Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

Internal polyhedral structures of a granular system can be investigated using the Voronoi tessellations.This technique has gained increasing recognition in research of kinetic properties of granular flows.For systems with mono-sized spherical particles,Voronoi tessellations can be utilized,while radial Voronoi tessellations are necessary for analyzing systems with multi-sized spherical particles.However,research about polyhedral structures of non-spherical particle systems is limited.We utilize the discrete element method to simulate a system of ellipsoidal particles,defined by the equation(x/a)^(2)+(y/1)^(2)+(z/1/a)^(2)=1,where a ranges from 1.1 to 2.0.The system is then dissected by using tangent planes at the contact points,and the geometric quantities of the resulting polyhedra in different shaped systems,such as surface area,volume,number of vertices,number of edges,and number of faces,are calculated.Meanwhile,the longitudinal and transverse wave velocities within the system are calculated with the time-of-flight method.The results demonstrate a strong correlation between the sound velocity of the system and the geometry of the dissected polyhedra.The sound velocity of the system increases with the increase in a,peaking at a=1.3,and then decreases as a continues to increase.The average volume,surface area,number of vertices,number of edges,and number of faces of the polyhedra decrease with the increase in sound velocity.That is,these quantities initially decrease with the increase in a,reaching minima at a=1.3,and then increase with further increase of a.The relationship between sound velocity and the geometric quantities of the dissected polyhedra can serve as a reference for acoustic material design.

Three-dimensional P-wave velocity structure of the crust beneath Hainan Island and its adjacent regions,China

Using over 3 500 first P arrival times recorded by nine digital seismic stations from Hainan Digital Seismic Net-work during 1999～2005,a 3-D P-wave velocity model of the crust under Hainan Island and adjacent regions has been determined. The results show that the pattern of velocity anomalies in the shallower upper crust is somewhat associated with the surface geological tectonics in the region. A relative low-velocity anomaly appears north of the Wangwu-Wenjiao fault zone and a relative high-velocity anomaly appears south of the Wangwu-Wenjiao fault zone,corresponding to the depressed areas in north Hainan Island,where many volcanoes are frequently active and geothermal values are relatively higher,and the uplifted and stable regions in central and south of the Hainan Is-land. In the middle and lower crust velocities are relatively lower in east Hainan than those in west Hainan,possi-bly suggesting the existence of the upwelling of hot materials from the mantle in east Hainan. The pattern of veloc-ity anomalies also indicates that NW faults,i.e.,the Puqian-Qinglan fault,may be shallower,while the E-W Wangwu-Wenjiao fault may be deeper,which perhaps extends down to Moho depth or deeper.

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in cen-tral-western China

采用中国中西部地区(2l°～36°N，98°～112°E)193个地震台在1992～1999年间记录到的9988次地震的Pg和Sg震相走时的读数资料，用Roecker的SPHYPIT90程序，反演了该地区三维地壳P波速度结构，并用SPHREL3D90程序进行了地震的重新定位．反演结果揭示了中国中西部地区地震P波速度结构明显的横向不均匀性，这些不同深度上波速的横向变化多以该地区的活动断裂为分界线．可以看出活动断裂两侧存在明显的速度反差．通过重新定位，得到了6459次地震的震源参数，这些精确定位的地震震中明显沿该区活动断裂呈现条带状分布，其范围和尺度清晰地表示了这一地区地震活动与活动断裂的紧密关系．其中，82％重新精确定位的事件的震源深度在20km以内．这一结果与笔者用双差地震定位法得到的重新定位的震源深度分布相一致．

Structural similarity of lithospheric velocity models of Chinese mainland

Existing lithospheric velocity models exhibit similar structures typically associated with the first-order tectonic features,with dissimilarities due to different data and methods used in model generation.The quantification of model structural similarity can help in interpreting the geophysical properties of Earth's interior and establishing unified models crucial in natural hazard assessment and resource exploration.Here we employ the complex wavelet structural similarity index measure(CW-SSIM)active in computer image processing to analyze the structural similarity of four lithospheric velocity models of Chinese mainland published in the past decade.We take advantage of this method in its multiscale definition and insensitivity to slight geometrical distortion like translation and scaling,which is particularly crucial in the structural similarity analysis of velocity models accounting for uncertainty and resolution.Our results show that the CW-SSIM values vary in different model pairs,horizontal locations,and depths.While variations in the inter-model CW-SSIM are partly owing to different databases in the model generation,the difference of tomography methods may significantly impact the similar structural features of models,such as the low similarities between the full-wave based FWEA18 and other three models in northeastern China.We finally suggest potential solutions for the next generation of tomographic modeling in different areas according to corresponding structural similarities of existing models.

Three-dimensional crustal P-wave velocity structure in the Yangbi and Eryuan earthquake regions, Yunnan, China

A magnitude 5.5 earthquakes occurred in Eryuan County,Dali Bai Autonomous Prefecture,Yunnan Province,China,on March 3.And a magnitude 5.0 earthquake occurred in the same place on April 17,2013,i.e.,45 days later.Then,on May 21,2021,multiple earthquakes,one with magnitude 6.4 and several at 5.0 or above,occurred in Yangbi County,Dali Bai Autonomous Prefecture,Yunnan Province,China.All of these occurred in the Weixi-QiaohouWeishan fault zone.In this study,1,874 seismic events in Yangbi and Eryuan counties were identified by automatic micro-seismic identification technology and the first arrivals were picked up manually.Following this,a total of 11,968 direct P-wave absolute arrivals and 73,987 high-quality Pwave relative arrivals were collected for joint inversion via the double difference tomography method.This was done to obtain the regional three-dimensional fine crustal P-wave velocity structure.The results show that the travel time residuals before and after inversion decreased from the initial–0.1–0.1 s to–0.06–0.06 s.The upper crust in the study area,which exhibited a low-velocity anomaly,corresponded to the basin region;this indicated that the low-velocity anomaly in the shallow part of the study area was affected by the basin.Results also showed some correlation between the distribution of the earthquakes and velocity structure,as there was a lowvelocity body Lv1 with a wide distribution at depths ranging from 15–20 km in the Yangbi and Eryuan earthquake regions.In addition,earthquakes occurred predominantly in the highlow velocity abnormal transition zone.The low-velocity body in the middle and lower crust may be prone to concentrating upper crustal stress,thus leading to the occurrence of earthquakes.

Three-dimensional P-wave Velocity Structure Modelling of the Middle and Lower Reaches of the Yangtze River Metallogenic Belt: Crustal Architecture and Metallogenic Implications

In this study,we compiled and analyzed 69310 P-wave travel-time data from 6639 earthquake events.These events(M≥2.0)occurred from 1980 s to June 2019 and were recorded at 319 seismic stations(Chinese Earthquake Networks Center)in the study area.We adopted the double-difference seismic tomographic method(tomo DD)to invert the 3-D P-wave velocity structure and constrain the crust-upper mantle architecture of the Middle and Lower Reaches of the Yangtze River Metallogenic Belt(MLYB).A 1-D initial model extracted from wide-angle seismic profiles was used in the seismic tomography,which greatly reduced the inversion residual.Our results indicate that reliable velocity structure of th e uppermost mantle can be obtained when Pn is involved in the tomography.Our results show that:(1)the pattern of the uppermost mantle velocity structure corresponds well with the geological partitioning:a nearly E-W-trending low-velocity zone is present beneath the Dabie Orogen,in contrast to the mainly NE-trending low-velocity anomalies beneath the Jiangnan Orogen.They suggest the presence of thickened lower crust beneath the orogens in the study area.In contrast,the Yangtze and Cathaysia blocks are characterized by relatively high-velocity anomalies;(2)both the ultra-high-pressure(UHP)metamorphic rocks in the Dabie Orogen and the low-pressure metamorphic rocks in the Zhangbaling dome are characterized by high-velocity anomalies.The upper crust in the Dabie Orogen is characterized by a low-velocity belt,sandwiched between two high velocity zones in a horizontal direction,with discontinuous low-velocity layers in the middle crust.The keel of the Dabie Orogen is mainly preserved beneath its northern section.We infer that the lower crustal delamination may have mainly occurred in the southern Dabie Orogen,which caused the mantle upwelling responsible for the formation of the granitic magmas emplaced in the middle crust as the low-velocity layers observed there.Continuous deep-level compression likely squeezed the granitic magma upward to intrude the upper crustal UHP metamorphic rocks,forming the'sandwich'velocity structure there;(3)high-velocity updoming is widespread in the crust-mantle transition zone beneath the MLYB.From the Anqing-Guichi ore field northeastward to the Luzong,Tongling,Ningwu and Ningzhen orefields,high-velocity anomalies in the crust-mantle transition zone increase rapidly in size and are widely distributed.The updoming also exists in the crust-mantle transition zone beneath the Jiurui and Edongnan orefields,but the high-velocity anomalies are mainly stellate distributed.The updoming high-velocity zone beneath the MLYB generally extends from the crust-mantle transition zone to the middle crust,different from the velocity structure in the upper crust.The upper crust beneath the Early Cretaceous extension-related Luzong and Ningwu volcanic basins is characterized by high velocity zones,in contrast to the low velocity anomalies beneath the Late Jurassic to Early Cretaceous compression-related Tongling ore field.The MLYB may have undergone a compressive-to-extensional transition during the Yanshanian(Jurassic-Cretaceous)period,during which extensive magmatism occurred.The near mantle-crustal boundary updoming was likely caused by asthenospheric underplating at the base of the lower crust.The magmas may have ascended through major crustal faults,undergoing AFC(assimilation and fractional crystallization)processes,became emplaced in the fault-bounded basins or Paleozoic sequences,eventually forming the many Cu-Fe polymetallic deposits there.

Imaging 3-D crustal P-wave velocity structure of western Yunnan with bulletin data

Western Yunnan is a region with intensive tectonic activity and serious earthquake risk. It is of significant importance to study three dimensional crustal structure of this region to understand the tectonic setting and disaster mechanism. Densification and digitalization of seismic networks in this region provides an opportunity to study the velocity structure with bulletin data. In this study, we collect P-wave data of 10 403 regional earthquakes recorded by 79 seismic stations from January 2008 to December 2010. In addition to first arrivals data （Pg with epieentral distance less than 200 km and Pn）, the Pg （or P） data with epicentral distance more than 200 km are also considered as later direct arrivals in the tomographic inversion. We also compare the quantity and the quality of the seismic data before 2010 and after 2010. The test results show that adding the follow-up Pg phase can effectively improve the inversion ability of crustal imaging, and quantity and the data quality are significantly improved since 2010. The tomographie results show that： （1） The Honghe fault zone, which is the major fault systems in this region, may cut through the entire crust, and the velocity contrasts between two sides at lower crust beneath the Honghe fault are estimated at higher than 10%, while the velocity difference below Nujiang fault zone extends only in the upper crust; （2） Most of the earthquakes in the region occurred at the interface of high-velocity media and low-velocity media, i.e., the areas with high velocity gradient, which has been validated in other areas.

Crustal velocity structures beneath North China revealed by ambient noise tomography

We collected continuous noise waveform data from January 2007 to February 2008 recorded by 190 broadband and 10 very broadband stations of the North China Seismic Array. The study region is divided into grid with interval 0.25°×0.25°, and group velocity distribution maps between 4 s and 30 s are obtained using ambient noise tomography method. The lateral resolution is estimated to be 20-50 km for most of the study area. We construct a 3-D S wave velocity model by inverting the pure path dispersion curve at each grid using a genetic algorithm with smoothing constraint. The crustal structure observed in the model includes sedimentary basins such as North China basin, Yanqing-Huailai basin and Datong basin. A well-defined low velocity zone is observed in the Beijing-Tianjin-Tangshan region in 22-30 km depth range, which may be related to the upwelling of hot mantle material. The high velocity zone near Datong, Shuozhou and Qingshuihe within the depth range of 1-23 km reveals stable characteristics of Ordos block. The Taihangshan front fault extends to 12 km depth at least.

Shallow crustal velocity structures revealed by active source tomography and fault activities of the Mianning–Xichang segment of the Anninghe fault zone, Southwest China

The Anninghe fault is a large left-lateral strike-slip fault in southwestern China. It has controlled deposition and magmatic activities since the Proterozoic, and seismic activity occurs frequently. The Mianning-Xichang segment of the Anninghe fault is a seismic gap that has been locked by high stress. Many studies suggest that this segment has great potential for large earthquakes(magnitude >7). We obtained three vertical velocity profiles of the Anninghe fault(between Mianning and Xichang) based on the inversion of P-wave first arrival times. The travel time data were picked from seismograms generated by methane gaseous sources and recorded by three linearly distributed across-fault dense arrays. The inversion results show that the P-wave velocity structures at depths of 0-2 km corresponds well with the local lithology. The Quaternary sediments have low seismic velocities, whereas the igneous rocks,metamorphic rocks, and bedrock have high seismic velocities. We then further discuss the fault activities of the two fault branches of the Anninghe fault in the study region based on small earthquakes(magnitudes between ML 0.5 and ML 2.5) detected by the Xichang array.The eastern fault branch is more active than the western branch and that the fault activities in the eastern branch are different in the northern and southern segments at the border of 28°21′N. The high-resolution models obtained are essential for future earthquake rupture simulations and hazard assessments of the Anninghe fault zone. Future studies of velocity models at greater depths may further explain the complex fault activities in the study region.

2-D P-wave velocity structure in the mideast segment of Zhangjiakou-Bohai tectonic zone: Anxin-Xianghe-Kuancheng DSS profile

In order to get the 3-D fine velocity structure in the Capital-circle area of China, 6 explosions, ranging from 1800 to 2500 kg, were conducted and recorded by an array of 240 seismographs. A reflection/refraction survey was carried out along the profile extending from Anxin county, Hebei Province northeastward to Yanshan Mountains, crossing the Zhangjiakou-Bohai tectonic zone. The 2-D velocity structure of P wave was imaging along the profile. The results show that abnormality exists in the deep structure of the Zhangjiakou-Bohai tectonic zone: The base- ment is significantly depressed, the interfaces and Moho are uplifted, and a strong velocity gradient layer is existed above the Moho that may be dislocated by deep fault. The crust of Huabei basin is thin and low velocity body ex- ists in the crust. The Yanshan Mountains′ crust is thick, the layers in the crust are quite clear and the velocity in the layer is homogeneous. Huabei basin differs from Yanshan Mountains in structure.

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in central-western China

A simultaneous inversion of earthquake relocation and three-dimensional crustal structure of P-wave velocity in central-western China (21癗~36癗, 98癊~112癊) were performed in this paper. The crustal P-wave velocity model and earthquake relocation for this region are obtained using Pg and Sg phase readings of 9 988 earthquakes from 1992 to 1999 recorded at 193 seismic stations within central-western China by SPHYPIT90 and SPHREL3D90 programs. A lateral inhomogeneous structure of P-wave velocity in this region was obtained. Ob-vious contrast of P-wave velocities was revealed on both sides of active fault zones. Relocated epicenters of 6 459 events show clear lineation along active faults, which indicated a close correlation between seismicity and the active faults in this region. Focal depths of 82% relocated events ranged from 0 to 20 km, which is in good agreement with that from double-difference earthquake location algorithm.

3D P-wave Velocity Structure and Active Tectonics in the Xinfengjiang Area of Guangdong

In this paper,we determined an earthquake sequence location in the Xingfengjiang area from June,2007 to July,2014 and the 3 D P-wave velocity structure by a simultaneous inversion method. On that basis,we studied the occurrence features of active tectonics and the earthquake source mechanism. The results show that the reservoir fracture system has a tendency to increase with gradual depth from southeast to northwest,consistent with gravitational field research results. There are 4 high velocity zones( HVZ) under the depth of the 7 km-12 km crust between the Xinfengjiang Reservoir dam and Xichang District,Dongyuan. The max velocity of the biggest HVZ which is under Xichang is 6. 3 km/s. Under the reservoir dam there is a strong tectonic deformation zone,as the center exit Renzishi fault( F_2),Nanshan-Aotou faults( F_4),Heyuan fault( F_1) and Shijiao-Xingang-Baitian fault( F_5),7 earthquakes with M_L≥ 5. 0( including M 6. 1 in March,1962) occurred at the high gradient zone of the HVZ Ⅲ and HVZ Ⅳ edge which has been under the reservoir dam since 1960, with relativity energy releasing more thoroughly. Moderate seismic activity occurred at the HVZ Ⅰ edge which has been under Xichang since 2012,and is a danger zone for M5. 0 earthquakes in the future.

MULTI-SCALE COHERENT STRUCTURES IN TURBULENT BOUNDARY LAYER DETECTED BY LOCALLY AVERAGED VELOCITY STRUCTURE FUNCTIONS

The time sequence of longitudinal velocity component at different vertical locations in turbulent boundary layer was finely measured in a wind tunnel. The concept of coarse_grained velocity structure functions, which describes the relative motions of straining and compressing for multi_scale eddy structures in turbulent flows, was put forward based on the theory of locally multi_scale average. Based on the consistency between coarse_grained velocity structure function and Harr wavelet transformation,detecting method was presented, by which the coherent structures and their intermittency was identified by multi_scale flatness factor calculated by locally average structure function. Phase_averaged evolution course for multi_scale coherent eddy structures in wall turbulence were extracted by this conditional sampling to educe scheme. The dynamics course of multi_scale coherent eddy structures and their effects on statistics of turbulent flows were studied.

P-wave velocity structure in the crust and the uppermost mantle of Chao Lake region of the Tan-Lu Fault inferred from teleseismic arrival time tomography

Chao Lake is a Geoheritage site on the active Tan-Lu Fault between the Yangtze craton,the North China craton,and the Dabie orogenic belt in the southeast.This segment of the fault is not well constrained at depth partly due to the overprinting of the fault zone by intrusive materials and its relatively low seismic activity and sparse seismic station coverage.This study took advantage of a dense seismic array deployed around Chao Lake to delineate the P-wave velocity variations in the crust and uppermost mantle using teleseismic earthquake arrival time tomography.The station-pair double-difference with waveform crosscorrelation technique was employed.We used a multiscale resolution 3-D initial model derived from the combination of highresolution 3-D v S models within the region of interest to account for the lateral heterogeneity in the upper crust.The results revealed that the velocity of the upper crust is segmented with structures trending in the direction of the strike of the fault.Sedimentary basins are delineated on both sides of the fault with slow velocities,while the fault zone is characterized by high velocity in the crust and uppermost mantle.The high-velocity structure in the fault zone shows characteristics of magma intrusion that may be connected to the Mesozoic magmatism in and around the Middle and Lower Yangtze River Metallogenic Belt(MLYMB),implying that the Tan-Lu fault might have formed a channel for magma intrusion.Magmatic material in Chao Lake is likely connected to the partial melting,assimilation,storage,and homogenization of the uppermost mantle and the lower crustal rocks.The intrusions,however,seem to have suffered severe regional extension along the Tan-Lu fault driven by the eastward Paleo-Pacific plate subduction,thereby losing its deep trail due to extensional erosion.

Three-Dimensional P-Wave Velocity Structure of the Crust of North China

Since the Xingtai （邢台） earthquake in 1966, China Earthquake Administration has carried out a survey campaign along more than thirty deep seismic sounding （DSS） profiles altogether about twenty thousand kilometers long in North China to study the velocity structure of the crust and the upper mantle in this region, and has obtained a great number of research findings. However, these researches have not provided a 3D velocity structure model of the crust of North China and cannot provide seismic evidence for the study of the deep tectonic characteristics of the crust of the whole region. Hence, based on the information from the published data of the DSS profiles, we have chosen 14 profiles to obtain a 3D velocity structure model of North China using the vectorization function of the GIS software （Arc/Info） and the Kriging data gridding method. With this velocity structure model, we have drawn the following conclusions： （1） The P-wave velocity of the uppermost crust of North China changes dramatically, exhibiting a complicated velocity structure in plane view. It can be divided into three velocity zones mainly trending towards north-west. In the research area, the lowest-velocity zones lie in the Haihe （海河） plain and Bohai （渤海） Bay. Although the geological structure of the sedimentary overburden in the study area is somewhat inherited by the upper crust, there are still several differences between them. （2） Generally, the P-wave velocity of the crust increases with depth in the study area, but there still exists local velocity reversion. In the east, low-velocity anomalies of the Haihe plain gradually disappear with increasing depth, and the Shanxi （山西） graben in the west is mainly characterized by relatively low velocity anomalies. Bounded by the Taihang （太行） Mountains, the eastern and western parts differ in structural trend of stratum above the crystalline basement. The structural trend of the Huanghuaihai （黄淮海） block in the east is mainly north-east, while that of the Shanxi block and the eastern edge of the Ordos block is mainly north-west. （3） According to the morphological features of Moho, the crust of the study area can be divided into six blocks. In the Shanxi block, Moho apppears like a nearly south-north trending depression belt with a large crustal thickness. In the southern edge of the Inner Mongolia block and the south of the Yanshan （燕山） block,the Moho exhibits a feature of fold belt, trending nearly towards east-west. In the eastern edge of the Ordos block, the structure of Moho is relatively complex, presenting a pattern of fold trending nearly towards north-west with alternating convexes and concaves. Beneath the Huanghuaihai block, the middle and northern parts of the North China rift zone, the Moho is the shallowest in the entire region, with alternating uplifts and depressions in its shape. For the anteclise zone in the west of Shandong （山东） Province, the Moho is discontinuous for the fault depression extending in the north-west direction along Zaozhuang （枣庄） -Qufu （曲阜）.

P-wave velocity structure beneath reservoirs and surrounding areas in the lower Jinsha River

The lower reaches of the Jinsha River are rich in hydropower resources because of the high mountains,deep valleys,and swift currents in this area.This region also features complex tectonic structures and frequent earthquakes.After the impoundment of the reservoirs,seismic activity increased significantly.Therefore,it is necessary to study the P-wave velocity structure and earthquake locations in the lower reaches of the Jinsha River and surrounds,thus providing seismological support for subsequent earthquake prevention and disaster reduction work in reservoir areas.In this study,we selected the data of 7.670 seismic events recorded by the seismic networks in Sichuan.Yunnan,and Chongqing and the temporary seismic arrays deployed nearby.We then applied the double-difference tomography method to this data,to obtain the P-wave velocity structure and earthquake locations in the lower reaches of the Jinsha River and surrounds.The results showed that the Jinsha River basin has a complex lateral P-wave velocity structure.Seismic events are mainly distributed in the transition zones between high-and low-velocity anomalies,and seismic events are particularly intense in the Xiluodu and Baihetan reservoir areas.Vertical cross-sections through the Xiangjiaba and Xiluodu reservoir areas revealed an apparent high-velocity anomaly at approximately 6 km depth:this high-velocity anomaly plays a role in stress accumulation,with few earthquakes distributed inside the high-velocity body.After the impoundment of the Baihetan reservoir,the number of earthquakes in the reservoir area increased significantly.The seismic events in the reservoir area north of 27°N were related to the enhanced activity of nearby faults after impoundment:the earthquakes in the reservoir area south of 27°N were probably induced by additional loads(or regional stress changes),and the multiple microseismic events may have been caused by rock rupture near the main faults under high pore pressure.

ROLE OF UNDERGROUND STRUCTURE DEFORMATION VELOCITY IN THE ANALYSIS OF BLAST-RESISTANT STRUCTURES

The structural deformation velocity plays a significant role in the dynamic calculation of underground blast-resistant structures. The motion differentiating equation of a structure system taking into account the role of deformation velocity of the structure will truthfully describe the actual situation of structural vibration. With the one-dimensional plane wave theory, the expression of load on the structural periphery is developed, and the generalized variation principle for the dynamic analysis of underground arched-bar structures is given. At the same time, the results of the numerical calculation are compared.

Crustal velocity structures and their tectonic implications in different tectonic block regions of the Chinese mainland

In this paper, the typical velocity structures and average velocities of the crust in six different active tectonic block regions are presented on the basis of previous studies and their tectonic implications are discussed. The results show that different tectonic units have different features of crustal velocity structures. In general, there are low velocity distributions in the crust in regions with strong tectonic activities, and the scales of low velocity distributions are related to the tectonic activities. The average velocities are relatively low in such regions. This reflects strong crustal deformation and the variations of states of matter in the crust resulting from strong tectonic movements. These regions are also seismically active zones frequented by strong earthquakes. Therefore, studying crustal velocity structures of these regions is of great importance to understanding crustal geodynamic process and seismogenic tectonic background.

Aerodynamic unstable critical wind velocity for three-dimensionalopen cable-membrane structures

The aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures is investigated. The geometric nonlinearity is introduced into the dynamic equilibrium equations of structures. The disturbances on the structural surface caused by the air flow are simulated by a vortex layer with infinite thickness in the structures. The unsteady Bernoulli equation and the circulation theorem are applied in order to express the aerodynamic pressure as the function of the vortex density. The vortex density is then obtained with the vortex lattice method considering the coupling boundary condition. From the analytical expressions of the unstable critical wind velocities, numerical results and some useful conclusions are obtained. It is found that the initial curvature of open cable-membrane structures has clear influence on the critical wind velocities of the structures.

Internal structures and high-velocity frictional properties of Longmenshan fault zone at Shenxigou activated during the 2008 Wenchuan earthquake

This paper reports internal structures of a wide fault zone at Shenxigou,Dujiangyan,Sichuan province,China,and high-velocity frictional properties of the fault gouge collected near the coseismic slip zone during the 2008 Wenchuan earthquake.Vertical offset and horizontal displacement at the trench site were 2.8 m（NW side up）and 4.8 m（right-lateral）,respectively.The fault zone formed in Triassic sandstone,siltstone,and shale about 500 m away from the Yingxiu-Beichuan fault,a major fault in the Longmenshan fault system.A trench survey across the coseismic fault,and observations of outcrops and drill cores down to a depth of 57 m revealed that the fault zone consists of fault gouge and fault breccia of about0.5 and 250-300 m in widths,respectively,and that the fault strikes N62°E and dips 68° to NW.Quaternary conglomerates were recovered beneath the fault in the drilling,so that the fault moved at least 55 m along the coseismic slip zone,experiencing about 18 events of similar sizes.The fault core is composed of grayish gouge（GG） and blackish gouge（BG） with very complex slip-zone structures.BG contains low-crystalline graphite of about 30 %.High-velocity friction experiments were conducted at normal stresses of 0.6-2.1 MPa and slip rates of 0.1-2.1 m/s.Both GG and BG exhibit dramatic slip weakening at constant high slip rates that can be described as an exponential decay from peak friction coefficient lpto steadystate friction coefficient lssover a slip-weakening distance Dc.Deformation of GG and BG is characterized by overlapped slip-zone structures and development of sharp slickenside surfaces,respectively.Comparison of our data with those reported for other outcrops indicates that the high-velocity frictional properties of the Longmenshan fault zones are quite uniform and the high-velocity weakening must have promoted dynamic rupture propagation during the Wenchuan earthquake.