Interaction between historical earthquakes and the 2021 Mw7.4 Maduo event and their impacts on the seismic gap areas along the East Kunlun fault

Abstract

On May 21, 2021 (UTC time), an Mw7.4 earthquake struck Maduo County, Qinghai Province, China. The rupture of this typical strike-slip event and its aftershocks along the Kunlun-Jiangcuo fault (JCF) propagated approximately 170 km from the epicenter. In this study, we calculated the coseismic and postseismic Coulomb stress changes induced by 14 historical earthquakes and investigated their impacts on the 2021 Maduo source area. We found that the JCF is in the stress shadow of these historical events with a combined ΔCFS range of approximately − 400 to − 200 kPa. Since the seismogenic fault of the 1937 event is nearly parallel and close to the JCF, the rupture of the 1937 event had the greatest inhibitory effect on Maduo source area. We hypothesize that the actual loading rate at the depth of the seismogenic layer in the Maduo source area is much higher than the simulated value (0.3 kPa/a). Consequently, the Maduo earthquake still occurred despite the considerable delaying effect of these historical earthquakes (especially the 1937 event). Our findings also indicate that the tectonic stress in the eastern Bayanhar block is still rapidly accumulating and adjusting. Our investigation further reveals the enhanced stress induced by the historical and Maduo events with ΔCFS values of approximately 30–300 kPa and 50–300 kPa on the Xidatan-Dongdatan segment (XDS) and the eastern end of the East Kunlun Fault (EKF), respectively, not only on the Maqin-Maqu segment (MMS) but also at the eastern end of each branch segment of the EKF. Hence, considering the accumulation of tectonic stress, we suggest that the seismic hazard in these two regions has been promoted.

Graphic Abstract

Introduction

On May 21, 2021 (UTC time), a Mw 7.4 earthquake struck Maduo County, Qinghai Province, China, with the hypocenter located at approximately (98.25°E, 34.59°N) and a focal depth of 10.0 km (USGS, Fig. 1). The focal mechanism solution (strike = 285°, dip = 85°, rake = 0°) and slip distribution model suggest that this earthquake was a typical strike-slip event. The total rupture of this event and its aftershocks along the Kunlun-Jiangcuo fault (JCF) propagated eastward and westward approximately 170 km from the epicenter (Wang et al., 2021).

Fig. 1

Tectonic setting, wherein the blue stars show epicenter of the M > 6.5 earthquakes spatial distribution on and around EFK; the red star shows the 2021 Maduo earthquake epicenter; the beach balls define the earthquake focal mechanism; the black solid lines define the faults. SMGB: South Margin Fault of Gonghe Basin; ELSF: Ela Shan Fault; KZHF: Kunzhong Fault; KSL: Kusai Lake segment of east Kunlun Fault; XDS: Xidatan-Dongdatan segment; ALS: Alake Lake segment; TLS: Tuosuo Lake segment; MMS: Maqu-Maqin segment; JZF: Jiangcuo Fault; MGF: Maduo-Gande Fault; DF: Dari Fault; GZ-YS: Ganzi-Yushu Fault; LMS: Longmenshan Fault. The detailed earthquake parameters (focal depths, focal mechanisms) are summarized in Table 1. The lower left inset presents the location of target area in the larger geological setting

The JCF, which is a branch fault of the East Kunlun Fault (EKF), is located in the eastern-central area of the Bayanhar block. Before the 2021 Maduo earthquake occurred, no M ≥ 5.0 earthquakes had been documented along the JCF. There were only two earthquakes (Ms6.2 in 1995 and Ms5.2 in 2015) occurred near south of the JCF (Wang et al., 2016; Ma et al., 2017). However, the seismicity in the surrounding area has been extremely active as of late: the western part of the EKF experienced the massive 2001 Kokoxili Ms8.1 earthquake, and the eastern margin of the Bayanhar block suffered the destructive 2008 Ms8.0 Wenchuan, 2013 Ms7.0 Lushan, and 2017 Jiuzhaigou Ms7.0 earthquakes. In addition, the Xidatan-Dongdatan segment (XDS, 93°E–95.5°E, Fig. 1) and Maqin-Maqu segment (MMS) of the EKF were thought to be seismic gap zones due to the lack of historical earthquake records for at least 300 years, especially the MMS, which is highly populated (Wen, 2018; Xu et al., 2014; Li et al., 2011a; Shan et al., 2015; Zhu et al., 2020; Pan et al., 2021). Geodesic research further suggests that multiple segments along the eastern section of the EKF, especially the MMS, are locked with a store of accumulated elastic strain energy, indicating the possible occurrence of strong earthquakes (Li et al., 2019; Zhu et al., 2020, 2021a). However, the 2021 Maduo earthquake, another strong event that occurred along the eastern section of the EKF after the 2017 M7.0 Jiuzhaigou earthquake, did not occur in the seismic gap of the main fault but on the branch fault to the south of the EKF. This seismic activity indicates that the eastern margin of the Bayanhar block, especially the eastern section of the EKF, is still in the stress adjustment stage. After the 2021 event, the value of estimating the seismic hazards within the seismic gaps has become increasingly significant for this region.

The occurrence of earthquakes is controlled predominantly by the regional tectonic stress field; however, comprehensive absolute stress data in the surrounding area of the rupture zone remain unknown. Nevertheless, we can calculate the stress perturbation to evaluate the seismic hazard. Many studies over the last few decades have suggested that a small stress loading can trigger large earthquakes if the fault system is sufficiently close to failure. Hence, calculating the Coulomb failure stress change (ΔCFS) prompted by a major shock can identify faults at an increased risk of triggering earthquakes and indicate future seismic activity (Stein and Lisowski, 1983; Harris, 1998; Parsons et al., 2008; Xiong et al., 2010; Liu et al., 2017). A stress change of 10 kPa is usually considered the threshold for triggering an earthquake (King et al., 1994; Stein, 1999). Using this theoretical method, numerous previous studies have analyzed the aftershocks triggered by main shocks (King et al., 1994; Stein, 1999; Toda et al., 2008) and the interactions between large earthquakes (Stein, 1994; Shan et al., 2015; Liu et al., 2018; Jia et al., 2012, 2018).

How did historical earthquakes impact the 2021 Maduo earthquake? More importantly, did the 2021 Maduo earthquake change the stress conditions on the active faults around the rupture zone and thus impact the seismic hazard along the eastern segment of the EKF? To investigate these questions, in this study, we simulated the stress perturbation induced by historical events on and around the JCF and the ΔCFS on the other active faults surrounding the JCF. Based on these results, we identified these faults as either close to or far from Coulomb failure. We also examined the sensitivities of the results to the various parameters of receiver fault and source slip models.

Tectonic setting and historical earthquakes

The Bayanhar block, one of the important tectonic units involved in the eastward extrusion of the Tibetan Plateau, is accelerating toward the east-southeast. The EKF, which is characterized by high-velocity sinistral strike-slip motion, constitutes the northern margin of this block and extends approximately 2000 km with an average strike of 270°–290° (Xu et al., 2002; Deng et al., 2014; Wen et al., 2018). Its slip rate gradually decreases from west to east, with the horizontal slip component being absorbed by the eastern margin thrust structure (the Longmen Shan fault zone, LSF) (Kirby et al., 2007; Li et al., 2011a).

Consequently, many strike-slip earthquakes have occurred on and around the EKF, such as the 1937 M7.6 earthquake that occurred on the Tuosuo Lake segment (TLS), the 1947 M7.6 earthquake that occurred on the Dari fault (DF) to the south of the EKF, and the 2001 M8.1 Kokoxili earthquake that occurred on the western Kusai Lake segment, which was the largest earthquake recorded along the EKF in recent decades with a surface rupture spanning 426 km (Xu et al., 2002). In contrast, primarily thrust and slip-strike earthquakes have occurred on and around the eastern margin of the Bayanhar block, including the 1879 M8.0 Wudu event, 1933 M7.8 Diexi event, 1976 Ms7.2 Songpan event, 2008 Ms8.0 Wenchuan event, 2013 Ms7.0 Lushan event, and 2017 Ms7.0 Jiuzhaigou event. In addition, the 2010 Ms7.1 Yushu earthquake occurred on the Ganzi-Yushu fault zone, which represents the southern margin of the Bayanhar block.

Several historical earthquakes have also been recorded to the north of the eastern segment of the EKF, such as the M7.0 and M6.6 events that struck in 1990 and 2000, respectively. However, these earthquakes were neglected by previous studies that modeled earthquake stress changes (Xiong et al., 2010; Shan et al., 2015; Jia et al., 2012; Li et al., 2021). Thus, this study quantified the contributions of these events to the ΔCFS on the EKF and other regions. Furthermore, although the 1920 M8.5 Haiyuan event did not occur on or around this block, probably had a certain impact on the study area due to its considerable magnitude, and hence, this event was also included in our study. However, the 2013 Lushan earthquake had a weak stress impact on the eastern segment of the EKF (Huang et al., 2019) and was excluded.

The source parameters, such as the epicenter location and focal mechanism solution, can be determined from previous studies and earthquake records. However, due to the scarcity of information, the slip distributions of historical earthquakes and less studied events (such as the 1879, 1920, 1933, 1937, 1947, 1963, 1976, 1990, and 2000 earthquakes) can be estimated only by the empirical formula of Wells and Coppersmith (1994). In contrast, the detailed rupture parameters and slip distribution models for other recent events (such as the 2001, 2008, 2010, and 2017 earthquakes) have usually been inverted through seismic and geodesy data (Lasserre et al., 2005; Wang et al., 2011; Li et al., 2011b; Liu et al., 2019). Fourteen historical events are included in this study, and the details are shown in Fig. 1 and Table 1.

Table 1 Information of the 14 historical earthquakes

Method and models

From the Coulomb friction criterion (Harris, 1998), the ΔCFS on a fault interface is defined as

$$ \Delta {\text{CFS}} = \Delta \tau + \mu^{\prime} \times \Delta \sigma_{n} , $$

(1)

where Δτ is the shear stress change on the receiver fault interface (positive along the inferred slip direction), Δσ_n is the normal stress change (positive for fault unclamping), and μ’ is the effective friction coefficient (0–1.0), reflecting the weight relationship between Δτ and Δσ_n in the value of ΔCFS. If Δτ and Δσ_n having opposite polarities, the polarity of ΔCFS depends on the value of μ’. This equation means that faults with increases in both shear stress and normal stress have a positive ΔCFS and thus are closer to failure. In contrast, faults with a negative ΔCFS are relatively far away from failure, which also means that they are in the stress shadow (Harris, 1998).

To calculate the ΔCFS induced by the rupture of earthquakes, it is necessary to calculate not only the coseismic stress release effects but also the viscous relaxation of the flexible middle and lower crust, which has a long-term stress adjustment effect on the upper elastic crust. According to previous seismic studies (Meissner et al., 2004; Silver, 2008; Shan et al., 2015; Jia et al., 2017), a four-layer crustal model is built, and the parameters (thickness, density, and coefficient of viscosity of each layer) of the layered model can be found in Table 2.

Table 2 Crustal model

We use the PSGRN/PSCMP software package (Wang et al., 2006) to calculate the stress changes and project them onto different receiver faults to calculate ΔCFS. Generally, the expected slip direction and geometric parameters of receiver faults are difficult to be constrained clearly. However, we can estimate these parameters through the earthquake focal mechanism solutions of historical earthquakes that occurred on or near those faults.

Results

The stress imparted to the hypocenter of the 2021 Maduo earthquake

To investigate the relationships between the 14 historical earthquakes and the 2021 Maduo event, we calculated the coseismic and postseismic stress changes at the hypocenter (98.34°E, 34.59°N, depth of 10 km) of the Maduo earthquake caused by those 14 events. Since the rupture direction of this event was approximately E–W, the E–W (x) and N–S (y) stress components probably had the greatest contributions to the ΔCFS. Figure 2 visualizes the values of ΔSxx, ΔSyy, and ΔSxy in detail. The 1937 M7.6 earthquake (No. 4) reduced the greatest impact with ΔSxx, ΔSyy, and ΔSxy values of − 60 kPa, − 280 kPa, and − 45 kPa, respectively. The 1947 M7.6 earthquake (No. 5) produced combined stress changes (ΔSxx, ΔSyy, ΔSxy) of − 106 kPa, 27 kPa, and − 72 kPa, respectively. As shown in Fig. 1, not only the epicenters of the 1937 and 1947 events were close to the Maduo earthquake, but also the magnitude is considerably great. While the magnitudes of the 1879 (No. 1), 1920 (No. 2), 1933 (No. 3), 2001 (No. 11), and 2008 (No. 12) earthquakes were greater than 7.8, they were far from the source area of the 2021 event, so these events had relatively small impacts. The impacts induced by other events (No. 7, No. 8, No. 9, No. 10, No. 13, and No. 14) were negligible due to their smaller magnitude (M ≤ 7.0) or relatively long distance (more than 500 km) from the target area, as shown in Fig. 1. Theoretical calculations indicate that the attenuation of elastic static stress is inversely proportional to the cubed distance from the seismic source zone, and the value of the long-distance stress change may be lower than the tidal stress level (Hill et al., 1993). Therefore, the impact of a large, distant earthquake on the Maduo area should be less than that of a nearby event with a relatively small magnitude.

Fig. 2

The combined stress change in three components caused by 14 historical earthquakes at the hypocenter of 2021 earthquake (depth = 10 km). Numbers (1)–(14) represent the 14 events, respectively, same as Table 1

The stress changes caused by the 1937 and 1947 earthquakes

The 1937 (No. 4) and 1947 (No. 5) events, both of which were sinistral strike-slip events, generated considerable stress changes near the JCF, as shown in Fig. 3. The 1937 event exhibited compressional deformation in the N–S and E–W directions, whereas the 1947 event resulted in slight tensile deformation in the E–W direction along the JCF. The JCF is located in the middle of the rupture zone of these two events and thus suffered west-to-east compression during the 1937 event and nearly east-to-west (that is, in the opposite direction) compression during the 1947 event.

Fig. 3

Stress changes caused by the 1937 and 1947 earthquake. a–c are the ΔSxx, ΔSyy, and ΔSxy caused by 1937 earthquake, respectively; d–f are the ΔSxx, ΔSyy, and ΔSxy caused by 1947 earthquake, respectively; black beach ball shows the Maduo earthquake, black circles represent the aftershock of Maduo event, and black stars define the epicenter of the earthquakes

The strike-slip fault interaction process is demonstrated in the sketch map of Fig. 4 by showing the relationship between the interseismic crustal displacement due to tectonic loading and earthquake-induced crustal deformation. However, the Bayanhar block is moving from west to east, and the southern side of the JCF (the interior of the block) moves faster than the northern side. Consequently, the JCF is characterized by sinistral strike-slip motion, as shown by the red arrow in Fig. 4. The 1937 event accelerated the movement to the north of the JCF; while the 1947 event suppressed the movement to the south of the JCF, both effects were contrary to the tectonic movement of the JCF. Therefore, the occurrence of these two events, especially the 1937 event, yielded a ΔCFS value of − 235 kPa and thus delayed the occurrence of the 2021 Maduo earthquake (Fig. 5). This finding is supported by the results of previous studies that interpreted the interactions of parallel strike-slip fault systems: when slip takes place on a model fault, the shear stress on other parallel faults is reduced, inhibiting the occurrence of another earthquake around the seismogenic fault (Kato and Lei, 2001; Yue et al., 2008).

Fig. 4

The sketch map of the impact of two earthquakes and the tectonic activity

Fig. 5

The coseismic and postseismic ΔCFS at the epicenter of 2021 Maduo earthquake induced by historical earthquakes, at different depth 10 km and 15 km

The total ΔCFS prior to 2021

We calculated the ΔCFS at the hypocenter of the Maduo event caused by each historical event. Since the focal depths of the 2021 event given by different research institutions are inconsistent, we calculated the ΔCFS at two depths: 10 km and 15 km. Then, the stress changes produced by the 14 historical events were projected to the receiver fault interface (strike = 285°, dip = 85°, slip = 0°, same as the mechanism of the Maduo event) while assuming an effective friction coefficient of μ' = 0.4. The result is shown in Fig. 5. Although the values vary at different depths, the polarity is the same, and the difference is small. The ΔCFS exhibited a maximum decrease of approximately − 235 kPa and − 241 kPa due to the 1937 event at depths of 10 km and 15 km, respectively. The corresponding values caused by events No. 2 and 5 were in the approximate range of − 15 to − 25 kPa, while other events (Nos. 3, 6, 10, 11, 12, and 13) increased the ΔCFS by only 1–4 kPa. Generally, a negative ΔCFS results in a decrease in seismic activity in the stress shadow (unloaded stress regions).

Figure 6 shows a map of the cumulative ΔCFS (coseismic and postseismic) prior to 2021, with the projection interface same as the focal mechanism solution of the Maduo earthquake. The results show that the ΔCFS in the Maduo source area was between − 400 and − 200 kPa, which obviously indicates that this segment is in a stress shadow. Accordingly, the 2021 Maduo earthquake was delayed by these 14 historical events, mainly by the 1937 event. The region was stress-loaded in the eastern part of each branch fault with a maximum value of 500 kPa, and the stress in the areas to the west of the DF and the XDS was enhanced also.

Fig. 6

The combined ΔCFS induced by 14 earthquakes at the depth of 10 km

Coulomb stress transfer on the major faults after 2021

The 2021 Maduo earthquake (based on USGS slip model, as shown in Table 1) enhanced the coseismic ΔCFS on the TLS, MMS, and the middle-west segments of the DF with more than 10 kPa (Li et al., 2021). In this study, we calculated the total effect caused by 14 historical earthquakes and this Maduo earthquake. Figure 7 provides details of the cumulative ΔCFS at a depth of 10 km along the major active faults in the target area just after the 2021 Maduo earthquake occurred. The geometric parameters of the major faults are shown in Table 3 with a coefficient frictional parameter μ’ of 0.4. The ΔCFS was positive over most of the major faults, such as the eastern and western segments of the branch faults of the EKF (A1, A2, B1, B2, B3, and B4 in Fig. 7), and the western segment of the DF exhibited an increase of approximately 200–300 kPa. Regions A and B in Fig. 7 represent typical apparent seismic gaps, especially segment B1, which is the MMS of the EKF. This seismic gap has been tectonically quiet with no large earthquake having been recorded for over 300 years. Generally, an enhanced ΔCFS corresponds to increased seismic risk.

Fig. 7

The combined ΔCFS on major faults caused by 14 historical events and 2021 event

Table 3 Geometric parameters of each fault

Figure 8 plots the ΔCFS of each section in these two gaps (parts A and B in Fig. 7). The values on segments A1 and A2 are approximately 50 kPa and 50–100 kPa, respectively. However, the value exceeds 300 kPa at the eastern end of A2. In the region B gap, the largest values (100–300 kPa) are detected on the southern segment (B4), while the values on the other 3 segments (B1, B2, and B3) are 0–200 kPa. Figure 9 illustrates the ΔCFS distributions on segments A2 and B1 at time intervals of 0, 10, 50, and 100 years after the 2021 earthquake occur under the assumption that no additional earthquakes will occur in the future. The stress gradually accumulates over time, especially on the western segments of A2 and B1, with the greatest increase of 50 kPa. All these increasing values of ΔCFS are higher than the earthquake triggering threshold of 10 kPa (King et al., 1994; Stein, 1999). In general, a positive ΔCFS brings a fault closer to failure. Based on this earthquake stress-triggering assumption, we suggest that the 2021 earthquake and other historical events have promoted the possible future failure of active faults east of the EKF and enhanced the seismic hazard therein.

Fig. 8

The combined ΔCFS on gap A and gap B area

Fig. 9

ΔCFS on A1 and B1 at time intervals of 0, 10, 50, and 100 years after 2021

Discussion and conclusion

Effect of the slip model

The value of ΔCFS depends on various parameters, such as the slip model of the earthquake, the effective friction coefficient μ’, the dip angle, the strike angle, and the rake angle. First, we investigated the sensitivity of the stress to the slip model. Previous studies have suggested that the stress change in the near field is probably impacted by different slip models, but there is no obvious difference in the far field (Qu et al., 2016; Liu et al., 2020). After the 2017 Ms7.0 Jiuzhaigou earthquake occurred, many scholars discussed whether the 2017 event was triggered by the 2008 Wenchuan earthquake (Jia et al., 2018; Huang et al., 2019). Our previous study suggested that the difference in the chosen source slip model for the 2008 earthquake is the main reason for this controversy (Dong et al., 2019).

Due to the scarcity of data, it is difficult to accurately determine the slip models for the 14 historical earthquakes selected in this paper, especially the older events. For example, for the 1933 M7.8 Diexi earthquake (event No. 3), different scholars have reported different focal mechanism solutions: sinistral strike-slip (Wang and Shen, 2011), dextral strike-slip (Chen et al., 1994), and tensile rupture (Ren et al., 2017). However, the location of this earthquake is far from the rupture zone of the Maduo event, and the impact on the hypocenter of the 2021 earthquake was less than 10 kPa (Fig. 2). Hence, it is not necessary to discuss the impact induced by this event.

However, the 1947 M7.6 Dari earthquake (event No. 5) had a certain impact on the calculated stress change. Previous studies reported two different mechanisms: the first mechanism involved a strike of 135°, dip of 90°, and rake angle of 0°, representing a typical sinistral strike-slip fracture model (Shen et al., 2003; Liu et al., 2021); the second mechanism involved a strike of 135°, dip of 60°, and rake angle of 60° (Molnar and Deng, 1984; Shan et al., 2015). In this study, we adopted the first mechanism, but it is still necessary to discuss the influence of the second rupture mechanism. Figure 10 shows the distributions of the stress perturbation components ΔSxx, ΔSyy, and ΔSxy under the second mechanism, the values of which at the epicenter of the Maduo earthquake are − 83.5 kPa, − 43.2 kPa, and − 33.2 kPa, respectively. The corresponding results under the first mechanism are − 106 kPa, 27.3 kPa, and − 71.9 kPa (Fig. 2), which are evidently different from the former, especially the polarity of ΔSyy. Accordingly, we calculated ΔCFS values (strike = 285°, dip = 85°, rake = 0°, μ’ = 0.4) of − 7.5 kPa and − 30 kPa under the first and second mechanisms, respectively. Although the results are different, the overall impact on the conclusion of this study is limited.

Fig. 10

Stress change induced by 1947 event with the other focal mechanism

Sensitivity to variations in the parameters of the receiver fault

To evaluate the sensitivity of the calculated stress change to difference in the parameters of the receiver fault, we changed one parameter in each case while keeping the remaining parameters constant. Here, the MMS (B1 segment in Fig. 7) is taken as an example. Figure 11 indicates that the ΔCFS varies with differences in the chosen parameters. The results based on the different strike angles, dip angles, and rake angles are shown in Fig. 11a–c, respectively. Figure 11a suggests that the larger the strike angle is, the smaller the ΔCFS, and the value even changes from positive to negative at the eastern end. Figure 11b, c shows that the ΔCFS is less sensitive to variations in the dip angle and rake angle. It should be noted that this conclusion can probably be satisfied only under the conditions in this study.

Fig. 11

ΔCFS in the MMS (B1) produced by 14 historical and 2021 Maduo events for various parameters

Figure 11d shows the impact caused by the effective friction coefficient μ’, indicating that the ΔCFS increases with an increase in the friction coefficient. However, a fault with a higher friction coefficient is less likely to rupture. The reason for this contradiction is that the shear stress change (Δτ) is negative, and the normal stress change (Δσ_n) is positive. According to formula (1), the larger μ’ is, the greater the weight of Δσ_n in the computation of ΔCFS. Consequently, ΔCFS increases as μ’ increases, as has been shown in the previous studies (Toda et al., 2011; Parsons et al., 1999); however, this conclusion is contrary to common sense in physics. Zhu and Miao (2016) discussed this problem and suggested that the tectonic background stress should be considered when calculating the variation in the ΔCFS caused by changes in μ’. Therefore, the selection of μ’ is important in the ΔCFS calculation without considering the tectonic stress field. In this research, we only analyzed the effect of stress disturbance induced by earthquakes. In addition, μ’ in major strike-slip faults is usually chosen as to be 0.4 (Stein et al., 1994; Lin and Stein 2004). Therefore, we suggest that it is reasonable to take an intermediate value of 0.4 for the effective friction coefficient μ’.

Interseismic stress loading rate

Based on the generalized Hooke’s law, Shan et al. (2015) evaluated that the tectonic Coulomb stress loading rate is approximately 2–3 kPa/a on the TLS and 0.2–0.5 kPa/a on the MMS based on the fault slip rate (11.2–4.9 mm/a). Generally, by assuming an elastic modulus of 3 GPa, a slip rate of 1 mm/a corresponds roughly to a loading rate of 0.3 kPa/a. Zhu et al. (2021b) determined the slip rate on the JCF to be 1.2 ± 0.8 (0.4–2.0) mm/a based on interseismic GPS observations across the Maduo region. We estimated the rate of stress accumulation on the JCF to be approximately 0.1–0.6 kPa/a. Liu et al. (2021) used the numerical finite-element method with average GPS velocity data from 1991 to 2015 to simulate the regional interseismic loading rate and computed the value on the DF of 0.21 kPa/a. The JCF is spatially close to the DF, and they are both characterized by left-lateral strike-slip motion, so we assume that their fault slip rates and stress accumulation rates are roughly equivalent and within the range of the estimated value (0.1–0.6 kPa/a).

Based on the estimated loading rate, the stress released by the 14 historical earthquakes (− 400 to − 200 kPa) is equivalent to 300–1000 years of an interseismic stress accumulation. However, the Maduo earthquake was delayed primarily by (and occurred less than 100 years after) the 1937 event. On one hand, the interseismic tectonic loading rate we estimated or modeled may be lower than the actual rate. Zhan et al. (2021) suggested that there are generally deep and undulating high-conductivity layers in the middle and lower crust within the Bayanhar block (that is, mechanically weak layers that easily deform) based on magnetotelluric profiles across the Maduo seismic source area. The source areas of the 2021 Maduo and 1947 Dari events are located at the junction of high-conductivity and high-resistivity bodies. Stress would migrate to the highly resistant brittle upper crust, causing stress to concentrate locally. These two events may have been controlled by the shear and shortening of these high-conductivity layers. Therefore, we hypothesize that the actual deep tectonic loading rate is much larger than the estimated value based on surface geodynamic data. On the other hand, the previous studies suggested that seismic vibrations can change the mechanical strength of rock bodies and faults, thereby modifying the hydrological characteristics of rocks and sediments (Taira et al., 2009; Moyer et al., 2018; Shi et al., 2021). As a result, the rupture conditions become more sensitive, the stress re-accumulates to a lower value, and rupture may occur. Therefore, we hypothesize that the actual deep fault loading rate is larger than the estimated value based on surface geodesy data and that the seismogenic conditions of the JCF may be suppressed. Consequently, the Maduo earthquake occurred despite the considerable delaying effects of the 14 historical earthquakes (especially the 1937 event). This finding further indicates that the tectonic stress in the eastern Bayanhar block is still rapidly accumulating and adjusting.

Seismic hazards of seismic gaps A and B after 2021

Based on geomorphological research, Van der Woerd et al. (2000) suggested that the average long-term slip rate of the EKF was approximately 11.7 ± 1.5 mm/a (94°E), 10 mm/a (99°E), and 12.5 ± 2.5 mm/a (100°E). More recent geodesy data indicate that the slip rate decreases gradually from west to east, with a rate of ~ 10 mm/a on the TLS that decays to 1–5 mm/a (Kirby et al., 2007; Lin and Guo, 2008; Li et al., 2019; Diao et al., 2019; Zhu et al., 2021a) on the MMS. We estimate that the tectonic stress loading rates of the XDS-ALS, TLS, and MMS are approximately 3 kPa/a, 2.7–1.5 kPa/a, and 1.5–0.3 kPa/a, respectively. However, the simulated results (Liu et al., 2021) show that the corresponding values are 0.29 kPa/a, 0.19 kPa/a, and 0.16 kPa/a, the first two of which (corresponding to the XDS-ALS and TLS, respectively) are roughly ten times smaller than the estimated values above.

As mentioned above, due to local anomalies within the crust, the simulated results (Liu et al., 2021) and estimated values are inconsistent, which may also be lower than the actual tectonic loading rates. Only under the calculations in this study do all 14 historical earthquakes and the Maduo event yield a total ΔCFS of 30–300 kPa in the gap A region. Given an interseismic tectonic loading rate of 3 kPa/a, the promoted stress is equivalent to tectonic loading for approximately 10–100 years. In the gap B region, the total ΔCFS values are 50, 50–200, 50–200, and 200–300 kPa for B1, B2, B3, and B4, respectively. With an interseismic tectonic stress loading rate of 1.5 kP/a, these increased values are equivalent to the accumulation of tectonic stress for approximately 30, 30–130, 30–130, and 130–200 years.

Conclusions

In this study, we calculate the coseismic and postseismic Coulomb stress changes induced by 14 historical earthquakes and investigate their influences on the 2021 Maduo source area. Furthermore, we investigate the influences of all these previous events and the Maduo event on the seismic hazard in the EKF. Combined with the consequences of tectonic loading, we examined the partitioning of stress and re-evaluated the seismic hazards of the EKF. We reached the following conclusions based on our results:

• (1) The 14 historical events considered herein released the stress in the rupture zone of the Maduo earthquake with a combined approximate ΔCFS range of − 400 to − 200 kPa. In particular, the 1937 event had the greatest contribution of − 235 kPa at the Maduo hypocenter. The JCF is the seismogenic fault of the 2021 Maduo event, which is almost parallel and close to the EKF (where the 1937 event occurred). Therefore, the rupture of the 1937 event delayed the occurrence of the Maduo event by inducing the typical inhibitory effect between parallel strike-slip faults on the JCF.

• (2) According to the fault slip rates based on surface geodesy data, we estimated that the loading rate on the JCF is only 0.3 kPa/a. However, magnetotelluric data reveal that the Maduo source area is located at the junction of high-conductivity and high-resistivity bodies in the middle and lower crust, where the tectonic stress easily concentrates locally. Therefore, we hypothesize that the actual loading rate at the depth of the seismogenic layer in the Maduo source area is much higher than the simulated value. We further suggest that although this area is in the stress shadow of historical events, long-term tectonic loading is the main control on the occurrence of this event.

• (3) Our investigation reveals the enhanced stress induced by the historical and Maduo events with ΔCFS values of approximately 30–300 kPa and 50–300 kPa on the XDS (gap A area) and the eastern end of the EKF (gap B area), respectively, not only on the MMS but also at the eastern end of each branch segment of the EKF. A positive ΔCFS brings a fault closer to Coulomb failure. Hence, combined with the accumulation of tectonic stress, the seismic hazard in these two regions has been promoted.