Time-advanced occurrence of moderate-size earthquakes in a stable intraplate region after a megathrust earthquake and their seismic properties

The distance-dependent coseismic and postseismic displacements produced by the 2011 MW9.0 Tohoku-Oki megathrust earthquake caused medium weakening and stress perturbation in the crust around the Korean Peninsula, increasing the seismicity with successive ML5-level earthquakes at the outskirts of high seismicity regions. The average ML5-level occurrence rate prior to the megathrust earthquake was 0.15 yr−1 (0.05–0.35 yr−1 at a 95% confidence level), and the rate has increased to 0.71 yr−1 (0.23–1.67 yr−1 at a 95% confidence level) since the megathrust earthquake. The 2016 ML5-level midcrustal earthquakes additionally changed the stress field in adjacent regions, inducing the 15 November 2017 ML5.4 earthquake. The successive 2016 and 2017 moderate-size earthquakes built complex stress fields in the southeastern Korean Peninsula, increasing the seismic hazard risks in the regions of long-term stress accumulation. The increased seismic risks may continue until the medium properties and stress field are recovered.

The Korean Peninsula is located in a stable intraplate region of the eastern Eurasian plate. The continental crust lies in the peninsula and the Yellow Sea. A transitional crust between continental and oceanic crusts has developed in the East Sea (Sea of Japan) [1][2][3][4][5] . The region around the peninsula is under the influence of a compressional stress field with an ENE-directional compression and SSE-directional tension 6,7 (Fig. 1). The instrumentally recorded earthquakes since 1978 indicated mild and diffused seismicity (Fig. 1).
However, the historical literature indicates large seismic damage on the Korean Peninsula. The largest seismic intensity reached IX on the modified Mercalli intensity (MMI) scale 8 . The historical seismicity displays high similarity with the instrumentally recorded seismicity over most regions in the Korean Peninsula, except the central peninsula around the Seoul metropolitan area 8,9 . The historical earthquake records present high seismicity with large earthquakes in the central peninsula.
The distance-dependent displacements produced tension stress over the Korea Peninsula 11 (Fig. 1), and the discriminative crustal extension decreased the seismic velocity in the crust 12,[16][17][18][19] . The seismicity increased abruptly after the megathrust earthquake, and unusual episodic earthquake swarms were observed for 60 days after 29 April 2013 and 120 days after 2 June 2013 at two regions in the Yellow Sea ( Fig. 1) 11 . The seismicity increase may have been caused by the decreasing yield strength of the medium due to instantaneous activation of the tension field by crustal extension 11 . It was suggested that a small change in stress field may induce significant seismicity changes 20 . The earthquakes occurred in both high seismicity regions and low seismicity regions, suggesting that the earthquakes were fostered in the low seismicity region 11,21 .
The stress field inferred from the focal mechanism solutions of earthquakes after the 2011 Tohoku-Oki megathrust earthquake is close to the ambient stress field inferred from the focal mechanism solutions of earthquakes before the 2011 Tohoku-Oki megathrust earthquake. The compression-axis directions of the 12 September 2016 M L 5.8 earthquake and its aftershocks were N70°E to N77°E 22 . The maximum compression-axis directions of the ambient stress field before the megathrust earthquake were ~N77°E (±1.2° at a 95% confidence level) 6 . Small changes in the stress field and medium properties produce earthquakes with new fault planes whose orientations conform to the stress field 11 . Earthquakes with different faulting types occurred after the megathrust earthquake 11 , possibly due to abrupt changes in differential stresses that develop new fault planes with different faulting behavior 23,24 .
Ten M L 5-level earthquakes have occurred on the Korean Peninsula since 1978, when national seismic monitoring was commenced (Fig. 1). The M L 5-level earthquakes were generally scattered around the suburbs of high seismicity regions (Fig. 1). The number of M L 5-level earthquakes has increased since the 2011 Tohoku-Oki megathrust earthquake: one-half of the moderate-size earthquakes (5 events) occurred since the 2011 Tohoku-Oki megathrust earthquake. We investigate the properties of the successive M L 5-level earthquakes and their induction mechanisms on the Korean Peninsula. The primary compression field is presented with solid bars 6 . The tension field and coseismic displacements incurred by the megathrust earthquake over the Korean Peninsula are presented 11 . The coseismic slip during the megathrust earthquake is presented on the map 10 . (b) Earthquakes with magnitudes greater than or equal to M L 5.0 since 1978. The seismicity densities of instrumentally recorded earthquakes since 1978 are presented with contours 35 . The locations of earthquake swarms since the 2011 megathrust earthquake are marked on the map. (c) Earthquake occurrence since 1978 in the Korean Peninsula. Events with magnitudes greater than or equal to 5.0 are indicated. The total seismic moments emitted by the earthquakes every seven years are shown. The emitted seismic moments increased after the megathrust earthquake. (d) Temporal variation in yearly numbers of earthquakes with magnitudes greater than or equal to 2.5 from a declustered catalog. The average number of earthquakes was 21 yr −1 before the 2011 Tohoku-Oki megathrust earthquake and 31 yr −1 after the earthquake. The dates of earthquakes with magnitudes of M ≥ 5.0 are marked with broken lines. The seismicity increased abruptly after the megathrust earthquake. The figure was created using GMT 4.5.14 (https://www.soest.hawaii. edu/gmt/) and Adobe Illustrator CS6 (https://www.adobe.com/kr/products/illustrator.html).

Results
Seismicity change. The seismic velocities in the crust of the Korean Peninsula decreased by ~3% instantly after the 2011 Tohoku-Oki megathrust earthquake 12 . Seismic velocities are recovered with time 12 . We examine the seismicity changes by declustering the seismicity, which excludes the aftershocks from the earthquake catalog ( Fig. 1) (see supplementary materials). The earthquake catalog since 1978 is complete for seismicity with magnitudes greater than or equal to M L 2.5 9,11 (see supplementary materials). The declustered seismicity of earthquakes with M L ≥ 2.5 presents seismicity rates of 21 yr −1 (18.72-23.25 yr −1 at a 95% confidence level) prior to the megathrust earthquake and 31 yr −1 (27.13-35.53 −1 at a 95% confidence level) since the megathrust earthquake (Fig. 1).
The increase in seismicity rate was caused an increase in seismic energy emission. The seismic moments emitted from the earthquakes on the Korean Peninsula for 82 months since the 2011 Tohoku-Oki megathrust earthquake were more than 10 times larger than those before the megathrust earthquake for the same time duration ( Fig. 1).
The seismicity before the megathrust earthquake may be a consequence of tectonic loading in the crust of the Korean Peninsula. The average occurrence rate of the ten M L 5-level earthquakes for the 40 years of 1978-2018 is 0.25 yr −1 (0.12-0.46 yr −1 at a 95% confidence level). The occurrence rate prior to the megathrust earthquake, 0.15 yr −1 (0.05-0.35 yr −1 at a 95% confidence level) changed to 0.71 yr −1 (0.23-1.67 yr −1 at a 95% confidence level) after the megathrust earthquake. The probabilities of having five M L 5-level earthquakes in the 7 years since the megathrust earthquake are less than 3% and 1% for occurrence rates of 0.25 yr −1 and 0.15 yr −1 in terms of Poissonian earthquake occurrence 25,26 (see supplementary materials). This observation suggests that the recent M L 5-level earthquakes since the 2011 megathrust earthquake may be time-advanced events that might otherwise have occurred at later times 27 .
The  (Fig. 2). However, the magnitudes of the aftershocks decreased with time at similar decay rates. The aftershocks of the 2017 M L 5.4 earthquake were located at depths between 4 and 11 km, while those of the 2016 M L 5.8 earthquake were distributed at depths between 11 and 16 km 22 (Fig. 2). The focal depths of the mainshocks and aftershocks of the 2016 M L 5.8 earthquake and the 2017 M L 5.4 earthquake were within the typical seismicity depths (4-20 km) on the Korean Peninsula 28 .
The seismic energy from the 2017 M L 5.4 earthquake was rich in low frequencies around ~0.5 Hz compared to that from the 2016 M L 5.8 earthquake (Fig. 2) 22 . The levels of displacement spectra of the 2016 M L 5.8 earthquake and the 2017 M L 5.4 earthquake at a common station at comparable distances were similar, despite an apparent magnitude difference in the local magnitude scale. The spatial distribution of the peak ground accelerations (PGAs) of the 2017 M L 5.4 earthquake was similar to that of the 2016 M L 5.8 earthquake (Fig. 2). The PGA decays gradually with distance on the Korean Peninsula 29 . The characteristic slow distance-dependent decay of PGAs suggests a high potential for seismic damage over wide regions when a large event occurs in the stable intraplate region.  (Fig. 3). The aftershocks of the 2017 M L 5.4 earthquake were distributed in a volume of 8 × 3 × 6 km 3 . The aftershock distribution and fault-plane solutions illuminate the geometry of the fault, which may be divided by three segments (Fig. 3).
Each fault segment developed at a different depth (Fig. 3). The focal depths of the earthquakes in the northeastern segment were shallow (4.5-7.2 km). On the other hand, most earthquakes in the southwestern segment were distributed at greater depths (≥6 km). The focal mechanism solutions of the earthquakes in the southwestern and northeastern segments indicate right-lateral strike-slip faults. By contrast, the focal mechanism solution of the M L 4.3 earthquake in the central segment suggests a reverse faulting with a strike of N18°E and a dip of 62°. The seismic moment was 3.66 × 10 22 Nm, and the corresponding moment magnitude was M w 4.3.
The mainshock occurred at the boundary between the southwestern and central segments. The early sequence of aftershocks was located mainly in the southwestern segment, accompanying some aftershocks in Induction mechanism of time-advanced earthquakes. The crust of the Korean Peninsula was stretched by the differential coseismic and postseismic displacements due to the 2011 Tohoku-Oki megathrust earthquake, reducing the yield strengths in the crust 12 .
The 2016 M L 5.1 and M L 5.8 earthquakes produced Coulomb stress changes of −4.9 to 2.5 bar for optimally oriented strike-slip faults at a depth of 10 km (Fig. 4). The induced Coulomb stress change for optimally ori-

Discussion and Conclusions
Seismicity varies with stress 31,32 . Tectonic loading may be the primary source of the stress that has accumulated in the crust. The long-term tectonic-loading stress over the Korean Peninsula may be homogeneous. The 2011 M W 9.0 Tohoku-Oki megathrust earthquake caused high perturbation in the medium and stress field. The induced stress change may play a crucial role in increasing the seismic hazard potential. A stress change may trigger earthquakes in regions of long-lived stress concentration 33,34 . The recent successive M L 5-level earthquakes may be time-advanced events that are a consequence of medium weakening and stress perturbation due to the 2011 M W 9.0 Tohoku-Oki megathrust earthquake and precedent adjacent events.
The recent inland M L 5-level earthquakes occurred in crustal blind faults that were not identified before the events. Historically, large earthquakes have been recorded on the Korean Peninsula 8,9,35 . The recent increased seismicity with moderate-size earthquakes suggests high probability of hazardous-earthquake occurrence on the Korean Peninsula.
The spatial distribution of previous events may allow us to constrain the potential locations of future earthquakes. The seismicity density functions of instrumentally recorded and historical earthquakes may provide information on the stress released by precedent earthquakes (Figs 1 and 4). It is intriguing to note that the M L 5-level earthquakes occurred in low seismicity regions (Fig. 1). The recent moderate-size earthquakes might occur around high prestressed regions with long-term cumulation of tectonic loading 36 . Faults in near-critical conditions might respond preferentially to additional stress changes induced by the 2011 Tohoku-Oki megathrust earthquake 32 . A major event releases the cumulated stress of the fault, triggering another event in adjacent regions.
The medium properties were recovered gradually with time, restoring the stress field. Several regions of high seismicity densities with low recent seismic activities exist (Fig. 4). The increased seismicity may continue until the medium properties and stress field are recovered. A combined interpretation of the instrumentally recorded and historical seismicity may suggest potential locations of devastating events that occurred historically (Fig. 4).

Methods
The observed seismicity can be expressed as a sum of background seismicity and triggered seismicity 37 : , t) is the observed seismicity rate density at time t at location x, λ 0 (x) is the background intensity function, and λ i (x, t) is the contribution of earthquake i that occurred in time t i at location x i . We decluster the earthquake catalog based on a nonparametric method that is useful for regions with low seismicity rates. The functions λ i (x, t) and λ 0 (x) are determined by an iterative process that assesses the numbers of event pairs in discrete bins of magnitudes, interevent times and distances 37-39 (see supplementary materials). We perform a long-period waveform inversion of earthquakes to determine the focal mechanism solutions 11,40 based on a global-averaged one-dimensional (1-D) velocity model 41 . We determine a set of hypocentral parameters that generate the best-fit synthetic waveforms 42 . The focal mechanism solutions of the earthquakes are determined based on 5 seismic records of 0.05-0.1 Hz in regional distance (Fig. 2).
The hypocentral parameters of the earthquakes are refined using VELHYPO based on the P and S arrival times (see supplementary materials) 43,44 . This method is effective for the determination of hypocentral parameters of earthquakes in media with poorly known velocity structures (see supplementary materials). We implement a 1-D velocity model as the initial model 45 . We analyze 14 to 34 three-component waveforms of each earthquake for the hypocentral-parameter inversion. The average P and S travel time residuals are 6.1 × 10 −6 s and 4.9 × 10 −3 s, and their standard deviations are 0.0489 s and 0.1948 s, respectively (see supplementary materials). The horizontal and vertical location errors at the 95% confidence level are 9.7 m and 24.3 m. The origin time and hypocenter errors are sufficiently small.
The induced Coulomb stress change, ΔCFS can be represented by 46,47 n where Δτ is the shear stress change, μ′ is the effective frictional coefficient, and Δσ n is the normal stress change.
We set the effective frictional coefficient μ′ to be 0.4 11,22,32,47,48 . The fault dimension is assumed to follow an empirical relationship with the seismic moment 49 . The ambient compressional stress field is oriented in the N77°E direction, with a strength of 65 bars 6,7,11,22 (Fig. 1). In addition, we set the lithospheric Young's modulus to be 80 GPa and the Poisson's ratio to be 0.25 11,22,46,47 . The Coulomb stress changes induced by the earthquakes are calculated for media with strike-slip faults in the optimal orientation or given orientation 50 .