions instead of theoretical transfer functions by the one-dimensional linear and equivalent linear analyses. The empirical transfer functions are not influenced by the assumptions of dynamic property models and subsurface structure models.
The seismic intensity by nonlinear site responses INON is modeled by seismic intensity by linear site responses ILIN and the equivalent predominant frequency fe=PGALIN /(2πPGVLIN). Here PGALIN and PGVLIN are the calculated peak ground acceleration and the peak ground velocity. The regression relation derived by the constrained least square method with ILIN≧INONis,
INON - ILIN =6.155-1.669 ILIN + 0.110 ILIN2-0.688log10fe.
Figure shows the relation between INON and ILIN and the regression relations. The maximum INON of data was 6.6 observed at KiK-net Hino during the 2000 Tottoriken Seibu earthquake. The range of ILIN used in the regression analysis is from 4.5 to 7.0. The number of transfer functions is 192. In the empirical equation, INON becomes smaller than ILIN beyond ILIN of about 5.0. We show that fe is better than Vs30 as a parameter of the equation because fe is influenced by not only site effects but also source and path effects. The higher fe is, the bigger the difference between INON and ILIN is. This feature reflects that amplification factors in the high frequency range decrease stronger than those in the low frequency range by the increase of damping factors due to nonlinearity of soil. In the obtained equation, INON is 6.4 in the case of ILIN =7.0 and fe=5Hz. INON is 6.7 in the case of ILIN =7.0 and fe=2Hz. Since ILIN2 term is added in the equation in order to represent the saturation of dynamic properties on the strain, the empirical equation of INON has the slight saturation effect on ILIN.
Acknowledgments: This research is supported by JSPS KAKENHI Grant Number 26242034 and 23241054. We use KiK-net records and P-S loggings by NIED and the hypocenter information by JMA.
Firstly, we select strong motion records with peak ground accelerations greater than 300 cm/s2 of 68 earthquakes observed at 124 KiK-net stations and the weak motion records of 520 earthquakes there. Then we remove some records affected by rocking or uplifting vibrations of seismometers, basements or structures from the selected records. The record most strongly affected by such vibration was the strong motion records observed at KiK-net Haga with equivalent intensity scale of 7 during the 2011 Tohoku earthquake.
Then we calculate empirical transfer functions which are defined by spectral ratios of ground motions at a surface to vertical motions at a borehole for weak motions to those for strong motions. The strong motions by linear site responses are estimated from strong motion records multiplied by the empirical transfer functions, which are complex Fourier spectra, in the frequency domain. The strong motions in the time domain are calculated by the Fourier inverse method. This idea means that we use empirical transfer functions instead of theoretical transfer functions by the one-dimensional linear and equivalent linear analyses. The empirical transfer functions are not influenced by the assumptions of dynamic property models and subsurface structure models.
The seismic intensity by nonlinear site responses INON is modeled by seismic intensity by linear site responses ILIN and the equivalent predominant frequency fe=PGALIN /(2πPGVLIN). Here PGALIN and PGVLIN are the calculated peak ground acceleration and the peak ground velocity. The regression relation derived by the constrained least square method with ILIN≧INONis,
INON - ILIN =6.155-1.669 ILIN + 0.110 ILIN2-0.688log10fe.
Figure shows the relation between INON and ILIN and the regression relations. The maximum INON of data was 6.6 observed at KiK-net Hino during the 2000 Tottoriken Seibu earthquake. The range of ILIN used in the regression analysis is from 4.5 to 7.0. The number of transfer functions is 192. In the empirical equation, INON becomes smaller than ILIN beyond ILIN of about 5.0. We show that fe is better than Vs30 as a parameter of the equation because fe is influenced by not only site effects but also source and path effects. The higher fe is, the bigger the difference between INON and ILIN is. This feature reflects that amplification factors in the high frequency range decrease stronger than those in the low frequency range by the increase of damping factors due to nonlinearity of soil. In the obtained equation, INON is 6.4 in the case of ILIN =7.0 and fe=5Hz. INON is 6.7 in the case of ILIN =7.0 and fe=2Hz. Since ILIN2 term is added in the equation in order to represent the saturation of dynamic properties on the strain, the empirical equation of INON has the slight saturation effect on ILIN.
Acknowledgments: This research is supported by JSPS KAKENHI Grant Number 26242034 and 23241054. We use KiK-net records and P-S loggings by NIED and the hypocenter information by JMA.