On 21 May 2021, a devastating M_S6.4 earthquake struck Yangbi County, Yunnan Province, China （25.68°N, 99.88°E） at a focal depth of 8 km. Within 72 hours preceding this mainshock, the source area experienced two M_S4.3 and one M_S5.6 foreshocks, constituting a typical foreshock-mainshock-aftershock sequence. The abundant foreshock activities of this sequence provide valuable observational data for investigating the physical processes of earthquake nucleation.

In this study, we collected seismic waveform records from 42 stations within a 200 km radius of the M_S6.4 main shock epicenter and adopted the double-difference relocation algorithm （hypoDD） to precisely relocate 4 345 seismic events （M_L≥0）, including 280 pre-mainshock events. The relocation achieved a success rate above 92%, with average 2σ location uncertainties of ±53 m in latitude, ±55 m in longitude, and ±130 m in depth.

The Yangbi earthquake occurred in a structurally complex region on the southeastern margin of the Qinghai−Xizang Plateau. Its seismogenic fault is interpreted as a concealed secondary fault branching from the Weixi−Qiaohou fault system. The earthquake sequence exhibits a dominant NW−SE trending distribution with predominant right-lateral strike-slip motion. Focal mechanism solutions reveal consistent right-lateral strike-slip faulting, which is compatible with the regional tectonic stress field dominated by NW−SE compression. Spatial distribution indicates that all foreshocks occurred on the mainshock fault plane and were concentrated southeast of the mainshock epicenter.

To guarantee the statistical completeness of seismic catalogs, we determined the magnitude of completeness M_c combined the maximum curvature （MAXC） and goodness-of-fit test （GFT） methods based on the national seismic network dataset. The results yield an overall M_c-GFT of 0.55 for the entire sequence, with sub-sequence M_c-GFT values ranging from 0.15 to 1.05, i.e., 0.55 for the first M_S4.3 foreshock sequence, 0.15 for the second M_S4.3 foreshock sequence, 1.05 for the M_S5.6 foreshock sequence, and 0.45 for the aftershock sequence. Time-dependent M_c analysis shows fluctuating completeness magnitudes with an average value of 0.38. Corresponding M_c-GFT thresholds （M≥0.55, M≥0.15, M≥1.05, and M≥0.45） were adopted for subsequent p-value calculations of individual sub-sequences.

We applied the modified Omori law to quantitatively characterize the temporal decay behavior of seismicity and estimated the p-values via the maximum likelihood method under the non-stationary Poisson assumption. The results show that the two M_S4.3 foreshock sequences yield p-values of 0.69±0.16 and 0.58±0.04, respectively, whereas the M_S5.6 foreshock sequence contains insufficient events for reliable estimation. By contrast, the M_S6.4 mainshock aftershock sequence yields p＝1.15±0.03, consistent with the global average value of about 1.1. Notably, foreshock sequences exhibit distinctly lower p-values, indicating much slower seismicity decay relative to typical aftershock sequences. b-value analysis reveals a continuous decreasing trend throughout the foreshock stage: b＝0.486±0.067 for the first M_S4.3 foreshock, 0.391±0.024 for the second M_S4.3 foreshock, and 0.316±0.046 for the M_S5.6 foreshock. Following the mainshock, the b-value recovered to 0.485±0.009, suggesting progressively elevated differential stress approaching the mainshock rupture.

A double-logarithmic plot of cumulative earthquake number N（t） against elapsed time t was constructed to clarify the physical implication of p-values, where the asymptotic slope equals 1−p. A positive slope （ p＜1） represents slow seismicity decay, whereas a negative slope （ p＞1） indicates rapid decay. The foreshock sequences exhibit positive slopes of 0.31 and 0.42 （corresponding to p＝0.69 and 0.58）, while the aftershock sequence shows a negative slope of −0.15 （ p＝1.15）, directly demonstrating the contrasting decay patterns between slowly decaying foreshocks and normally decaying aftershocks.

These observations can be physically interpreted within the framework of rate-and-state friction and meta-instability theories. Low p-values of foreshock sequences reflect inefficient stress transfer when the fault plane is locked under high ambient stress, which prolongs secondary rupture triggering. This mechanism is also supported by laboratory results revealing a negative correlation between strain rate and p-value. The meta-instability stage refers to the transitional period from peak stress accumulation to dynamic instability, characterized by heterogeneous stress adjustment: localized stress weakening triggers foreshock activity, while the mainshock rupture plane remains highly stressed and locked. The declining b-values further verify enhanced stress heterogeneity as the stress release front propagates toward the earthquake nucleation zone.

Spatiotemporal migration analysis indicates that foreshock activities continuously contracted toward the mainshock epicenter, with contraction velocities of about 6.5 km/d and 4.0 km/d for the two M_S4.3 foreshock sequences, respectively, demonstrating progressive strain localization during the pre-mainshock stage. Overall, these lines of evidence suggest that the seismogenic fault entered a meta-instability state prior to the 2021 Yangbi M_S6.4 earthquake. This study provides new observational constraints for understanding earthquake nucleation mechanisms and improving precursor identification in the northwestern Yunnan tectonic region.