Generating Input Ground Motions for Seismic Risk Assessment Using Recorded Ground Motions from the Moderate Magnitude Earthquake

Abstract

To secure the seismic performance of structures, seismic risk assessment is necessary to quantify safety against beyond-design-based earthquakes and seismic design. For the seismic risk assessment of structures, the input ground motions corresponding to the seismic intensity for evaluation are required as seismic loads, which must reflect the tectonic characteristics and site conditions. In this study, ground motions recorded in regions of low to moderate seismicity were used to generate examples of input ground motions for seismic risk assessment. A uniform hazard spectrum (UHS) was used as the target spectrum for risk assessment, following the guidelines. The magnitude and distance parameters of the scenario earthquake for seismic risk assessment were determined via hazard de-aggregation. The empirical Green’s function method (EGFM) was used to match the ground motion recorded at the site with the seismic intensity required for seismic risk assessment. In addition, a spectral matching process was applied to ensure that the input ground motion was compatible with the response spectrum used in seismic risk assessment. In this process, the convergence characteristics of the spectral matching to the target spectrum were analyzed. Consequently, the spectral conditions for selecting the ground motion for the seismic risk assessment were determined.

1. Introduction

For the response history analysis of structures, the input ground motion time histories as seismic loads are required. The selection of input ground motions recorded at the site under consideration or others with similar site conditions, considering site-specific characteristics, is recommended to evaluate appropriate analysis results [1]. The ground motion time history recorded at a site captures the seismic wave from the earthquake rupture process and the propagation effect from the earthquake source to the site, along with site effects such as site amplification, all of which can affect the input ground motion for response analysis of structures [2,3,4]. The frequency of the input ground motions is closely related to topographic irregularities and affects site amplification; therefore, the use of recorded ground motions for structural response analysis should be considered [5].

In low to moderate seismicity regions, there is a scarcity of recorded earthquake accelerograms corresponding to credible intensities that can damage structures. Where the required number of recorded ground motions is not available, appropriate simulated ground motions are generated stochastically, or ground motion time histories recorded in regions with similar seismicity to the site under consideration are used. For stochastically simulated ground motions, it is possible to generate multiple ground motion time histories compatible with the target spectrum [6]. Stochastically simulated ground motion time histories have faced challenges in accurately reflecting the features of actual earthquakes, which are important for structural seismic response predictions [7]. However, recent methodologies have been developed for the stochastic generation of artificial accelerograms that capture actual earthquake characteristics, such as non-stationary time histories [8,9], and ensure compatibility with ground motion prediction equations [10]. Despite these advancements, guidelines and standards for critical structures such as nuclear power plants continue to recommend generating input ground motions for seismic loads by using and expanding recorded ground motions, although the use of artificial ground motions is permitted [11,12,13]. In this regard, a methodology based on a site-based variant approach was developed, utilizing recorded ground motions as seed motions and considering actual earthquake characteristics to generate ground motions compatible with the target spectrum [14].

Alternatively, the use of ground motions recorded from other high seismicity regions as input seismic loads can satisfy the seismic intensity level being considered. Chandramohan et al. [15] and Lu et al. [16] selected ground motions from the pacific earthquake engineering research center’s ground motion database, instead of using recorded ground motions from the target region. Chandramohan et al. [15] classified seismic source types into three categories and identified scenario earthquakes from seismic hazard de-aggregation results for ground motion selection. The effects of the selected ground motion characteristics on the structural response were analyzed. Lu et al. [16] selected ground motions matching specific magnitude-distance conditions for structural seismic risk assessment. However, seismic waves generated in different tectonic environments exhibit distinct properties, and design standards generally recommend using seismic input motions recorded from the relevant region [17,18,19]. Nevertheless, few studies have presented procedures for generating ground motions for the risk assessment of critical structures by scaling the magnitude of the recorded motions in low to moderate seismicity regions to spectrally match the risk assessment spectrum.

Therefore, it is necessary to conduct research on generating appropriate input ground motions for analyzing the behavior of a structure under seismic loads using the recorded ground motion that reflects the characteristics of the site under consideration. In addition, the recorded ground motion must be converted into the target seismic intensity level. For seismic risk assessment, a seismic intensity level that damages structures and exceeds the intensity applied in the seismic design must be considered. Accordingly, this study focused on presenting a procedure to generate input ground motion time histories of seismic intensity corresponding to seismic risk assessment, based on recorded ground motions from moderate-magnitude earthquakes. In addition, the optimal selection conditions suitable for risk assessment purposes, where conservatism must be eliminated, are presented when selecting the input ground motion.

2. Guidelines for Using Recorded Ground Motions in Response History Analysis

As discussed in Section 1, various guidelines and standards recommend using recorded ground motions for conducting the structural response. The guidelines and standards for ground motion generation in seismic design and risk assessment are as follows.

2.1. Seismic Intensity and Spectrum Shape

For nuclear power plant structures, detailed guidelines for seismic risk assessment are provided to evaluate the safety and quantify risks for potential scenario earthquakes using probabilistic seismic hazard analysis (PSHA). Regulatory guideline 1.208 [13] by the United States Nuclear Regulatory Commission recommends using PSHA to determine earthquakes of a magnitude and distance that significantly contribute to the hazard at the site and to use input ground motion based on these parameters. The guidelines outline an approach for developing a design response spectrum, as referenced in the ASCE 43-05 guidelines [20]. This approach is based on site-specific ground motions at the free-field ground surface with a uniform hazard spectrum (UHS) for the annual frequency of exceedance, which is the first step in developing a safe shutdown earthquake (SSE) for a site to characterize regional and local seismic hazard characteristics. This shows that site-specific characteristics must be considered when generating the input ground motion for seismic design or risk assessment. In addition, a technical report [21] by the Electric Power Research Institute (EPRI) provided guidelines on seismic fragility for seismic probabilistic risk assessment. It recommends selecting the level of seismic input that dominates the risk as the reference earthquake, which typically corresponds to the UHS values of 1 × 10⁻⁴, 1 × 10⁻⁵, and 1 × 10⁻⁶ evaluated from the PSHA. Appendix A of the ASCE 4-16 guidelines [11] provides an overview of the methodologies used in seismic probabilistic risk assessment (SPRA) to evaluate whether facilities can safely withstand seismic ground motions greater than design level ground motions.

2.2. Selection of Ground Motions

ASCE 7-10 guidelines [12] recommend that when performing a linear response history procedure for a structure, the ground motions should consist of a selected horizontal acceleration time history from the recorded ground motions. The selection of ground motion time histories is based on factors such as magnitude, distance from the fault, and earthquake rupture mechanism. To select the ground motion acceleration time histories, the recorded ground motions should be selected for events that are consistent with the seismic magnitude and fault distance controlling the ground motion. The selected ground motions must be scaled to be compatible with the spectrum over the natural period range of significance of the structural response. However, in low to moderate seismicity regions where strong earthquakes rarely occur, the recorded ground motion data for risk assessment are insufficient and require excessive scaling or modification. If the ground motion time history is excessively modified, leading to a significant difference in earthquake intensity, the actual earthquake characteristics of the seed ground motions may be lost. Alternatively, ground motions recorded in regions with high seismicity may be used to select the appropriate intensity for the input seismic loads. These ground motion data do not reflect the site-specific characteristics of low to moderate seismicity regions. Differences in seismicity between high and low to moderate regions are caused not only by the mechanism of fault rupture but also by the attenuation characteristics from the earthquake source to the site. These differences support the proposal in the guidelines and standards that input ground motions based on recorded ground motions are necessary for a seismic risk assessment.

3. Procedure Considering Guidelines for Generating Ground Motions

This study focuses on nuclear power plant structures as critical structures and is therefore subject to constraints imposed by relevant guidelines. The generation of ground motions for risk assessment involves the application of multiple guidelines related to the selection of ground motions based on the seismic intensity, spectral shape, and hazard de-aggregation. Owing to these complex considerations, the relevant criteria are somewhat unclear, and appropriate selection and conversion of recorded ground motions are necessary to generate input ground motions for risk assessment that match the shape and seismic intensity of the risk assessment spectrum. In this study, we propose a procedure to generate an input ground motion that matches the shape and seismic intensity of the risk assessment spectrum, using the recorded motion from regions with low to moderate seismicity where only low-intensity accelerograms are available. Figure 1 presents the procedure in a flowchart. As an example of this procedure, a simple PSHA was performed by selecting the optimal annual frequency of exceedance to evaluate the UHS as a spectrum for risk assessment. Based on the PSHA results, hazard de-aggregation was conducted to select ground motions appropriate for the UHS, and the scenario earthquake was identified, focusing on the magnitude-distance that contributed the most to the hazard. Since recorded ground motion data corresponding to the scenario earthquake are not available, a finite fault was modeled using the empirical Green’s function method (EGFM) based on actual fault information from an existing earthquake event. An example of an earthquake event is the largest recent Mw 5.5 earthquake in Korea for which recorded ground motions exist [22]. This example earthquake was converted into the magnitude-distance of the scenario earthquake obtained from seismic hazard de-aggregation using finite fault modeling. The characteristic of the finite fault model using the EGFM is the generation of a diverse set of ground motion time histories for the same magnitude and distance. Therefore, it is necessary to analyze the spectral shape of the generated ground motions according to the spatial distribution from the EGFM and select the ground motion with a response spectrum similar to the risk assessment spectrum shape. In this process, a spectral shape considering the conservatism of the UHS is proposed. Ground motions were selected from two distinct target spectra to compare conservatism in a uniform hazard spectral shape. The two selected ground motions were considered as the seed motion of the input ground motion for the risk assessment. Spectral matching in the time domain was performed on the selected ground motions to ensure compatibility with the risk assessment spectrum. Finally, the impact of the target spectrum when selecting the ground motion in the spectral matching process was analyzed, and the selection conditions were presented in the input ground motion generation procedure for risk assessment.

Based on the procedures applied at each step of the flowchart, ground motions that comply with each of the risk assessment guidelines can be generated using the recorded ground motions in low to moderate seismicity regions. Detailed descriptions of each step of the procedures depicted in the flowchart are provided in the following sections.

4. Probabilistic Seismic Hazard Analysis and Evaluation of Example Scenario Earthquake

In this section, for the input ground motion generation procedure for seismic risk assessment, a PSHA is performed using a simple parameter as an example owing to the absence of suitable seismic hazard curves for de-aggregation. Subsequently, seismic hazard de-aggregation was performed, and the magnitude-distance bins according to hazard contribution were estimated to select the magnitude-distance of the scenario earthquake for the input ground motion.

4.1. Development of a Uniform Hazard Spectrum as the Risk Assessment Spectrum

PSHA calculates the probability of exceeding a specific ground motion intensity within a specific spectral period and uses one of the approaches to efficiently quantify large uncertainties in earthquakes [23]. The uncertainties in earthquake ground motions to be quantified were associated with the seismic characteristics of the source, path, and site effects. These uncertainties can be quantified using the following equation with the magnitude, distance, and epsilon as parameters [24]:

$$\nu \left(Sa>y\right)=\sum _k\sum _j{\nu }_j\iiint f_{M, R, E}\left(m,r,\epsilon \right)P(Sa>y\left|m,r,\epsilon ,{GMPE}_k)\right.dmdrd\epsilon P({GMPE}_k)$$

(1)

The frequency of earthquake occurrences was calculated through a statistical analysis of the recorded historical earthquake data. In Equation (1), ${\nu }_j$ represents the annual rate of occurrence associated with the potential earthquake sources [24]. This rate represents the occurrence of earthquakes with magnitudes greater than the minimum magnitude defined by the Gutenberg-Richter law [25].

The function $f_{M, R, E}\left(m,r,\epsilon \right)$ is a joint probability density function for magnitude ($m$), distance ($r$), and epsilon ($\epsilon$). As path and site effects, to predict the probability of ground motion intensity at the site, the distribution of ground motion intensity according to the magnitude and distance from the earthquake source to the site must be considered. Therefore, the ground motion prediction equation (GMPE) calculated for a specific region of seismic activity considers the attenuation characteristics of ground motion intensity based on different magnitudes and distances. In GMPE, the uncertainty of ground motions is modeled as a log-normally distributed random variable. Therefore, epsilon (ε) is defined as the number of logarithmic standard deviations by which ground motions deviate from the median values for a given magnitude (m) and distance (r) scenario. $P(Sa>y\left|m,r,\epsilon ,GMP{E}_k)\right.$ is the probability that the ground motion intensity measure ($Sa$) exceeds intensity level ($y$) given magnitude, distance, epsilon, and $GMP{E}_k$. $P\left(GMP{E}_k\right)$ denotes the weight of each GMPE. Finally, $\nu \left(Sa>y\right)$ is the result of the PSHA, indicating the annual frequency of exceedance for the ground motion intensity measure exceeding a specified intensity level. By integrating these steps, the PSHA result is expressed as a seismic hazard curve, which is defined as the relationship between the ground motion intensity and the annual frequency of exceedance for a site of interest.

In addition, the calculation of seismic hazard across a wide range of natural periods allows for the determination of the UHS based on the value of the ground motion intensity at which all spectral periods exhibit a uniform annual frequency of exceedance. The UHS is a seismic design or assessment spectrum used to select ground motions for the seismic response analysis of structures at a site of interest. According to regulatory guideline 1.208 [13], the 1 × 10⁻⁴ and 1 × 10⁻⁵ UHS of free-field motions are site-specific earthquake ground motions. The design-based earthquake (DBE) ground motion is now defined using modern probabilistic techniques and is referred to as the SSE ground motion. Appendix A of the ASCE 4-16 guidelines [11] provides an overview of the methodologies used in seismic margin assessment and seismic probabilistic risk assessment with respect to plant facility integrity for ground motions greater than the design level ground motion. In SECY-93-087 [26], a seismic margins analysis based on probabilistic risk assessment considered the sequence-level high confidence of the low probability of failures and fragilities for all sequences that result in core damage or containment failures of up to approximately twice the magnitude of the SSE. As stated above, many criteria require the evaluation of structures with seismic intensities that exceed the design level.

Accordingly, the aim of this study is to present a spectrum for risk assessment of intensities greater than the design level and a procedure for generating a ground motion time history compatible with this spectrum. In this study, a simplified PSHA model with a homogeneous area seismic source and one GMPE was assumed. PSHA was performed using the OpenQuake engine (version 3.21.0) [27], open-source software supported by the Global Earthquake Model. The input parameters used are listed in Table 1 below.

The area of the source model was determined to be 100 $\times$ 100 km², which was sufficiently large to avoid affecting PSHA results. Gutenberg-Richter $a$ and $b$ values for the Korean peninsula vary depending on research results, with a value generally ranging at 4.32–6.25 [28]. Considering a simplified single-area source model, parameter $a$ was set to 2.843. To test the validity of the selected parameter values of $a$, an analysis was conducted based on the ratio of the area of the simplified single-area source model to that of the Korean Peninsula. The area of the Korean Peninsula is 300,000 km², which is 30 times larger than the simplified single-area source model used in this study. That is, the parameter value of a decreases by log30 from 4.32 and 6.25, as described in Equation (2), in relation to the frequency of occurrence and magnitude of earthquakes:

$$\log N\left(N\ge M\right)=a-bM$$

(2)

where $N$ is the cumulative number of earthquakes with magnitudes greater than or equal to magnitude ($M$). The range of the value converted to 30 times the area reduction was 2.843–4.773; thus, a value of 2.843 for the seismic source area in this study is reasonable. The value of parameter $b$ was set to 0.95, which has been suggested to be optimal for Korea, which has low to moderate seismic activity [29].

A GMPE model developed for an area with a seismic environment similar to that of Korea was reviewed, and the selected GMPE model was developed by Atkinson and Boore (2006) [30]. A truncation level of two standard deviations (2σ) was applied. The GMPE model supported a stable, shallow continental tectonic region. The selected GMPE was validated by comparing the response spectra of the two horizontal components of the MKL station from the 912 Gyeongju Earthquake, which was the largest instrumental earthquake in Korea. This comparison was conducted using median GMPE values corresponding to the magnitude and distance of the MKL station from the 912 Gyeongju Earthquake (Figure 2). The PSHA calculation results from these parameters are shown as seismic hazard curves in Figure 3a.

Table 1. Seismic hazard parameters for PSHA.

Parameter		Value
Seismic Source Model		100 km $\times$ 100 km single area source
Gutenberg-Richter	$a$ value	2.843
	$b$ value	0.95
	Min Magnitude	5.0 Mw
	Max Magnitude	7.0 Mw
Ground Motion Prediction Equation		Atkinson and Boore (2006) [30]
Annual Frequency of Exceedance		0.2 × 10−4 (/year)

Table 1. Seismic hazard parameters for PSHA.

Parameter		Value
Seismic Source Model		100 km $\times$ 100 km single area source
Gutenberg-Richter	$a$ value	2.843
	$b$ value	0.95
	Min Magnitude	5.0 Mw
	Max Magnitude	7.0 Mw
Ground Motion Prediction Equation		Atkinson and Boore (2006) [30]
Annual Frequency of Exceedance		0.2 × 10−4 (/year)

For critical structures such as nuclear power plants, a risk assessment against a design basis earthquake must be considered to quantitatively evaluate the safety as well as conservative seismic design. For this purpose, the seismic intensity must be determined for seismic risk assessment. For example, a stress test conducted on the Wolseong Unit 1 in Korea evaluated whether the seismic safety of a nuclear power plant was maintained beyond the design basis earthquake, which exceeded the design criteria [31]. In the stress test, the ground motion level (0.3 g), corresponding to a return period of 10,000 years, was evaluated as a beyond design basis earthquake. In the EPRI technical report [15] and ASME standard [32], the input level that dominated the risk—such as the level at which the cumulative risk reached 50% of the total risk and the level at which the risk density reaches its maximum—is selected as the reference earthquake. Typically, a reference earthquake is given as a UHS of 1 × 10⁻⁴, 1 × 10⁻⁵, or 1 × 10⁻⁶ annual frequency of exceedance. Additionally, the ASCE 43-05 guidelines [20] recommend using a mean annual frequency of exceedance of 1 × 10⁻⁴ for the minimum structural damage state, which is described by elastic behavior. Appendix A of the ASCE 4-16 guidelines [11] provides an overview of methodologies for identifying seismic vulnerabilities and risks at the plant level and discusses the structural integrity of nuclear power plants when facing ground motions exceeding the design basis.

Considering these standards, the annual frequency of exceedance of the UHS, the target spectrum for seismic risk assessment, was set at 0.2 × 10⁻⁴ and is presented in Figure 3b. This frequency corresponds to a return period of 50,000 years and represents a seismic intensity greater than the design level, which has an annual frequency of exceedance of 1 × 10⁻⁴.

4.2. Seismic Hazard De-Aggregation for Selection of Scenario Earthquake

Although a UHS is used for risk assessment, it does not indicate the specific magnitude or distance of a single earthquake. Therefore, a method of de-aggregating seismic hazards, an extension of PSHA, has been developed for selecting the input ground motion required for seismic risk assessment [33]. Seismic hazard de-aggregation calculates the contribution of magnitude-distance pairs (M-R bins) of earthquakes at a specific annual frequency of exceedance and spectral period. These contributions were grouped into their respective bins.

If considering epsilon (ε), which represents the number of standard deviations used to scatter ground motions about the median GMPE values, based on the calculated contribution, the combination of the dominant magnitude-distance-epsilon pairs (M-R-ε bin) is defined as a probabilistic scenario earthquake [34,35]. For instance, the conditional distribution of magnitudes is calculated as follows [24]:

$$f_{M\left|Sa>y\right.}\left(m,y\right)={\displaystyle \frac{1}{\nu \left(Sa>y\right)}}\sum _k\sum _j{\nu }_j\iint f_{M,R,E}\left(m,r,\epsilon \right)P\left(Sa>y\left|m,r,\epsilon ,{GMPE}_k\right.\right)drd\epsilon P\left({GMPE}_k\right)$$

(3)

where each variable is defined in Equation (1). By adjusting the variables in Equation (3), the de-aggregation of distance and epsilon can be computed. The distribution for each magnitude-distance-epsilon bin pair is calculated to establish the contribution of each pair to the annual frequency of exceedance, and the magnitude-distance pair with the highest contribution is defined as the scenario earthquake. The spectral period of interest was set to 0.2 s in the de-aggregation process, considering that nuclear power plant structures typically have natural periods in the short period range of 0.1 to 0.25 s. The hazard curves in Figure 3a were de-aggregated for an annual frequency of exceedance of 0.2 × 10⁻⁴ at a spectral period of 0.2 s, with the de-aggregation results shown in Figure 4. Most hazard contributions were concentrated over a short distance of 20 km. Considering the low annual frequency of exceedance in hazard de-aggregation resulted in significant contributions from large magnitudes and short distances. At the same distance, as the magnitude approaches its maximum, the contribution to the hazard increases. The contribution to the hazard was greatest at the maximum magnitude or slightly lower. Most contributions fell within the positive epsilon bin, indicating that ground motions larger than the median value of the GMPE were considered. The magnitude-distance-epsilon pair (M-R-ε bin) with the highest contribution to the hazard is shown in

Table 2. Parameters for scenario earthquake based on the PSHA de-aggregation results.

Parameter	Value
Magnitude bin (Mw)	6.4–6.6
Distance * bin (km)	0–10
$\epsilon$ bin	0.5–1.0
Contribution to Hazard (%)	3.93

* Closest distance to the coseismic fault rupture plane.

. Based on the de-aggregation results expressed in bins, a moment magnitude of 6.5 and an epsilon of 0.75 were selected from Table 2 to specify the parameters of the scenario earthquake, with 10.0 km selected as the optimal distance value.

4.3. Target Spectrum for Selecting Seed Ground Motions in Risk Assessment

Based on the preceding steps, once the risk assessment spectrum has been evaluated and the scenario earthquake has been identified, the next step is to select appropriate ground motion records that match both the spectrum shape and seismic characteristics. The risk assessment spectrum, UHS, assumes a uniform annual frequency of exceedance at all periods; however, this does not represent a single ground motion because the hazard curves of each period are obtained independently. This means that selecting a ground motion compatible with the UHS conservatively implies large amplitude spectral acceleration values for most spectral periods for a single ground motion. Due to the conservatism in the UHS, the scenario earthquake defined by magnitude-distance-epsilon pairs may have lower spectral acceleration values except at the target period specified in the de-aggregation procedure. When selecting ground motions compatible with the UHS, those with spectral acceleration values lower than the target were selected. To exclude the conservatism of the UHS, a conditional mean spectrum (CMS) was developed that considered both the natural period of the structure and scenario earthquake [36]. CMS provides the mean response spectrum conditioned on the occurrence of the UHS spectral acceleration value at the natural period of the structure. In other words, the specific natural period of the CMS represents the UHS values, and other period bands of the CMS are determined based on the values between the median of the GMPE and the UHS, considering the correlation between periods [36]. Therefore, when ground motions are selected based on the CMS, they can preserve the scenario earthquake conditions estimated by hazard de-aggregation. In this study, the CMS was calculated based on the de-aggregation results in Table 2, and the selection of ground motion time histories based on the CMS was presented as a procedure for generating the acceleration ground motion for seismic risk assessment. The CMS calculation equation is given by Equation (4):

$$\ln {Sa}^{CMS}\left(T_i\right)\left|\ln {Sa}^{CMS}\left(T^{*}\right)=\overline{\ln Sa}\right.\left(M,R,T_i\right)+\rho \left(T_i,T^{*}\right)\times {\sigma }_{\ln Sa\left(T_i\right)}\times \epsilon \left(T^{*}\right)$$

(4)

where $\ln {Sa}^{CMS}\left(T_i\right)\left|\ln {Sa}^{CMS}\left(T^{*}\right)\right.$ represents the CMS at all periods ($T_i)$ and target period $\left(T^{*}\right)$ and $\overline{\ln Sa}\left(M,R,T_i\right)$ is the logarithmic mean spectral acceleration value for magnitude ($M$) and distance ($R$) at all periods, and $\rho \left(T_i,T^{*}\right)$ is the correlation coefficient between spectral accelerations at all periods and target period. ${\sigma }_{\ln Sa\left(T_i\right)}$ is the standard deviation of mean spectral acceleration from GMPE at all periods, and $\epsilon \left(T^{*}\right)$ is the number of standard deviations by which given target spectral acceleration differs from the logarithmic mean spectral acceleration value. The risk assessment spectrum, UHS, and calculated CMS for the scenario earthquakes in Table 2 are shown in Figure 5. As shown in Figure 5, at the target period of 0.2 s, the spectral acceleration of the CMS matches that of the UHS. In other periods, the spectral acceleration appeared as a conditional mean relative to the GMPE median value, depending on the ground motion correlation coefficient.

5. Finite-Fault Modeling for Scenario Earthquake Utilizing Empirical Green’s Function Method

The magnitude of the scenario earthquake for risk assessment was determined to be 6.5, and the distance was determined to be 10.0 km, respectively. The use of recorded ground motion time histories for magnitudes and distances consistent with the scenario earthquake is recommended as the input ground motion for seismic risk assessment. However, the Korean Peninsula is characterized by low to moderate seismic activity, and strong earthquakes rarely occur. The largest recorded ground motion accelerogram was from the 912 Gyeongju Earthquake, which had a moment magnitude of 5.5 and occurred in 2016. When strong ground motion records are absent, scaling or modifying moderate-magnitude ground motion time history records from the site can be used as an alternative. However, simple intensity scaling cannot reflect the earthquake magnitude characteristics corresponding to the annual frequency of exceedance. Accordingly, the EGFM, which utilized the similarity of the seismic source scaling law, was used to adjust the ground motion of the recorded 912 Gyeongju Earthquake to match the magnitude and distance of the scenario earthquake. The EGFM was first developed to estimate large-magnitude mainshocks using small-magnitude aftershocks [37,38]. This method utilizes the similarity law of large and small earthquakes [39] and the characteristics of two earthquakes recorded at close distances with similar fault characteristics, path effects, and site effects [40]. The equation for synthesizing a large-magnitude earthquake by superposing small-magnitude earthquakes is given in Equation (5):

$$U\left(t\right)=C{\sum }_{i=1}^N{\sum }_{j=1}^N{\displaystyle \frac{r}{r_{ij}}}F\left(t-t_{ij}\right)\ast u(t)$$

(5)

where $U\left(t\right)$ is the ground motion time history of the synthesized large-magnitude earthquake (main-event), $u\left(t\right)$ is the small-magnitude earthquake (i.e., element-event) used for superimposition, and * indicates the convolution. $C$ is the stress drop ratio between large and small magnitude earthquakes, and $N$ is the ratio of the fault dimensions between large and small magnitude earthquakes. Here, $i$ and $j$ represent the increased dimensions in the strike and dip directions of a large-scale fault, respectively, compared with a small-scale fault. Parameters $r$ and $r_{ij}$ denote the hypocenter distance to the seismic station of a small and large magnitude earthquake, respectively. $F\left(t\right)$ is the correction function for the difference in slip velocity time between large and small magnitude earthquakes. Parameters $t$ and $t_{ij}$ denote the rise times of large and small magnitude earthquakes, respectively.

As demonstrated in Equation (5), the synthesized main event from the EGFM preserves the characteristics of the actual faults and path effects by utilizing the recorded ground motion as an element event in the finite fault model. Accordingly, many studies have focused on large-magnitude earthquake synthesis or estimation of seismic source parameters and wave propagation using EGFM [3]. In this study, the limitations due to the lack of recorded ground motions were addressed using EGFM. The generation of the scenario earthquake ground motion in accordance with the de-aggregation of the PSHA is presented. To synthesize the ground motion time histories suitable for the PSHA de-aggregation results presented in Figure 4 and Table 2, a finite fault model was constructed as shown in Figure 6. The fault parameters for the 912 Gyeongju Earthquake [22] and EGFM are listed in

Table 3. Comparison of fault geometry between the 912 Gyeongju earthquake and the EGFM finite fault model.

Parameter		912 Gyeongju Earthquake	EGFM Finite Fault Model
Magnitude		5.5 Mw	6.5 Mw
Focal Mechanism	Strike	26°	26°
	Dip	67°	67°
	Rake	175°	175°
Fault dimension	Width	4.0 km	12.0 km
	Length	4.0 km	16.0 km
Hypocentral Depth		12.0 km	(Min) 8.5 km, (Max) 12.2 km
S-wave Velocity		3.5 km/s	3.5 km/s
Rupture Velocity		2.8 km/s	2.8 km/s

.

The size of the finite fault model that matches the PSHA de-aggregation results is calculated by converting it to the rupture area-moment magnitude relationship [41]:

$${\log }_{10}A=M_W-4.25$$

(6)

Parameters $A$ and $M_W$ correspond to the fault rupture area (km²) and the moment magnitude of the earthquake, respectively. The element event used in the EGFM was the fault rupture area of the 912 Gyeongju Earthquake. The fault rupture area with a moment magnitude of 6.5, which was the result of PSHA de-aggregation, was estimated to be approximately 177.83 km² using Equation (6). In consideration of the element event rupture area of 16.0 km², which can be assumed to be a 4 km $\times$ 4 km square shape, the finite fault model can be converted into a fault with a width of 12.0 km in the dip direction and a length of 16.0 km in the strike direction, as shown in Figure 6a. The converted finite fault rupture area was determined to be 192.0 km², which is slightly different from 177.83 km². Nonetheless, this corresponds to a moment magnitude of 6.5 according to Equation (6), indicating that finite fault modeling is reasonable. The strike and dip angle of the finite fault were determined using fault values from the 912 Gyeongju Earthquake. The estimated crustal thickness of Korea is about 15.0 km, and the width of the finite fault model in the deep direction is 12.0 km. Therefore, the depth at the top of the fault in this study was determined to be 3.0 km, as shown in Figure 6b. Assuming that the rupture starts at the bottom of the finite fault model according to the EGFM, eight rupture starting points can be considered, as shown in Figure 6c. As shown in Figure 6b, the distance to each finite seismic station was considered the closest distance to the coseismic fault rupture plane, and this distance was determined to be 10 km by PSHA de-aggregation. Five virtual seismic stations were positioned at the same closest distance to the coseismic fault rupture plane, as shown in Figure 6a,c, to consider the directivity effect of the seismic wave propagation. Forty ground motion time histories with different characteristics for each direction were synthesized for the two horizontal components from the finite fault using the EGFM. Figure 7 shows the response spectrum of the ground motion time histories synthesized using the EGFM modeled in Figure 6, with the 912 Gyeongju Earthquake as the element event.

6. Selection of Seed Ground Motions for UHS and CMS

Another important aspect of the procedures in this study was to determine whether differences in the target spectrum used to select the ground motion time histories affected the generation of earthquake input ground motions for risk assessment. Although the selection of the ground motion time histories based on the CMS is appropriate considering the consistency with hazard de-aggregation, the differences in selection based on the UHS, which is used for risk assessment, need to be analyzed. Therefore, the CMS obtained for a 0.2 s target period, corresponding to the UHS, and the UHS were used as the target spectra for selecting the ground motion time histories. The time history selection criteria were based on the mean squared error (MSE) between the response spectra of the ground motion time histories and the target spectra, as given by Equation (7). The assumption of a fundamental spectral period of 0.2 s is used; however, shorter period ranges owing to higher vibration modes and longer period ranges owing to nonlinear structural behavior can affect the dynamic behavior of structures. Therefore, the MSE was calculated for the range of 0.01 to 2.0 s from a structural engineering perspective.

$$MSE={\displaystyle \frac{\sum _{i=1}^n{(\left(\ln {Sa}_{SYN}\left(T_i\right)-\ln {Sa}_{CM{S}_{or}UHS}\left(T_i\right)\right)}^2}{n}}$$

(7)

where $n$ refers to the overall number of spectral periods assessed, and ${Sa}_{SYN}\left(T_i\right)$ represents the acceleration response spectral value of the synthesized ground motion time history at the $i$-th period, as determined by the EGFM. ${Sa}_{CM{S}_{or}UHS}\left(T_i\right)$ represents the acceleration spectral value of the CMS and UHS at the $i$-th period. A smaller MSE indicates a better match between the two response spectra.

The results of calculating the MSE for the response spectra of the 40 ground motion time histories in each direction in Figure 7 are listed in

Table 4. MSE values for the two horizontal direction components between the response spectra of the synthesized time histories and the UHS.

Rupture Starting Point	Horizontal Direction Components	Virtual Seismic Station Number
		1	2	3	4	5
1	EW	0.2048	0.1083	0.2539	0.0842	0.138
	NS	0.1048	0.094	0.1175	0.0648	0.0604
2	EW	0.1787	0.1291	0.2327	0.1002	0.0903
	NS	0.1413	0.1412	0.2382	0.0548	0.0686
3	EW	0.0837	0.2154	0.2976	0.125	0.2029
	NS	0.0381	0.1698	0.2304	0.072	0.0672
4	EW	0.2806	0.3341	0.5171	0.2514	0.1657
	NS	0.2685	0.3338	0.5095	0.1642	0.0962
5	EW	0.2082	0.0998	0.2416	0.0833	0.1183
	NS	0.1179	0.0801	0.1139	0.0715	0.0756
6	EW	0.1604	0.128	0.244	0.1056	0.0954
	NS	0.1490	0.1198	0.2159	0.058	0.0574
7	EW	0.1012	0.2263	0.3249	0.1149	0.1990
	NS	0.0294	0.2725	0.2681	0.0782	0.0715
8	EW	0.2753	0.3003	0.5439	0.2181	0.1645
	NS	0.2056	0.2602	0.5095	0.1211	0.0788

and

Table 5. MSE values for the two horizontal direction components between the response spectra of the synthesized time histories and the CMS.

Rupture Starting Point	Horizontal Direction Components	Virtual Seismic Station Number
		1	2	3	4	5
1	EW	0.1514	0.0857	0.1932	0.1122	0.1605
	NS	0.0515	0.0552	0.0697	0.0823	0.0738
2	EW	0.1469	0.0973	0.1661	0.1209	0.1202
	NS	0.0654	0.0743	0.132	0.0619	0.0588
3	EW	0.1036	0.1554	0.2099	0.1441	0.2932
	NS	0.0434	0.0801	0.1222	0.0476	0.1317
4	EW	0.2004	0.2161	0.3568	0.1777	0.1586
	NS	0.1466	0.1974	0.3274	0.0803	0.0558
5	EW	0.1613	0.0837	0.1849	0.1021	0.1272
	NS	0.0569	0.055	0.0689	0.0869	0.085
6	EW	0.1283	0.0997	0.1734	0.1305	0.1147
	NS	0.0717	0.0612	0.1212	0.0743	0.0565
7	EW	0.1406	0.154	0.2185	0.1168	0.2883
	NS	0.0501	0.1671	0.15	0.0496	0.1411
8	EW	0.1953	0.1952	0.3766	0.1695	0.1555
	NS	0.1075	0.1436	0.3254	0.0532	0.0452

. Table 4 presents the MSE values for the response spectra of the synthesized ground motion time histories compared with those of the UHS, while Table 5 presents the MSE values compared with those of the CMS.

The total MSE values for the analysis were calculated as the sum of the MSE values of the two horizontal components. Figure 8 shows the total MSE values according to the hypocentral distance presented in Table 4 and Table 5. Comparing the MSE values, the response spectra of the time histories synthesized from the finite fault of the EGFM were lower in the CMS (as shown in Figure 8b) than in the UHS (in Figure 8a). The ground motion synthesized using the finite fault model of the EGFM is expected to preserve the actual seismic characteristics. This was supported by the fact that the CMS was closer to the response spectra of the recorded ground motions than the UHS. Despite having the closest distance from the fault to the seismic station, a large deviation in the MSE was obtained. This deviation may occur because of forward or backward directivity effects. The directivity of seismic waves depends on the rupture direction and direction of seismic wave propagation. Therefore, the MSE values for station 3 in Figure 8 are strongly related to the hypocentral distance because this station is located in the direction of the fault plane. Accordingly, when the seismic station is determined first, the directivity effect must be considered based on the trends shown in Figure 8a,b. If the closest distance to the fault is the same and the hypocentral distance is the largest, the rupture direction aligns with the direction of the seismic wave propagation, and a high directivity effect is expected. The forward directivity effect caused larger amplitudes in long-period motion, resulting in the smallest MSE in this example model.

A virtual seismic station and rupture starting point were selected based on the minimum value of the total MSE according to the target spectrum for ground motion selection. By selecting the case with the minimum total MSE value, the response spectrum of the synthesized ground motion time history at seismic station 2 with rupture starting point 5 was selected as the best match for the CMS. For the UHS, the response spectrum of the synthetic ground motion time history at seismic station 1, with rupture starting point 3, was selected. Figure 9 shows the acceleration response spectrum and time history selected based on the CMS, whereas Figure 10 shows those selected based on the UHS. The synthesized acceleration time histories selected to best match the CMS and UHS were used as seed ground motions to obtain spectrum-compatible ground motions for risk assessment.

As shown in Figure 9a and Figure 10a, the acceleration response spectra of the synthesized time histories, obtained by increasing the magnitude of the earthquake using the EGFM, showed greater similarity to the CMS and UHS than to those of the 912 Gyeongju Earthquake. Therefore, by using ground motions recorded during moderate earthquakes, it is possible to synthesize ground motions that are compatible with the risk assessment spectrum while maintaining the actual seismic characteristics of the site. The acceleration response spectrum selected to match the CMS lacks a spectral value compared with the UHS in the short-period range of less than 1.0 s, as shown in Figure 9a. However, because the UHS has a larger spectral value than the CMS, the acceleration response spectrum selected to match the UHS exceeds that of the UHS in the short-period range of less than 1.0 s, as shown in Figure 10a.

Figure 9b and Figure 10b present the recorded acceleration time histories of the 912 Gyeongju Earthquake, while the synthesized acceleration time histories generated using the EGFM are shown in Figure 9c and Figure 10c. Because the magnitude increased from finite fault modeling, there was a corresponding increase in both the seismic intensity and strong motion duration of the synthesized acceleration time histories. In addition, although the acceleration time histories were synthesized for the same closest distance using the EGFM, there were differences in both the time histories and response spectra. These results indicate that the EGFM can be utilized to generate ground motion time histories that reflect earthquake characteristics of the target magnitude and distance at the site.

7. Spectral Matching of Seed Ground Motions to Risk Assessment Spectrum

To utilize the ground motion time history generated using the EGFM as the input ground motion for seismic risk assessment, a spectral matching procedure is necessary to modify its response spectrum to be compatible with the UHS. In the spectral matching process, compatibility with the target spectrum and preservation of the seed ground motion characteristics in the time domain are important. For this purpose, the spectral matching method that adjusts wavelets in the time domain proposed by Al Atik and Abrahamson (2010) [42] was used to preserve the non-stationary characteristics of the original acceleration time history. As in the selection step of the synthesized ground motion time history from finite fault modeling using the EGFM, the range of 0.01 to 1.0 s spectral period was considered during the spectral matching. In general, the spectral matching process in the frequency domain is effectively performed. However, in the time domain, it may not perform well in some cases, depending on the selection of the seed motion. To evaluate the effectiveness of selecting ground motion matched to the UHS or CMS as seed motions, a matching process was conducted using the seed motion time histories from the two previously selected cases. The matching conditions were identical in both cases.

In the first case, the ground motion time history presented in Figure 9, which was selected based on the CMS, was matched to be compatible with the UHS shown in Figure 11. In another case, the ground motion time history presented in Figure 10, which was selected based on the UHS, was matched to be compatible with the UHS shown in Figure 12. As shown in Figure 11, the acceleration time histories are closely compatible with the UHS after only the first iteration. However, when selected based on the UHS (Figure 12a), the EW component did not change before or after matching with the first iteration. That is, at least the second iteration is necessary for spectral matching to proceed.

In addition, 15 iterations were conducted to analyze the convergence of compatibility with the UHS across iterations. The degree of compatibility with the UHS is represented by the MSE using Equation (7). Figure 13a,b show the MSE for each of the EW and NS components for the time histories selected based on the UHS and CMS, respectively, as the number of iterations increased. Regardless of the selected ground motions, the MSE converged remarkably around the fourth iteration of matching and almost converged after the eighth iteration. However, there was a difference in the converged MSE values between the two seed motion selection methods. Figure 14a,b show the response spectra for the EW and NS components, respectively, when spectral matching corresponding to the fourth iteration in Figure 13 was performed.

The initial MSE before applying the spectral matching process indicated that the ground motion time history selected based on the UHS was lower than that selected based on the CMS, as illustrated in Figure 13. However, even with just the first iteration, the MSE was lower when the ground motion time history was selected based on the CMS, and the MSE values improved with an increasing number of iterations. Although a small difference between the initial MSE and converged MSE results in minimal adjustments to the acceleration time history when the seed motion is selected based on the UHS, the effectiveness is low because of the relatively large MSE after convergence. In other words, even after the 15th iteration, MSE converged to a high value. As shown in the fourth iteration results in Figure 14b, owing to the characteristics of spectral matching with the addition of wavelets in the time domain, offsetting the spectral values exceeding the UHS, especially in the short period range, is difficult. These results show that the response spectrum used to select the ground motion time histories for risk assessment impacts spectral matching. Therefore, considering the spectral matching method using wavelet time history functions, it is recommended to use the ground motion selected by the CMS as the seed motion because it is consistent with the scenario earthquake and less conservative.

8. Conclusions

This study proposes a procedure for generating input ground motion time histories for seismic risk assessment using recorded data from a moderate-magnitude earthquake. A simplified PSHA was used to generate a spectrum for seismic risk assessment, and the magnitude and distance of scenario earthquakes were identified by PSHA de-aggregation. A CMS was constructed to reflect the actual ground motion characteristics and the natural period of structure for seed motion selection. A moderate-magnitude earthquake in Korea was utilized in the EGFM and synthesized to represent the scenario earthquake’s magnitude. Subsequently, the ground motion time histories were selected and matched to ensure compatibility with a UHS.

In the process of the finite fault modeling process using the EGFM, multiple candidate seed motions consistent with the scenario earthquake were generated. Among these, it is reasonable to select a seed motion that matches the CMS. This is because it is similar to the spectral characteristics of actual earthquakes and the natural period of structure, compared to the UHS. Additionally, performing spectral matching to the UHS using such a seed motion improves the process by reducing the MSE. These results highlight the advantage of using the CMS for seed motion selection or synthesis. In conclusion, this approach differs from traditional methods, which commonly suggest that the seed motion selection should focus on the spectrum most similar to the target spectrum, such as UHS. seed motion selection based on the UHS. This procedure also improves the efficiency of ground motion generation for seismic risk assessments in regions of low to moderate seismicity.