11:00 AM - 11:15 AM
[SSS11-13] Toward developing GMPE for acceleration response spectra using Pacific plate boundary earthquakes (2)
Keywords:GMPE, Acceleration response spectra, Interplate earthquakes
1.Introduction
In this study, we revisited the ground motion prediction equation (GMPE) and residuals, focusing on the magnitude dependence and the effect of velocity structure noted in previous studies. We used 10,400 records from 1,034 stations for 38 earthquakes with Mw 5.5 to 8.7.
2.Modeling of velocity structure dependence
First, each parameter related to the velocity structure was added to the basic equations and regression analysis was performed, to see which parameters are most effected to explain the observed acceleration response spectra. The regression coefficient of the source characteristic was estimated for each earthquake, while other regression coefficients were common to all earthquakes and estimated simultaneously.
The residuals between the observed and the predicted values and their standard deviations (σ) were compared and analyzed for each parameter related to the velocity structure. Based on the analysis, we decided to add Vs30, D1400, and mantle thickness to the basic equations as parameters.
3.Analysis of magnitude dependence
We then performed a regression analysis on the relationship between the regression coefficients of the source characteristics and Mw for each earthquake. Three cases of equations were tested in regression analysis: a linear equation, two linear equations with different slopes, and a quadratic equation. Source characteristics with Mw 5.5 to 8.7 were well explained by the latter two cases. s for the linear equation with two slopes was slightly smaller than for the quadratic equation.
4.Constructed GMPE and future prospects
The following equations were developed based on the studies described above.
log10Sa = A - bΔ - βlog10Δ -dδ0 + G(Vs30,D1400) ± σ
A = Aw1Mw + Ac (if Mw≦Mth)
A = Aw1Mth + Aw2(Mw - Mth) + Ac (if Mth<Mw)
δ0 = δmin (if δ<δmin)
δ0 = δ (if δmin≦δ<δmax)
δ0 = δmax (if δmax≦δ)
G(Vs30,D1400) = gVlog10(min[Vs30,Vmax]) + gDlog10(max[D1400,Dmin])
Where
Sa: Acceleration response spectrum with 5% damping [cm/s2]
*RotD50 by Boore (2010), five periods of 0.5, 1.0, 2.0, 3.0, and 5.0 seconds
Aw1,Aw2,Ac: Regression coefficient for source characteristics
Mw: Moment magnitude
Mth: Mw, where the earthquake scale dependence of source characteristics changes
b, β: Regression coefficient for attenuation characteristics
Δ: Shortest distance to fault [km] *Fault is assumed as ellipse
d: Regression coefficient for velocity structure (propagation path)
δ: Thickness of the mantle [km]
*From the top of the mantle to the top of the Pacific plate, based on the JIVSM model
dmin, dmax: Lower and upper limits for the thickness of the mantle [km]
*The upper limit applies only to western Japan
(the depth remains the same for northern Hokkaido)
gV: Regression coefficient for velocity structure (shallow ground)
Vs30: Average S-wave velocity at 30m below the surface [m/s]
PS logging + Midorikawa and Nogi (2015)
Vmax: Upper limit of Vs30
gD: Regression coefficient for ground amplification characteristics
D1400: Depth to the layer where Vs>=1400 m/s [m]
*J-SHIS deep velocity geological structure model (V4)
Dmin: Lower limit of D1400
σ: Standard deviation
We obtained σ of approximately 0.25-0.3 for the constructed GMPE. Due to the differences in the data sets, direct comparisons with previous studies were difficult. We plan to analyze the residuals using the Strong Motion Data Flat File 2023 Edition from the National Research Institute for Earth Science and Disaster Prevention.
Acknowledgements
This study was done as a part of the Supporting Project for the Headquarters for Earthquake Research Promotion (HERP) sponsored by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We used K-NET and KiK-net data. The figures were created using GMT.
In this study, we revisited the ground motion prediction equation (GMPE) and residuals, focusing on the magnitude dependence and the effect of velocity structure noted in previous studies. We used 10,400 records from 1,034 stations for 38 earthquakes with Mw 5.5 to 8.7.
2.Modeling of velocity structure dependence
First, each parameter related to the velocity structure was added to the basic equations and regression analysis was performed, to see which parameters are most effected to explain the observed acceleration response spectra. The regression coefficient of the source characteristic was estimated for each earthquake, while other regression coefficients were common to all earthquakes and estimated simultaneously.
The residuals between the observed and the predicted values and their standard deviations (σ) were compared and analyzed for each parameter related to the velocity structure. Based on the analysis, we decided to add Vs30, D1400, and mantle thickness to the basic equations as parameters.
3.Analysis of magnitude dependence
We then performed a regression analysis on the relationship between the regression coefficients of the source characteristics and Mw for each earthquake. Three cases of equations were tested in regression analysis: a linear equation, two linear equations with different slopes, and a quadratic equation. Source characteristics with Mw 5.5 to 8.7 were well explained by the latter two cases. s for the linear equation with two slopes was slightly smaller than for the quadratic equation.
4.Constructed GMPE and future prospects
The following equations were developed based on the studies described above.
log10Sa = A - bΔ - βlog10Δ -dδ0 + G(Vs30,D1400) ± σ
A = Aw1Mw + Ac (if Mw≦Mth)
A = Aw1Mth + Aw2(Mw - Mth) + Ac (if Mth<Mw)
δ0 = δmin (if δ<δmin)
δ0 = δ (if δmin≦δ<δmax)
δ0 = δmax (if δmax≦δ)
G(Vs30,D1400) = gVlog10(min[Vs30,Vmax]) + gDlog10(max[D1400,Dmin])
Where
Sa: Acceleration response spectrum with 5% damping [cm/s2]
*RotD50 by Boore (2010), five periods of 0.5, 1.0, 2.0, 3.0, and 5.0 seconds
Aw1,Aw2,Ac: Regression coefficient for source characteristics
Mw: Moment magnitude
Mth: Mw, where the earthquake scale dependence of source characteristics changes
b, β: Regression coefficient for attenuation characteristics
Δ: Shortest distance to fault [km] *Fault is assumed as ellipse
d: Regression coefficient for velocity structure (propagation path)
δ: Thickness of the mantle [km]
*From the top of the mantle to the top of the Pacific plate, based on the JIVSM model
dmin, dmax: Lower and upper limits for the thickness of the mantle [km]
*The upper limit applies only to western Japan
(the depth remains the same for northern Hokkaido)
gV: Regression coefficient for velocity structure (shallow ground)
Vs30: Average S-wave velocity at 30m below the surface [m/s]
PS logging + Midorikawa and Nogi (2015)
Vmax: Upper limit of Vs30
gD: Regression coefficient for ground amplification characteristics
D1400: Depth to the layer where Vs>=1400 m/s [m]
*J-SHIS deep velocity geological structure model (V4)
Dmin: Lower limit of D1400
σ: Standard deviation
We obtained σ of approximately 0.25-0.3 for the constructed GMPE. Due to the differences in the data sets, direct comparisons with previous studies were difficult. We plan to analyze the residuals using the Strong Motion Data Flat File 2023 Edition from the National Research Institute for Earth Science and Disaster Prevention.
Acknowledgements
This study was done as a part of the Supporting Project for the Headquarters for Earthquake Research Promotion (HERP) sponsored by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We used K-NET and KiK-net data. The figures were created using GMT.