Simulation of ground motions in the Korean peninsula using a stochastic model with generalized inversion technique

Abstract

In low to moderate seismic regions such as the Korean peninsula, it is difficult to perform seismic hazard analyses to construct hazard maps and curves because only a limited number of strong ground motion records is available. In this study, to solve such obstacles, ground motions are simulated using a stochastic model for Fourier amplitude spectrum (FAS) in frequency domain and shaping window model in time domain. The generalized inversion technique is adopted to determine the seismological characteristics (source, path, and site effects) of the FAS for Korean region. The validity of the source, path, and site effects obtained from the GIT and that of simulated ground motions is verified.

Appendices

Appendix A

See Figs. 14 and 15.

Fig. 14

Matrix formulation for FAS

Fig. 15

Matrix formulation for $FAS$ without path effect

Appendix B: Extrapolation of the GMS to simulate strong ground motions

The GMS model proposed in this study could be used to simulate strong ground motions, which could be used to conduct seismic hazard analyses and to construct the seismic map. It is important to acquire strong ground motion data for low-to-moderate seismicity regions such as the Korean Peninsula.

For this purpose, ground motions should be simulated for any given event with a specific magnitude and ${R}_{H}$. In previous sections, the source effect is determined using the GIT only for earthquake events collected in the database.

Equation B1 can be used to determine the source effect, which was proposed by Brune (1970, 1971), which was used in previous studies (Atkinson and Boore 1995, 2006; Toro et al. 1997; Boore 1983, 2003 Campbell 2003; Pezeshk et al. 2011; Atkinson et al. 2015; Yenier and Atkinson 2015).

$$Source\left(f,{M}_{o},{f}_{c},{\kappa }_{Source}\right)=\left(\frac{{R}_{\theta \varnothing }FV}{4\pi {\rho }_{s}{\beta }_{s}^{3}}\right)\cdot \frac{{M}_{o}}{1+{\left(f/{f}_{c}\right)}^{2}}\cdot {\text{exp}}\left(-\pi f{\kappa }_{Source}\right)\cdot {\left(2\pi f\right)}^{p}$$

(B1)

where ${M}_{o}$, ${f}_{c}$, and ${\kappa }_{Source}$ are the seismic moment in dyne-cm, corner frequency in Hz (Boore 1983), and source attenuation parameter for a given earthquake, respectively. The ${M}_{o}$ value can be calculated using equations proposed by Hanks and Kanamori (1979) by which source effect for a given earthquake magnitude can be estimated. The ${f}_{c}$ value can be calculated using an equation developed by Brune (1970, 1971), whereas the ${\kappa }_{Source}$ value can be found in Jee and Han (2022). In Eq. 13, ${R}_{\theta \varnothing }\left(=0.55\right)$ is the S-wave averaged radiation pattern coefficient (Boore and Boatwright 1984), $F\left(=2\right)$ is the free surface effect, $V\left(=1/\sqrt{2}\right)$ is the partition value of a vector into two horizontal components (Boore 1983), ${\rho }_{s}$ is the near source S-wave soil density in ${\text{g}}/{{\text{cm}}}^{3}$, ${\beta }_{s}$ is the near source S-wave shear wave velocity in ${\text{km}}/{\text{s}}$, and $p$ ($=$ 0, 1, and 2 for displacement, velocity, and acceleration) is the type of ground motion coefficient (Boore 1983). In Eq. 13, ${R}_{\theta \varnothing }$, $F$, and $V$ are parameters that use the same fixed values regardless of locations.

In addition to reproducing the ground motions recorded in the past in stable continental region (SCR) such as the Korean Peninsula, it is necessary to use methods that can extrapolate the magnitude of earthquakes in order to generate strong ground motions that may occur in future. According to previous studies (Hanks and Kanamori 1979; Boore 1983; Frankel 1994; Jee and Han 2022), it has been reported that the parameters ${M}_{o}$, ${f}_{c}$, and ${\kappa }_{Source}$ of the source effect can be determined for large moment magnitude (${M}_{W}$) in the stable continental region using Eq. B2, where ${M}_{o}$ can be calculated using Eq. B2 proposed by Hanks and Kanamori (1979).

$${M}_{o}={10}^{\frac{2}{3}\left({M}_{W}+10.7\right)}$$

(B2)

However, there is no simple way to calculate ${f}_{c}$ only with ${M}_{W}$. This problem can be circumvented by using the stress drop (∆σ) before and after an earthquake event. Equation B3 is an equation proposed by Boore (1983) to calculate ${f}_{c}$ using $\Delta \sigma$ and ${M}_{o}$ (Frankel 1994; Jee and Han 2022).

$${f}_{c}=4.906{\beta }_{s}{\left(\Delta \sigma /{M}_{o}\right)}^{1/3}$$

(B3)

Figure 16a shows the stress drop (∆σ) values for each earthquake event derived by Eq. B3 according to ${M}_{W}$. As shown in Fig. 16a, ∆σ is proportional to the increase in ${M}_{W}$, but above a certain ${M}_{W}$ value, ∆σ is a relatively stable.

Fig. 16

Estimated values of $\Delta\upsigma$ and ${\kappa }_{Source}$ according to ${M}_{W}$

Frankel (1994) reported that stable continental regions (SCRs) such as the Korean Peninsula have stable ∆σ for ${M}_{W}$ of 4.0 or higher, and Jee and Han (2022) also reported that stable ∆σ was obtained for ${M}_{W}$ of 3.63 or higher in the Korean peninsula. Considering this aspect, in a stable continental region such as the Korean Peninsula, ${f}_{c}$ can be calculated using Eq. B3 with a fixed value of ∆σ for ${M}_{W}$ of 4.0 or higher. Figure 16b shows the values of source attenuation parameter (${\kappa }_{Source}$) estimated using Eq. B1 for earthquake events collected in this study according to ${M}_{W}$. Similarly with ∆σ, ${\kappa }_{Source}$ increases in proportion to ${M}_{W}$, but it has almost constant value irrespective of ${M}_{W}$ when ${M}_{W}$ exceeds a certain value (= 3.63). Thus, based on such observations, ∆σ of 69.27 and ${\kappa }_{Source}$ of 0.0099 are used when ${M}_{W}$ = 4.0 or higher. Ground motions induced by earthquakes with ${M}_{W} =$ 4.0 or higher can be generated using the proposed ground motion simulation model with calculated ${M}_{o}$, ${f}_{c}$, and ${\kappa }_{Source}$. This indicates that the GIT-based ground motion simulation model proposed in this study can generate strong ground motions from future earthquakes with ${M}_{W}\ge 4.0$, which can be used when conducting seismic hazard analyses and developing ground motion prediction equation.

As an example, ground motions were generated at the YOW2 station for earthquakes of ${M}_{W}$= 6.0, 6.5, and 7.0 occurred at a latitude of 37.18, longitude of 128.71, and depth of 6 km. The epicentral distance was 23.21 km. Figure 17 shows the FAS and acceleration time histories of the ground motions.

Fig. 17

Sample Fourier amplitude spectrum and ground motion acceleration data generated from ground motion simulation model: a ${M}_{W}=6.0$, b ${M}_{W}=6.5$, c ${M}_{W}=7.0$

To simulate the strong ground motions for conducting seismic hazard analyses, the site effect should be determined at any locations in the Korean peninsula. There are ergodic amplification models, developed in different regions in the world. Nevertheless, to the best of our knowledge, there is no equation to determine the site effect for the Korean peninsula. The procedure calculating site effect proposed by this study makes it possible to determine site effect at any location of Korea. Without the proposed procedure, ground motions should be simulated only at the same locations of seismic stations in Korea. Otherwise, some assumptions should be made that all locations are the same site condition as the reference stations.

Once the source effect is determined, strong ground motions can be simulated according to the procedure in Sect. 7.