Compatible Ground Motion Models for South Korea Using Moderate Earthquakes

Abstract

Due to a heightened interest in the field of earthquakes after two moderately sized earthquakes occurred in Gyeongju and Pohang, this study explores which ground motion prediction equations are compatible for the South Korea region. Due to data availability, ground motions from five earthquakes of moderate magnitude were used for comparing against selected ground motion models. Median rotated response spectral ordinates at a period of 0.2 s were extracted from these ground motions, which served as a basis for comparison. Twelve ground motion models were considered from the Next Generation Attenuation West, West2, and East programs due to their extensive databases and robust analytical techniques. A comparison of relative residuals, z-score, and each event found that the subset of Next Generation Attenuation—East ground motion prediction equations did not perform as well as the suite of Next Generation Attenuation—West2 ground motion prediction equations, most likely due to the regional simulations involved in developing the database. Interestingly, the ground motion models that performed relatively well were from the set designed for rock conditions.

1. Introduction

A ground motion model (GMM), also known as a ground motion prediction equation or attenuation relationship, is used to estimate ground motion intensity measures at a specific location as a result of an earthquake. GMMs make such estimates using parameters, such as earthquake magnitude, site-to-source distance, local site effects, and source effects [1]. Numerous comprehensive studies have actively explored these factors. The Pacific Earthquake Engineering Research Center (PEER) became one of the leaders in this field from the time of its establishment in 1997. PEER initiated comprehensive earthquake research and published extensive studies, including GMM and seismic hazard analyses, with a primary focus on the frequent seismic activity in the Western United States [1,2,3,4,5,6,7,8,9,10,11,12].

On the other hand, in the context of South Korea, earthquake-related studies have received limited attention due to the region’s perceived low seismicity, where South Korea is classified as a moderate seismic-hazard zone, which corresponds to a maximum acceleration on a rock site of 0.2–0.8 m/s², with a 10% probability of exceedance in 50 years or, in other words, having a 475-year return period [13]. Between the initiation of earthquake observation in 1905 until 2006, approximately 1000 earthquakes have been recorded, with the majority being small events with a magnitude of less than 4.0 [14]. Additionally, the average annual frequency of earthquakes stood at 19.1 from 1978 to 1998. However, there was a significant increase in the average frequency to 70.6 after 1999, following the initiation of digital recording for earthquake monitoring [15]. This notable rise can be attributed, in part, to the occurrence of major earthquakes in Gyeongju (M_W 5.5, 2016) and Pohang (M_W 5.5, 2017) [16,17]. These events led to heightened concerns about earthquake vulnerability on the Korean Peninsula and to increased attention.

With the growing focus on earthquake and earthquake risk studies on the Korean peninsula, several challenges have emerged in local seismology and earthquake engineering analyses. For example, studies on active faults in the Korean peninsula were insufficient from the government’s perspective, which started programs to investigate specific faults in South Korea in 2017, and the Korean Ministry of the Interior and Safety announced that this research will be completed in 2041 [18]. Moreover, there have been additional issues in how earthquake data are processed by the Korea Meteorological Agency (KMA). The KMA has reported earthquake magnitude measurements using the local magnitude scale (M_L) derived from Japanese studies since 1978 [19]. Regrettably, the M_L equation was formulated based on Japanese earthquake events over M_L 5.0, incorporating geological characteristics specific to Japan, making it inappropriate for South Korea [20,21]. KMA has made a series of adjustments, continues to employ M_L, and does not show a willingness to adopt moment magnitude (M_W) as an earthquake magnitude scale, one that is widely utilized throughout the world. To compound the problem, the aforementioned data are crucial elements in GMMs, making it very difficult to apply robust GMMs in earthquake and seismic risk studies around the Korean peninsula. Additionally, there is a lack of guidance on which GMMs are appropriate for use in the Korean peninsula, with only one model developed using small-magnitude earthquakes from 2007 to 2012 [22].

Other countries and regions have also shown an interest in comparing appropriate GMMs for seismic hazard studies [23,24,25] or developing localized GMMs for better use [6,7,26,27,28]. These studies generally evaluate performance using secondary computations on residuals, with some selecting a small band of relevant intensity measures for evaluation [23,24].

Given this backdrop, this study aims to identify several suitable GMMs, if any, for use in South Korea among a subset of PEER GMMs, as PEER GMMs are derived from an extensive database through relatively robust techniques. In doing so, users are able to more confidently select appropriate GMMs for their earthquake and seismic risk studies in the Korean peninsula. This study starts by compiling earthquake event data and the necessary processing to derive useful ground shaking intensity measures from local ground motion recordings. These are compared to NGA ground motion model estimates per event with an evaluation on each model. Although not shown yet, a unique element of this study is that it considers mainland and offshore events; foreshocks, main shocks, and aftershocks; as well as a potentially triggered event.

2. Materials and Methods

The materials and methods used in this study focus on the processes used to extract as much useable and relevant information as possible to allow for comparisons between South Korean earthquake data and relevant GMMs. This requires earthquake location data, recorded magnitude, and ground motion recordings. Such data are obtained from government sources and then processed to align with PEER GMM output formats.

2.1. Data Sources for Earthquake Events

All earthquake events within South Korea are recorded by KMA and published using M_L through the National Earthquake Comprehensive Information System [29]. Bibliographic sources with more detailed earthquake data were used for M_W and fault geometry [30,31,32,33]. Any earthquake data not present in the aforementioned bibliographic sources were taken from the Global Centroid Moment Tensor (GCMT) project [34,35]. However, ground motion data were taken from the Korea Institute of Geoscience sand Mineral (KIGAM) [36] as KIGAM had a more user-friendly interface and record details. Unfortunately, KIGAM started recording earthquake ground motions from 2016. Moreover, the amount of useful data is further limited as this study is interested in events that hold both M_W and M_L records, which admittedly reduces the possible dataset to earthquakes of, at best, moderate magnitudes. The benefit is the network is composed of mostly newer equipment. Despite these limitations, five earthquakes, including the famous 2016 Gyeongju and 2017 Pohang events, were selected, and their information is listed in

Table 1. Earthquake events considered in this study.

Name	Date	Time (UTC)	Lat. (°)	Lon. (°)	Depth (km)	MW	ML	Fault Plane (°)
								Strike	Dip	Slip
Ulsan	2016/07/05	11:33:07	35.51	129.99	12.0	4.5	5.0	114	87	−15
Gyeongju FS	2016/09/12 F	10:44:34	35.77	129.19	14.0	5.1	5.1	26	65	−179
Gyeongju	2016/09/12	11:32:57	35.76	129.20	13.6	5.5	5.8	26	69	171
Pohang	2017/11/15 P	05:29:33	36.12	129.36	4.6	5.5	5.4	222	60	136
Pohang AS	2018/02/10 A	20:03:04	36.08	129.33	4.2	4.7	4.6	21	55	116

^F foreshock. ^A aftershock. ^P possible induced or triggered earthquake.

. Note that the table shows a positive relationship between M_W and M_L, with increased variability at M > 5 [21].

2.2. Earthquake Data Sources

The ground motion data were sourced from KIGAM. KIGAM operates a network of ground motion recording stations across South Korea, with each station assigned an abbreviated name, suggesting the location [36]. A list of KIGAM recording stations is provided in

Table 2. Ground motion recording stations operated by KIGAM with measured V_S30.

Station	VS30 (m/s)	Station	VS30 (m/s)	Station	VS30 (m/s)	Station	VS30 (m/s)	Station	VS30 (m/s)
AJD	660 *	DOKDO	704 *	HWSB	1264	MGB	680	TJN	584 *
BBK	601 *	DUC	463 *	IBA	556	MKL	660 *	UNI	524
BGD	512 *	GCN	544 *	JJB	580 *	MRD	416 *	WDL	306
BOG	475 *	GHR	544	JRB	641	MUN	545 *	WID	530 *
BRN	427 *	GKP1	438 *	JSB	618 *	NPR	478 *	YIN	632 *
BRS	466 *	GKP2	847	JUC	459 *	OJR	1092	YKB	736 *
CGD	638 *	GRE	505 *	KIP	518 *	PCH	559 *	YPD	482 *
CGU	581 *	GSU	1333	KJM	301 *	PKNU	313 *	YSB	533 *
CHNB	659 *	HAK	631 *	KMC	698 *	POHB	562 *	YSUK	166
CHS	672 *	HCH	599 *	KNUC	338	POSB	539 *	YSUM	899
CRB	859	HDB	587 *	KNUD	791 *	SIG	625 *	-	-
DES	642 *	HKU	506	KSA	615 *	SND	772 *	-	-
DKJ	615 *	HSB	914	MAK	642 *	SNU	718 *	-	-

* derived value [37].

. Also listed in the table are the measured shear wave velocities in the upper 30 m (V_S30) for certain stations. Note that not all stations have a measured V_S30. This parameter is typically used to describe local-site effects in many GMMs and is required in several NGA GMMs. For purposes of GMM computations, results from another study utilizing geologic and topographic features to estimate V_S30 are used [37].

Each station recorded data in three directions, indicating the axis of movement: east–west (E), north–south (N), and up–down (Z). For each azimuth, the recorded data underwent essential processing and baseline correction procedures. These included downloading an unprocessed earthquake acceleration record with 10 s of data before and 200 s of data after the listed start time. The instrument response was removed and a cosine taper of 5% was applied to both the front and back of the series. The data were then filtered using a 4th-order low-pass filter with a corner frequency of 0.1 Hz and a 5th-order high-pass filter with a corner frequency of 50 Hz, which happened to be the Nyquist frequency. These resultant frequencies were the result of varying the corner frequencies and performing a visual analysis of the plotted ground motions and their corresponding Fourier spectra. An additional cosine taper of 5% was applied to both the front and back of the filtered data. Baseline correction involved fitting and removing a 4th-order polynomial to the velocity version of the ground motion data. Acceleration ground motions were computed as the derivative of the velocity data.

Table 3. Ground motion processing and baseline correction program.

Time Window	At the beginnings (s)	Event time −10
	At the end (s)	Event time +200
Cosine Taper	At the beginning (%)	5
	At the end (%)	5
High-Pass Filter	Low-Pass (Hz)	0.1, 4th order
	High-Pass (Hz)	49.9, 5th order
Post-Cosine Taper	At the beginning (%)	5
	At the end (%)	5
Baseline Correction	Fitting Domain	Velocity
	Polynomial Order	4

summarizes the raw ground motion data processing parameters.

With the resultant ground motions, 5% damped acceleration response spectral ordinates for periods, T = 0.02, 0.2, 1.0, and 10.0 s were estimated for comparison with PEER GMMs. There are several reasons for selecting these periods. The reason for selecting T = 0.2 s as a basis of comparison is because it is a compromise between the acceleration and velocity-sensitive period ranges, while T = 1.0 s is a compromise between the velocity and displacement-sensitive period ranges. Additionally, spectral ordinates at and near T = 0.2 and 1.0 s generally control practical response spectra design [38,39]. A period of T = 0.02 s was selected in lieu of a peak ground acceleration (PGA) estimation because some GMMs use short periods, typically below 0.05 s, as representative of PGA and that PGA is not generally used in practical design. Using the same logic, peak ground velocity was not considered because it is also not very prominent nor frequent in design practice. Nonetheless, estimations for PGA and at T = 0.02 s are not significantly different. A long period of T = 10.0 s was selected for displacement-based interests. The two orthogonal horizontal recordings, i.e., E and N, were projected onto a single azimuth given by an increment of rotation angle across 1° to 180°. A 5% damped elastic acceleration response spectrum (SA) was estimated for each rotation angle increment with the median across all SA at a specific period denoted as Rot50 [40]. Note that this implies not all Rot50 will come from the same azimuth.

2.3. GMMs Considered

PEER separated ground motion work into generational and geographical segments. The first set of GMMs was released under the program Next Generation of Ground Attenuation Models for the Western United States (NGA West). This initial set was based on a comprehensive and extensive earthquake ground motion database and consisted of 5 GMMs for active shallow crustal regions. The program concluded in 2008 and produced GMMs, named by their developers as Abrahamson and Silva, Boore and Atkins, Campbell and Bozorgnia, Chiou and Youngs, and Idriss, which will be abbreviated to AS08, BA08, CB08, CY08, and I08, respectively, herein [1,2,3,4,5]. These NGA West GMMs estimated the natural log of the pseudo spectral accelerations (PSAs) using the geometric mean of a period and azimuth-decoupled version of the Rot50 intensity measure (GMRotI50) [41] as well as their associated uncertainties. Studies show that the differences between Rot50 and GMRotI50 were similar in short periods, with a maximum difference of about 7% in longer periods [40].

The subsequent NGA program was aptly named NGA-West2, which utilized an expanded database as well as a better understanding and quantification of earthquake and wave propagation phenomena. This set of 5 GMMs was again applied to active shallow crustal regions and named by their developers as Abrahamson, Silva, and Kamai; Boore, Stewart, Seyhan, and Atkins; Campbell and Bozorgnia; Chiou and Youngs; and Idriss. These are abbreviated as ASK14, BSSA14, CB14, CY14, and I14, respectively, herein [6,7,8,9,10]. However, the NGA-West2 GMMs estimated the natural log of the PSA from the aforementioned Rot50.

The final NGA GMM project was NGA-East. This project focused on developing GMMs for Central and Eastern North America (CENA), a relatively stable region with low seismicity [42]. Like NGA-West2, NGA-East estimated the natural log of the PSA using Rot50. Although NGA-East offers multiple GMMs, only two by Darragh, Abrahamson, Silva, and Gregor and Pezeshk, Zandieh, Campbell, and Tavakoli, abbreviated as DASG15 and PZCT18, respectively, are considered in this study [11,12]. Both were selected for consideration because they seemed to have survived the test of time, with one having been updated. We use the newer version herein [12]. Additionally, some of the proposed NGA-East GMMs are slight modifications to an NGA-West or NGA-West2 counterpart, some require parameters that are unobtainable at this point, and at least one did not offer a quantifiable relationship within the document. It should be noted that DASG15 offers 4 versions of their GMM. These four versions are binary combinations of a corner frequency (1 or 2) and stress parameter (constant or variable) used in their simulation technique [11]. Interestingly, DASG15 did not seem to offer practical guidance on which version to use; therefore, all four will be initially considered herein as DASG15-1CC, DASG15-1CV, DASG15-2CC, and DASG15-2CV. PZCT18 also has two versions, and the one designated for CENA is considered herein. The NGA GMM models considered in this study are detailed in

Table 4. The NGA GMMs used for comparison analysis.

Category	GMM	Magnitude Range (MW)	Distance Range (km)	VS30 Range (m/s)
NGA-West.	AS08 [2]	5.0–8.5	0–200	N/A
	BA08 [1]	5.0–8.0	0–200 B	180–1300
	CB08 [3]	4.0–8.5 A	0–200	150–1500
	CY08 [4]	4.0–8.5 A	0–200	150–1500
	I08 [5]	5.0–8.5 A	0–200	>450
NGA-West 2	ASK14 [6]	3.0–8.5	0–300	180–1500
	BSSA14 [7]	3.0–8.5 A	0–400	150–1500
	CB14 [8]	3.3–8.5 A	0–300	150–1500
	CY14 [9]	3.5–8.5 A	0–300	180–1500
	I14 [10]	5.0–8.0	0–150	450–2000
NGA-East	DASG15-1CC [11] DASG15-1CV [11] DASG15-2CC [11] DASG15-2CV [11]	4.5–8.5	<1000	N/A
	PZCT18 [12]	4.0–8.0	<1000	3000

N/A not available, not an input parameter, or not clearly stated. ^A dependent on faulting mechanism. ^B distance is treated as closest distance to surface projection of fault rupture plane.

.

With respect to the NGA-West and NGA-West2 GMMs, there are several input parameters, which are very difficult to obtain or are not typically used in seismology or earthquake engineering analyses. Fortunately, there are some relationships that can help an analyst estimate such parameters [43].

2.4. Comparisons

Relative residuals, which are essentially z-scores, were calculated to assess the differences between observed recordings and GMM predictions using the following equation:

$$Z_i=\frac{{\ln SA}_{Observed,i}-\ln {PSA}_{GMPE,i}}{{\sigma }_{ln,GMPE,i}}$$

(1)

where i is the station ground motion recording as an index identifier, SA_Observed,i is the acceleration response spectral ordinate from Rot50 for the ith recording station, PSA_GMM,i is the PSA from one of the aforementioned NGA GMMs for conditions at the ith recording station, and σ_ln,GMM,i is the corresponding standard deviation given in the GMM description in natural log units for the ith recording station conditions. Although this formulation might seem strange and can show some bias, this was implemented because the standard deviation is in natural log units and allows for a better interpretation of how compatible the GMMs are given the available data. This approach was also used in a European study [26].

With respect to determining which GMMs would be a good fit, a summation of the squares is taken of the relative residual:

$$Score=\frac{1}{n}\sum _i^n{\left(Z_i\right)}^2$$

(2)

where n is the number of recordings per earthquake. This makes Score a metric per earthquake. In this case, the lower these metrics are, the better the GMM compatibility with moderate South Korean earthquakes.

3. Results

3.1. Comparisons with Site-to-Source Distance

For plotting purposes, the median of the measured and inferred V_S30 = 610 m/s was used as input to GMMs that required a V_S30 value. For brevity, a series of acceleration plots against distance will be made for the major events, 2016 Gyeongju and 2017 Pohang, for NGA-West GMMs. An example showing the dependent events will also be shown as well as NGA-West2 and NGA-East GMMs for the major events. These are made to help the reader familiarize the environment and dataset available.

An example of the data comparison is shown in Figure 1. The figure plots NGA-West GMMs for PSA(T = 0.2 s) against processed SA(T = 0.2 s) data for both the 2016 M_W 5.5 Gyeongju earthquake and the 2017 M_W 5.5 Pohang earthquake. With respect to the 2016 Gyeongju event, the data appear to plot somewhat below the NGA-West GMMs on average but do relatively well in the 100 to 200 km range. Although originally not intended for distances past 200 km, the data appear to be bound by all 5 NGA-West GMMs. With respect to the 2017 Pohang event, the GMMs appear to predict relatively well at the 100 to 200 km distances, with some slight overprediction scattered across the available distance range.

For comparison, Figure 2 is similar to Figure 1 except for PSA(T = 1.0 s) against processed SA(T = 1.0 s) data. The figure shows the GMMs to be relatively more linear with respect to log–log space, with an overall overprediction of accelerations, especially for the 2017 Pohang event. Interestingly, the variability in these GMMs is wider at T = 0.2 s than at T = 1.0 s for distances greater than 200 km.

Figure 3 is a plot of spectral accelerations at T = 0.02 s. Interestingly, the plot shows similar patterns as seen in Figure 1, with visual inspection suggesting that the NGA-West GMMs tend to overestimate accelerations on the Korean peninsula, at least for-moderate sized earthquakes.

Figure 4 plots PSA(T = 10.0 s) against processed SA(T = 10.0 s) data. The absolute values of the data are quite small and perhaps insignificant but are kept here for completeness and comparison. Such small values will have an impact on the residuals. What is noticeable is that the 2017 Pohang earthquake does not seem to show significant signs of attenuation with distance relative to the 2016 Gyeongju earthquake. Interestingly, the scatter in NGA-West GMMs at T = 10.0 s is significant, with about two orders of magnitude in difference at the longer distances considered.

A similar plot is made for dependent events in Figure 5. Figure 5a shows the results for an M_W 5.1 foreshock to the 2016 Gyeongju earthquake. The recordings seem to show similar levels of ground shaking to the M_W 5.5 main shock and plot quite closely, from a visual sense, to NGA-West GMMs in the 100 to 200 km range. Figure 5b shows the results for an M_W 4.7 aftershock to the 2017 Pohang earthquake. Unlike the foreshock in the figure, the NGA-West GMMs tend to overestimate ground shaking on average. Also, in Figure 5b, the AS08 and CY08 GMMs are noticeably lower than the other NGA-West GMMs because they can account for aftershocks, noting that spectral accelerations are generally lower than main shock ordinates. Interestingly, the data for SA(T = 0.2 s) still show an overestimation at distances less than 100 km but an underestimation at distances greater than 200 km. It is noted that the NGA-West GMMs are slated for sites less than 200 km away.

Figure 6 plots the results when considering NGA-West2 GMMs. It shows that the 2014 versions of the NGA GMMs work in a narrower range relative to their 2008 versions. In doing so, Figure 6a shows that the GMMs underestimate ground shaking for sites greater than 200 km away. It is noted that most NGA-West2 GMMs have a range of up to 300 km. Similarly, for the 2017 Pohang event shown in Figure 6b, the NGA-West2 GMMs appear to underestimate ground shaking at distances greater than 200 km and also overestimate accelerations at distances less than 100 km.

Interestingly, Figure 7 plots the results for a subset of NGA-East GMMs and appears to show that the DASG15 suite of GMMs tended to very slightly overestimate both 2016 Gyeongju and 2017 Pohang recordings, especially for site-to-source distances greater than 60 km. Similar observations were made for the PZCT18 relationship but at all considered site-to-source distances. Since all four versions of the DASG15 GMM produce similar outputs and taking into account the validation notes in their section, only the GMM for one corner frequency and variable stress parameter (DASG15-1CVSP) is considered hereafter [40].

3.2. Comparing Residuals

Residuals were calculated based on Equation (1), comparing GMMs, and plotted along distance for familiarization. For plotting purposes, the residuals are based on spectral acceleration at T = 0.2 s. Moreover, specific V_S30s were taken from Table 2 in calculations. Figure 8 plots the relative residuals for each recording relative to NGA West GMMs for all events considered in this study. Figure 8a shows the variability in the residuals for the 2016 Gyeongju event, with a majority of the relative residuals within two lognormal standard deviations at distances less than 200 km. After 200 km, the figure shows that the relative residuals for three of the five NGA-West GMMs (AS08, BA08, CB08) continue to increase, signifying a pattern of underprediction, while one of the five NGA-West GMMs (CB08) continued to decrease, signifying a pattern of overprediction. For the 2017 Pohang event shown in Figure 8b, the NGA-West GMMs generally show overprediction at distances less than 100 km. One of the GMMs (CB08) consistently overpredicted across the distances considered. Similar to the 2016 Gyeongju event, three of the five NGA-West GMMs underpredicted at distances greater than 100 km. Figure 8c shows similar patterns of increasing scatter at larger distances. Interestingly, all NGA-West GMMs overpredicted the Pohang aftershock event at distances less than 100 km, even though two GMMs have built-in considerations for aftershocks. The GMM estimates increasingly scattered with distance after about 130 km. Results for the offshore Ulsan earthquake are shown in Figure 8e. The scatter is considerable, going across 4 log normal standard deviations.

For comparison, Figure 9 shows the results when NGA-West2 GMMs are applied to the earthquakes under study in a similar format to Figure 8. Figure 9 shows the same patterns as NGA-West GMMs for each event. However, the variability appears to tighten per recording when NGA-West2 GMMs are considered. This is due, in part, to the higher standard deviations in the NGA-West2 suite.

Relative residuals were also calculated for both M_W 5.5 events using the subset of NGA-East GMMs and are shown in Figure 10. This plot suggests that both DASG15 and PZCT18 GMMs performed relatively well at long distances, especially the DASG15 GMM. For the 2017 Pohang aftershock, the GMMs also show a similar tendency to overestimate earthquake ground shaking but perhaps not as variable as the M_W 5.5 events.

Table 5. Score for each GMM per earthquake event for SA(T = 0.2 s). Numbers in bold are the lowest in the group. Ends of rows and columns are the summation of the previous metrics for comparison.

GMM	2016 MW 5.5	2017 MW 5.5 P	MW 5.1 F	MW 4.7 A	MW 4.5	Sum
AS08	1.38	2.03	1.29	1.67	2.48	8.85
BA08	1.70	2.11	1.67	4.25	2.40	12.13
CB08	2.70	6.15	2.82	8.85	2.95	23.47
CY08	1.78	0.49	2.11	2.56	8.09	15.03
I08	1.06	1.16	0.93	1.94	1.52	6.61
ASK14	1.95	2.93	1.78	2.08	4.92	13.66
BSSA14	1.55	1.71	1.67	1.05	4.47	10.45
CB14	1.63	2.24	1.70	1.63	4.08	11.28
CY14	2.17	2.77	1.80	1.69	4.99	13.42
I14	1.50	1.26	1.22	1.58	2.29	7.85
DASG15	0.99	1.35	1.01	1.77	1.24	6.36
PCZT18	2.14	2.72	1.80	1.78	1.67	10.11
SUM	20.55	26.92	20.52	28.85	16.13

^F foreshock. ^A aftershock. ^P possible induced or triggered earthquake.

presents the relative residual scores for each GMM compared at SA(T = 0.2s). What is somewhat simultaneously surprising and unsurprising is that both NGA-East GMMs considered herein outperformed their NGA-West and NGA-West2 GMMs in the South Korean region. It is surprising because NGA-East GMMs incorporated simulated results into their regressions, which were local to CENA conditions, most likely different from the Korean peninsula. What is unsurprising is the relative improvement, from the perspectives of residuals, that NGA-East GMMs have over NGA-West and NGA-West2 GMMs as they were later derived from active crustal regions, which the Korean peninsula is not, at least not yet. However, the I08 and I14 GMMs did well for all moderate earthquakes considered, which is perhaps not surprising as the original intent of that GMM was to revolve around rock sites, i.e., sites with relatively higher V_S30.

Similar observations are shown in

Table 6. Score for each GMM per earthquake event for SA(T = 1.0 s). Numbers in bold are the lowest in the group. Ends of rows and columns are the summation of the previous metrics for comparison.

GMM	2016 MW 5.5	2017 MW 5.5 P	MW 5.1 F	MW 4.7 A	MW 4.5	Sum
AS08	1.17	2.43	2.54	1.70	1.16	8.00
BA08	1.43	3.57	3.13	3.27	1.53	12.93
CB08	1.54	5.92	3.23	4.19	1.53	16.41
CY08	1.22	0.48	2.52	1.34	1.49	7.05
I08	0.72	2.11	1.66	2.03	0.93	7.45
ASK14	1.23	1.29	1.42	1.83	3.30	9.07
BSSA14	1.03	1.42	1.31	1.38	2.86	8.00
CB14	0.96	2.54	1.42	1.59	2.67	9.18
CY14	0.97	1.42	1.20	1.28	3.47	8.34
I14	1.72	1.40	1.31	2.04	1.84	8.31
DASG15	0.93	2.33	1.82	1.32	0.95	7.35
PCZT18	1.18	2.10	1.97	0.62	1.63	7.50
SUM	14.10	27.01	23.53	22.59	23.36

^F foreshock. ^A aftershock. ^P possible induced or triggered earthquake.

, which presents the relative residual scores for each GMM compared at SA(T = 1.0 s). However, relative to Table 5, the relative residuals here are much smaller. Again, the NGA-East GMMs and the I08 and I14 GMMs showed some of the lowest scores, but CY08, AS08, and all NGA-West2 GMMs did well, all things considered. Interestingly, all GMMs did well for the 2016 Gyeongju main shock at SA(T = 1.0 s). This is in contrast to Table 5, showing better performance for the smallest earthquake, which also happened to be the farthest from most seismic recoding stations, the 2016 Ulsan earthquake.

Table 7. Score for each GMM per earthquake event for SA(T = 0.02 s). Numbers in bold are the lowest in the group. Ends of rows and columns are the summation of the previous metrics for comparison.

GMM	2016 MW 5.5	2017 MW 5.5 P	MW 5.1 F	MW 4.7 A	MW 4.5	Sum
AS08	1.38	1.62	1.18	1.77	1.58	7.53
BA08	3.15	2.68	2.53	4.03	3.64	16.03
CB08	3.91	9.06	4.71	10.87	5.04	33.59
CY08	2.32	2.45	2.28	3.29	6.92	17.26
I08	1.36	1.43	1.24	2.67	1.42	8.12
ASK14	1.56	1.86	1.16	1.75	2.48	8.81
BSSA14	1.65	1.85	1.75	1.40	3.80	10.45
CB14	1.75	2.19	1.29	2.00	1.94	9.17
CY14	2.03	2.21	1.86	3.28	5.15	14.53
I14	1.82	1.15	1.23	1.98	1.45	7.63
DASG15	1.88	3.67	2.09	5.00	1.66	14.30
PCZT18	2.93	5.07	2.93	5.47	1.47	17.87
SUM	25.74	35.24	24.25	43.51	36.55

^F foreshock. ^A aftershock. ^P possible induced or triggered earthquake.

presents the relative residual scores for each GMM compared at SA(T = 0.02 s). Surprisingly, the NGA-East GMMs did not score as well at the stiffer range of ground shaking. Notable performances were observed for both the I08/I14 and AS08/ASK14 GMMs. All GMMs considered tended to do well for both Gyeongju events.

Table 8. Score for each GMM per earthquake event for SA(T = 10.0 s). Numbers in bold are the lowest in the group. Ends of rows and columns are the summation of the previous metrics for comparison.

GMM	2016 MW 5.5	2017 MW 5.5 P	MW 5.1 F	MW 4.7 A	MW 4.5	Sum
AS08	1.00	1.12	1.14	1.21	1.77	6.24
BA08	2.41	1.65	3.18	1.59	2.14	10.97
CB08	0.73	0.76	0.95	0.93	1.56	4.93
CY08	1.15	1.42	1.35	0.95	5.14	10.01
I08	4.55	5.75	3.65	3.50	8.82	26.27
ASK14	1.08	1.09	1.27	1.97	5.32	10.73
BSSA14	1.07	1.47	1.17	1.30	3.84	8.85
CB14	1.44	1.90	1.74	2.52	7.70	15.30
CY14	2.39	2.46	2.56	2.25	9.12	18.78
I14	1.78	2.40	1.57	1.89	5.15	12.79
DASG15	0.41	0.26	0.54	0.47	1.72	3.4
PCZT18	1.38	1.08	1.58	0.67	3.36	8.07
SUM	19.39	21.36	20.70	19.25	55.64

^F foreshock. ^A aftershock. ^P possible induced or triggered earthquake.

presents the relative residual scores for each GMM compared at SA(T = 10.0 s). Interestingly, the overall Scores are not as large as expected as the accuracy of the GMMs might not match at such low levels of shaking. For long periods of shaking, the I08/I14 performed poorly and was overtaken by CB08 and BSSA14. Again, both NGA-East GMMs did well, with DASG15 scoring the lowest total across all earthquakes studied.

4. Discussion and Conclusions

To ascertain which, if any, of the PEER NGA GMMs would be applicable to the Korean peninsula, collections of earthquake and ground motion data were compiled and processed. This resulted in data from five diverse earthquakes of moderate magnitude around the Korean peninsula from 2016. There were three main shocks, one of which may be a potentially induced or triggered event, with another being offshore, one foreshock, and one aftershock. Plots of distance against spectral acceleration at T = 0.02, 0.2, 1.0, and 10.0 s showed appreciable scatter at distances less than 100 km but would monotonically increase or decrease, representing underestimation and overestimation, respectively, at distances farther than 200 km, the typical limit of the NGA-West/West2 GMMs considered. NGA-East GMMs also showed similar patterns with distance but did not exhibit the considerable monotonic increase or decrease, as shown in the NGA-West/West2 GMMs. Tabulating the relative residuals across all earthquake events showed that the NGA-East GMMs performed well except at T = 0.02 s. The results also suggested the NGA-West/West2 GMMs I08/I14 also performed comparatively well across the board.

In terms of rankings, the NGA-East GMMs DASG15 and PCZT18 did relatively well and would be recommended for earthquake- and seismic-related studies in the Korean peninsula. Surprisingly, the I08 and I14 GMMs did well overall, with the only major setback being at an evaluation of SA(T = 10.0 s). For long periods, both GMMs by CB08 and BSSA14 can perform well; however, the earthquake magnitudes considered herein are not conducive to long periods of strong ground motion. Therefore, it is better to consider DASG15 or PCZT18 instead. An interesting outcome of this study is the consideration of aftershocks. AS08, ASK14, and CY08 integrate aftershocks into their GMMs, and the results suggest AS08 performs well for such earthquake types, better than ASK14, surprisingly.

There were many challenges with this investigation, with most revolving around a lack of information. An important one was the lack of geological and seismological data available for ground motion recording sites and past earthquakes. Much of the missing information used to compensate for missing parameters was inferred or taken from specific studies, such as the V_S30 dataset. However, this investigation did not consider earthquakes without an M_W, which restricted the availably of data. Hopefully, the authorities will attempt to integrate a system for estimating and publicizing M_W estimates. Estimating the magnitude was out of scope for this study. Another issue was the confusion with ground motion recordings and a lack of appropriate technical support. Much of the time was spent searching for ground motion data, which ended up being KIGAM instead of KMA. Additionally, much of this investigation was spent on determining how to process the data. These issues suggest that the results of the processed ground motions can have externally incorporated uncertainties.

Of course, the resultant response spectra might have been biased as a result of these factors. What is interesting is that the NGA-West and NGA-West2 suite of GMMs showed relative compatibility with South Korean earthquakes of moderate magnitude. Although the database used for NGA-West and NGA-West2 GMMs is quite exhaustive for events in seismically active regions, the database for NGA-East was more geared towards the rocky CENA, which is more similar to South Korea than the Western United States and other seismically active regions. It would be helpful if there were more quality data to work with, such as site and instrument parameters. Additionally, if there are more significant earthquakes involving the Korean peninsula, perhaps this study can be expanded and provide better results with newer and more robust evaluation techniques.