The Stress State before the M_S 6.8 Luding Earthquake on 5 September 2022 in Sichuan, China: A Retrospective View Based on the b-Value

Abstract

On 5 September 2022 (BJT), Luding, located in southwestern Sichuan Province, China, experienced an M_S 6.8 earthquake. This earthquake occurred within the historical rupture zone of the 1786 M_S 7.75 event, part of the southern section of the Xianshui He Fault belt. Given the average 155-year recurrence interval for strong earthquakes in this area, the 236 years since the last event made this earthquake somewhat expected. However, prior to this event, we did not detect any anomalies indicating low surface b-values, which are often indicative of a high-stress state in the source area before strong earthquakes, as highlighted by numerous studies. Our research focused on the northern section of the eastern boundary of the Sichuan–Yunnan sub-block, encompassing the Xianshui He, Anning He, Zemu He, and Daliang Shan fault belts. We meticulously located earthquakes of M_L ≥ 1.5 from 2009 to May 2022. The catalog was divided into two periods: 2009–2014 and 2015–May 2022. Using an AIC-constraint method, we analyzed the changes in b-values (Δb) in the latter period compared to the former. Our findings revealed a significant abnormal Δb zone (Δb < −0.3), with a radius of approximately 50 km, when ΔAIC ≥ 2 was selected. Intriguingly, the epicenter of the recent Luding M_S 6.8 earthquake fell within this abnormal zone. Furthermore, we calculated the b-value cross-section for the southern section of the Xianshui He fault belt using a directory of precisely located small earthquakes. This revealed that the location, scale, and shape of the abnormally low-b-value area corresponded with the large displacement co-seismic area of the main earthquake, affirming the b-value’s effectiveness in identifying asperities. The b-value’s temporal evolution prior to the mainshock exhibited a nearly decade-long continuous decrease, signifying a long-term stress-loading process akin to that observed before many strong earthquakes. The b-value anomalies observed from different profiles before the Luding earthquake underline the necessity of a comprehensive, multi-dimensional analysis of such anomalies. Finally, our analysis indicates that nine earthquakes with M_S ≥ 6.5, including the Luding M_S 6.8 event, have contributed to increased Coulomb Failure Stress change (ΔCFS) in the Daofu (DF)–Kangding (KD) section of the Xianshui He fault belt and the northern section of the Anning He fault belt south of Shimian (SM), with amplitudes surpassing the 0.01 MPa threshold. This suggests the potential for strong earthquakes in these zones.

1. Introduction

The b-value is a pivotal parameter in seismology, quantifying the relationship between earthquake magnitudes and their occurrence frequency in a specific area. This metric plays a crucial role in decoding earthquake patterns and assessing future seismic risks. It transcends a mere statistical measure, serving as a vital gauge of the Earth’s crustal stress state. Generally, lower b-values signal higher stress levels in a region, while higher b-values often denote lower stress conditions. This inverse relationship has been substantiated through extensive studies on fault systems’ physical properties, creep–slip dynamics along fault lines, and the movement of pore pressures within the crust, as evidenced by seminal works [1,2,3,4,5].

The study of the b-value’s spatial and temporal evolution in areas prone to frequent, strong earthquakes is particularly fascinating. There is a rich history of successfully predicting the location and magnitude of potential strong earthquakes by identifying regions with low b-values, known as asperities. Notable examples include the San Jacinto–Elsinore fault system in Southern California [6], the Parkfield segment of the San Andreas fault [7], and the 2014 Parkfield M 6.0 earthquake analysis [5]. A consistent pattern observed before some major earthquakes is a prolonged, steady decrease in b-values, culminating in a significant seismic event, such as the 2008 Wenchuan M_w 7.9 earthquake in China [8] and the 2011 East Japan M_w 9.0 earthquake [9]. Regular monitoring of b-values’ spatial and temporal heterogeneity serves as a standard method for identifying precursors to potential large earthquakes.

In our quest to apply b-values more effectively in assessing seismic hazard in zones with a high probability of strong earthquakes, we conducted a retrospective analysis of the b-value’s temporal and spatial evolution before the M_s 6.8 Luding earthquake on 5 September 2022 in Sichuan, China. This study also explores the potential risks of strong earthquakes in the northern section of the eastern boundary of the Sichuan–Yunnan block.

2. b-Value Calculation Methods

In our estimation process of the b-value, we employed the widely recognized Gutenberg–Richter relationship [10] in statistical seismology, which is expressed as $\mathit{log}N=a-bM$, where N denotes the cumulative number of earthquakes with magnitude equal to or greater than M, and a and b represent constants. Here, the a-value indicates the level of seismic activity within the region, while the b-value, representing the slope of the magnitude–frequency distribution, is typically associated with the region’s geological structure and prevailing stress state.

Given the linear nature of this relationship, the Least Squares Method (LSM) has been traditionally utilized to estimate a- and b-values. However, LSM tends to assign equal weight across all magnitude bins, which can lead to disproportionate influences from smaller sample sizes in higher-magnitude bins on the estimated b-value. Such disproportionate effects can result in unstable b-value estimates, which might lead to unreliable predictions in seismic risk assessments.

To address these limitations, we recommend and have utilized the maximum likelihood estimation (MLE) method in this study. The MLE method treats the magnitude M as a continuous random variable and assumes that it follows a power-law distribution, as outlined by Aki [11] and Utsu [12]. They provided foundational formulas for the maximum likelihood estimation of the b-value, enhancing the precision of b-value calculations by effectively accounting for different sample sizes across magnitude bins. This approach significantly reduces the biases associated with LSM, thereby providing more stable and reliable estimates of b-values. Based on this, Aki and Utsu separately provided expressions for the maximum likelihood estimation of the b-value:

$$\widehat{b}=\frac{\log \left(e\right)}{\overline{M}-M_C}$$

(1)

$\overline{M}$ represents the average magnitude, and $M_C$ is the magnitude of completeness. Utsu [13] further refined this method, improving the accuracy of the b-value estimations under varied seismic conditions:

$$\widehat{b}=\frac{\log \left(e\right)}{\overline{M}-(M_C-\Delta M/2)}$$

(2)

The MLE method calculates the b-value based on the probability density values across different magnitude segments, avoiding the disproportionate weight issues characteristic of the LSM. This enhancement in methodological approach leads to more accurate and stable b-value estimates, which are crucial for understanding the underlying stress states in seismic regions.

Recent research emphasizes the critical role of accurate b-value estimation in understanding regional stress levels and seismic risk. Studies have demonstrated that lower b-values are often associated with high seismic coupling and geological asperities, particularly in regions like the Chilean megathrust, highlighting areas of significant stress accumulation that are prone to large earthquakes [14]. For instance, Tormann et al. (2015) observed rapid changes in b-values before and after the Tohoku-oki earthquake, providing insights into the randomness of megathrust earthquakes and the dynamics of stress recovery [15]. This study further illustrates how sudden shifts in b-values can signify underlying stress adjustments that might not be apparent from surface observations alone.

Other investigations have linked rapid changes in reservoir water levels to lower b-values, suggesting that such environmental modifications can induce seismic activity through increased pore pressure and resultant stress [16]. Moreover, a trend of decreasing b-values preceding major earthquakes has been observed, indicating rising shear stress within fault zones. These findings collectively validate the use of b-values as reliable indicators of stress variations, serving as essential tools for seismic risk assessment and the development of mitigation strategies [17].

Thus, by employing Utsu’s refined MLE formula for b-value calculation, we aim to enhance the reliability of seismic activity forecasts. The uncertainty of the b-value can becan be estimated by

$$\widehat{\sigma }=\frac{\widehat{b}}{\sqrt{N}}$$

(3)

3. Tectonic Setting

The clockwise rotation of the Tibetan Plateau, as delineated by Niu et al. [18], has fragmented the tectonic landscape into distinct sub-blocks [19] (illustrated in Figure 1). These sub-blocks are traversed by deep, major faults, each with unique kinematic attributes. The northward Bayan Har sub-block’s eastward trajectory is halted by the stable South China sub-block, culminating in the formation of the thrust-type Longmen Shan fault zone at their interface [20]. This zone has witnessed significant seismic events—notably, the 2008 Wenchuan M_W 7.9 [21] and the 2013 Lushan M_W 6.6 earthquakes [22]. After these events, Gui noted a decrease in stress levels in the Dayi area but an increase between Tianquan and Baoxin, suggesting dynamic stress redistributions, which have implications for future seismic activities [23]. South of Bayan Har, the Sichuan–Yunnan sub-block, emerging from the southeastern escape of the Qinghai–Tibet Plateau [24], is characterized predominantly be strike-slip and combined strike-slip with normal faults.

The Xianshui He–Anning He–Zemu He fault zone, marking the northern boundary of the Sichuan–Yunnan sub-block’s eastern edge, has been extensively studied due to its rich history of strong earthquakes [25]. Jin discussed the locking and slip deficit of the Xianshuihe fault, indicating that the varying locking depths across this fault have significant implications for earthquake potential, suggesting that different segments might respond differently to tectonic stresses [26]. Shao et al. examined the evolution of Coulomb stress over 200 years, noting that areas like Bamei, Selaha, and Kangding, which exhibit stress enhancement, are likely to experience strong earthquakes [27].

The Xianshui He fault belt (F1 in Figure 1b), commencing in Ganzi (GZ) and tapering off near Shimian (SM), stretches southeastward through Luhuo (LH), Daofu (DF), Kangding (KD), and Luding (LD), covering approximately 400 km. Since the late Cenozoic era, it has experienced notable sinistral strike-slip movement, amassing a total displacement of 60 km [28]. This fault belt is characterized by significant segmentation, with its slip rate diminishing from northwest to southeast, averaging around 10 mm/a [29,30,31,32,33,34,35].

To the north, the Anning He fault belt (F2 in Figure 1b) extends from Shimian (SM) and continues southward past Mianning (MN) to just south of Xichang (XC). Since the late Quaternary Period, it has displayed pronounced sinistral strike-slip and thrust movements. This 160 km long fault strikes north–south and dips either east or west, with angles ranging from 60° to 80° [33,36]. Zhu et al. developed a three-dimensional finite element model to analyze the stress state and fault segmentation within the Anninghe–Zemuhe–Xiaojiang faults region [37], finding that some locations with higher stress correspond to low-b-value areas, suggesting a complex interplay of factors that influence fault behavior [38]. The northern and southern segments exhibit slip rates of approximately 2.8–3.7 mm/a and 5–8 mm/a, respectively, with six of the eight recorded M_S > 6.0 earthquakes occurring in its southern segment [39].

The Zemu He fault belt (F3 in Figure 1b) continues the sinistral strike-slip pattern of the Xianshui He and Anning He faults. Starting from Xichang (XC) and extending to Qiaojia (QJ) in the south, GPS studies indicate a slip rate of about 6 mm/a [40]. Paleoseismic research suggests that eight M_S ≥ 7 earthquakes have occurred from the end of the Late Pleistocene Period to the present, with a recurrence interval estimated at approximately 1000 years [41].

Lastly, the Daliang Shan fault belt (F4 in Figure 1b), located east of the Anning He fault, is characterized by sinistral strike-slip movement. Since the Holocene Period, its slip rate has been recorded at approximately 3–4 mm/a [40,42,43,44,45,46]. Recent GPS analyses further highlight its evolving seismic potential by revealing substantial slip deficits and a strong potential for significant earthquakes [47].

The Luding earthquake, registering a magnitude of 6.8, struck in the Moxi area, located in the southeastern part of the Xianshui He fault belt. This area forms a crucial link between the northern termini of the Anning He and Daliang Shan fault belts [44,48]. The southeastern segment of the Xianshui He fault zone is notable for having one of the longest intervals without seismic activity in the history of the fault [25,49,50]. The accumulated strain, calculated from the slip rate and the elapsed time since the last significant event, is estimated to be between 2.3 and 3.2 m [49]. This led researchers, prior to the earthquake, to classify this segment as a high-risk area for a major seismic event, potentially reaching magnitudes of 7.0 to 7.37 [49,50].

The study region, outlined by polygons with blue lines in Figure 2, is situated in the northern portion of the eastern boundary of the Sichuan–Yunnan sub-block. The 2022 Luding M_S 6.8 earthquake occurred centrally within this designated area. This area encompasses not only a section of the southern Longmen Shan fault belt but also the Xianshui He, Anning He, Zemu He, and Daliang Shan fault belts in its core. Collectively, these fault belts form the northern segment of the eastern boundary of the Sichuan–Yunnan sub-block, sharing a common dynamism and movement pattern—a left-lateral strike-slip motion attributed to the southeastward shift of the Qinghai–Tibet Plateau. The completion of the “post-disaster reconstruction project” following the 2009 Wenchuan M_W 7.9 earthquake significantly enhanced earthquake monitoring capabilities in Sichuan [51]. To ensure data completeness and continuity, the year 2009 was selected as the starting point for our analysis.

4. Accurate Earthquake Locating

To ensure precise initial data for the subsequent b-value cross-section calculations, we need more seismic phase samples with more accurate arrival time data to form reasonable constraints on earthquake locating. We selected all M_L ≥ 1.5 earthquakes, over 130,000, recorded by 230 stations across Sichuan from 2009 to the end of 2022. To streamline the computation and mitigate large-scale ellipsoid correction errors, we divided Sichuan into 2° × 2° sub-areas. An AI-based auto-picker constructed by the CNN network was applied to refine and supplement the phase arrival times [52]. To keep the phase arrival time more accurate, we double-checked the phases whose arrival time differences were equal to or greater than 0.5 s between the AI and manual phase files. This workflow was proven to be valid and effective in the M_S 6.8 Luding earthquake sequence recognition [53]. We compared the results of manual and artificial intelligence recognition in a sub-area, and it can be seen that artificial intelligence corrected the errors of manual recognition and increased the amount of data by about 5% (Figure 3).

The earthquake location procedure adopted here is described in the following. Initially, Hypoinverse2000 [54] was employed for initial locating in each sub-area using a unified velocity model [55], yielding absolute location results. Subsequently, tomoDD [56] was used for high-precision relative locating, leveraging a detailed 0.2° × 0.2° three-dimensional velocity structure of the Sichuan–Yunnan area provided by Liu et al. [57]. We then amalgamated the location results from each sub-area, prioritizing the relative location results from tomoDD (marked as 2, black circle in Figure 4a). Events that were not amenable to relative locating due to factors like “air quakes” or connection loss were assigned absolute locating results from Hypoinverse2000 (marked as 1, green circle in Figure 4a). The few remaining earthquakes with fewer than three observations, which could not be numerically calculated for source location, were cataloged using their original parameters (marked as 0, purple circle in Figure 4a).

Ultimately, we identified 16,203 earthquakes with M_L ≥ 1.5 in the study area. The distribution of these events by flags 0, 1, and 2 is 689 (4%), 1959 (12%), and 13555 (84%), respectively. The average horizontal error for events flagged as 2 is less than 1 km, and the vertical error ranges between 1 and 2 km, as determined by the bootstrap test [58]. Flag = 0 events predominantly occur at the boundaries of the seismic network. The average deviation between flag = 1 and flag = 2 events is 0.4 km horizontally and 1.3 km vertically. The focal depth is mostly within 10 km (Figure 4b), but it escalates to nearly 30 km in a small area south of Shimian (SM), a phenomenon previously reported [59] that is yet to be fully explained.

Given the occurrence of the Lushan M_S 6.1 earthquake on 1 June 2022 along the southern section of the Longmen Shan fault belt adjacent to our study area, we designated the study period from 2009 to 31 May 2022 to preclude the influence of seismic sequences and mainshock-triggered effects. We computed the minimum magnitude of completeness (M_C) using the Maximum Curvature method [60,61] with a 0.1° × 0.1° step and a 30 km search radius. The M_C predominantly hovers around M_L = 1.5 across the study area, coinciding with our earthquake locating work’s starting magnitude. It increases to about M_L = 1.7 south of Ganzi (GZ) due to fewer stations, and, near Qiaojia (QJ) in the southern study area, the Mc ascends to M_L 1.8–1.9, being at the seismic network’s edge (Figure 5a). Using the maximum likelihood method [11] and the M_C-varied results from Figure 5a, we generated a b-value map, setting the sample’s lower limit in each grid to 30, with magnitudes exceeding Mc. This map reveals that most areas, including the future Luding M_S 6.8 earthquake’s epicenter, fall within a normal range of 0.7~1.1. The only exception is the abnormally low-b-value area (b < 0.7) in the southern section of the Longmen Shan fault belt (Figure 5b).

Acknowledging the potential for underestimation of the minimum magnitude of completeness (M_C) when using the Maximum Curvature method [62], we opted to set M_C at a conservative M_L = 2.0. The newly calculated b-value map (Figure 5c) revealed no significant deviation from the earlier version. To minimize the impact of arbitrary parameter selection on the outcomes, we employed the Hierarchical Space-Time Point-Process Model [63] for recalculating the b-value map, based on M_C = M_L 2.0 (Figure 5d). This approach yielded a smoother distribution of b-values, yet the overall trend remained consistent with the previous maps. Intriguingly, regardless of the method applied, the epicenter of the impending Luding M_S 6.8 earthquake was not situated in a low-b-value zone.

This observation contradicts conventional wisdom, which typically associates strong earthquakes with low-b-value areas [6,7,64]. To unravel this anomaly, we investigated the stress distribution in the Xianshui He fault zone prior to the Luding M_S 6.8 earthquake, examining the temporal and spatial characteristics of the b-value. The 2014 Kangding M_S 6.3 earthquake, which occurred north of the Luding M_S 6.8 event on the same fault belt, had exerted a positive Coulomb stress influence on the southern section of the Xianshui He fault belt [65]. To isolate the impact of this earthquake, we divided the study period into two phases, using 2015 as the demarcation point: the first phase spanned from 2009 to 2014, and the second from 2015 to 31 May 2022.

We applied a P-test based on the Akaike Information Criterion [66] to quantitatively evaluate the b-value trends across these two stages. As proposed by Utsu [67], the difference in AIC (i.e., ΔAIC) for the same statistical window between different stages can be defined as follows:

$$\Delta AIC=2\left({\displaystyle {\sum }_{\mathrm{i}=1}^2{N}_{\mathrm{i}}\ln b_i}\right)-2$$

(4)

N_i and b_i are the sample size and b-value in the ith window, respectively. The probability that the events in the two sample windows are from the same population can be derived from the AIC:

$$P=\exp (\frac{-\Delta AIC}{2}-2)$$

(5)

A significant change in the b-value is considered to have occurred when ΔAIC ≥ 2 (P ≈ 0.05); when ΔAIC > 5 (P ≈ 0.01), it is judged to be highly significant.

The results show that, when we choose ΔAIC ≥ 2, the southern segment of the Xianshui He fault belt has the only large-scale anomaly area in the study area, with a radius of about 50 km and a ΔAIC value of around 5 (Figure 5a), corresponding to Δb ≤ −0.3, reflecting significant changes in b-values between the two periods of 2009–2014 and 2015–31 May 2022. Additionally, the b-value in the latter period significantly decreased compared to the former. The anomaly area was set at the intersection and bending parts of faults, where significant strains can accumulate [68,69]. The future Luding M_S 6.8 earthquake (yellow star in Figure 6) is located in this anomaly area (Figure 6b). Considering that some earthquake cases indicate an increase in seismic activity before strong earthquakes [70,71,72,73] or some special spatiotemporal migration patterns [74,75], we analyzed the spatiotemporal distribution characteristics of earthquakes of M_L ≥ 3.0 within a 100 km range, with the Luding M_S 6.8 earthquake as the center (Figure 6c). We noticed that, since 2015, the seismicity rate of earthquakes of M_L ≥ 3.0 within a range of 50 km has been higher than that of the background period, which is also the spatiotemporal domain where the b-value exhibits anomalies. Although we did not observe any obvious migration pattern before the mainshock, a small magnitude swarm near the future mainshock occurred from December 2021 to March 2022 (red rectangle in Figure 6c). More detailed research is needed to determine the relationship between these small earthquakes and the major earthquakes that will occur in the recent future that will occur six months later. The ΔAIC value of the adjacent southern segment of the Longmen Shan fault belt is as high as 15, indicating that seismic activity changes intensely there. However, the Δb-value in this area is positive. The Qiaojia (QJ) area in the southern part of the study area also has a high ΔAIC value, which may be due to weak monitoring capabilities at the boundary of the station network (Figure 6a).

Along the strike of the Xianshui He fault belt, we have drawn a seismic profile from Daofu (DF) to the south of Shimian (SM) (see Figure 3b for the location of the profile). The projected width of the profile is 30 km on each side, and the b-value is calculated using a rectangular statistical window with a horizontal width of 10 km and a vertical width of 3 km. The sliding increment in both directions is 1 km. At the same time, it is required that there be at least 30 samples with M_L ≥ 2 in the statistical window.

The focal profile from 2009 to 2014 shows (Figure 7a) that the clustering characteristic is significant. The earthquakes from Daofu (DF) to Shimian (SM) are mainly distributed within a depth of 10 km (cluster1, C1), while the number of earthquakes within a depth of 8 km to the Shimian (SM) area is scarce, and the earthquakes are clustered between 8 and 14 km in depth (cluster2, C2). Another cluster is located south of Shimian (SM), which is clustered in the depth range of 17–30 km (cluster 3, C3). We noticed that the three clusters are not spatially continuous, especially since there is a seismic gap of about 20 km in length between C1 and C2 (Figure 7a dotted box), and the future Luding M_S 6.8 earthquake sequence occurred near the boundary of this seismic gap. The entire profile does not show a significant low-b-value region in this period.

From 2015 to May 2022, the earthquake distribution showed significant changes compared to the previous period (Figure 7b): earthquakes in C1 extended into and broke the earthquake gap. At the same time, the scale of C2 and C3 expanded and connected. The b-value profile showed that, during this period, a 50 km low-b-value anomaly area (b < 0.7) formed in the lower boundary area of C1 near the seismic gap. The future Luding M_S 6.8 earthquake is just located in this anomaly area. Combined with the co-seismic slip map (Figure 7c), we can see that the location, scale, and shape of the large co-seismic slip area are highly consistent with the low-b-value area, and the earthquake gap is filled with the Luding M_S 6.8 aftershock. The low-b-value anomaly area and the seismic gap constitute this earthquake sequence’s rupture range.

5. Temporal Evolution of b-Value before the M_S 6.8 Luding Earthquake

We selected the earthquake catalog within a 50 km radius centered on the Luding M_S 6.8 earthquake (the abnormal region identified in Figure 6) from 2009 to 31 May 2022. Using a statistical window of 300 events and an increment of 1 event, we calculated the temporal evolution of b-values before the Luding M_S 6.8 earthquake using the maximum likelihood method with M_C = M_L 2.0. The results showed that there had been a decline from the second half of 2012 to the end of 2021, from 1.3 in 2012 to 1.0 in 2022 (Figure 8a). Considering that the b-value error is around 0.1, we believe that this decline is significant. The main period of decrease in the b-value was from 2013 to 2018, during which more earthquakes with M_L ≥ 3.0 occurred compared to other periods (Figure 8b). Since the end of 2021, there had been a slight rebound of b-values for about four months, with a magnitude of 0.05, corresponding to a small-magnitude earthquake cluster near the future mainshock (red rectangle in Figure 6c). This small-scale, short-term phenomenon has occurred multiple times in the past, but there has been no subsequent strong earthquake, so it is difficult to say that it was a precursor to the Luding M_S 6.8 earthquake. The long-term decrease in b-values reflects the continuous accumulation of stress in the region; similar phenomena have occurred before many strong earthquakes [8,9].

To validate the observed phenomena, this study plotted the Gutenberg–Richter (G–R) relationship, fitting graphs for two different periods. Specifically, data from 2010 to 2013 are represented by red dots in Figure 9, while data from 2018 to 2021 are shown with blue dots. Comparison of Figure 9 clearly shows that, despite the identical duration and similar levels of seismic activity (in terms of both frequency and intensity) between the two periods, the later period recorded more earthquakes of magnitude 3.5 and above (4 compared to 3 in the earlier period), and the maximum magnitude increased from 4.0 in the earlier period to 4.9 in the later period. Consequently, the b-value for the later period dropped to 0.91, below the earlier period’s 1.18. This discrepancy is clearly reflected in the b-value temporal evolution curve, thereby supporting the reliability of the observed decrease in b-values over time.

6. Discussion

The occurrence of the Luding earthquake was inevitable, whether considering the historical seismic recurrence cycle or the high deformation-locking area. Since 1400, 23 M_S ≥ 6.5 earthquakes have been recorded in the study region, and the rupture zones almost cover the entire boundary fault (Figure 10). Since the 21st century, there have been two M_S ≥ 6.0 earthquakes on the Xianshui He fault belt, namely, the Kangding M_S 6.3 in 2014 [76] and the Luding 6.8 in 2022 [77]. The section from Kangding (KD) to Shimian (SM) is located in the historic rupture zone of the Kangding south M_S 7¾ in 1786; the epicenter of the Luding M_S 6.8 earthquake is located at the southern end of the historic rupture zone [35]. The Xianshuihe Fault Zone, as one of the fault zones with the most frequent strong seismic activity, has a significant segmented seismic recurrence cycle. The Moxi section where the Luding M_S 6.8 earthquake is located has a characteristic seismic recurrence cycle of 155 years [50]. Before the Luding M_S 6.8 earthquake, the 236-year elapsed time had already passed far beyond the recurrence period.

Li et al. [78] explained this inevitability from another perspective. They used the DEFNODE algorithm [79] to invert the fault locking of the Xianshui He fault belt based on GNSS data from 2016 to 2020. The results showed that the Luding M_S 6.8 earthquake sequence was located in the high-locking region of the southern section of the Xianshui He fault belt (PHI close to 1, Figure 11), indicating that the Luding seismic source area was in a state of stress accumulation during this period. The Luding M_S 6.8 earthquake tore the southern part of the 1786 M_S 7.75 rupture zone. However, considering the relatively low fault-locking degree, the strong earthquakes are not urgent in the northern part of the historic rupture zone (Figure 11).

Although numerous examples of earthquakes have demonstrated that the low-b-value area obtained from surface scanning is effective in predicting the location and magnitude of future strong earthquakes [5,6,7], our research indicates that neither the fixed-window method nor the non-fixed-window method (HIST-PPM) revealed a significant low-b-value state in the future epicenter area, resulting in false negatives, whereas Δb could somewhat solve this problem. It seems feasible to use AIC constraints to highlight the Δb-abnormal areas and delineate the location of future strong earthquakes from our example. In addition, using a precise location catalog to calculate the spatial and temporal b-value profiles can help discover the regions and periods of b-value anomalies from different perspectives.

The co-seismic stress transfer produced by large earthquakes has a profound impact on the occurrence of successive earthquakes [80], while the Changes in Coulomb Failure Stress (ΔCFS) can describe the transfer pattern quantitatively, which is defined as ΔCFS = Δτ + μΔσ, where Δτ is the change in shear stress, Δσ is normal stress change, and μ is the coefficient of friction [81]. We took 10 M_S ≥ 6.5 earthquakes in the Sichuan region since 1973 as sources (including the 2022 Luding M_S 6.8 earthquake, [82]). We used Coulomb 3.3 [83] to calculate the ΔCFS maps in our study region based on the Xianshui He fault belt (Figure 12a) and the Anning He fault belt (Figure 12b) as the receiving faults. Two segments with significant stress increases can be found in the two maps: the DF–KD segment in the Xianshui He fault belt and south of SM in the northern Anning He fault belt. The ΔCFS of the two segments is greater than the trigger threshold of 0.01 MPa [84,85], which could, therefore, infer that the segments carry a high risk of strong earthquakes.

7. Conclusions

In the retrospective analysis of the 2022 Luding M_S 6.8 earthquake, the event appeared inevitable based on the recurrence interval of strong earthquakes in the region. However, conventional surface b-value scanning prior to the earthquake did not detect any low-b-value anomalies at the epicenter. This lack of detection resulted in a prediction failure.

To gain a deeper understanding of the b-value response before the earthquake and to assess the potential risk of strong earthquakes in the study area, we divided the earthquake catalog into two stages, from 2009 to 2014 and from 2015 to May 2022, and conducted segmented analysis. The AIC-constrained Δb (change in b-value) effectively revealed significant areas of b-value change, pointing out potential locations for future strong earthquakes. The Δb and ΔAIC maps calculated for these two periods show that, under the condition of ΔAIC ≥ 2, there is a clear abnormal Δb area with a radius of about 50 km (Δb < −0.3) where the Luding M_S 6.8 earthquake occurred. This low-Δb-value anomaly area provides a spatial reference for the spatiotemporal evolution analysis of b-values.

Furthermore, the b-value profiles derived from precise relocation show that the abnormal low-b-value area corresponds to the position, size, and shape of the mainshock’s large-slip co-seismic zone, confirming that b-values can reveal areas of stress concentration on faults and that the aftershocks triggered by the mainshock filled the seismic gaps that existed before the earthquake. The continuous decline in b-values over the past decade reveals that the Luding M_S 6.8 earthquake source area has undergone a long-term stress-loading process, a pattern that is consistent with the b-value evolution before other major earthquakes and the fault-locking results inverted from GNSS data. Given that b-values are dynamic functions of time and space, one-dimensional analysis may lose multidimensional information; therefore, comprehensive analysis from multiple dimensions such as surface, cross-section, and time is crucial for accurately identifying b-value anomalies.

Finally, the Coulomb failure stress change analysis shows that 10 historical significant earthquakes, including the Luding M_S 6.8 earthquake, have increased the stress along the Dadukou (DF) to Kangding (KD) section of the Xianshuihe fault zone south of Ya’an (SM) and the northern section of the Anning River fault zone, with the stress magnitude exceeding the threshold of 0.01 MPa, indicating that these areas still have the potential for strong earthquakes.