The rupture process of earthquake generally involves multiple fault activities. The seismogenic fault is generally not a single fault plane, but a combination of multiple fault planes. Based on the principle that clustered small earthquakes often occur near the fault plane, and assuming that the hypocenters obey three-dimensional normal distribution around the center of the sub-fault planes, the three-dimensional spatial structure of the Yangbi earthquake fault in Yunnan Province is estimated based on the fuzzy clustering algorithm. The results in this paper are estimated from the perspective of data analysis. The results will be more accurate if the comprehensive analysis can be carried out in combination with geological, geophysical exploration and other means. The fuzzy clustering analysis is mainly carried out for regions with dense seismic source data. Because the program compiled by this method runs fast on an ordinary computer and can be calculated many times in a short time, the best result can be obtained. In this study, the shape of fault zone can be quickly calculated and analyzed, the shape and spatial distribution of branch fault zone is roughly consistent with the seismic distribution, which verifies that this method has certain predictive effect and application value.
Firstly, GK(Gustafson, Kessel)fuzzy clustering method is used to obtain the partition matrix for all sub classes of hypocenter, then the outliers are removed by using the partition matrix and appropriate threshold, and the subclasses containing fault planes are extracted. Finally, the parameters of each fault plane(including position, strike and dip)with 95%confidence level are determined. It is inferred from the results that the hypocenters are distributed along the fault zone almost parallel to the Weixi-Qiaohou Fault and gradually divided into three fault branches to southeast direction. The east branch dips to southwest, which is the main fault, corresponding to two sub fault planes, with strike of 134.22°, 132.65°and dip angle of 87.14°, 81.96°, respectively; the west branch nearly parallels to the east branch with strike and dip of 129.45°and 74.77°, respectively. Except for the three main faults, a blind fault near the Weixi Qiaohou fault zone is identified in this study, with a strike of 235.66°and dip of 66.30°. In this study, we determined the fault structure of the Yunnan Yangbi earthquake sequence by fuzzy clustering algorithm, which is independent of other methods by using seismic wave data, geodetic data and geological data. It is of significance for tectonic and geodynamic studies.
This data analysis algorithm can be applied to the shape analysis and prediction of fault zone by a large number of such source data. In consideration of earthquake prediction and earthquake disaster assessment, the knowledge of fault network structure in the vicinity of large earthquakes will also help to test different assumptions about stress transfer effects.

The occurrence of earthquake is closely related to the crustal stress field. Earthquakes are caused by the failure of faults, driven by tectonic stress build-up in the Earth’s crust. The change of the stress field before a large earthquake is directly related to the earthquake preparation process. In order to understand the relationship between the tectonic stress field and the low-level seismicity of the Longmenshan Fault and adjacent region before the 2008 Wenchuan earthquake, the composite focal mechanism method based on P wave first motions of small and medium earthquakes is used to determine the tectonic stress field before the Wenchuan earthquake and analyze the temporal and spatial characteristics of the composite focal mechanisms.
Accurate earthquake location is a necessary factor to determine the focal mechanism and the stress field, especially to invert the focal mechanism and the stress field using P wave first motion of the near-field and local earthquake. Firstly, we estimated the hypocentral location and its uncertainty of a large number of small and medium earthquakes in Sichuan, China with a relatively accurate earthquake location method by considering the arrival time uncertainty. Secondly, the azimuth and take-off angle of the P wave first motion of a large number of small and medium earthquakes were calculated, whose focal mechanisms usually cannot be determined from small amount of P wave first motions, and the different weight values were given to the P wave first motion according to the hypocentral distance. Then we determine the composite focal mechanisms on the 0.5°×0.5° grid point in Sichuan area before the Wenchuan earthquake by using the composite focal mechanism method. The results show that the principal compressive stress(P)axes and principal tensile stress(T)axes of the composite focal mechanisms have obvious zoning characteristics, divided roughly by the Longmenshan Fault, the Xianshuihe Fault, and the Huayingshan Fault. The direction of the compressive axis of the northern Sichuan block from the west of the Longmenshan fault zone to the Longriba Fault is near EES-WWN, and that of the extension axis is nearly vertical, which results in the movement pattern of thrusting with right-lateral strike-slip in the Longmenshan fault zone and promoted the accumulation of stress field before the Wenchuan earthquake. The composite focal mechanisms in the south of the Xianshuihe Fault show a strike-slip pattern, which perfectly explains the sliding behavior of a series of major strike-slip earthquakes on the Xianshuihe Fault. The southeast segment of Huayingshan Fault presents a thrust pattern, which is consistent with the paleostress model proposed by predecessors. Thirdly, in order to understand the temporal variation of the crustal stress field before the Wenchuan earthquake, we calculate the focal mechanism rotation angles(FMOAs)of the annual composite focal mechanisms taking the Wenchuan earthquake as the time end to the focal mechanism of the Wenchuan earthquake obtained by different authors and institutions before the Wenchuan earthquake. It is found that the FMOAs of all the focal mechanisms of different authors and institutions reached its minimum value and were lower than its standard deviation 1 year before the Wenchuan earthquake. In view of the large rupture scale of the Wenchuan earthquake, we calculate the FMOAs of the annual composite focal mechanisms to the focal mechanisms of the Yingxiu-Hongkou initial rupture segment and Beichuan rupture segment before the Wenchuan earthquake. The results show that the FMOA of the Yingxiu Hongkou section decreased obviously, which indicates that this method can predict the location of future earthquake to some extent. Finally, in order to verify the uniqueness of convergence of stress field before the Wenchuan earthquake, we calculated the FMOAs of the annual composite focal mechanisms to the focal mechanisms of the other four reference points except the location of the Wenchuan earthquake in Sichuan area, and the results did not show the phenomenon that the stress direction of the four points tends to be consistent.
Above all, the temporal and spatial variation characteristics of the FMOAs of the stress field show that the focal mechanism and location of the Wenchuan earthquake are closely related to the convergence of the composite focal mechanism around the epicenter before the Wenchuan earthquake, which illustrates that the convergence tendency of the stress field to the Wenchuan earthquake rupture may provide a new idea to explore large earthquake precursor from tectonic stress field.

Based on the rupture model of Mainling M6.9 earthquake in Tibet on November 18, 2017, the spatial distribution of static Coulomb failure stress change at different depths are calculated respectively according to two different receiving fault selection schemes. The one scheme is that we set the parameters of receiving fault at different position to be consistent with the main shock; The other scheme is on the assumption that fault's orientation is randomly distributed under the ground, and we select the receiving fault which is most prone to slide under the influence of coseismic stress field produced by main shock. Therefore, the geometrical orientation of receiving fault will vary with space. According to the above two results of static Coulomb failure stress change, we discussed the static Coulomb stress influence produced by the main shock to short-term aftershocks and the Medog M6.3 earthquake in Tibet on April 24, 2019, respectively. The result shows that: 1)When the parameters of receiving fault are same with the main shock, the proportion of aftershocks in the positive zone of static Coulomb failure stress change is small at each depth. The focal mechanisms of aftershocks in the positive zone of static coulomb fracture stress are deemed similar to the main shock. We thought that they are motivated by the continuous rupture of the main shock. 2)Most of the aftershocks are in the negative zone of static Coulomb failure stress change at each depth. We inferred that this phenomenon which may be on account of the focal mechanisms of these aftershocks is quite different with the main shock. From the result of receiving fault to choose the most prone to slide under the coseismic stress field produced by main shock, we can clearly see that all the aftershocks are within the zone of static Coulomb failure stress change greater than the trigger threshold of 0.01MPa at different depths. It indicates that all the aftershocks are likely to be triggered. It was speculated that the aftershocks in the negative zone of static Coulomb failure stress change occurred in the crushed zone caused by violent rupture of the main shock. There are countless cracks in the crushed zone, and the orientation of these cracks is abundant. Perhaps, because most aftershocks occurred on these various cracks, their focal mechanisms are quite different from the main shock. The value of elastic constants will be reduced significantly in the crushed zone. All the results in this paper also indicate that considering the elastic constants difference between in and out of the source region is beneficial to accurately estimate the static Coulomb stress influence between earthquakes in the source region. 3)Different institutes and authors used different data and methods to get several different focal mechanisms of the Medog earthquake. According to these results, we calculated a central focal mechanism solution, which has a minimum difference with these focal mechanisms. On the basis of this central focal mechanism solution, the static Coulomb stress influence of the Mainling earthquake to the Medog earthquake is calculated quantitatively. Result indicates that the magnitude of static Coulomb failure stress change generated by the Mainling earthquake is quite small on both two nodal planes of the central focal mechanism solution of the Medog earthquake, this means that the Medog earthquake is independent of the Mainling earthquake.

Under the background of thrusting stress regime, a large number of strike-slip earthquakes occurred on the Miyaluo Fault during the Wenchuan earthquake sequence process, which is in the southern part of the Longmenshan Fault. In order to find the cause of their occurrence, stress tensors in subregions near the Miyaluo Fault are estimated. The result shows that in both north and south side of the Miyaluo Fault, the direction of principal compressive stress is nearly perpendicular to the Longmenshan Fault, and its dip is nearly horizontal, and the direction of tensile stress is nearly vertical. While in the Miyaluo fault zone, the direction of principal compressive stress is SWW-NEE, and its dip is nearly horizontal, the direction of principal tensile stress is NNW-SSE, also its dip is nearly horizontal. It is consistent with sinistral shear stress state in the Miyaluo fault zone. It was referred that the behavior of Miyaluo Fault during the Wenchuan earthquake sequence process was caused by tearing effect generated from unbalanced forces of two sides of the fault. To understand the rupture mode of the aftershocks in subregions as described above, the total seismic moment tensors are estimated by adding the corresponding component separately of the seismic moment tensor of aftershocks in each region. The result shows the similar trend of total seismic moment tensor components in the north and south side of the Miyaluo Fault(indicating the consistency of rupture mode in the north and south side of the Miyaluo Fault), and most seismic moment tensor components in the south side is higher than that in the north side, especially the compression component perpendicular to Longmenshan Fault and expansion component in the vertical direction. It indicates that thrusting component in the southeast direction in the south side is greater than that in the north side, and the thrusting difference causes the sinistral tearing effect of the Miyaluo Fault. We also find that the sinistral tearing component of the Miyaluo Fault is the same order of magnitude with the thrusting difference of its two sides, which indicates that the tearing effect of Miyaluo Fault can be completely explained by thrusting difference of its two sides. According to the analysis, we put forward the dynamic model of the Miyaluo Fault, which can explain the above phenomenon.

Based on the rupture models of the 2015 Pishan M_W6.4 earthquake and half space homogeneous elastic model, the Coulomb stress changes generated by the earthquake are calculated on the active faults near the earthquake region. The horizontal stress changes and the displacement field are estimated on the area around the epicenter. Results show that:(1)The Coulomb stress is decreased in the west of the western Kunlun frontal thrust fault(9.5×10³Pa), and increased in the east of the western Kunlun frontal thrust fault and the middle of the Kangxiwa faults. More attention should be taken to the seismic rick of the east of the western Kunlun frontal thrust fault; (2)Based on the analysis on the location of the aftershocks, it is found that most of the aftershocks are triggered by the earthquake. In the region of increased Coulomb attraction, the aftershock distribution is more intensive, and in the area of the Coulomb stress reduction, the distribution of aftershocks is relatively sparse; (3)The horizontal area stress increases in the north and south of the earthquake(most part of the Qaidam Basin and the northwest of the Qinghai-Tibet plateau), and decreases in the east and west of the earthquake(northern part of the Qinghai-Tibet plateau and eastern part of the Pamir Mountains). In the epicenter area, the principal compressive stress presents nearly NS direction and the principal extensional stress presents nearly EW direction. The principal compressive stress shows an outward radiation pattern centered on the epicenter with the principal extensional stress along the direction of concentric circles. The principal compressive stress presents NW direction to the west of the epicenter, and NE to the east of the epicenter. With the increase of radius, the stress level gradually decays with 10⁷Pa in the epicenter and hundreds Pa in the Maidan Fault which is in the north of the Qaidam Basin.

Based on the rupture models of the 2015 Nepal earthquake sequence and half space homogeneous elastic model, the displacement field near the epicenters is estimated. The horizontal components converge to the epicenters from north and south with maximum value of 871~962mm. The farther the epicenter distance is, the smaller of the horizontal displacement occurred. The displacement on the south side of the epicenters decreases more rapidly than that on the north side as the distance from the epicenter increased. Significant settlement occurred on the north side of the epicenters with maximum of 376~474mm, while large uplift occurred on the epicenters and its south side with maximum value of 626~677mm. Then, the displacement of the peaks of the Himalaya near the epicenters is estimated. The largest displacement occurred at the peak of Shishapangma with 393mm horizontal component and 36mm settlement. Mt. Everest, the world's highest peak, moves 36mm in nearly southward direction with 9mm settlement. The displacements of other peaks of the Himalaya are different with the epicentral distance and azimuth of the 2015 Nepal earthquake sequence.

A collapse happened in Pingyi County, Shandong Province, on December 25, 2015. The displacement field, stress field and Coulomb failure stress change on the Mengshan frontal fault generated by the collapse are calculated by using point collapse model in isotropic medium. The result shows that: (1) The maximum horizontal displacement is located at the center of the collapse with value of~18mm. The horizontal displacements are greater than 1mm within~5km of the collapse with its direction pointing to the collapse center. The maximum subsidence is located at the center of the collapse with the value of 4mm. The subsidence is greater than 1mm within ~3km of the collapse. The displacement field decays so rapidly that can be ignored at far away from the collapse for the shallow source, which caused local displacement field. (2) Influenced by the free surface, the contraction area stress within ~5km of the collapse with the order of 1000Pa and expansion area stress in farther away areas at depth of 2km are estimated. the expansion area stress of 1000Pa is estimated at the~5km from the collapse center. Then the expansion area stress decays to 100Pa at the distance of ~10km from the collapse. The maximum compressive and extensional principal stresses are estimated as 10000Pa at the depth of 2km. The compressive stress axes present radical direction pointing to the collapse within ~5km of the center. In farther away from the collapse, The extensional principal stress axes present radical direction pointing to the center of the collapse. With farther distance to the collapse, the compressive and extensional stress decay rapidly to the order of 100Pa. (3) The Coulomb failure stress on the northwestern part of the Mengshan frontal fault, which is known as active segment of the Mengshan frontal fault, is decreased by the collapse with maximum value of 2500Pa. Whereas, the Coulomb failure stress on the southeastern part of the Mengshan frontal fault, which is known as left-lateral normal slip fault segment in Quaternary period, is increased by the collapse with maximum of 2400Pa, to which attention would be paid in seismic hazard analysis.

Gansu and its adjacent areas are on the northeastern margin of the Qinghai-Tibet plateau. The study area locates at the junction of Alashan,Qilian,Qaidam and Ordos blocks. The tectonic structure is complicated in this area. The research of tectonic stress field in the study area has an important scientific significance for earthquake prediction of Gansu. Characteristics of present-day tectonic stress field is studied based on 245 M_L≥3.5 focal mechanism solutions since January 2001 to June 2012 in Gansu and its adjacent areas.
For solving the stress field,we follow Wan's(2000)method to solve the rake angle according to two nodal planes' strikes and dips of the focal mechanisms. We treat the stress tensor solution of each fault plane as the optimal solution of the area when the slip on the fault plane minus the angle between shear stress direction and strike is minimal. We use F test to get the confidence interval of the four parameters, as well as the confidence interval of the principal compressive and tensile stress axes. We divide the whole area into 1°×1°grids. In order to cover the whole study region and get the smoothed stress field,we select the data within the square areas of 2°×2° centered at the grid point. The direction and the relative size of the tectonic stress field in 2°×2° grid in Gansu and its adjacent areas are presented for the first time. These results show that the dip angles of maximum principal compressive stress axes of the whole region are generally small. And the dip angles of maximum principal tensile stress axes vary widely,which are small in the western part,and relatively larger in the east. It indicates that the tectonic stress field with horizontal action of compression acts as the major in the west. Many deep large strike-slip faults in Qilian seismic belt correspond with the results. The geological structure of southeastern area of Gansu is complex,and the characteristics of stress field indicate that strike-slip reverse faulting is likely to occur. Result of the inverted tectonic stresses also shows that maximum principal compressive stress axis strikes near NE on the plate margin of Tibet plateau. This is caused by Qinghai-Tibet plateau moving to the northeast. At the outer edge of the Tibet plateau plate,its strikes show a radiated pattern,i.e. NS in west part,NNE in the middle section,and NNW in the east. The reason is that Qinghai-Tibet plateau,when moving to the northeast,is encountered with stable Ordos and Alashan blocks,therefore the material moves to southeast. The stress directions show that the source of the stress field in Gansu and its adjacent areas is extrusion of the India plate to Eurasian plate. Our inversion results are similar with the previous results,indicating the correctness of the approach. The relative stress values are more than 0.5 in the western areas and less than 0.5 in the eastern areas. According to Wan's research(2011), the maximum principle compressive stress solutions are more reliable in the western area,while the maximum principle tensile stress solutions are more reliable in the eastern areas.
The results indicate a non-uniform stress field spatial distribution in Gansu area,and have certain reference significance for explaining the seismo-geological background and earthquake prediction research.

In this paper,we present a method which allows to calculate the mean stress field according to the total seismic moment released by earthquakes.The exact method is as follows: First,we calculate the scalar seismic moment released by each earthquake according to the statistical relationship between earthquake magnitude and its seismic moment; Second,we calculate the seismic moment tensor released by each earthquake according to the relationship between focal mechanism solution and seismic moment tensor; Then,we can get the total seismic moment tensor released in a specific time period of the study area; Finally,we calculate the eigenvector and eigenvalue of the total seismic moment tensor,the obtained eigenvector is corresponding to the mean stress field direction released by the study area. We tested the method by using the synthetic focal mechanism to which random error was added and with the focal mechanism data of Tangshan aftershock zone.The testing results show that,the released stress field of the study area obtained by our method is in consistency with the regional stress field. So our method can be applied to solve regional stress field.The more focal mechanism data used,the more stable the result would be,and closer to the real regional stress field. One of the advantages of this method is that it uses magnitude as the weight of each earthquake,so the contribution difference of the earthquake size in the stress field inversion can be better reflected. Another advantage is that it does not need to know which nodal plane of the focal mechanism is the real fault plane when we calculate stress field.

In this research,we made a primary research on the Coulomb stress triggering of the March 11,2011 M_W=9.0 Tohoku earthquake sequence by using the software of Coulomb 3.2,the earthquake rupture models obtained by Hayes and Guangfu Shao et al. , and the aftershocks data from Harvard CMT catalogue(Centroid Moment Tensor)and Japan F-net catalogue. Our results suggest that: Firstly,the M_W7.2 foreshock,which occurred on March 9,has stress triggering effect on the M_W9.0 main shock; Secondly,the statistical result of the aftershocks triggered by the main shock shows that different statistical results would be obtained when using different main shock rupture model,aftershock catalogue,equivalent friction coefficient and different nodal plane of focal mechanism as the receive plane. The minimum and maximum triggering rates of main shock to aftershock are 56.8%and 75.3%,respectively; and thirdly,when calculating the Coulomb stress by using earthquake focal mechanism,the shear stress on the two nodal planes is the same theoretically. However,in actual calculation,the shear stress would be different between the two nodal planes,due to the non-orthogonality of the two nodal planes or rounding off decimal places in the focal mechanism results. But,the difference of the shear stress on the two nodal planes is relatively small. More attention should be paid on the selection of receiver fault plane from the two nodal planes,when discussing the stress triggering of one specific earthquake or making statistics of aftershock triggering rate,because the selection of receiver fault plane would have a certain effect on the shear stress,and have greater effect on the normal stress,thus the Coulomb stress would be affected.

The precisely located earthquake catalogue is important to seismicity, seismic tomography and crustal stress inversion studies. It also has great application value in rapid report of an earthquake that just occurred. By considering the arrival time uncertainty, and the constraints on station elevation and seismic depth, we propose a relatively accurate method to estimate hypocentral location and its uncertainty based on inversion theory. Our method can combine the arrival times of Pg wave, Sg wave, Pn wave and Sn wave in hypocenter location, so it increases the location accuracy by involving more data; and it can be also used in local and regional earthquake location simultaneously. In order to test our location method, we located earthquakes by using the simulated data with different uncertainty of Pg,Sg,Pn,Sn arrivals. The result shows that the location determined by using our method is more accurate than that by using other method. We apply it to earthquakes occurring in the period from 2001 to 2008 in Sichuan area, and obtained a more clustered hypocentral distribution convergent to the fault zones. The result provides a solid foundation for studies of seismicity, geometry of the active faults and seismic tomography in Sichuan region. It is also helpful to study the seismicity precursors before the Wenchuan earthquake.

The co-seismic displacement field of the 2001 west of Kunlun Mountain Pass earthquake is obtained through the analysis of GPS data measured before and after the earthquake and leveling data measured in 1979 and 2002. Adopting these data,constrained by detail surface rupture data measured after the earthquake,we inverted the co seismic slip distribution along the seismic fault. The result shows that the depth of rupture lower limit is 14.2～21km (with 70% confidence level),with 17km as the optimal value. The result also shows that left lateral strike slip of 2～3m exists in the area between the Sun Lake segment and the west end of the main rupture zone,although surface rupture is not observed there. This is consistent with the result of InSAR data analysis. The subsurface rupture of this earthquake is ended at the Sun Lake in the west,but it seems that left lateral slip of 1.5～ 2.0m still exists within the range of 30km to the east of the surface rupture zone. The vertical displacement inverted in this study shows that to the west of 93°E the southern side of the fault is elevated,while to the east of 93°E the northern side of the fault is elevated. The released seismic moment estimated by geodetic data and surface rupture surveying is 6.1×10²⁰ N·m,consistent with the result inverted by seismic wave records.