1 Introduction

The seismotectonics is a tectonic framework combining seismicity, geology and geophysical properties, which are useful for inference of seismic hazard potentials (Gasparini et al., 1982; Powell et al., 1994; Lavecchia et al., 1994, Costa et al., 1996; De and Kayal 2003). A region can be divided into seismotectonic provinces considering the seismotectonic properties that are represented by maximum magnitudes, earthquake occurrence rates and potential peak ground accelerations. Each seismotectonic province can be defined by its unique seismicity properties and tectonic environments (Cornell 1968). Seismotectonic province models have been proposed for a number of regions (Nowroozi 1976; Tavakoli and Ghafory-Ashtiany 1999; Meletti et al. 2000; Singh et al. 2011). These regionalized provinces are used for seismic hazard analysis (e.g., Frankel 1995; Menon et al., 2010). However, a routine procedure for constructing seismotectonic province models has not been established. Also, it remains unclear how many seismotectonic provinces are appropriate for each region.

It is difficult to assess the seismotectonic properties of low-seismicity intraplate regions with short seismic records. In particular, the intraplate regions adjacent to continental margins comprise paleo-tectonic structures that respond to the regional stress field (Choi et al. 2012; Hong et al. 2015). The monitoring of seismogenic paleo-tectonic structures in oceanic regions by inland seismic networks can be poor. Also, tectonic-loading stress is accumulated slowly in intraplate regions, inducing destructive large earthquakes with long recurrence time intervals (e.g., Talwani and Cox 1985).

Seismicity with long recurrence intervals is limitedly observable in short-term earthquake catalogs. Long-term seismicity records may contribute to the assessment of potential seismic hazards. Historical earthquake records may be useful for long-term seismicity analysis. Thus, analysis of both instrumental and historical earthquake records may be desirable. However, historical earthquake records suffer from inherent incompleteness, and the source parameters are poorly constrained. Thus, it remains unclear how historical earthquake catalogs should be combined with instrumental earthquake catalogs for seismic hazard analysis. Also, the necessary time period of earthquake catalogs for seismic hazard analysis remains unclear.

We propose a seismotectonic province model for the Korean Peninsula that belongs to a stable intraplate regime where major earthquakes occur with long recurrence intervals. Seismotectonic province models based on both the tectonics and seismicity have been rarely proposed for the Korean Peninsula (e.g., Kim and Lee 2000). The early models generally resembled the geological province structures. In this study, the seismicity and geophysical properties, and geological and tectonic features are combined to determine the seismotectonic province models. Both the instrumental and historical earthquake records are combined for the analysis of seismicity properties and maximum magnitudes. The variation of seismicity properties and maximum magnitudes depending on the seismotectonic province model is investigated. Also, the effect of seismotectonic province models on the determination of seismicity properties and maximum magnitudes is examined.

2 Geology and Tectonics

The Korean Peninsula is located in an intraplate region adjacent to the far-eastern Eurasian plate margin (Fig. 1). The far-eastern Eurasian plate converges with the Philippines Sea plate at the region off the southern Japanese islands, and with the Okhotsk plate at the eastern margin of the East Sea (Sea of Japan). The collisions of Eurasian plate inducing an tectonic-loading stress field composed of ENE-directional compression and WNW-directional tension around the Korean Peninsula (Choi et al. 2012) (Fig. 1). The current appearance of the Korean Peninsula was formed by a continental collision between North China and South China blocks during late Permian to Jurassic, which was followed by a continental-rifting opening the East Sea (Sea of Japan) during the Oligocene to mid-Miocene (Jolivet et al. 1994; Chough et al. 2000; Oh 2006). The continental collision developed a characteristic NE-trending geological provinces. The surface of the peninsula is composed of three precambrian massif blocks and two intervening belts (Chough et al. 2000).

The paleo-continental-collision developed an EW-trending subparallel structures in the central Yellow Sea, which were reactivated by the ambient NS-directional tension and Ryukyu trench rollback and produce normal-faulting earthquakes (Fig. 1). Also, the paleo-rifting developed NS-trending offshore paleo-normal-faulting structures subparallel with the east coast of the peninsula. The paleo-normal-faulting structures were reactivated by the EW-directional lithostatic compression, producing thrustal earthquakes (Choi et al. 2012). A solidified underplated magma associated with the East Sea opening appears to be present in the lower crust off the east coast of the peninsula, which is illuminated by high Pn velocity, high magnetic anomalies and high \(V_P/V_S\) ratios (Cho et al. 2004; Hong and Kang 2009; Jo and Hong 2013) (Fig. 2).

The massif blocks (Gyeonggi massif, Yeongnam massif) are illuminated as high seismic velocity regions (Hong and Kang 2009). Geophysical and seismic properties of the crust (crustal shear wave velocity, gravity anomaly, crustal P amplification, Lg Q, Pn tomography, heat flow) generally follow the geological structures in the surface (Fig. 2). The Pn seismic velocities are observed to be low along the east coast. The southeastern peninsula (Gyeongsang basin) is covered by Cretaceous volcanic sediments where high heat flows, low shear wave velocities, high gravity anomalies, low Pn velocities, low Lg Q, and high P amplification are observed.

The inland peninsula and Yellow Sea display typical features of continental crusts with thicknesses of 29–36 km (Chang et al., 2004; Hong et al. 2008; He and Hong 2010). The paleo-continental-rifting developed transitional crusts between continental and oceanic crusts in the East Sea (Fig. 1). The crustal thicknesses in the East Sea decrease abruptly across the east coast, and reach 8.5–10 km in the Japan basin (Hirata et al. 1992; Kim et al. 1998). Continental shelves cover the most regions of the Yellow Sea, while are extended only for several tens of kilometers in the East Sea. A number of faults were investigated (e.g., Lee and Um 1992; Kyung 2003; Lee and Yang 2007). Only several faults were identified to be capable (Choi 2012) (Fig. 1). The faults in the peninsula strike dominantly in NE, displaying acute angles to the ambient compressional stress field. These strikes of faults are consistent with the geometry of geological structures, which might result from the paleo-continental collision.

3 Seismicity and Earthquake Records

The instrumental seismic monitoring in the Korean Peninsula began in 1978, and the number of reported earthquakes until 2013 is 14,992 (Fig. 3). We collect the event information of the instrumentally-recorded earthquakes from the Korea Meteorological Administration (KMA), Japan Meteorological Agency (JMA), and China Earthquake Network Center (CENC). The largest magnitude of the instrumentally-recorded events is 5.3 (Fig. 4). Six earthquakes with magnitudes equal to or greater than 5.0 occurred in the Korean Peninsula since 1978. It is noteworthy that an M6.5 earthquake was reported to have occurred at the northwestern peninsula in 1952 (Engdahl and Villasenor 2002). Most events occur at depths less than 20 km, and the largest focal depth is 35 km (Fig. 5).

Strike-slip earthquakes are dominant in the peninsula (Fig. 5). Characteristic normal-faulting earthquakes are observed around the paleo-continental collision belt in the central Yellow Sea (Hong and Choi 2012). Thrust earthquakes occur along the NS-trending paleo-rifting structure off the east coast of the peninsula (Choi et al. 2012). These normal-faulting and thrustal earthquakes result from the response of paleo-tectonic structures to the ambient stress field. It is observed that the instrumental seismicity is weakly correlated with known capable faults (cf., Figs. 1, 3)

The historical earthquake records are analyzed to reflect the seismicity with long recurrence time intervals. A number of historical earthquakes were recorded in historical literatures including Samgooksagi, Koryosa and Choseonwangjosillog. Some devastating earthquakes produced seismic damages with seismic intensities of VIII in the modified Mercalli intensity (MMI) scale (Lee and Yang 2006). Most historical earthquakes were recorded during Joseon dynasty (1393–1904), and the number of events is 1893 (Figs. 3, 4). The event information for the historical earthquakes is collected from Houng and Hong (2013). However, the magnitudes of the historical earthquakes are redetermined based on a recently-developed magnitude–intensity relationship that is given by (Park and Hong 2014):

$$\begin{aligned}&I(M_\mathrm{L}, l, h) = 1.72 M_\mathrm{L} - 0.322 \,\mathrm {ln} (l^2 + h^2) - 0.00608 \, \sqrt{l^2 + h^2}\,-0.998, \end{aligned}$$
(1)

where I is the seismic intensity in the MMI scale, \(M_\mathrm{L}\) is the event magnitude in the local magnitude scale, h is the focal depth in kilometer, and l is the epicentral distance in kilometer.

4 Theory

4.1 Gutenberg–Richter Seismicity Constants

The minimum magnitude, \(M_{\min }\), represents the threshold magnitude above which the event catalog is complete (e.g., Rydelek and Sacks 1989; Gomberg 1991). An earthquake catalog for events with magnitudes greater than \(M_{\min }\) generally satisfies the Gutenberg–Richter frequency–magnitude relationship:

$$\begin{aligned}&\log N=a -b M, \end{aligned}$$
(2)

where a and b are constants, M is the magnitude, and N is the number of events with magnitudes greater than or equal to M. The fitness between the seismicity data and theoretical curve is estimated by

$$\begin{aligned}&R=1-\frac{\sum _{j=1}^{n}|B_j-S_j|}{\sum _{j=1}^{n} B_j}, \end{aligned}$$
(3)

where \(B_j\) is the number of events with magnitudes greater than or equal to \(M_j\), \(S_j\) is the reference value from the Gutenberg–Richter relationship, and n is the total number of events in the dataset. From Eq. (2), the Gutenberg–Richter b value for an event catalog with a minimum magnitude of \(M_{\min }\) satisfies (Aki 1965)

$$\begin{aligned}&b=\frac{1}{\ln (10) \times (\bar{M}-M_{\min })}, \end{aligned}$$
(4)

where \(\bar{M}\) is the average of the observed magnitudes.

If the magnitude-dependent earthquake distribution follows a probability density function, f(m), the number of earthquakes (N) with magnitudes greater than or equal to M satisfies (Tinti and Mulargia 1985)

$$\begin{aligned}&N=10^{a} \int _M^{\infty } f(m)\, \mathrm{d}m=10^{a}\left[ 1-\int _0^{M} f(m)\, \mathrm{d}m\right] =10^{a}\left[ 1-F(M)\right] , \end{aligned}$$
(5)

where the function F(M) is the cumulative distribution function that is the integral function of f(m). Function F(M) is given by

$$\begin{aligned}&F(M)=1-10^{-bM}. \end{aligned}$$
(6)

The probability density function, f(M), is calculated by differentiating F(M):

$$\begin{aligned}&f(M)=\beta \mathrm{e}^{-\beta M}, \end{aligned}$$
(7)

where \(\beta \) is given by

$$\begin{aligned}&\beta =b\ln (10). \end{aligned}$$
(8)

The probability density function, f(M), is normalized for events with magnitudes greater than or equal to \(M_{\min }\). The normalized probability density function, \(\hat{f}(M)\), is defined to be

$$\begin{aligned}&\hat{f}(M)=\frac{\beta \mathrm{e}^{-\beta M}}{\int _{M_{\min }}^{\infty } f(m)\, \mathrm{d}m }= \beta \mathrm{e}^{-\beta (M-M_{\min })}. \end{aligned}$$
(9)

Hereafter, function \(\hat{f}(M)\) is used for f(M). The population mean (E(M)) and population variation (\(\mathrm{Var}(M)\)) of magnitude distribution f(m) are given by

$$\begin{aligned}&E(M)=\int _{M_{\min }}^{\infty } m f(m)\, \mathrm{d}m= M_{\min }+\frac{1}{\beta }, \nonumber \\&\mathrm{Var}(M)=\int _{M_{\min }}^{\infty } m^2 f(m)\, \mathrm{d}m - \left[ E(M) \right] ^2= \frac{1}{\beta ^2}. \end{aligned}$$
(10)

Thus, an earthquake catalog with a sufficiently large number (n) of events displays a normal distribution with a mean of \(M_{\min }+1/\beta \) and variation of \(1/(n\beta ^2)\).

When the event catalog satisfies a normal distribution, the \(\beta \) estimate, \(\hat{\beta }\), for an event catalog with mean magnitude of \(\bar{M}\) can be written as

$$\begin{aligned}&\hat{\beta }=\int _{-\infty }^{\infty } \beta \, \exp \left[ -\frac{1}{2}\times \frac{\left\{ \bar{M}-\left( M_{\min }+\frac{1}{\beta }\right) \right\} ^2 }{\frac{1}{n\beta ^2}} \right] \,\mathrm{d}\beta =\frac{1}{\bar{M}-M_{\min }}. \end{aligned}$$
(11)

The b value based on the earthquake catalog is estimated to be

$$\begin{aligned}&\hat{b}=\frac{\hat{\beta }}{\ln (10) }=\frac{1}{\ln (10) (\bar{M}-M_{\min })}. \end{aligned}$$
(12)

The accuracy of the minimum magnitude (\(M_{\min }\)) is dependent on the magnitude precision in the catalog. When the apparent minimum magnitude for an event catalog with a discrete magnitude interval of \(\Delta M\) is given by \(M_\mathrm{thre}\), the practical minimum magnitude is given by

$$\begin{aligned}&M_{\min }=M_\mathrm{thre}-\frac{\Delta M}{2}. \end{aligned}$$
(13)

Thus, the b value for the earthquake catalog can be written as

$$\begin{aligned}&\hat{b}=\frac{1}{\ln (10) \times [ (\bar{M}-(M_\mathrm{thre}-\Delta M/2)]}. \end{aligned}$$
(14)

Also, the \(\hat{a}\) value for the event catalog is given by

$$\begin{aligned}&\hat{a}=\log (N)+\hat{b} M_{\min }. \end{aligned}$$
(15)

4.2 Determination of Maximum Magnitude, \(M_{\max }\)

The maximum magnitude, \(M_{\max }\), is the upper limit of event magnitudes that can occur in the given region (Kijko and Singh 2011). The maximum magnitudes can be estimated deterministically based on empirical relationships between magnitudes and fault parameters (e.g., Wells and Coppersmith 1994). Also, numerous probabilistic methods were proposed to determine the maximum magnitudes from earthquake catalogs. Probabilistic methods are based on either parametric or non-parametric statistical analyses of seismicity (Robson and Whitlock 1964; Cooke 1979; Pisarenko et al. 1996; Kijko and Graham 1998; Kijko and Singh 2011). The probabilistic approaches may yield different estimates depending on the properties of event catalogs such as the completeness of catalogs and the number of composing events. Representative probabilistic methods are introduced in this study.

The parametric approach is applicable to the event catalog that satisfies the Gutenberg–Richter frequency–magnitude relationship. The set of magnitudes satisfies the probability density function, f(M), which can be written as

$$\begin{aligned}&f(M)=\frac{\beta \exp \left[ -\beta (M-M_{\min }) \right] }{\int _{M_{\min }}^{M_{\max }} \beta \exp \left[ -\beta (m-M_{\min }) \right] \, \mathrm{d}m } = \frac{\beta \exp \left[ -\beta (M-M_{\min }) \right] }{1- \exp \left[ -\beta (M_{\max }-M_{\min }) \right] }. \end{aligned}$$
(16)

Also, the cumulative distribution function, F(M), is given by

$$\begin{aligned}&F(M)=\int _{M_{\min }}^M f(m)\, \mathrm{d}m =\frac{1- \exp \left[ -\beta (M-M_{\min }) \right] }{1- \exp \left[ -\beta (M_{\max }-M_{\min }) \right] }. \end{aligned}$$
(17)

The maximum magnitude based on the Tate–Pisarenko method is given by (Appendix 1)

$$\begin{aligned}&M_{\max }=M_n+\left( \frac{1}{n}\right) \times \frac{1- \exp \left[ -\beta (M_{\max }-M_{\min }) \right] }{\beta \exp \left[ -\beta (M_{\max }-M_{\min }) \right] }. \end{aligned}$$
(18)

A grid-searching algorithm is applied to determine the maximum magnitudes with the Tate–Pisarenko approach.

The Tate–Pisarenko method is applicable to earthquake catalogs that satisfy the Gutenberg–Richter frequency–magnitude relationship. Large-magnitude earthquakes with long recurrence intervals can be included in short-term earthquake catalogs in which the expected upper-bound magnitudes (\(M_{\max }^\mathrm{exp}\)) are much smaller than the observed maximum magnitudes (\(M_{\max }^\mathrm{obs}\)) (Fig. 6). Earthquake catalogs including exceptionally large events often yield unstable \(M_{\max }\) estimates with the Tate–Pisarenko method. A reasonable \(M_{\max }\) estimate may be achieved when an appropriate number of events (n in Eq. (18)) is considered (Fig. 6). This procedure is applicable to incomplete catalogs in which minimum magnitudes are not be determined correctly. There is the possibility that earthquakes of any magnitude can be missed in historical earthquake catalogs. In this case, the Gutenberg–Richter frequency–magnitude relationship for instrumental earthquake catalogs can be applied.

The maximum magnitude based on non-parametric analysis with order statistics is given by (Kijko and Singh 2011; Appendix 1)

$$\begin{aligned}&M_{\max }=2 M_n-(1-{\mathrm{e}}^{-1})\sum _{i=0}^{n-1} ({\mathrm{e}}^{-i} M_{n-i}). \end{aligned}$$
(19)

The Robson–Whitlock (RW) method for \(M_{\max }\) uses the largest two magnitudes in the catalog (Robson and Whitlock 1964). The maximum magnitude is determined to be

$$\begin{aligned}&M_{\max }=(n+1)M_n-n M_{n-1}'=2M_n-M_{n-1}. \end{aligned}$$
(20)

The Robson–Whitlock–Cooke (RWC) method for \(M_{\max }\) is modified from the RW method, which is given by (Cooke 1979; Kijko and Singh 2011)

$$\begin{aligned}&M_{\max }=M_n+\nu (M_n-M_{n-1}), \end{aligned}$$
(21)

where \(\nu \) is a constant.

These methods have been applied widely to estimate maximum magnitudes in a number of regions including both active and stable regions (e.g., Kijko 2004; Kijko and Singh 2011; Anbazhagan et al. 2015). The four methods are used to determine the maximum magnitudes of events in the Korean Peninsula based on instrumental and historical earthquake catalogs.

5 Procedure

5.1 Construction of a Seismicity Density Map

The seismicity density map is constructed by combining the epicenters of earthquakes with magnitudes greater than or equal to the minimum magnitudes. The minimum magnitudes of instrumental and historical earthquake records are determined to be \(M_\mathrm{L}\) 2.5 and 4.7, respectively (Fig. 7). The seismicity density represents the population of seismic events, suggesting earthquake occurrence frequencies. The Korean Peninsula is discretized into 0.1\(^\circ \)-by-0.1\(^\circ \) cells. A Gaussian function is applied for spatial smoothing of earthquake occurrence frequencies. Spatial smoothing enables us to accommodate events with low-precision location information (Houng and Hong 2013). The correlation distance of the Gaussian function is set to 20 km, which is sufficiently large considering the hypocenter precision. The seismicity density is calculated by assessing the smoothed number of events.

5.2 Determination of Seismotectonic Provinces and Seismicity Parameters

The damage related to large events was well documented in the historical literature. Historical earthquakes are useful for assessment of long-term seismicity, which should be considered in the construction of seismotectonic provinces. The occurrence of earthquakes is related to both the tectonics and geological features. It is necessary to implement complete earthquake catalogs for correct determination of seismicity properties. The minimum magnitudes ensuring the completeness of earthquake catalogs vary with the spatial coverage of stations, which is dependent on the physical environment. The minimum magnitudes of the offshore regions are inherently higher than those of inland regions.

The seismotectonics characterizes the interaction between seismicity and tectonics by consolidating the seismic, geological, geophysical and geodetic properties in the context of a tectonic framework (Scholz 2002). The seismotectonic provinces are regionalized such that each province has unique seismicity and tectonics properties. The seismicity properties and seismic hazards are controlled by various factors including the medium properties and stress field. The medium properties can be inferred from the seismic, geophysical and geological features. Thus, the differences in the seismic, geophysical and geological features suggest different seismotectonic environments. The boundaries of seismotectonic provinces are constructed considering the spatial distribution of geophysical, geological and seismic properties.

We firstly divide the regions based on the seismicity density adequately. Uniform seismicity regions are adjusted considering the spatial distribution of focal mechanisms and geophysical signatures. The seismotectonic province boundaries are constructed considering the geological province boundaries, and seismic and geophysical properties. Also, we determine the minimum magnitudes (\(M_{\min }\)) and the Gutenberg–Richter parameters (a, b) for each province. The earthquake frequency parameter, a value, is normalized for time (year) and area (1 km\(^2\)). The estimates of maximum magnitudes are generally dependent on the observed maximum magnitudes and the completeness of the catalogs.

The minimum magnitude may vary by the b value, which is dependent on the method implemented. The maximum likelihood method considers every earthquake to be an independent event satisfying the Gutenberg–Richter frequency–magnitude relationship (Aki 1965; Tinti and Mulargia 1985). However, the b values for catalogs composed small numbers of events may not be determined accurately using a maximum likelihood method that assigns high weights to small earthquakes and low weights to large earthquakes (Wiemer and Wyss 2000). For better fit of both small and large events, a least-squares method is applied in this study. The range of magnitudes yielding fitnesses less than the threshold level is constrained. We set a magnitude allowing stable estimation of the Gutenberg–Richter relationship to be the minimum magnitude (Houng and Hong 2013). Also, we apply four different methods to determine the maximum magnitudes. All analyses are based on the magnitudes in the local magnitude scale (\(M_\mathrm{L}\)).

6 Synthetic Test of Maximum Magnitude Estimation

We test the validity and limitations of methods for estimation of maximum magnitudes using synthetic data. We produce synthetic earthquake catalogs composed of 100, 200, 500, 1000, 2000, 5000, and 10,000 events. The synthetic earthquake catalogs have a \(M_{\min }\) of 2.5 and a b value of 0.92 for tests of instrumental earthquake records, and have a \(M_{\min }\) of 4.7 and a b value of 0.82 for tests of historical earthquake records. The maximum magnitude (\(M_{\max }\)) is set to 7.5. We generate 1000 different sets of event catalogs to assess the variation in \(M_{\max }\) estimates depending on the event catalog. Four methods including the Tate–Pisarenko (TP) method, non-parametric determination based on order statistics (NPOS), Robson–Whitlock (RW) method, and Robson–Whitlock–Cooke (RWC) method are applied to estimate the maximum magnitudes.

It is observed that maximum magnitude estimates generally approach to the correct maximum magnitude with an increasing number of events in the catalogs (Figs. 8, 9). Also, the standard deviations of the maximum magnitude estimates decrease with the number of events. The parametric method (TP) produces more accurate \(M_{\max }\) estimates than non-parametric methods (NPOS, RW, RWC). Also, the Robson–Whitlock (RW) method is the most accurate of the non-parametric methods.

The standard deviations of \(M_{\max }\) estimates from the parametric method are greater than those from the non-parametric methods. This observation suggests that \(M_{\max }\) estimates are unstable when the event catalog is composed of a small number of events. On the other hand, the non-parametric methods display relatively stable \(M_{\max }\) estimates with catalogs with small numbers of events. However, non-parametric methods generally underestimate the maximum magnitudes for catalogs composed of small numbers of events.

It is intriguing to note that the convergence of \(M_{\max }\) estimates to the correct value is dependent on the implemented \(M_{\min }\) as well as the number of events in the catalog (Figs. 8, 9). A larger number of events in the catalog appears to be needed for correct estimation when a smaller \(M_{\min }\) is applied. This is because small events are naturally more frequent than large events according to the Gutenberg–Richter frequency–magnitude relationship.

7 Seismicity Density

The seismicity density models are calculated based on instrumental and historical earthquake records (Fig. 10). Long-term seismicity is represented by historical earthquakes. The historical seismicity density model is observed to be similar to the instrumental seismicity density model in most inland regions. High seismicity densities are found in the Okcheon belt (region A in 10), Taebaeksan basin (region B), Pyeongan basin (region C), and Yeongnam massif (region D) in both the instrumental and historical seismic densities. Low seismicity is observed at the Gyeonggi massif (region G) and northeastern peninsula (region H) in both seismic densities.

We find differences between the historical and instrumental seismicity density models in several regions including the Seoul metropolitan area in the central peninsula (region I) and offshore regions in the Yellow Sea, East Sea, and South Sea (regions E, F, J, K, L). Historical earthquakes suggest high seismicity densities in the Seoul metropolitan region, while instrumental earthquakes display low seismicity densities. This observation suggests that large events in the Seoul metropolitan region may have long recurrence time intervals. The apparent differences in offshore seismicity between the instrumental and historical earthquake records may be associated with the limited observation of offshore events without help of modern seismic instruments due to physical inaccessibility.

8 Seismotectonic Provinces

Seismotectonic province models are constructed for the region of latitudes between 33\(^{\circ }\) and 40\(^{\circ }\) and longitudes between 124\(^{\circ }\) and 131\(^{\circ }\). We first consider a seismotectonic province model composed of 17 provinces (Fig. 11). Province 2 is constructed for the highest seismicity region in the northwestern peninsula (Pyeongnam massif). This high seismicity is clearly observed in both the instrumental and historical seismicities. Province 1 is located to the west of province 2. Province 3 is an inland region located to the east of province 2.

Province 4 is an offshore region to the east of province 3. Both provinces 3 and 4 are low seismicity regions. Province 3 includes the eastern Pyeongnam and eastern Gyeonggi massifs. Provinces 3 and 4 are divided considering the physical environment and crustal thickness. Note that the crustal thickness changes abruptly across the east coast of the peninsula. Province 5 includes the region around Baekyeong island and Ongjin basin, which is adjacent to provinces 1 and 2. Province 5 is a high seismicity offshore region. The dominant focal mechanism in the province is normal faulting. Provinces 1 and 5 are divided considering the geological provinces and faulting systems. It was reported that the paleo-collision belt between the North and South China blocks may be placed in province 5 (Hong and Choi 2012).

Province 6 includes the western Gyeonggi massif, which is placed to the west of province 3 and to the south of province 2. Province 6 represents the high historical seismicity region around the Seoul metropolitan area in the central peninsula. Localized high heat flows and low Moho P (Pn) velocities are observed in the region. This province displays a characteristic seismicity with long recurrence time intervals (high historical seismicity but low instrumental seismicity). Province 7 includes the central and southern Yellow Sea regions, which display low and diffuse seismicity. Province 8 is a region including the southern Gyeonggi massif and central Okcheon belt displaying high seismicity in both the instrumental and historical earthquake records. This province displays low heat flows and high Pn velocities. Province 9 represents a localized high seismicity region in the eastern Okcheon belt (Taebaeksan basin). Low Pn velocities and high shallow-crustal S velocities are observed in the region.

Province 10 covers the eastern Yeongnam massif and northeastern Gyeongsang basin, presenting low Pn velocities. Province 11 is the the East Sea region to the south of province 4. This province includes the NS-directional paleo-continental-rifting structure that produces reverse-faulting earthquakes by the ambient compressional stress (Choi et al. 2012). High Pn velocities, localized high Lg Q, and high Bouguer gravity anomalies are observed along the paleo-rifting structure. A transitional structure between the continental and oceanic crusts develops in the region. Province 12 includes the southwestern peninsula of mild seismicity. This province includes the southwestern Okcheon belt and southern Yeongnam massif that are characterized by low heat flows, high Pn velocities, high Lg Q, and high Bouguer gravity anomalies.

Province 13 is located in the south-central peninsula, which includes the central Yeongnam massif and the western Gyeongsang basin. The province is a high seismicity region with low \(V_P/V_S\) ratios, low heat flows, high Pn, and high P amplification. Province 14 represents the southeastern Gyeongsang basin, which is characterized by high \(V_P/V_S\) ratios, low shallow-crustal S velocities, high Pn velocities, and low Lg Q. Province 15 is assigned for the western South Sea region including Jeju island where strong instrumental seismicity is observed. Province 16 includes the eastern South Sea region including Tsushima island. Province 17 is the region around the southern Japanese mainland.

We also construct a simplified model composed of 7 provinces by merging the provinces of the 17-province-composite model (Fig. 11). Provinces 1, 2 and 5 in the 17-province-composite model are combined into province 1 in the 7-province-composite model. Provinces 3 and 4 in the 17-province-composite model are assembled into province 2 in the 7-province-composite model. Provinces 6 and 8 in the 17-province-composite model are merged into province 4 in the 7-provinces model. Provinces 9, 10, 11, 13 and 14 in the 17-province-composite model comprise province 5 in the 7-province-composite model. Provinces 12 and 15 in the 17-province-composite model comprise province 6 in the 7-province-composite model. Also, provinces 16 and 17 in the 17-province-composite model are combined into province 7 in the 7-province-composite model.

9 Seismicity Properties and Maximum Magnitudes

The Gutenberg–Richter a values for instrumental earthquake catalogs are observed to be larger than those for historical earthquake catalogs. This may be because the historical earthquake catalog is not complete. Note that inhomogeneous distribution of major towns and cities causes location-dependent records of historical earthquakes (Houng and Hong 2013). The b values for instrumental earthquakes vary between 0.54 and 1.25 in the 7-province-composite model, and between 0.31 and 1.45 in the 17-province-composite model. The b values for the historical earthquakes are 0.55–0.91 in the 7-province-composite model and 0.34–0.85 in the 17-province-composite model. It is noteworthy that the b values of the 7-province-composite model are close to those of the 17-province-composite model for the same regions. The b values for the instrumental earthquakes are applied in the determination of maximum magnitudes of historical earthquakes considering possible incomplete historical earthquake records.

The expected maximum magnitudes (\(M_{\max }^\mathrm{exp}\)) are calculated with estimated a and b values for the duration of the earthquake catalogs, and are compared with the observed maximum magnitudes (\(M_{\max }^\mathrm{obs}\)). The differences between \(M_{\max }^\mathrm{obs}\) and \(M_{\max }^\mathrm{exp}\) for instrumental earthquake catalogs are less than 0.5 magnitude unit in most regions except province 7 of the 7-province-composite model and province 17 of the 17-province-composite model where the differences are found to be 1.10 and 1.11. The large differences suggest possible unstable estimation of \(M_{\max }\) with a parametric method (TP method).

The maximum magnitudes are estimated using four different methods (TP, NPOS, RW, RWC). In addition, the maximum magnitudes for \(T_\mathrm{exp}\) are estimated using the TP method. The maximum magnitude estimates of the instrumental earthquakes are 4.90–7.50 (TP*), 4.62–7.51 (NPOS), 4.80–8.20 (RW), and 4.65–7.60 (RWC) for the 7-province-composite model, and 3.75–7.51 (TP*), 3.51–7.51 (NPOS), 3.60–8.20 (RW), and 3.50–7.60 (RWC) for the 17-province-composite model (Fig. 12). The interval between the upper and lower bounds of the maximum magnitude estimates for the seismotectonic province model generally increases with the number of constituent provinces. This observation suggests that we may need an appropriate number of constituent provinces for reasonable estimation of maximum magnitudes.

Analysis based on the instrumental earthquake catalog suggests that province 2 of the 17-province-composite model has relatively low estimated maximum magnitudes despite characteristic high seismicity with a large b value. This may be because the observed maximum magnitude of province 2 is lower than those of other provinces (Table 2). Also, characteristic regional variation in maximum magnitude estimates is observed in the 17-province-composite model where province 10, a low seismicity region surrounded by high-seismicity neighbors, displays noticeably low maximum magnitude estimates.

The maximum magnitudes of the historical earthquake catalog are found to be \(\sim \)2.0 magnitude units greater than those of the instrumental earthquake catalog for both the 7- and 17-province-composite models. Maximum magnitudes are not estimated for provinces 3 and 7 in the 7-province-composite model and provinces 4, 15, 16 and 17 in the 17-province-composite model in which historical earthquake records are limitedly available. The maximum magnitude estimates are found to be 7.13–7.68 (TP*), 6.79–7.10 (NPOS), 6.95–7.13 (RW), and 6.80–7.10 (RWC) for the 7-province-composite model, and 6.49–7.64 (TP*), 6.29–7.10 (NPOS), 6.41–7.44 (RW), and 6.27–7.10 (RWC) for the 17-province-composite model (Fig. 13). The maximum magnitudes of most provinces in the 7-province-composite model are comparable. The distribution of maximum magnitudes suggests a high possibility of large events with magnitudes greater than 7.0 around the peninsula.

The parametric method (the TP method) produces larger maximum magnitude estimates than the non-parametric methods for both instrumental and historical earthquake catalogs. The RW method yields slightly larger estimates than the other non-parametric methods (NPOS, RWC). The NPOS and RWC methods produce comparable maximum magnitudes. These observations are consistent with the synthetic tests (Figs. 8, 9). However, the synthetic experiments suggest that the maximum magnitudes can be under- or over-estimated depending on the number of events in the catalogs (Figs. 8, 9). Also, the error size is dependent on the method and true maximum magnitude. Thus, it may be useful to compare the maximum magnitude estimates from the four methods to identify possible under- or over-estimation.

Maximum magnitude estimates based on the historical earthquake catalog are greater than those based on the instrumental earthquake catalog due to differences in the observed maximum magnitudes (\(M_{\max }^\mathrm{obs}\)) (Tables 1, 2, 3, 4). The maximum magnitude estimates based on the historical earthquake catalog appear to be more suitable for assessment of seismic hazard potentials than those based on the instrumental earthquake catalog. There were several studies investigating \(M_{\max }\) in the Korean Peninsula (Kim et al. 2000; Lee 2001; Noh 2014). Kim et al. 2000 presented maximum magnitudes of 6.97–7.45, and Lee (2001) suggested 7.06–7.88 from analysis of historical earthquakes. On the other hand, Noh (2014) suggested the maximum magnitude of events in the Korean Peninsula to be 6.98 from the analysis of instrumental earthquakes. The maximum magnitudes of the previous studies are generally comparable or slightly greater than those seen in this study.

10 Discussion and Conclusions

We analyzed long-period earthquake records combining instrumental and historical earthquake catalogs for assessment of seismic hazard potentials. Seismotectonic province models were proposed for the Korean Peninsula, which belongs to an intraplate regime with low and diffuse seismicity. The seismotectonic provinces were identified from the seismicity properties models, and their boundaries were defined considering the geological, geophysical and tectonic properties. Seismotectonic province models that are composed of 7 and 17 provinces were proposed. The maximum magnitudes and seismicity properties were calculated for the proposed seismotectonic province models. The maximum magnitudes were determined using four methods (TP, NPOS, RW, RWC).

The validity and accuracy of the four methods were tested thorough synthetic experiments. The synthetic tests indicated that the accuracy of the estimated maximum magnitudes generally increases with the number of events in the catalog. It was observed that the parametric method (TP) yields more accurate maximum magnitude estimates than non-parametric methods (NPOS, RW, RWC). A modified parametric approach (modified Tate–Pisarenko method) was proposed for reasonable estimation of maximum magnitudes for short-period or incomplete catalogs with large \(M_{\max }^\mathrm{obs}\). The modified TP method allowed us to determine the maximum magnitudes of potential earthquakes using the Gutenberg–Richter frequency–magnitude relationship.

The synthetic experiments indicated that the standard deviations of maximum magnitude estimates from the parametric method are greater than those from the non-parametric methods. It was suggested that the maximum magnitudes can be under- or over-estimated using earthquake catalogs composed of a small number of events. It appeared that comparisons of maximum magnitude estimates among the four methods may be useful for identification of correct maximum magnitudes.

It was observed that the upper bound of estimated maximum magnitudes apparently increases with the number of constituent seismotectonic provinces. Also, when one province is divided into several provinces, the maximum magnitude and b value for the original single province are approximately equal to the averages of the maximum magnitudes and b values for the subdivided provinces. These observations suggested that an appropriate number of constituent provinces are needed for correct assessment of seismic hazard potentials. Analysis based on the historical earthquake catalog yielded larger maximum magnitudes than those based on the instrumental earthquake catalog. The maximum magnitudes estimated in this study were generally smaller than those of previous studies. The maximum magnitudes suggested a high possibility of large events with magnitudes greater than 7.0 around the peninsula.