Coseismic Coulomb stress changes induced by a 2020-2021 M_(W)>7.0 Alaska earthquake sequence in and around the Shumagin gap and its influence on the Alaska-Aleutian subduction interface

Three M_(W)>7.0 earthquakes in 2020-2021 occurred in the Shumagin seismic gap and its adjacent area of the Alaska-Aleutian subduction zone,including the Mw7.8 Simeonof thrust earthquake on July 22,2020,the M_(W)7.6 Sand Point strike-slip earthquake on October 19,2020,and the M_(W)8.2 Chignik thrust earthquake on July 29,2021.The spatial and temporal proximity of these three earthquakes prompts us to probe stress-triggering effects among them.Here we examine the coseismic Coulomb stress change imparted by the three earthquakes and their influence on the subduction interface.Our results show that:(1)The Simeonof earthquake has strong loading effects on the subsequent Sand Point and Chignik earthquakes,with the Coulomb stress changes of 3.95 bars and 2.89 bars,respectively.The Coulomb stress change caused by the Sand Point earthquake at the hypocenter of the Chignik earthquake is merely around 0.01 bars,suggesting the negligible triggering effect on the latter earthquake;(2)The triggering effects of the Simeonof,Sand Point,and Chignik earthquakes on aftershocks within three months are not well pronounced because of the triggering rates of 38%,14%,and 43%respectively.Other factors may have played an important role in promoting the occurrence of these aftershocks,such as the roughness of the subduction interface,the complicated velocity structure of the lithosphere,and the heterogeneous prestress therein;(3)The three earthquakes caused remarkable coseismic Coulomb stress changes at the subduction interface nearby these mainshocks,with an average Coulomb stress change of 3.2 bars in the shallow region directly inwards the trench.

Investigation of Coulomb stress changes in south Tibet(central Himalayas) due to the 25th April 2015 M_W 7.8 Nepal earthquake using a Coulomb stress transfer model

After Mw 7.8 Nepal earthquake occurred, the rearrangement of stresses in the crust commonly leads to subsequent damaging earthquakes. We present the calculations of the coseismic stress changes that resulted from the 25th April event using models of regional faults designed according to south Tibet-Nepal structure, and show that some indicative significant stress increases. We calculate static stress changes caused by the displacement of a fault on which dislocations happen and an earthquake occurs. A Mw 7.3 earthquake broke on 12 May at a distance of - 130 km SEE of the Mw 7.8 earthquake, whose focus roughly located on high Coulomb stress change （CSC） site. Aftershocks （first 15 days after the mainshock） are associated with stress increase zone caused by the main rupture. We set receiver faults with specified strikes, dips, and rakes, on which the stresses imparted by the source fault are resolved. Four group normal faults to the north of the Nepal earthquake seismogenic fault were set as receiver faults and variant results followed. We provide a discussion on Coulomb stress transfer for the seismogenic fault, which is useful to identify potential future rupture zones.

Co-seismic Coulomb stress changes on the northern Tanlu fault zone caused by the Tohoku-Oki M_(W)9.0 earthquake

Based on the spherical earth dislocation theory and a fault slip model of the Tohoku-Oki M_(W)9.0 earthquake,the co-seismic Coulomb failure stress changes(ΔCFS)on the northern Tanlu fault zone at depths of 0–40 km are calculated.By comparing two sets of results from the spherical earth dislocation theory and the semi-infinite space one,the effect of earth curvature on the calculation results is analyzed quantitatively.First,we systematically summarize previous researches related to the northern Tanlu fault zone,divide the fault zone as detailed as possible,give the geometric parameters of each segment,and establish a segmented structural model of the northern Tanlu fault zone.Second,we calculate the Coulomb stress changes on the northern Tanlu fault zone by using the spherical earth dislocation theory.The result shows the Coulomb stress changes are no more than 0.003 MPa,which proves the great earthquake did not significantly change the stress state of the fault zone.Finally,we quantitatively analyze the disparities between the results of semi-infinite space dislocation theory and the spherical earth one.The average disparity between them is about 7.7%on the northern Tanlu fault zone and is 16.8%on the Fangzheng graben,the maximum disparity on this graben reaches up to 25.5%.It indicates that the effect of earth curvature can not be ignored.So it’s necessary to use the spherical earth dislocation theory instead of the semi-infinite space one to study the Coulomb stress change in the far field.

Viscoelastic stress change from the 1931 M_(w)7.8 Fuyun earthquake and its impacts on seismic activity around the Altai mountains

The 1931 M_(w)7.8 Fuyun earthquake occurred around the Altai mountains, an intracontinental deformation belt with limited active strain-rate accumulation. To explore whether seismic activity in this deformation belt was affected by stress interaction among different active faults, we calculate the Coulomb failure stress change(ΔCFS) induced by the Fuyun earthquake due to coseismic deformation of the elastic crust and postseismic viscoelastic relaxation of the lower crust and upper mantle. Numerical results show that the total ΔCFS at a 10-km depth produced by the Fuyun earthquake attains approximately 0.015-0.134 bar near the epicenter, and just before the occurrence of the 2003 M_(w)7.2 Chuya earthquake, which distances about 400 km away from the Fuyun earthquake. Among the increased ΔCFS,viscoelastic relaxation from 1931 to 2003 contributes to approximately 0.014-0.131 bar, accounting for>90% of the total ΔCFS. More importantly, we find that for the recorded seismicity in the region with a radius of about 270 km to the Fuyun earthquake from 1970 to 2018, the percentage of earthquakes that fall in positive lobes of ΔCFS resolved on the NNW-SSE Fuyun strike-slip fault, on the NWW-SEE Irtysh strike-slip fault, and on the NW-SE Kurti reverse fault is up to 67.22%-91.36%. Therefore, the predictedΔCFS suggests that the impact of the 1931 M_(w)7.8 Fuyun earthquake on seismic activity around the Altai mountains is still significant as to hasten occurrence of the 2003 M_(w)7.2 Chuya earthquake at a relatively far distance and to trigger its aftershocks in the near-field even after several decades of the mainshock.

Study of electromagnetic characteristics of stress distribution and sudden changes in the mining of gob-surrounded coal face

The incidence of dynamic coal or rock disasters is closely related to the distribution of stress in the surrounding rock. Our experiments show that electromagnetic radiation （EMR） signals are related to the state of stress of a coal body. The higher the stress, the more intense the deformation and fractures of a coal body and the stronger the EMR signals. EMR signals reflect the degrees of concentrated stress of a coal body and danger of a rock burst. We selected EMR intensity as the test index of the No.237 gob-surrounded coal face in the Nanshan coal mine. We tested the EMR characteristics of the stress distribution on the strike, on the incline and in the interior of the coal body. The EMR rule of rock bursts, caused by sudden changes in stress, is analyzed. Our research shows that EMR technology can be not only used to test qualitatively the stress distribution of the surrounding rock, but also to predict a possible occurrence of rock burst. Based on this, effective distress measures are used to eliminate or at least weaken the incidence of rock bursts. We hooe that safetv in coalmines will be enhanced.

Coulomb stress changes due to the 2021 MS7.4 Maduo Earthquake and expected seismicity rate changes in the surroundings

On May 22 nd,2021,an MS7.4 earthquake occurred near the Maduo county of the Qinghai Province,China,within the Bayan Har Block.Seismic activities have been intense in this block,thus whether the Maduo Earthquake will bring subsequent seismic hazards to its surrounding regions raises wide concerns.In this paper,we first calculated the Coulomb failure stress changes caused by the Maduo Earthquake on nearby faults,and estimated how much these faults are brought closer or further from their next failures based on their stressing rates.Next,we combined the Coulomb failure stress changes with the rate-state frictional law to estimate the seismicity rate in the study region in the next decade.A declustered catalogue before the Maduo Earthquake was adopted to calculate background seismicity rate,and rate-state parameters are constrained by fault slip rates.Our results show that the Maduo Earthquake increases stress accumulations in the northwestern portion of the Qingshuihe fault(0.02 MPa at maximum),the two ends of the Kunlun Mountain Pass-Jiangcuo fault(0.01 MPa at maximum),and the northwestern portion of the Maduo-Gande fault(on average~0.09 MPa),and seismicity rates are expected to increase near these faults.What is especially worth noting is the seismic hazard in the region extending from the eastern end of the Kunlun Mountain Pass-Jiangcuo fault to the Maqin-Maqu seismic gap on the Eastern Kunlun fault,which is calculated to have experienced a maximum stress increase of 0.67 MPa after the Maduo Earthquake.On the other hand,stress accumulations are reduced in the southern end of the Elashan fault,the Eastern Kunlun fault segment to the west of Maduo,and the northwestern portion of the Dari fault.Seismic hazards are expected to be low in these regions.For the study region as a whole,the probability of an M≥6 earthquake taking place in the next decade is estimated to be 59%,about twice the value calculated for the time period before the Maduo Earthquake.

Finite element simulation of deformation and stress changes of Kalpin-Kemin fault system in the Southwest Tianshan Orogenic Belt

Under the shadow of the far-field effect of the India-Eurasia collision,the Tianshan orogenic belt underwent tectonic re-activation in the Cenozoic,accompanied by strong tectonic deformation and frequent large earthquakes.Bounded by two rigid cratonic blocks located in its north and south,a series of marginal foreland fold-and-thrust belts are developed within the Tianshan orogenic belt and continue to develop to the bilateral pull-apart basins.Meanwhile,the faults in the orogenic belt are reactivated.The deformation caused by thrust-related structure accounts for larger than 50%of the total convergence of the Tianshan Mountains,which results in the most active structure with large earthquakes in the Tianshan area.Therefore,it is of great significance to study the dynamic process of the newly generated and reactivated thrust-nappe structures in Tianshan orogen via numerical modeling.This paper selects a classical cross-section profile in the western segment of the Southwest Tianshan Mountains,which contains the Kalpin-Maidan-Nalati-Kemin fault system from the south to the north.We attempt to establish a two-dimensional plane strain,viscoelastic finite element model,by treating the regional faults as a whole fault system and considering the topography,fault geometry,and GPS data.The displacement and stress fields of the model are retrieved,the short-term cumulative deformation field of the overall fault system is analyzed,and the rate of Coulomb failure stress change of each fault is also considered.The results show that the deformation is concentrated in the middle and southern parts of the Southwest Tianshan Mountains.In contrast,the deformation of the Kemin fault in the north is relatively small.According to the Coulomb failure stress changes of these four faults and the historical earthquake catalog,the potential seismicity of each fault is qualitatively analyzed.Our preliminary results suggest that the possibility of large earthquake occurrence is higher in the Kalpin fault,Maidan fault,and Nalati fault but lower in the Kemin fault in the near future。

Monitoring the change in horizontal stress with multi-wave time-lapse seismic response based on nonlinear elasticity theory

Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (CO_(2)) injection and storage, shallow surface prospecting and deep-earth structure description. The change in in-situ stress induced by hydrocarbon production and localized tectonic movements causes the changes in rock mechanic properties (e.g. wave velocities, density and anisotropy) and further causes the changes in seismic amplitudes, phases and travel times. In this study, the nonlinear elasticity theory that regards the rock skeleton (solid phase) and pore fluid as an effective whole is used to characterize the effect of horizontal principal stress on rock overall elastic properties and the stress-dependent anisotropy parameters are therefore formulated. Then the approximate P-wave, SV-wave and SH-wave angle-dependent reflection coefficient equations for the horizontal-stress-induced anisotropic media are proposed. It is shown that, on the different reflectors, the stress-induced relative changes in reflectivities (i.e., relative difference) of elastic parameters (i.e., P- and S-wave velocities and density) are much less than the changes in contrasts of anisotropy parameters. Therefore, the effects of stress change on the reflectivities of three elastic parameters are reasonably neglected to further propose an AVO inversion approach incorporating P-, SH- and SV-wave information to estimate the change in horizontal principal stress from the corresponding time-lapse seismic data. Compared with the existing methods, our method eliminates the need for man-made rock-physical or fitting parameters, providing more stable predictive power. 1D test illustrates that the estimated result from time-lapse P-wave reflection data shows the most reasonable agreement with the real model, while the estimated result from SH-wave reflection data shows the largest bias. 2D test illustrates the feasibility of the proposed inversion method for estimating the change in horizontal stress from P-wave time-lapse seismic data.

Advances in experiments and numerical simulations on the effects of stress perturbations on fault slip

Laboratory experiments and numerical simulations on rock friction perturbations,an important means for understanding the mechanism and influencing factors of stress-triggered earthquakes,are of great significance for studying earthquake mechanisms and earthquake hazard analysis.We reviews the experiments and numerical simulations on the effects of stress perturbations on fault slip,and the results show that stress perturbations can change fault stress and trigger earthquakes.The Coulomb failure criterion can shed light on some questions about stress-triggering earthquakes but cannot explain the time dependence of earthquake triggering nor be used to investigate the effect of heterogeneous stress perturbations.The amplitude and period are important factors affecting the correlation between stress perturbation and fault instability.The effect of the perturbation period on fault instability is still controversial,and the effect of the high-frequency perturbation on earthquakes may be underestimated.Normal and shear stress perturbation can trigger fault instability,but their effects on fault slip differ.It is necessary to distinguish whether the stress perturbation is dominated by shear or normal stress change when it triggers fault instability.Fault tectonic stress plays a decisive effect on the mode of fault instability and earthquake magnitude.Acoustic emission activity can reflect the changes in fault stress and the progression of fault nucleation,and identify the meta-instability stage and precursor of fault instability,providing a reference for earthquake prediction.

Co and postseismic fault slip models of the 2022 M_(W)6.7 Menyuan earthquake reveal conjugated faulting tectonics at the central section of the Lenglongling fault

The 2022 M_(W)6.7 Menyuan earthquake ruptured the western end of the Tianzhu seismic gap,providing an opportunity to study the regional seismogenic characteristics and seismic hazards.Here we use interferometric synthetic aperture radar(InSAR)and seismic data to study the mainshock rupture,early afterslip and the second largest aftershock of the 2022 Menyuan earthquake sequences.Our modeling results show that the mainshock ruptured the Lenglongling fault and the Tuolaishan fault with a maximum slip of~3 m.Rapid postseismic transient deformation occurred at the center of the Lenglongling fault.Our afterslip modeling reveals that the majority of afterslip occurred in the deeper part of the Lenglongling fault.A high-angle conjugated faulting event is found at the middle section of the Lenglongling fault.We use the stress inversion to investigate the possible triggering mechanism of the conjugated rupture event.The results indicate the maximum principal stress direction is in~222°,forming a~22°angle between the conjugated fault of second largest aftershock and the mainshock.The calculated normal stress changes indicate the region is within a pull-apart stress field,which favors such a conjugated rupturing event.Our study will help understand the rupture behavior of such kind of conjugated fault in other regions.

On Estimating Magnitude of a Maximum Sequent Earthquake by Viscoelastic Coulomb Stress Change and a Discussion of the Relationship between the M_S7.3 Earthquakes in Yutian 2008 and 2014

On the basis of the previous studies of the layered crustal model in the Yutian area,combined with the field GPS continuous observation data,we roughly estimate the viscous coefficient of each layer. With the viscoelastic horizontal layer model,we calculate the viscoelastic co-seismic Coulomb stress change caused by the Yutian M_S7. 3 earthquakes 2008 and 2014 respectively. Based on the Coulomb stress change,using the calculation method of "direct "aftershock frequency,we come up with the theoretical earthquake frequency directly related to the mainshock and the co-seismic Coulomb stress change in the study area. Then we put forward a method,based on the comparison of theoretical and actual earthquake frequency or the comparison between theoretical and practical earthquake frequency-distance decay curve fitting residuals,to estimate the magnitude of a maximum sequent earthquake,directly related to the mainshock co-seismic Coulomb stress change. Results calculated by different methods show that the maximum follow-up earthquake magnitude caused by the coseismic Coulomb stress change lies from M_S7. 2 to M_S7. 5 following Yutian M_S7. 3 earthquake in 2008; but that of the 2014 Yutian M_S7. 3 earthquake is M_S6. 3. The former is very close to the Yutian M_S7. 3 earthquake in 2014.Because of the same magnitude,relatively close spatial distance,short time interval,the same region of the external force,the strong correlation between two seismic tectonic and a clear stress interaction,we thus consider that the two Yutian M_S7. 3 earthquakes in 2008 and 2014 constitute a pair of generalized double shock type earthquake. This is consistent with the sequence type characteristic of past "double shock"earthquakes in the region. In this paper,the influence of the magnitude lower limit and the b-value in the relationship of G-R on the results is discussed. As a result,when the viscoelastic coseismic Coulomb stress variation is determined,the lower limit of magnitude has little effect on the maximum sequent earthquake magnitude estimation,but b-value of G-R has a greater impact on the results.

The Effect of Static Stress Triggering of the M_S 7. 1 Yushu Earthquake

This paper calculates the static stress changes generated by the Yushu M_S 7. 1 earthquake in Qinghai Province. On the basis of regional stress,we take account of the static stress change triggered by the Yushu M_S 7. 1 earthquake to find the optimally oriented fault planes,then calculate the Coulomb stress change on the optimally oriented fault plane. The results indicate that most of the aftershocks are triggered by the mainshock. The image of Coulomb stress changes is also in accord with regional earthquakes ( M_L ≥3. 0 ) distribution,but the value is lower than 0. 01MPa. In addition,this paper calculates the Coulomb stress changes in the case that the aftershock fault plane is the same as the main shock. Through comparison,we find that the image of Coulomb stress changes obtained using the "optimally oriented fault"approach is more consistent with the distribution of Yushu aftershocks and regional earthquakes.

Stress triggering" between different rupture events in several earthquakes

Most strong earthquakes have complex rupture processes. As an approximation, each earthquake can be described as two or more subevents of rupture with time interval of several seconds to several days. In order to discuss the relationship between different subevents, we investigated the rupture process of the 1966 Xingtai, the 1976 Tangshan, the 1990 Gonghe and the 1996 Lijiang earthquake by calculating the static Coulomb failure stress changes produced by the first subevent. The calculation of static stress changes produced by fault slip is based on the formulation of Okada (1992). The result suggests that the static Coulomb failure stress changes (ΔCFS) produced by the first subevent have 'triggering' effect on the subsequent subevents which locate in the region where the Coulomb stress change produced by the first event is positive, with the order of magnitude 10-2 [similar to] 10-1 MPa.

Regional seismicity triggered by the M_s=7.8 Tangshan event on July 28, 1976 and the stati cstress field change

We studied the seismicity before and after the M_s=7.8 Tangshan event on July 28, 1976 (39°28'N, 1 18° 11'E) and the results show that in 3 regions outside of the source zone, seismicity rate increasing were observed, which was significant in 0.99 significance level using Z-statistic test and was proposed to be triggered by the M_s=7.8 Tangshan earthquake. The magnitude of the greatest triggered event was 5.5. The epicenter distances of these earthquakes were several ten kilometers to 300 km. The static stress change △CFS of Coulomb failure was calculated using an elastic dislocation model in half space and the △CFS on the major rupture directions in these three regions were positive.

Evolution of cumulative Coulomb failure stress in northeastern Qinghai-Xizang (Tibetan) Plateau and its effect on large earthquake occurrence

We simulate accumulative Coulomb failure stress change in a layered Maxwell viscoelastic media in the northeastern Qinghai-Xizang （Tibetan） Plateau since 1920. Lithospheric stress/strain evolution is assumed to be driven by dislocations of large earthquakes （M≥7.0） and secular tectonic loading. The earthquake rupture parameters such as the fault rupture length, width, and slip are either adopted from field investigations or estimated from their statistic relationships with the earthquake magnitudes and seismic moments. Our study shows that among 20 large earthquakes （M≥7.0） investigated, 17 occurred in areas where the Coulomb failure stress change is positive, with a triggering rate of 85%. This study provides essential data for the intermediate to long-term likelihood estimation of large earthquakes in the northeastern Tibetan Plateau.

Finite element simulation of stress change for the M_(S)7.4 Madoi earthquake and implications for regional seismic hazards

On May 22,2021,the M_(S)7.4 earthquake occurred in Madoi County,Qinghai Province;it was another strong event that occurred within the Bayan Har block after the Dari M_(S)7.7 earthquake in 1947.An earthquake is bound to cast stress to the surrounding faults,thus affecting the regional seismic hazard.To understand these issues,a three-dimensional viscoelastic finite element model of the eastern Bayan Har block and its adjacent areas was constructed.Based on the co-seismic rupture model of the Madoi earthquake,we analyzed the co-and postseismic Coulomb stress change caused by the Madoi earthquake on the surrounding major faults.The results show that the Madoi earthquake caused significant co-seismic stress increases in the Tuosuo Lake and Maqin-Maqu segments of the East Kunlun fault(>10 kPa),which exceeded the proposed threshold of stress triggering.By integrating the accumulation rate of the inter-seismic tectonic stress,we conclude that the Madoi earthquake caused future strong earthquakes in the Tuosuo Lake and Maqin-Maqu segments of the East Kunlun fault to advance by 55.6-623 and 24.7-123 a,respectively.Combined with the influence of the Madoi earthquake and the elapsed time of the last strong earthquake,these two segments have approached or even exceeded the recurrence interval of the fault prescribed by previous research.In the future,it is necessary to focus greater attention on the seismic hazard of the Maqin-Maqu and Tuosuo Lake segments.This study provides a mechanical reference to understand the seismic hazard of the East Kunlun fault in the future,particularly to determine the seismic potential region.

Crustal Stress Evolution over the Past 700 Years in North China and Earthquake Occurrence

Fault interaction and earthquake occurrence have attracted much attention in seismological community during recent years. Many studies have shown that the rupture of one fault could encourage or discourage earthquake nucleation on a neighboring fault, depending on the relative geometry of the two faults and the earthquake rupture mechanisms. In this paper, we simulate the evolutionary process of cumulative Coulomb failure stress change （ CCFSC ） in North China since 1303, manifested by secular tectonic stress loading and occurrence of large earthquakes. Secular tectonic stress loading is averaged from crustal strain rates derived from GPS. Fault rupture parameters of historical earthquakes are estimated as follows： the earthquake rupture length and the amount of slip are derived based on their statistical relationships with the earthquake intensity distribution and magnitude, calibrated using parameters of instrumentally measured contemporary earthquakes. The earthquake rake angle is derived based on geologically determined fault orientational parameters and seismically estimated orientation of regional tectonic stresses. Assuming a layered visco-elastic medium, we calculate stress evolution resulting from secular tectonic loading and coseismic and postseismic deformation. On the eve of each large earthquake, the accumulated stress field is projected to the fault surface of that earthquake and the CCFSC is evaluated to assess the triggering effect of CCFSC. Forty-nine earthquakes with M≥6.5 have occurred in North China since 1303. Statistics shows that 39 out of the 48 subsequent events were triggered by positive CCFSC, yielding a triggering rate of 81.3%. If we use the accumulative stress field to evaluate the CCFSC for the M ≥ 5.0 earthquakes that occurred in North China since 1303, we find that 75.5% of those events were triggered. The triggering rate for the M ≥ 5.0 earthquakes after the 1976 Ninghe earthquake is up to 82.1%. The triggering rates can be higher if corrections are made for some aftershocks which were wrongly identified as occurring in stress shadow zones because of errors in parameter estimates of historical earthquakes. Our study shows a very high correlation between positive CCFSC and earthquake occurrences. Relatively high CCFSC in North China at present is concentrated around the Bohai Sea, the west segment of the Northern Qinling fault, the western end of the Zhangjiakou-Bohai Sea seismic zone, and the shiyuan basin, Shanxi graben, suggesting relatively higher earthquake potential in these areas.

Research on the Dynamic Change of Regional Stress Fields before the M_S8.0 Wenchuan Earthquake

Using the digital telemetric seismic waveform data of Chengdu and Kunming, this article studies the focal mechanism solutions and the apparent stress values of a large number of small earthquakes, and then analyzes the dynamic variation of regional stress fields and the spatio- temporal distribution of apparent stress values. The annual variation values of the azimuth of average principal stress field before the May 12, 2008 Ms8.0 Wenchuan earthquake in the Sichuan-Yunnan region were 58° from 2003 to 2004, 85° from 2003 to 2005,61° from 2006 to 2007 and 90° from 2006 to April 2008 respectively. In recent years, deflection or disturbances occurred in the azimuth of the average principal stress field in the Sichuan-Yunnan region. Analysis shows that this may be related to the change of stress field states of crustal blocks before and after the December 26, 2004 Ms9.0 Sumatra earthquake and the 2008 Ms8.0 Wenchuan earthquake. The ratio of thrust-type earthquakes in the Sichnan-Qinghai block was on the higher side in the period from 2006 to 2007, and the source faulting type of the regional moderate and small earthquakes had changed before the Ms8.0 Wenchnan earthquake. The change of state of the stress field is consistent with the changes in block displacement fields revealed by GPS data and the crustal shortening velocity vertical to the Longmenshan fault zone. Based on the radiation energy calculated from all bands of the seismic waveform, the value of apparent stress σapp is obtained. The fluctuation shape of the fitting trend of the apparent stress is related to the intensity of regional seismicity. It reveals that the micro- dynamic fluctuation process of the regional stress value is similar to the azimuth transition of the regional principal compressive stress field, which can be used to probe for pregnant physical processes. Areas with a higher value of apparent stress σapp are possible areas of potential seismic risk. It can be seen from the spatial distribution of the medium and shortterm apparent stress σapp before the Ms8.0 Wenchuan earthquake, the Longmenshan fault zone is in a low stress distribution area, and the relatively high apparent stress is in the peripheral area. These images may show medium and short-term locking phenomena near the seismogenic tectonics of the Ms8.0 Wenchuan earthquake. For example, changes with time of the focal parameter consistency of the sub-blocks in Sichuan and Yunnan Provinces, continual increase of thrust-type earthquakes in the Sichuan-Qinghai block and the appearance of spatial distribution areas of high apparent σapp stress. The work on this aspect was continued after the Ms8.0 Wenchuan earthquake, and the results seem to be shown a clearer relationship between these phenomena and future great earthquakes.

Research on seismic stress triggering

This paper briefly reviews basic theory of seismic stress triggering. Recent development on seismic stress triggering has been reviewed in the views of seismic static and dynamic stress triggering, application of viscoelastic model in seismic stress triggering, the relation between earthquake triggering and volcanic eruption or explosion, other explanation of earthquake triggering, etc. And some suggestions for further study on seismic stress triggering in near future are given.

Failure time variation derived from R–S relation: the role of the static stress perturbation

In general, earthquake cycle related to earthquake faulting could include four major processes which could be described by （1） fault locking, （2） self-acceleration or nucleation （possible foreshocks）, （3） coseismic slip, and （4） post-stress relaxation and afterslip. A sudden static stress change/perturbation in the surrounding crust can advance/ delay the fault instability or failure time and modify earth- quake rates. Based on a simple one-dimensional spring-sli- der block model with the combination of rate-and-state- dependent friction relation, in this study, we have approxi- mately derived the simple analytical solutions of clock advance/delay of fault failures caused by a sudden static Coulomb stress change applied in the different temporal evolution periods during an earthquake faulting. The results have been used in the physics-based explanation of delayed characteristic earthquake in Parkfield region, California, in which the next characteristic earthquake of M 6.0 after 1966 occurred in 2004 instead of around 1988 according to its characteristic return period of 22 years. At the same time, the analytical solutions also indicate that the time advance/ delay in Coulomb stress change derived by the dislocation model has a certain limitation and fundamental flaw. Fur- thermore, we discussed the essential difference between rate- and state-variable constitutive （R-S） model and Coulomb stress model used commonly in current earthquake triggering study, and demonstrated that, in fact, the Coulomb stress model could be involved in the R-S model. The results, we have obtained in this study, could be used in the development of time-dependent fault interaction model and the probability calculation related to the time-dependent and renewal earthquake prediction model.