Investigating relationships between temporally- and spatially-related continental earthquakes is important for a better understanding of the crustal deformation, the mechanism of earthquake nucleation and occurrence, and the triggering effect between earthquakes. Here we utilize Global Positioning System (GPS) velocities before and after the 2008 Mw 7.9 Wenchuan earthquake to invert the fault coupling of the Longmenshan Fault (LMSF) and investigate the impact of the 2008 Mw 7.9 Wenchuan earthquake on the 2013 Mw 6.6 Lushan earthquake. The results indicate that, before the 2008 Mw 7.9 Wenchuan earthquake, fault segments were strongly coupled and locked at a depth of ~18 km along the central and northern LMSF. The seismic gap between the two earthquake rupture zones was only locked at a depth < 5 km. The southern LMSF was coupled at a depth of ~10 km. However, regions around the hypocenter of the 2013 Mw 6.6 Lushan earthquake were not coupled, with an average coupling coefficient ~0.3. After the 2008 Mw 7.9 Wenchuan earthquake, the central and northern LMSF, including part of the seismic gap, were decoupled, with an average coupling coefficient smaller than 0.2. The southern LMSF, however, was coupled to ~20 km depth. Regions around the hypocenter of the 2013 Mw 6.6 Lushan earthquake were also coupled. Moreover, by interpreting changes of the GPS velocities before and after the 2008 Mw 7.9 Wenchuan earthquake, we find that the upper crust of the eastern Tibet (i.e., the Bayan Har block), which was driven by the postseismic relaxation of the 2008 Mw 7.9 Wenchuan earthquake, thrust at an accelerating pace to the Sichuan block and result in enhanced compression and shear stress on the LMSF. Consequently, downdip coupling of the fault, together with the rapid accumulation of the elastic strain, lead to the occurrence of the 2013 Mw 6.6 Lushan earthquake. Finally, the quantity analysis on the seismic moment accumulated and released along the southern LMSF show that the 2013 Mw 6.6 Lushan earthquake should be defined as a “delayed” aftershock of the 2008 Mw 7.9 Wenchuan earthquake. The seismic risk is low along the seismic gap, but high on the unruptured southwesternmost area of the 2013 Mw 6.6 Lushan earthquake.

Because of the nonlinearity nature of contacts, real contact information in discontinuous computation is unknown before analysis. In standard three-dimensional (3D) discontinuous deformation analysis (3D DDA), the indeterminacies of the contacts arise from two aspects: the singular block boundaries and the nonsmooth frictional behavior. Because the contact occurs only at the first entrance position, the first entrance theory is the general physical law of block contacts. Therefore, the first entrance approach is proposed in this study to select the first entrance plane and to evaluate the related first entrance points, along which the contact forces would be applied. Furthermore, the procedure and criteria of the open-close iteration (OCI) for the 3D frictional contact problem is presented to determine the most suitable status and force of each contact. With this rigorous method, the information of each contact can be determined, such that the two kinds of the contact indeterminacies are resolved. The effectiveness of the proposed method is verified by three numerical tests, suggesting that the proposed method works at a practical level in accuracy and robustness.

The Xianshuihe Fault Zone is one of the most historically seismically active regions in mainland China. However, the seismicity along this fault zone has been quiescent for the past 40 years, since the Daofu M6.9 earthquake in 1981. Understanding its current deformation patterns and fault coupling characteristics is of great significance to estimate the potential risk of strong earthquakes. In this study, we analyzed the dynamic deformation and fault coupling characteristics along the Xianshuihe Fault Zone using Global Navigation Satellite System (GNSS) data for 1999–2007 and 2016–2020. The results show that the deformation pattern of the Xianshuihe fault zone underwent a dynamic adjustment after the 2008 Wenchuan M_w7.9 and 2013 Lushan M_w6.6 earthquakes, i.e., the maximum shear strain accumulation rates of the Luhuo and Daofu sections significantly decreased from 6.0 × 10^–8/a to 3.2 × 10^–8/a, while that of the southeastern segment (i.e., Kangding and Moxi sections) increased from 4.5 × 10^–8/a to 6.2 × 10^–8/a. Additionally, the slip rate and deformation width of the Xianshuihe Fault Zone also changed during these two periods. Combined with the near-field cross-fault observation data, we suggest that the surrounding strong earthquakes Wenchuan and Lushan had evident differential impacts on the deformation pattern of the Xianshuihe Fault Zone. The fault-coupling inversion results show that the locking degree of the Xianshuihe Fault Zone continued to increase after the Wenchuan and Lushan earthquakes, especially the Qianning and Moxi sections increased significantly, with an average coupling coefficient of greater than 0.9 and left-lateral slip-rate deficits of ~ 5 mm/a and ~ 8 mm/a, respectively. In contrast, the locking degree of the Kangding section decreased with almost no slip-rate deficit, which is in a state of creeping status. The analysis of the recent rupture history and strain accumulation characteristics of the Xianshuihe Fault Zone indicates that both the Qianning and Moxi sections have a high seismic potential for the next strong earthquake in the Xianshuihe Fault Zone. Graphical Abstract