The HYPOINVERSE-2000 (HYPO 2000) location algorithm was adopted to determine the absolute position of the master event (Klein, 2002); this approach has been successfully applied to multiple earthquake sequences (Langin, 2003; Clinton et al., 2006; Konstantinou et al., 2006; 2009a; 2009b; Choi and Noh, 2010; Hauksson et al., 2012; Caciagli et al., 2015; Schoenball and Ellsworth, 2017; Yao et al., 2021). In the DD earthquake location algorithm, developed by Waldhause and Ellsworth (2000), the relative positions of event pairs are determined through minimum residuals between observed and theoretical travel-time differences (or double-difference). The DD method has been widely used to improve earthquake locations (Waldhauser and Ellsworth, 2002; Hauksson and Shearer, 2005; Mandal and Horton, 2007; Waldhauser and Schaff, 2008; Mottaghi et al., 2010; Zhao et al., 2013; Fang et al., 2015; Kato et al., 2016; Sippl et al., 2018; Fan et al., 2022).

In the M&L method, the DD travel-time is used to detect micro-earthquakes; the detection depends only weakly on the accuracy of the velocity model. A brief description of the M&L detection algorithm applied in this study is as follows (Zhang and Wen, 2015a). First, seismic events located by the DD method were chosen as template events with low SNR. The study area was then gridded in longitude, latitude, and depth with the positions of template events used as centers. The travel-time difference of the reference phases (S waves) between each potential small event (i.e., grid point) and template event at each station was calculated. Subsequently, based on travel-time differences of multiple stations, sliding window cross-correlation was performed between reference phases of the template events and the continuous data stream at each station and data component. Finally, the mean correlation coefficient (CC) and SNR after the stacking cross-correlation were calculated. When the mean CC and SNR exceeded defined thresholds, a small event was deemed to be a positive detection, and its position was determined as the grid point with the maximum mean CC. The magnitudes of the detected small events were determined based on the median of the amplitude ratios for the reference phases in all station components (Peng and Zhao, 2009).

Continuous waveform data recorded by 24 stations (Figure 1) within 100 km of the Alxa M _s 5.8 earthquake (i.e., mainshock) epicenter were selected. The study period was from 1 January 2015, to 28 February 2016 (i.e., 3 months before and 10 months after the mainshock). In order to obtain accurate arrival-times and reliable earthquake locations, event waveforms recorded clearly by at least four stations were first selected and the arrival-times of the direct P and S seismic phases were picked manually. The arrival-time data for each earthquake event were checked and corrected using the Wadati diagram, and data that greatly deviated from the fitting line were removed based on regional-phase travel-time curves for Pg and Sg.

Based on the observation data from permanent seismic stations, 90 localizable earthquakes in the Alxa M _s 5.8 (i.e., mainshock) earthquake sequence were obtained using the HYPO2000 method. After the inclusion of data from the campaign arrays, 175 localizable earthquakes were obtained (i.e., the number of localizable earthquakes almost doubled), the minimum complete magnitude decreased from M _L1.2 to M _L0.8 (Figure 2), and the completeness of the earthquake catalog was significantly improved.

The study area was located in the Hetao Basin. Velocity data for the area are available in the CRUST1.0 velocity model (Laske et al., 2013); however, these data are low resolution. Based on the results of previous research into the one-dimensional crustal velocity structure in Alxa, the subsurface structure of the study area was divided into four layers (Song and Ge, 2018).

Based on corrected seismic phase data and uniform station coverage, reliable hypocenter positions can be obtained using the HYPO2000 method. The horizontal and vertical position errors of the mainshock are 0.25 and 0.83 km, respectively. For the earthquake sequence, the horizontal position errors of nearly 95% of earthquakes are within 1 km; the vertical position errors of more than 95% of earthquakes are within 3 km; the arrival residuals of ∼95% earthquakes are within 0.3 s. The average values of horizontal and vertical position errors and arrival residual are 0.55 km, 1.53 km, and 0.175 s, respectively. Thus, the hypocenter position of the Alxa M _s 5.8 earthquake sequence obtained by the HYPO2000 method is reliable.

The HYPO2000 location parameters were taken as input parameters for the DD method. The relative location accuracy of earthquake source was improved and the directional distribution of the occurrence of earthquakes was clearer, representing a difference from the disordered distribution before relocation (Figure 3). The spatial distribution of aftershocks appears to be very similar before and after relocation. In comparison, it was found that the hypocenters of most earthquakes were very close before relocation, and the hypocenters is layered distribution, as shown in Figure 3B. After the relocation, the linear distribution characteristics of the hypocentres became more obvious, as well as the seismic gap.

Earthquakes at the eastern end of the aftershock zone were found to have undergone an eastward shift after relocation, with an increased spread length of aftershocks (Figure 3A). The focal depths mainly ranged between 16 and 22 km before relocation, while after relocation, the depth spread increased to 15–25 km (Figure 3B). The dominant distribution of the focal depth of the Alxa M _s 5.8 earthquake sequence shows that the seismogenic layer was located in the middle–upper crust.

Under the premise of uniform azimuthal distribution of stations and waveforms with high SNR, the number of stations used for micro-earthquake detection should be appropriate, and stations close to the epicenter should be selected to the extent possible. Therefore, six stations were selected for micro-earthquake detection, and 25 earthquakes of > M _L2.5 with high SNR waveforms were selected as template events (Table 1); waveforms 1 s before and 3 s after the Sg seismic phases of the template events were chosen as template waveforms. Wave filtering at 2–8 Hz was then performed for the template and continuous waveform data. In accordance with the M&L method, the study area was gridded at 0.01° × 0.01° × 0.5 km (longitude, latitude, depth), with the positions of the template earthquakes used as the centers. Finally, the origin times, seismic-source locations, and magnitudes of the micro-earthquakes were determined using a grid search method. In this study, the average CC threshold value was set as 0.3 (Zhang and Wen, 2015a; 2015b; 2015c) based on existing studies, and the event magnitude was decided based on the median of the amplitude ratios for the reference seismic phases in all station components. When the S wave amplitude is barely above the noise level, the principal component fit method can be used to calibrate the magnitude (Shelly et al., 2016; Meng et al., 2018; Yao et al., 2020; Daniels and Peng, 2022). The Sg seismic phase parameters were calculated using the TauP Toolkit (Crotwell et al., 1999) based on the Preliminary Reference Earth Model (Dziewonski and Anderson, 1981). The event with the largest CC in each 6-s time window was chosen as the detected earthquake to avoid duplicate detection.

A total of 803 micro-earthquakes (including 208 DD-located earthquakes) were detected using the M&L method (Figure 4); these were mainly distributed near the mainshock. In addition, two areas of micro-earthquakes were concentrated ∼30 km north of the mainshock. The number of earthquakes showed a sharp increase to nearly four times the number of events before micro-earthquake detection.

After micro-earthquake detection using the M&L method, the minimum complete magnitude decreased from M _L0.8 to M _L0.6 (Figure 5), and the seismic gap of the earthquake catalog was improved. The resultant richer aftershocks provided an improved basis for detailed analysis of aftershock evolution and seismogenic structure.

After micro-earthquake detection using the M&L method, 25 template events were all self-detected, with CCs of 1.0. Figure 6A shows the self-detected result of the mainshock, and Figure 6B shows the detection result of a single M _L0.3 micro-earthquake with an average CC of 0.3259.

The results of the 208 DD-located earthquakes were compared with those of the M&L method for the same earthquake to illustrate the effectiveness of micro-earthquake detection (Figure 7). More than 70% of earthquakes (i.e., 155 events) had an origin time difference of <0.5 s, and >92% of earthquakes (i.e., 195 events) had a magnitude difference of <0.3. In addition, the distance between epicenter positions was <3 km for >95% of earthquakes (i.e., 201 events), while the focal depth difference of >95% of earthquakes (i.e., 199 events) was <4 km. In general, the detection results are similar to the DD location of the same earthquake, confirming the reliability of the micro-earthquake detection.

The Cut and Paste (i.e., CAP) method (Zhao and Helmberger, 1994; Zhu and Helmberger, 1996) was applied to invert focal mechanism solutions for the mainshock and the four aftershocks of > M _L4.0. The focal mechanism parameters are shown in Table 2.

The focal mechanism solution and waveform fitting results were analyzed by taking the mainshock as an example. As shown in Figure 8, the phases and amplitudes of the theoretical and observed seismic waveforms at different stations had a good fit. The nodal plane solution of the focal mechanism of the mainshock was characterized by 86° strike, 84° dip, and −9° rake; the strike, dip, and rake of the alternative nodal plane solution were 177°, 81°, and −174°, respectively. The azimuth and plunge of the P axis were 41° and 11°, whereas those of the T axis were 132° and 2°, respectively. The moment magnitude of the mainshock was M _w5.6. The fit errors corresponding to the mechanism solutions of the mainshock at different focal depths are shown in Figure 9A. The fit error was smallest for a focal depth of 21 km; the mechanism solutions were relatively stable within a depth range from 15km to 31 km and were dominated by strike-slip with some normal components.

The mechanism solutions of the four aftershocks of > M _L4.0 were also well fitted (Figures 9B–E). The mechanism solutions at different depths were relatively stable and primarily characterized by strike-slip with a smaller number of normal or thrust components. These results are consistent with the focal mechanism solution of the mainshock. Overall, the seismogenic structure of the mainshock was a strike-slip fault, which is consistent with the development of multiple strike-slip faults in the study area (Research Group of Active Fault System around the Ordos Massif, 1988).

The focal mechanism solutions of the Alxa M _s 5.8 earthquake were determined using data from previous literature (Han et al., 2015; Wang et al., 2019) and several institutions, including GFZ, USGS, GCMT, Institute of Geophysics, China Earthquake Administration (CEA-IGP). Focal depths obtained through inversion ranged from 13 to 30 km, with the relocated focal depth of the mainshock being 22.7 km. This depth falls within the upper crust and is essentially consistent with the results of Wang et al. (2019) [20.597 km], but is significantly deeper than the inverted focal depth (18 km) of Song and Ge (2018), the focal depth determined by the China Earthquake Network Center (10 km), the relocated depth (13.2 km) of Wei et al. (2017), and relocated depth (13 ± 1 km) of Han et al. (2015). However, the lack of significant ground surface rupture, major building damage, or casualties (Wang et al., 2019) is inconsistent with such shallow focal depths. Furthermore, the P wave velocity structure in the epicenter region, inverted by Wang et al. (2019) via the TomoDD method, shows a high- and low-velocity conversion zone at 20-km depth in the Alxa Left Banner focus region. Previous studies have shown that the presence of intracrustal high-velocity bodies is essential for high stress concentrations, and strong earthquakes are prone to occur in the transition zone between intracrustal high- and low-velocity zones or on the sides of high-velocity bodies (Lees and Malin, 1990; Zeng et al., 2014; 2017a; Wu et al., 2022). Thus, the above analysis and previous studies of seismogenic dynamics confirm that the focal depth of 22.7 km for the Alxa M _s 5.8 earthquake determined in this study is likely a realistic value.

According to the M-t diagram and 2-day frequency diagram for the Alxa M _s 5.8 earthquake sequence (Figure 10), there were fluctuations in the development of the sequence. Aftershocks mainly occurred before 30 June 2015, followed by a rapid decrease in number. In December 2015, the number of aftershocks abruptly rose; however, these were mostly earthquakes with small magnitudes. Therefore, we selected only earthquakes from before 30 June 2015, for the analysis of aftershock evolution. Notably, after a period of quiescence following the aftershock decay, three larger aftershocks occurred between March and June 2016, including M _L4.2, M _L3.2 and M _L4.1 earthquakes.

From analysis of the distribution characteristics of the Alxa M _s 5.8 earthquake sequence from April 15 to 30 June 2015 (Figure 11), we found that the aftershock sequence extended in an NEE direction (N70°–75°E) with a length of 12 km, likely indicating the rupture length of the mainshock. The mainshock rupture started from the eastern end of the aftershock zone and gradually extended to the western end, suggesting unilateral rupture. Aftershock activity was segmented, with eastern and western segments separated by an area of low seismicity extending 5 km horizontally. Both the mainshock and two aftershocks of > M _L 4.0 occurred on the eastern segment, with significantly fewer aftershocks on the western segment. The aftershock zone was ∼4 km wide on the western segment and 5 km wide on the eastern segment. From March to June 2016, M _L 4.2, M _L 3.2 and M _L 4.1 earthquakes occurred in the low-seismicity gap.

The NE-oriented DBF lies near the location of the Alxa M _s 5.8 earthquake, with an angle of ∼15° between the spread direction of the earthquake sequence and the direction of the DBF. More, the strike of the DBF does not match the focal mechanism solution of the mainshock. Therefore, the earthquake sequence is tentatively determined to have occurred on an unknown blind fault to the west of the DBF.

The mainshock epicenter (i.e., the starting point of earthquake rupture) was located at the eastern segment of the aftershock zone (Figure 12A), demonstrating a unilateral rupture of the main shock. In addition, it shows that the eastern segment of the aftershock zone should belong to the asperity zone on the seismogenic fault zone. The two largest aftershocks (>M _L4.0) also occurred on the eastern segment of the aftershock zone, indicating that mainshock did not release all of the strain in the main asperity zone. The focal depth profile (Figure 12B) illustrates that most aftershocks were shallower than the mainshock (22.7 km), which is consistent with the theory that strong earthquakes nucleation tend to the deeper and propagate upwards (Scholz, 1990). Aftershocks predominantly occurred at depths of 15–25 km, largely consistent with the depth of the mainshock rupture from previous studies (Wang et al., 2019). Few aftershocks above 15 km is compatible with field survey findings that no significant surface rupture was found after the mainshock (Wang et al., 2019). Figure 12A shows an obvious area of low seismicity (∼5 km² × 5 km²) between the western and eastern segments of the aftershock zone, located at a depth of 20–25 km (Figure 12B). This zone potentially relates to a high strength barrier on the fault (Aki, 1979), and it was also consistent with an Coulomb stress triggering area of the mainshock (Gao et al., 2015). From March to June 2016, three earthquakes of > M _L3.0, including two M _L4 earthquakes, occurred in a low seismicity zone, indicating that the three large aftershocks were caused by the rupture of this barrier.

In summary, the eastern segment of the aftershock zone formed the main asperity of the seismogenic fault zone. The main rupture was initiated at the eastern segment of the fault, and propagated west, before being blocked by a barrier in the western section of the fault zone. Subsequently, the rupture crossed the barrier and continued for another 2 km. Between the mainshock and February 2016, there were very few aftershocks in the low seismicity zone, and those earthquake that did occur had very low magnitudes. It suggested that the barrier zone remained in a state of high stress until 24 March 2016, after which M _L4.2, M _L3.2, and M _L4.1 earthquakes occurred. Therefore, the location and magnitude of larger aftershocks can be determined through the analysis of aftershock evolution.