A Numerical Model for Simulating Ground Motions for the Korean Peninsula

Featured Application: Developing a numerical model for simulating ground motions for low ‐ to ‐ moderate seismic regions such as the Korean Peninsula. Abstract: Ground motions are used as input for the response history analyses of a structure. However, the number of ground motions recorded at a site located in low ‐ to ‐ moderate seismic regions such as the Korean Peninsula is few. In this case, artificial ground motions need to be used, which can reflect the characteristics of source mechanism, travel path, and site geology. On 15 November, 2017, the Pohang earthquake, with a magnitude of 5.4 and a focal depth of 9 km, occurred near the city of Pohang. This earthquake caused the most significant economic loss among the earthquakes that occurred in the Korean Peninsula. During the Pohang earthquake, valuable ground motions were recorded at stations distributed in the Korean Peninsula. In this study, a ground motion model is proposed based on ground motions recorded during the 2017 Pohang earthquake. The accuracy of the proposed model is verified by comparing measured and simulated ground motions at 111 recording stations.


Introduction
The Korean Peninsula is located in stable continental regions about 400 km from the boundaries of four plates: the Philippine Sea, Pacific, North American, and Eurasian Plates [1,2]. The seismic activity in this region is lower than that in regions located near plate boundaries such as Japan, Indonesia, or the Western United States. However, Korean historical documents reported that big earthquakes with a magnitude of 6 or larger occurred in the peninsula from 2 A.D. to 1904 A.D. [3]. The Pohang earthquake, with a magnitude of 5.4 and focal depth of 9 km, occurred near the city of Pohang, located in the Korean South-East province. This earthquake caused the largest casualties and economic loss among the earthquakes that have occurred in Korea.
To protect structures from earthquakes, it is necessary to conduct the seismic performance evaluation of structures with reliable input ground motions, and to retrofit the structures based on the results of the seismic performance evaluation [4][5][6]. However, it is difficult to collect available ground motions recorded from mid-to large-size earthquakes that have occurred in sites located in low-to-moderate seismic regions. In this case, artificial ground motions can be simulated and used in seismic performance evaluation. Simulated ground motions should retain the characteristics of the local source mechanism, travel path, and geology of a site.
Previous studies [7][8][9][10][11][12] have developed and improved the ground motion simulation model to generate artificial ground motions by considering key components of seismological characteristics. Ground motions can be simulated using the stochastic point-source model in the frequency domain and the shaping window model in the time domain.
In this study, a ground motion simulation model is proposed. The ground motion parameters are determined based on the ground motions recorded from the mainshock of the 2017 Pohang earthquake.
To verify the accuracy of the proposed model, the key components of measured and simulated ground motions are compared, such as peak ground acceleration (PGA) and 5% damped pseudo spectral acceleration (PSA).
In order to develop the proper ground motion simulation model for the Korean Peninsula, this article is organized into three sections. In Section 2, the collected ground motions in three orthogonal directions (East-West, North-South, and Vertical) are presented, which were recorded from 111 stations in the inland Korean Peninsula during past earthquakes. In Section 3, a stochastic pointsource model and shape window model are proposed to simulate the ground motions recorded during past earthquakes that occurred in the Korean Peninsula. In Section 4, the proposed model is verified by comparing the generated artificial ground motions and ground motions recorded during the 2017 Pohang earthquake event.

Ground Motions Collected for Developing the Ground Motion Simulation Model
To develop a numerical model for simulating ground motions in the Korean Peninsula, the ground motions recorded at 111 seismic stations during the 2017 Pohang earthquake were collected from the National Earthquake Comprehensive Information System (NECIS) of Korea Meteorological Administration (KMA). Figure 1 shows the distribution of 111 stations out of 157 stations in Korea, which provided ground motion records with a high signal-to-noise ratio (SNR). To exclude ground motions with signal distortion due to noise, we only collected recordings with a signal-to-noise ratio (SNR) greater than 2.0. Each station provided three components (North-South, East-West, and Vertical) of ground motions. Thus, the total number of recorded ground motions is 333 (=3 × 111).
All collected ground motions were recorded with a sampling rate of 0.01 s (100 samples per second), and the NECIS provided these records after applying a high cut anti-aliasing filter to remove the noise with a frequency greater than 40 Hz. In this study, low-frequency noise was also removed by using the 0.1 Hz (corresponding period 10 s) low-cut filter, and baseline correction was done using a technique proposed by Papazafeiropoulos and Plevris [13]. Table 1 summarizes the information on the 2017 Pohang earthquake.    The site amplification effect was also removed from the ground motion records because a ground motion model has been developed for hard rock conditions without considering site effects. In general, site effects are considered in numerical models by applying a site amplification factor to the ground motions generated for hard rock site conditions. In this study, the site amplification effect was removed from the recorded ground motions by using a horizontal-to-vertical spectral ratio (HVSR) technique, which has been widely used for site amplification factor calculation [14][15][16][17].
The site amplification factor,   AMP f , can be calculated from Equation (1). from the East-West, North-South, and Vertical components of ground motions, respectively. Figure  3 shows the calculated site amplification factor function estimated from the ground motions recorded at stations BUS2, CEA, and CEJA during the 2017 Pohang earthquake. This function was applied to the Fourier spectrum of a ground motion at each frequency. Figure 4 shows the ground acceleration time histories and Fourier spectra before and after applying Equation (1).

Ground Motion Simulation Model
The numerical model to simulate ground motions in the Korean Peninsula is proposed based on the stochastic point-source model in the frequency domain and the shaping window model in the time domain. The point source model is an effective tool for generating ground motions for a site with limited seismological information.
The Fourier amplitude spectrum (FAS) of a ground motion can be determined using the stochastic point-source model [8][9][10][11][12], which was developed based on the omega-square model [18,19]. This model consists of three main seismological characteristics, namely source, path, and site effects [12].
The shaping window model consists of a ground motion envelope and duration time. Saragoni and Hart [7] proposed the envelope of ground motion records, which was adopted in this study. The duration of a ground motion affects the incidence of the collapse of a structure [20].

Stochastic Point-Source Model Estimation
In the stochastic point-source model, the Fourier amplitude spectrum [   A f ] of a ground motion is calculated using Equation (2).  [21]. Figure 5 shows the original and smoothed   : S-wave averaged radiation pattern coefficient [22]   2 F  : free surface effect [9]   : geometrical attenuation function [24]    0.48 348 Q f f  : quality factor of the anelastic attenuation function [24]   AMP f : site amplification factor function at each station Site effect function function [25] In this study, the site attenuation coefficient, 0  , was determined first. Since the contribution of 0  in Equation (2) is determined without interaction with path effect and site amplification, the contribution of path effect and site amplification were removed from Equation (2). The Fourier amplitude spectrum without path effect and site amplification [ ] was calculated using Equation Anderson and Hough [25] estimated the site attenuation coefficient ( 0  ) using a residual slope of ( ) A f  between 10 Hz and 40 Hz, which was also used in this study. Figure 6 shows ( ) Figure 6. The values of 0  estimated for individual stations are summarized in Table A1 of Appendix A.   Figure 7 shows and . Corner frequency, , can be estimated using Equations (5)-(8), which were proposed by Andrews [29] and Jo and Baag [27].
Seismic moment, 0 M , can be also calculated from Equation (9), which was proposed by Joshi et al. [28].  cm, respectively, which were used to calculate (Equations (2)-(4)). Figure 9 shows the measured and calculated for three sample stations. It can be observed that the calculated matches the measured , by which the accuracy of the proposed procedure is verified.

Shaping Window Model Estimation
In order to generate a ground acceleration in the time domain ( ( ) shaping window function should be applied [12]. A shaping window model consists of a ground motion envelope shape and duration time. Boore [12] simulated ground motion recordings using an envelope shape proposed by Saragoni and Hart [7] and a duration time proposed by Atkinson and Boore [11]. However, the shaping window model used by Boore [12] may not properly reflect the envelope shape of the ground motions recorded in the Korean Peninsula. In this study, a shaping window model (   W t ) is proposed based on the ground motions recorded during the 2017 Pohang earthquake (Equation (10)).
where t is the time, and D T is the duration time. The duration time is calculated from the S-wave arrival time to the time corresponding to the 95% normalized arias intensity energy (   E t ).   E t is estimated using Equation (11).
where T E is the total energy of ( ) . Figure 10a-c show the estimated duration time of a ground motion recorded at the BUS2 station,   E t , and estimated shaping window, respectively. Figure 11 shows the estimated shaping window and duration of ground motions recorded at 111 stations during the 2017 Pohang earthquake. The coefficients 0 c , 1 c , and 2 c in Equation (10) are estimated to match the median envelope shape denoted with a thick solid line in Figure 7a.   Figure 11b shows the estimated duration time ( D T ) at each station. Previous studies [10,11,30] reported that duration time is mainly affected by corner frequency ( c f ) and source-to-site distance ( H R ). In this study, the following equation is proposed for D T , according to H R and c f . Figure 11b shows the duration time calculated using Equation (12). This figure also shows that D T calculated from Equation (12) distinctively differs from that calculated using the equations proposed by Atkinson and Boore [11].

Ground Motion Simulation for the 2017 Pohang Earthquake
Ground motions were generated using the proposed numerical model, consisting of the stochastic point-source model and shaping window model. The procedure is briefly summarized as follows: (1) White noise is first generated in time domain for a duration time of the ground motion (Equation (12)). (2) The noise is then windowed using the shaping window model (Equation (10)).
(3) The windowed noise is transformed into the frequency domain.

) The normalized ( )
A f is then multiplied by the stochastic simulation model (Equation (2)).
(6) The resulting ( ) A f is transformed back to the time domain, which is a simulated ground motion. Figure 12a,b show two horizontal components' ground motions at station BUS2 during the 2017 Pohang earthquake, whereas Figure 12c presents one ground motion simulated using the proposed procedure. Figure 12d presents the geomean of ( ) A f for recorded ground motions. In this figure, ( ) A f calculated using Equation (2) is also included, which shows that the calculated ( ) A f matches that obtained from recorded ground motions. Figure 12e shows the geomean of 5% damped-pseudo spectral acceleration

Residual( ) log[ ( ) ] log[ ( ) ]
sim measured Residuals were calculated for all ground motions of the 111 stations. Figure 13 shows the residuals according to hypocentral distance. As shown in Figure 13a, the mean value of residuals is near zero, which indicates that the ground motions in the Korean Peninsula can be adequately simulated using the proposed numerical model with the source, path effect, and site amplification functions.
If the path effect function proposed by Boor (2003) is used in the numerical model, the mean residual deviates from zero, as shown in Figure 13b. The degree of deviation varies according to the period. In the case of using the source function and site amplification function proposed by others when simulating ground motions with the proposed numerical model, similar observations were made, which are not included in the paper.

Conclusions
In this study, a