The b-value is an important parameter in the empirical magnitude-frequency formula, , which was derived from the study of global seismicity patterns (Gutenberg and Richter 1944). In the formula, N denotes the frequency of earthquakes above magnitude M, a denotes the level of seismicity in the region, and b denotes the proportional relationship between earthquakes of different magnitudes in the region. Experimental rock results have shown that the b-value is inversely proportional to the stress magnitude, and that low b-value regions have high stress accumulations (Scholz 1968; Amitrano 2003; Schorlemmer et al. 2005). In particular, there is a clear trend of decreasing b-values before a rock rupture or an earthquake tremor.
Many seismologists have studied the physical significance of the b-value in depth, and many case studies have corroborated the phenomenon of lower b-values often occurring in the source and adjacent areas before earthquakes. For example, Nanjo and Yoshida (2021) studied the variation in the b-value in and around the source area of magnitude 6.9 and 6.8 earthquakes off the coast of Miyagi Prefecture, Japan. The authors found that the earthquakes occurred near a region with very small b-values, even after the earthquake. Zeng et al. (2020) studied the changes in the b-values before an Ms-6.0 earthquake in Changning, China, and found that low b-value anomalies (≤ 0.85) were present in the epicenter area and adjacent areas before the Changning earthquake, with a decrease in the b-values near the epicenter five months before the earthquake. Jiang and Feng (2021) studied the characteristics of the pre-earthquake b-value anomaly in Jiuzhaigou, China, for a 7.0-magnitude earthquake and found that this region had significantly low b-value anomalies before the earthquake.
Furthermore, Xie et al. (2022) studied the pre-seismic b-value variation of a 6.0-magnitude earthquake in Luxian, China, and found that anomalous low b-value features occurred in and around the source area. In summary, a long-term b-value decrease in a certain area reflects the high internal stress of the medium. The possibility of a significant rupture and a strong earthquake increases in these cases, so special attention should be paid to these areas. Spatiotemporal b-value scan results can provide information about the locations of future strong earthquakes and can be used to analyze the likelihood of strong earthquakes. They can reveal and infer the relative levels of stress accumulation in active ruptures at different stages, outline possible concave and convex bodies or closed fracture segments, and further determine the substantial earthquake hazard posed by active ruptures. The b-value has gradually become an effective tool for judging the level of regional stress, inferring the locations of future strong earthquakes, and determining potential earthquake source areas.
On September 5, 2022, at 12:52, a 6.8-magnitude earthquake occurred in Luding County, Ganzi Prefecture, Sichuan Province, China, at a depth of 16 km. The epicenter was located near the Moxi Fracture in the southeastern section of the Xianshui River Fracture Zone (29.59°N, 102.08°E), and the earthquake was a mainshock-aftershock type earthquake with a maximum intensity of IX. This earthquake caused 97 deaths, and 20 people were missing. The direct economic losses amounted to 154.80 billion yuan. Located on the eastern edge of the Qinghai-Tibet Plateau, the Xianshui River Fracture Zone is a northwest-trending arc-shaped left-lateral strike-slip fracture zone. This zone is also the boundary of the slip activity between the Bayankara Block and the Sichuan-Yunnan Block, starting in the north near the east valley of Ganzi and extending in the northwest-southeast direction, with a dip angle of roughly 55–80°. The zone passes through Luhuo, Daofu, Qianning, and Kangding and intersects with the Longmenshan Fault Zone and the Anning River Fault near asbestos, having a total length of approximately 400 km.
The Xianshui River Fracture Zone is divided into two major sections, northwest and southeast, with the Huiyuan Temple La Division Basin as the boundary. The northwest section has a sliding rate of less than 8.4 mm/yr, while the southeast section has a sliding rate of 4.0–5.2 mm/yr (Liang, 2019). The northwest section can be subdivided into the Luhuo section (sliding rate of 9.13 mm/a), the Daofu section (sliding rate of 8.57 mm/a), and the Qianning section (sliding rate of 7.67 mm/a), with a relatively homogeneous geometry. The southeast section can be subdivided into the Kangding section (sliding rate of 6.14 mm/a) and the Moxi section (sliding rate of 4.41 mm/a) (Li et al., 2019). The structure of the Kangding section is relatively complex, and it is mainly composed of three fractures, including the Seraha Fracture (sliding rate of 1.2 mm/yr), Foldotang Fracture (sliding rate of 1.3–3.4 mm/yr), and Yala River Fracture (sliding rate of 0.7–1.0 mm/yr), which are nearly parallel to each other.
The seismic activity within the Xianshui River Rift Zone is strong, with more than 50 earthquakes with magnitudes of 5.0 or higher occurring since 1700, including eight earthquakes with magnitudes of 7.0 or higher (Fig. 1). The surface rupture caused by the earthquakes covers almost the entire section of the rupture. The most recent strong earthquake with magnitudes of 5.8–6.3 occurred on November 22, 2014, more than a year before the strong earthquake in Luding. The Sichuan–Yunnan rhombic massif and the Bayankara massif exhibit the characteristic of strong earthquake activity with a high frequency. There have been a number of earthquakes in the Sichuan–Yunnan rhombic massif and in the boundary or interior of the Bayankara massif: on May 21, 2021, there were 5.8–6.4-magnitude earthquakes in Yangbi County, Dali, Yunnan; on May 22, 2021, there was a 7.4-magnitude earthquake in Maduo County, Qinghai; on January 2, 2022, there was a 5.5-magnitude earthquake in Ninglang County, Lijiang, Yunnan; on June 1, 2022, there was a 6.1-magnitude earthquake in Lushan County, Yaan, Sichuan; and on June 10, 2022, there was a 6-magnitude earthquake in Markang, Sichuan.
In view of this, we calculated the spatial and temporal b-value scans of the earthquake catalog before the Luding 6.8-magnitude earthquake in a large-scale region (100–103.1°E, 29–32°N) and a small-scale region (29–30.5°N, 101.5–103°E). Based on error analysis, we also analyzed the spatial and temporal variation characteristics of the pre-earthquake b-values and the influence of different scales on the spatial and temporal variation characteristics of the pre-earthquake b-value. In addition, the spatiotemporal image characteristics of the b-value were interpreted in relation to the distribution of moderate to strong earthquakes and active ruptures. The low b-value zones were further delineated to determine the potential seismic hazard zones.