The spatio-temporal evolution characteristics of the M_S6.0 Barkam earthquake sequence in Sichuan on June 10，2022

According to the China Earthquake Networks Center, at 00:03 on June 10, 2022, local time, an earthquake with M_S5.8 （M_L6.3） struck Barkam City （32.27°N, 101.82°E）, Aba Prefecture, Sichuan Province, with a focal depth of 10 km. Subsequently, at 01:28 local time, another M_S6.0 （M_L6.5） earthquake occurred in the same location （32.25°N, 101.82°E), with a focal depth of 13 km. These two earthquakes were located in the southeast part of the Bayan Har block, approximately two kilometers apart. According to the definition of earthquake sequence type, the magnitude difference between the two earthquakes ΔM＝0.2 constitutes a swarm type earthquake, which is hereinafter referred to as “M_S6.0 Barkam earthquake swarm”. The M_S6.0 Barkam earthquake swarm exhibited numerous minor earthquakes, up until 23:00 on June 30, 2022, a total of 4 821 earthquakes of magnitude 0 and above were recorded, including seven earthquakes with magnitude ranging from M_S3.0 to M_S3.9, three earthquakes with magnitude ranging from M_S4.0 to M_S4.9, two earthquakes with magnitude ranging from M_S5.0 to M_S5.9, and one M_S6.0 earthquake. The largest aftershock recorded was an earthquake with M_S5.2 （M_L5.6） at 03:27 local time on June 10. Considering the significant event of an earthquake with M_S5.8 preceding the occurrence of the main shock with M_S6.0, it is important to investigate the characteristics of the M_S5.8 earthquake sequence as a foreshock and the sequence features before and after the main shock. Existing seismological methods indicate that earthquake sequences can intuitively reflect differences in tectonic stress fields, seismic structures, and the seismogenic environment medium. Moreover, the rupturing properties of the main shock often influence the evolution of aftershock sequences. This study utilizes seismic data from the Sichuan regional seismic network, based on parameters such as the b-value and p-value of the sequence, in combination with regional structure and focal mechanism solution parameters of the strong aftershock, to investigate the spatio-temporal evolution characteristics of the Barkam M_S6.0 earthquake swarm sequence and to explore the sequence evolution characteristics before major earthquakes in Barkam.

Regional geological settings and M≥5.0 historical earthquakes

The Barkam region is situated in the eastern part of the southeastern margin of the Bayan Har block within the Songpan-Garze orogenic belt. The Longriba fault in the studied area divides the eastern part of the Bayan Har block into two parts, including the secondary Longmenshan block on the east and the Aba secondary block on the west. The Longmenshan block primarily features the NE-trending Longmenshan fault zone, the nearly SN-trending Minjiang fault, and the Huya fault. On the other hand, the Aba secondary block, features a series of large-scale strike-slip faults trending NW that have exhibited activity in the Late Quaternary period. These faults, along with the Garze-Yushu fault, the Xianshuihe fault, and the east Kunlun fault at the southern and northern boundaries of the Bayan Har block, collectively constitute the tectonic framework of the Bayan Har block. The Barkam M_S6.0 earthquake swarm occurred near the intersection of the NW-trending Songgang fault and the NE-trending Longriba fault within a relatively complex fault structure. The Songgang fault is approximately 100 kilometers in length, with a maximum width of about 300 meters, trending between 320° and 330°, dipping to the northeast with an angle of 50° to 70°. It extends from the northern slope of Mengbi Mountain on the south side of Barkam, along a NW direction, and disappears near Zoigê. This fault exhibits relatively complex activity, featuring characteristics of multiple periods of activity. Its southern segment is a Late Pleistocene active fault, and historical records indicate that it has experienced three M_S≥5.0 earthquakes, with the largest M_S6.0 earthquake occurred on October 8, 1941 in Heishui area. The northern segment of the fault does not exhibit obvious surface activity since the Late Pleistocene. Apart from the Maerkang M_S6.0 earthquake swarm, no M_S≥5.0 earthquake was shown in historical records. Minor earthquakes are relatively active in the central part of the fault, concentrated in deep-seated dense activity along the NW direction. This reflects the existence of a northwest-trending ruptured surface and suggests that the northern segment of the fault possesses potential seismic risk. The Longriba fault is considered to be resulted from the strong obstruction of the southeastern movement of the Bayan Har block from the South China block during the Late Cenozoic, and it constitutes the backthrust-overthrust tectonic system of the Longmenshan structural belt, bearing the role of crustal deformation on the eastern edge of the Qinghai-Xizang Plateau since the Late Cenozoic. This fault is a new fault primarily characterized by right-lateral strike-slip movement in the NE direction, consisting mainly of two parallel branch faults: the Longriba fault and the Maoergai fault. It exhibits a series of distinct fault landforms and demonstrates Late Quaternary activity. Historical records indicate that the Longriba fault has not experienced any M_S≥5.0 earthquakes. The M≥5.0 earthquakes that occurred within a 50 km range from the epicenter were all earthquake swarms. There were a total of two swarms, which took place on September 26 and November 6, 1969, with M_S5.1 and M_S5.3 in Aba, and on September 5 and November 8, 1970, with M_S5.5 and M_S5.5 in Rangtang.

Basic situation of the sequence

Using the multi-stage positioning method to locate the Barkam M_S6.0 earthquake sequence. The results indicate that the sequence is situated to the northeastern side of the Songgang fault, with an overall parallel distribution along the NW-SE direction, forming two branches running in an east-west direction, parallel to the Songgang fault. The western branch spans approximately 12 km in length and 3 km in width, while the eastern branch extends about 15 km in length and 2 km in width, with a separation of roughly 2 km between the two. The sequence experienced a total of three M_S≥5.0 earthquakes, with the M_S5.8 earthquake occurred closer to the eastern side of the western branch, the M_S6.0 earthquake located within the eastern branch, and the largest aftershock of M_S5.2 situated to the east of the eastern branch. Prior to the M_S6.0 earthquake, seismicity was primarily distributed along the western branch, while after the M_S6.0 earthquake, the activity shifted to the eastern branch, indicating the spatial migration over time. Additionally, the distribution of seismicity is more scattered in the western branch and more concentrated in the eastern branch, suggesting potential differences in the seismicity patterns between the two branches and indicating that the sequence does not occur on a single fault structure, but rather on different branch faults.

Using the CAP （cut and paste） method to calculate the focal mechanism solutions of the M_S5.8, M_S6.0, and some M_S≥3.5 earthquakes of the sequence. The results revealed that the M_S5.8 earthquake had best double-couple solutions with strike 324°, dip 76°, and slip 0° for nodal plane I, while strike 234°, dip 90°, and slip 166° for nodal plane Ⅱ . The M_S6.0 earthquake had best double-couple solutions with strike 329°, dip 90°, and slip −3° for nodal plane I, and strike 58°, dip 87°, and slip −180° for nodal plane Ⅱ . Both main shocks and the focal mechanisms of the larger aftershocks exhibited consistent strike-slip motion, which is consistent with the regional predominance of reverse and strike-slip faulting. The strike of nodal plane I in the NW direction is consistent with the strike of the Songgang fault near the epicenter. Furthermore, the focal mechanism solutions for some M_S≥3.5 events of the Barkam M_S6.0 earthquake sequence indicated a concentrated depth distribution ranging from 5 to 8 km （Table 1）. Combining the results of precise positioning and the study of the sequence’s seismogenic structure by Long et al （2023), it is suggested that the seismogenic structure of the Barkam M_S6.0 earthquake swarm is complex, which is resulted from the simultaneous activity of several faults of different scales. These faults are located close to the Songgang fault, not exposed at the surface, and may be connected to the Songgang fault at depth, indicating that the seismogenic structure may be a concealed branch fault of the Songgang fault. It is noteworthy that there are traces of a NE-oriented distribution within the sequence, implying that the seismicity in this area may exhibit conjugate rupture characteristics.

Early sequence parameter evolution characteristics

The early temporal evolution of the sequence encapsulates the processes of nucleation and stress changes. The analysis of the temporal evolution characteristics is helpful to understand the mechanism and development of the sequence. In commonly used statistical seismological models, the regression parameter b value in the Gutenberg-Richter （G-R） relationship and the p value in the modified Omori’s law carry specific physical properties and are widely considered as statistical quantities characterizing the sequence. The G-R relationship is expressed as lgN＝a－bM, where b value represents the maximum likelihood solution ${b}={\mathrm{lg}\mathrm{e}}/ （ {\overline{M}－{M}_{\mathrm{C}}} ）$, a value represents the overall level of seismic activity, N represents seismic frequency, M_C represents the minimum completeness magnitude, $\overline{M}$ represents the average magnitude, and lge＝0.4343. The rock fracture experiments indicate that the b value decreases with the increase of stress level. A smaller b value reflects higher regional stress levels, while a larger b value indicates lower stress levels. So the b value, as a means of assessing regional stress accumulation levels, has been widely used in seismic hazard assessment and post-earthquake trend analysis. Laura and Stefan （2019） studied the b values of the earthquake sequences of the AmatriceNorcia M_W6.2, M_W6.6 in central Italy on August 24 and October 30, 2016; the Kumamoto M_W6.5, M_W7.3 sequence in Japan; and the Tohoku M_W7.3, M_W9.0 sequence in Japan. They concluded that the b value of the foreshock sequence would significantly decrease. Jiang et al （2021） found that the b value of the Yongping M_S6.4 earthquake sequence in Yunnan showed a decrease followed by fluctuation before and after the main shock, reflecting the intense stress adjustment state in the sequence’s continuous process. Wang et al （2023） discovered the phenomenon of b value decreasing after the foreshock and increasing after the main shock, clearly reflecting the development process of the foreshock-main shock-aftershock sequence. In the actual calculation process, calculation error of the b value is obtained through the construction of a bootstrap process. Additionally, assuming N＝1, M corresponds to the theoretical maximum earthquake magnitude M_max, expressed as M_max＝a/b. The expression of the modified Omori’s law is n（t）$＝{K}/{{ （ t+c ） }^{p}}$, where n（t） represents the number of aftershocks at time interval t after the main shock, K represents the aftershock occurrence rate, and p is referred to as the aftershock frequency decay coefficient, representing the rate of sequence decay. A larger p value indicates faster decay, while a smaller p value suggests slower decay, typically varying between 0.9 and 1.5. Its variation characteristics may be related to the uneven structure, temperature changes, and stress accumulation levels in the crust. Discretizing frequency statistics over time periods can result in information loss, thus we obtained the p value and other coefficients in cumulative frequency form. The final integrated form of the modified Omori’s law is: when p≠1, $N （ t ） ＝ K[{c^{1－ p}}－ { （ t ＋ c ） ^{1－ p}}] /{{ （ p － 1 ） }}$, and when p＝1, N（t）＝Kln（c+t）. In the actual inversion process, both equations are simultaneously calculated, and the fitting error is computed to select the smaller error value as the final p value calculation result. Due to the small sample size, conventional least squares methods may lead to local optimal solutions, hence genetic algorithms were used to solve the parameters. This study attempts to calculate the b value, p value, and other sequence parameters to identify evidence of the M_S5.8 serving as a foreshock to the M_S6.0 in the Barkam earthquake sequence.

In this sequence, three M_S≥5.0 events occurred within three hours of the sequence’s onset, indicating rapid sequence development. When we attempted to analyze the evolution characteristics between these three events, the short time intervals resulted in the signals of smaller earthquakes submerged in strong seismic waves, leading to incomplete aftershock records and insufficient statistical sample size. In order to increase the required seismic sample size for the study, a template matching method was used to detect missed earthquakes in the data from June 10th. Using 764 seismic events recorded by the network as templates, events with a correlation coefficient R≥0.85 were identified as individual earthquake events, and DBSCAN method was employed for earthquake correlation, ultimately obtaining 1 713 precise earthquake records, which is 2.2 times as much as the number of templates used. Since the identified earthquakes were similar to the template earthquakes in terms of location and nearly identical in terms of source mechanism solutions, the magnitudes of the missed earthquakes can be obtained by comparing their maximum S-wave amplitudes with the corresponding templates. The supplemented missed earthquakes mainly occurred before 10:00 a.m. , indicating significant interference of strong seismic waves in the manual identification of earthquakes, and also demonstrating the effectiveness of template matching in picking up missed earthquakes. The GFT method was used to compare and analyze the network catalog and the supplemented earthquake catalog before 10:00 a.m. , calculating the minimum completeness magnitudes, showing M_L1.8 and M_L1.3, respectively, proving the effectiveness of the template matching method in supplementing small magnitude earthquakes.

On June 10, three seismic events of M_S≥5.0 divided the seismic sequence into different stages. To ensure data comparability and control variables, each stage was defined as Ⅰ , Ⅱ , and Ⅲ , with each stage beginning one hour after each of the three M_S≥5.0 events. For each stage, the Gutenberg-Richter-Frohlich （GFT） method was used to calculate the minimum completeness magnitude （M_C） of the seismic sequence. Events above the M_C were selected, and their b values, M_max values, and p values were calculated. The analysis aimed to identify potential differences in stress states and seismic activity characteristics across the different stages and to understand the early evolution patterns of the sequence. We have listed the amount of data used and the calculation results for each stage in Table 2. From the table, it can be seen that the sample sizes for each stage （above the completeness magnitude） were all over 50, with 69, 57, and 66 events, respectively, ensuring robust calculation results. The M_C values for the three stages were M_L2.1, M_L2.3, and M_L1.7, indicating a significant impact of strong earthquakes on short-term monitoring capabilities, with the degree of impact varying with the magnitude. Compared to stages Ⅱ and Ⅲ , stageⅠexhibited a significantly lower b value （0.59). Over time, the b value gradually increased, with the subsequent two stages being 0.84 and 0.86, respectively. The low b value of stage Ⅰ suggests a high stress level in the seismic zone, indicating that the M_S5.8 earthquake could be considered as a foreshock of the M_S6.0 earthquake. The M_max values also demonstrated differences across the stages, with an M_max value of M_L5.0 in stage Ⅰ , the highest among the three stages. The subsequent stages showed a gradual decrease of M_max from M_L4.2 to M_L3.7, reflecting the potential foreshock nature of the seismic sequence in stage Ⅰ .

The a value of stage Ⅰ （3.1） was not significantly different from that of stage Ⅲ （3.2）, but was lower than that of stage Ⅱ （3.6), suggesting that the a value alone cannot distinguish between foreshocks and aftershocks. When calculating the p value for events above the M_C for each stage, the p value for stage Ⅰ was 0.76, significantly lower than those of the subsequent two stages, which were 1.81 and 1.64, respectively. This suggested that the seismic sequence in stage Ⅰ exhibited slower decay and insufficient stress release, while the subsequent two stages were opposite, possibly indicating differences in the temporal evolution between the foreshock sequence and the aftershock sequence.

Conclusions

The spatial distribution characteristics of the Barkam M_S6.0 earthquake swarm in the region indicated a significant spatial migration feature, suggesting that the sequence was not a simple single rupture event, but a complex seismic sequence. Given the presence of two branches in the sequence, the evolution characteristics over time were discussed separately for the east and west branches. Calculations for the west branch yielded M_C of M_L1.5, b value of 0.71, and p value of 0.81, while the corresponding parameters for the east branch were M_L1.6, 0.93, and 0.94, respectively. The differences in the parameters between the west and east branches reflected that the two branches were formed not by a single fault structure. The lower b and p values in the west branch indicated insufficient stress release, a high stress level, and slow decay, possibly related to the occurrence of the foreshock sequence.

In summary, the seismic cluster of the M_S6.0 event in Barkam on June 10, 2022 occurred near the intersection of the Songgang fault and the Longriba fault, indicating a complex fault structure. The seismic cluster exhibited rich small earthquakes, slow overall decay, and segmental spatial characteristics. Several conclusions were drawn from the analysis:

1） The Barkam M_S6.0 earthquake swarm occurred near the intersection of the NW-trending Songgang fault and the NE-trending Longriba fault, indicating a complex fault structure. The precise positioning results showed that the sequence was located along the NE direction of the Songgang fault, with an overall NW-SE orientation and parallel east and west branches. The east and west branches exhibited spatial migration features and different spatial distribution patterns. The source mechanisms of the larger earthquakes in the sequence were consistent, all being strike-slip type, which aligns with the regional background and the nature of the Songgang fault. It is speculated that this sequence was caused by several different-sized faults, which are close to the Songgang fault, not exposed at the surface, and may be connected to the Songgang fault at depth, representing concealed branch faults of the Songgang fault.

2） Using template matching, 1 713 precise earthquake events were identified, which was 2.2 times as much as the number of templates used. This reflected the significant interference of strong seismic waves on manual earthquake identification and demonstrates the effectiveness of template matching in detecting missed earthquakes.

3） By dividing the sequence into three stages following each M_S5.0 event, the b and p values were compared and analyzed. The results showed a significantly lower b values in stage Ⅰ , reflecting a higher stress level in the seismic zone during this stage. The M5.8 earthquake can be considered as a foreshock before the M_S6.0 earthquake. Additionally, the p value for stage Ⅰ was significantly lower than the subsequent two stages, indicating differences in the temporal evolution between the foreshock sequence and the aftershock sequence.

4） When analyzing the east and west segments separately, we found that the west segment exhibited lower b and p values, indicating insufficient stress release, high stress level, and slow decay, possibly related to the occurrence of the M_S5.8 foreshock sequence in this segment.

5） In summary, the comprehensive analysis suggests that the M_S5.8 earthquake was a foreshock of M_S6.0 event in Barkam. Temporally, the M_S5.8 earthquake sequence before the main shock exhibited characteristics of low b and p values. Spatially, the west segment of the M_S5.8 earthquake sequence also showed lower b and p values, indicating slow decay of the foreshock sequence of the Barkam M_S6.0 earthquake swarm and the presence of insufficient stress release and high stress levels in the foreshock area.