3.1 Relocation results
After ten iterations of the HypoDD program, the average changes in hypocenter location along the longitude, latitude and depth directions (DX, DY, DZ) decrease from 0.98 km, 0.75 km and 0.81 km at the beginning to 0.03 km, 0.09 km and 0.1km at the end, the iteration tend to be stable. The average travel time residual decreases from 0.08 s at the beginning of iteration to 0.01 s after iteration. After relocation, the travel time residual is significantly reduced, and the accuracy of the relative location of earthquakes is significantly improved. Finally, we obtain 4204 relocation results of the 2014 earthquake sequence.
Before relocation (Fig. 1a), the epicenter distribution of the 2014 sequence was more scattered. After relocation (Fig. 2), the distribution becomes more concentrated and its relationship to the tectonics becomes clearer. The epicenters show an NW-SE dominant direction, with an angle of about 135° to the north. The total length of the long axis of the epicenter distribution is about 15 km, so the rupture scale of this earthquake sequence is estimated to be about 15 km. The epicenters are mainly located in the central northeast part of the reservoir area, on the NW segment of the Shuangxi-Jiaoxiyang (f11 − 3) fault. The earthquake distribution along the Shuangxi-Jiaoxiyang fault is segmented (Fig. 2). In order to have a clear understanding of their vertical depth distribution characteristics, we divide the area into five regions, from R1 to R5, and project them separately (Fig. 2c, Fig. 3).
In terms of the occurrence time (Fig. 2a), earthquakes start in the R2/3 regions, and then gradually spread to the R1/4/5 regions on both sides and deeper places. Earthquakes begin to occur in the area where multiple faults (for example, f5 and f11, etc.) converge, in the area with dense structural planes and good permeability. The geometric complexity of faults may cause localized stress concentration, leading to the initial rupture of this earthquake sequence. Then, the earthquakes rupture from the initial location to both sides along the SE and NW directions, and the sequence gradually terminates at both ends of the dominant spreading direction. The NW spread terminates at the intersection of f11 and f3 faults, which may be related to the change of fault slip and the blockage of reservoir water infiltration (Yang et al., 2021).
Figure 2b and Fig. 3 show that the average hypocenter depth is 4 km, the minimum depth is less than 2 km, and the maximum depth is more than 6 km. Most earthquakes are shallow, and even though their magnitude is small, they are easily perceived and prone to cause serious impacts and injuries. The profile projection perpendicular to the dominant direction (Fig. 2c, profile AA’) of epicenters can reflect the dip characteristics of seismogenic structure (Fig. 3). It is roughly estimated that the dominant dip angles in the R1-3 region are about 84° (Figs. 3a-c, f-h); the seismogenic faults are characterized by high dip angle and dipping to SW. Especially in the R4 region, there are several secondary faults dipping to NE with a high-dipping angle of 86°, and the structure of the seismogenic faults is relatively complex. Therefore, we speculate that the f11 fault is relatively broken, and the secondary structures are most developed near the R4 region.
The earthquake magnitude (Figs. 2c and 3) combined with the occurrence time (Fig. 2a) shows that the earthquakes are strong at the beginning of the sequence. With the occurrence of the sequence, the magnitude gradually decreases and the earthquake location extends towards both NW and SE ends. We also calculate the spatial distribution of b-values (Fig. 2d) based on the magnitude distribution in Fig. 2c.
In the magnitude-frequency relation log10N = a-b*M proposed by Gutenberg and Richter (1944), the value of b describes the proportionality of large and small earthquakes in the sequence. Rock mechanics experiments, statistical analysis, and numerical simulations found that the b-value is usually negatively correlated with regional stress (e.g., Schorlemmer et al., 2005; Kun et al., 2013; Main et al., 1992; Nuannin et al., 2012; Scholz, 2015; Wiemer and Benoit, 1996). That is, the stress accumulation is more significant in areas with lower b-values. Mogi (1962) considered the inhomogeneity of the underground medium as an important factor influencing the value of b, and the higher the degree of inhomogeneity, the larger the b-value. Figure 2d shows that the b-values are lower at the location where the earthquake sequence started (black dashed circle in Fig. 2d). We hypothesize that this is because the faults intersect at the earthquake starting location, and the stress is more likely to concentrate in the area where structural surfaces intersect. Furthermore, the white dashed line in Fig. 2d circles the area where high and low b-values coexist. The high b-values are in the area where the water body is located. We hypothesize that the infiltration of the reservoir water led to higher water content in the rock below, i.e., higher degree of heterogeneity in the underground medium. The low b-value areas are located on land, indicating that the stress is relatively concentrated here.
According to the results of relocation, it can be concluded that the strike of the seismogenic fault is NW-SE, with an angle of 129° to north, a higher dip of about 84°, dipping to SW. The earthquake sequence began in the R2 region and progressed to both the NW and SE sides. The seismogenic fault structure is relatively complex, and there may be multiple sub-faults.
3.2 Focal mechanism results
The ML ≥ 3 focal mechanisms calculated by the HASH and CAP methods are shown in Fig. 4a and c. The azimuth and inclination of the P and T axis (Fig. 4b and d) can be calculated using the focal mechanism parameters. The consistency of both the focal mechanism and the P/T-axis azimuth for the 2014 sequence around Shanxi Reservoir is high (Fig. 4). It is inferred that the seismogenic characteristics of these events are similar, and there is no obvious stress rotation during the occurrence of earthquake sequence. In order to have a clearer understanding of the overall characteristics of the above parameters, we count the frequencies of the strike, dip, and rake for each nodal plane, and the azimuth and inclination for the P/T axis (Fig. 5).
From Figs. 4a, c and 5a, the plane I is dominant in NW-SE direction, and the plane II is dominant in NE-SW. The dip angles of nodal planes I and II are concentrated in the range of 70°-90°, so the dip angle of seismogenic surface is relatively steep. The rake angle is close to horizontal, and the fault surface movement is characterized by strike-slip, which indicates that the slip of seismogenic faults is mainly horizontal dislocation. Combined with the dominant NW-SE strike of the earthquake sequence (Figs. 2 and 3), it can be inferred that the nodal plane I is the main rupture surface of the earthquakes, with a SW dipping, and the strike of the fault surface is close to that of Shuangxi-Jiaoxiyang fault (f11, Fig. 1). Then, in Figs. 4b, 4d, 5b and 5d, the compressive P-axis is dominantly distributed in the NNW, near north direction; and the tensile T-axis is oriented in the NEE, near east direction. The inclination angles of the P and T axes are mostly less than 20°, which are nearly horizontal. The stresses near the fault show a sub-horizontal north-south compression, and a sub-horizontal east-west tension, resulting in a right-lateral strike-slip movement of the seismogenic fault.
To verify the reliability of the statistical results, we use the method proposed by Wan (2019) to obtain the center solution of focal mechanism for earthquakes with magnitude ML ≥ 3: the strike, dip and rake of nodal plane I are 131°, 82° and − 173°, respectively; and the strike, dip and rake of nodal plane II are 40°, 83° and − 8° respectively. The P-axis azimuth of the central solution is NNW 355° with an inclination of 11°, and the T-axis azimuth is NEE 85° with an inclination of 1°. Above results are consistent with the statistical rose chart (Fig. 5).
Based on the focal mechanisms and stress axis results, we infer that the 2014 earthquake sequence around Shanxi Reservoir was a right-lateral strike-slip activity with a strike NW-SE, dipping SW, and high dip angel, under the stress conditions of gentle-inclination N-S compression and W-E tension.