Spatial and Temporal Variations in Earthquake Stress Drops between the 2008 Wenchuan and 2013 Lushan Earthquakes

As a case study of spatial and temporal variations in earthquake stress drops between the 2008 Ms 8.0 Wenchuan and 2013 Ms 7.0 Lushan earthquakes,we computed 1828 stress-drop values for earthquakes with magnitudes 1.7≤ML≤5.0 during an eight-year time span before and after major earthquakes.We divide the study area into three subregions(the southern segment of the Longmen Shan fault zone;the southwestern junction of the Longmen Shan and Sichuan Basin;and the southwestern margin of the Sichuan Basin)and calculate individual event stress drops in each.The results show that regions of alternating high and low stress drop are found on either side of the southwestern segment of the Longmen Shan fault zone.During the two-year period after the 2008 Ms 8.0 Wenchuan earthquake,the stress state of the southern Longmen Shan fault shows no significant change.A marked increase in stress level appears about 18 months before the 2013 Ms 7.0 Lushan earthquake near the Lushan hypocenter zone.Two months after the Ms 7.0 event,the stress drops suddenly attenuate,with significantly less seismic energy release per event.We find that changes in the patterns of high and low stress drop values are consistent with the process of stress accumulation or transfer from the pre-mainshock to postmainshock periods.The results indicate that major earthquakes are the dominant cause of temporal and spatial evolution in stress levels.Stress drop variations show obvious temporal and spatial patterns that may suggests subtle changes in the character of stress fields on faults and spatial variations related to local intense compression and tectonic effects.

Stress evolution of deep surrounding rock under characteristics of bi-modulus and strength drop

Aiming at the circular chamber under uniform stress field in deep energy storage and mining,analytical solutions of stress and plastic zone of the surrounding rock under different far-field stress and internal pressure were derived based on bi-modulus theory and the elastic-brittle-ideal plastic constitutive model.Evolution trend of the elasticplastic stress and plastic region with different elastic constant ratios and residual strength coefficients were analyzed in details.Results revealed that when the internal pressure was small,the three-direction principal stress was compressive stress and the stress field distribution of the surrounding rock was not affected by the moduli difference.The obtained solution was consistent with the solution from the elastic-brittle plastic drop model under the equal modulus theory.On the other hand,when the internal pressure was large,the tangential stress was changed.The surrounding rock can be divided into three zones,i.e.,tensile plastic zone(TPZ),tensile elastic zone(TEZ)and compressive elastic zone(CEZ).The tensile and compressive dual modulus had significant influence on the demarcation point between TEZ and CEZ.In addition,the strength drop and the dual modulus characteristic had a coupling effect on the stress distribution in the surrounding rock.The related achievements further enrich the theory of deep rock mechanics.

On the excavation-induced stress drop in damaged coal considering a coupled yield and failure criterion

Investigating the stress drop of abutment pressure is the key to a deep quantitative analysis of the discontinuous stress redistribution under mining.In the present study,uniaxial and triaxial compression tests are carried out separately to determine the bulk and shear moduli,the cohesion,and the internal friction angle of the coal samples.By extending the meaning of Mohr’s circle referring to yield stress instead of the maximum principal stress,a yield line is introduced to illustrate the stress drop of Mohr’s circle referring to yield stress instead of the maximum principal stress at the elastoplastic boundary.Furthermore,a theoretical solution of the stress drop as a function of the damage is proposed to investigate how the abutment pressure differs considering the yield line and failure line.In addition,applying the stress drop at the yield line in non-pillar mining,top coal mining,and protective coal mining shows that the damage has a nonlinearly positive influence on the stress drop.The results shows that the bulk modulus and internal friction angle have a more sensitive influence on the stress drop than do the shear modulus and cohesion.Finally,the stress drop is divided into a discontinuous stress drop at the yield line and a structural stress drop at the failure line.The stress drop is effective in describing the discontinuous stress redistribution and shows a clear difference in the movement direction of Mohr’s circle considering the unloading pressure.

Scaling of stress drop and high-frequencyfall-off of source spectra

It has been observed for a long time that the high-frequency fall-off constant of source spectra is about 2 for 'large'earthquakes and about 3 for 'small' earthquakes. For earthquakes between 'large' and 'small', the high-frequencyfall-off constant is not an integer and varies with the size of the earthquake. In this article such a variation is explainedin the perspective of the scaling of stress drop, which proposes a new approach to the study of the scaling of stress dropusing seismic data with lower quality of completeness and high-frequency characteristics. The study on the sourcespectra of the aftershocks of the 1988 Lancang-Gengma, Yunnan, China earthquake shows that the high-frequencyfall-off of source spectra and its variation with the size of earthquake can be well explained by the model that for 'large'earthquakes the stress drop is a constant while for ',small' earthquakes the stress drop increases with the size of theearthquake.

Study on determination of stress level by seismic stress drops and the stress axis de-flections before and after large earthquakes

To obtain the stress level at the earthquake source, this paper sets forth the solution of the stress magnitude at the earthquake source by seismic stress drop and the stress axis deflections before and after large earthquakes. The pre-seismic and post-seismic stress direction can be statistically determined by a large collection of foreshock and aftershock focal mechanism data while the stress drop can be determined through the source fracture inversion from seismic wave data or crust deformation data. The paper attempts to make a fundamental contribution to seismic dynamics.

Stress drop assessment of the August 8, 2017, Jiuzhaigou earthquake sequence and its tectonic implications

By using a broadband Lg attenuation model developed for the Tibetan Plateau,we isolate source terms by removing attenuation and site effects from the observed Lg-wave displacement spectra of the M 7.0 earthquake that occurred on August 8,2017,in Jiuzhaigou,China,and its aftershock sequence.Thus,the source parameters,including the scalar seismic moment,comer frequency and stress drop,of these events can be further estimated.The estimated stress drops vary from 47.1 kPa to 7149.6 kPa,with a median value of 59.4 kPa and most values falling between 50 kPa and 75 kPa.The estimated stress drops show significant spatial variations.Lower stress drops were mainly found close to the mainshock and on the seismogenic fault plane with large coseismic slip.In contrast,the highest stress drop was 7.1 MPa for the mainshock,and relatively large stress drops were also found for aftershocks away from the major seismogenic fault and at depths deeper than the zone with large coseismic slip.By using a statistical method,we found self-similarity among some of the aftershocks with a nearly constant stress drop.In contrast,the stress drop increased with the seismic moment for other aftershocks.The amount of stress released during earthquakes is a fundamental characteristic of the earthquake rupture process.As such,the stress drop represents a key parameter for improving our understanding of earthquake source physics.

Period Doubling Bifurcation of Stress Drop for Stick-slip and Its Physical Implication

It is revealed in frictional experiments on medium-scale samples that period doubling bifurcation of stress drop for stick-slip occurs due to macroscopic heterogeneity of the sliding surface under conditions for typical stick-slip.The observed data show that the period doubling bifurcation of stress drop results from the alternate occurrence of strain release along the whole fault and along part of fault.This implies that complicated nonlinear behavior corresponds to clear physical implication in some cases.

Estimation of seismic stress drop from the peak velocity of ground motion

According to the source dislocation model suggested by Brune(1970), the authors have calculated the displacement spectra of S wave and source parameters of the Heqing M S 5 3 earthquake sequence, using the digital data of this sequence obtained in the Western Yunnan Earthquake Prediction Experimental Field (WYEPEF). Based on this calculation we have studied the dependence of the peak velocity ( rv ) of ground motion on the seismic stress drop Δ σ . From the seismic scaling law we obtained ( rv )∝Δ σ 2/3 , thus the three formulae of calculating seismic stress drop Δ σ using the peak velocity parameters can be derived: lg( rv)=d 1+13lg M 0+23lgΔ σ ; lg( rv) =d 2+13 M L+23lgΔ σ ; lgΔ σ =-1 0+1 5lg( rv ) Assuming that the average stress drop Δ σ =3.0×10 6 Pa for great and small earthquakes, then the constants d 1=-3 88 and d 2=-0 38 are determined by the observational data of the Heqing M S5 3 sequence. Results of the source parameters for this sequence show that the seismic moment M 0 is between 10 11 N·m and 10 15 N·m, the rupture radius a of the source is between 200 m and 600 m, the stress drop Δ σ is between 0 1 MPa and 10 MPa and the average stress drop Δ σ =3 7 MPa calculated from the peak velocity parameter of the ground motion. Δσ values measured from these scaling relations are basically in agreement with the results given by Brune′s method( 1970). Results of this study show that the dependence of the ground motion peak velocity parameter (rv) on the stress drop Δσ is even stronger than that on the seismic moment M 0 .

Research on Stress Drops and the Focal Mechanisms of the Xinyuan- Hejing ML6.8 Earthquake Sequences

Based on the digital waveform data recorded by Xinjiang Digital Seismic Network for the Xinyuan-Hejing M_L6.8 earthquake sequences of June 30,2012,this paper analyzes the stress drops of earthquake sequences and the correlation coefficients of focal mechanisms significant for strong aftershocks.Firstly,the source parameters of the Xinyuan-Hejing M_L6.8 earthquake sequences are obtained by applying the spectrum analysis and the Brunes source model.Then,the correlation coefficients of spectral amplitudes are calculated using the low-frequency spectral amplitude recorded by the same station for the different events.Finally,based on the results of the correlation coefficients of spectral amplitudes,the events with similar focal mechanisms are grouped using the clustering method.The results show that:(1)The stress drop values show a steady trend in the aftershock sequence calm period and the stress drop values show a rise-fall in strong aftershocks.(2)The moving average correlation coefficient of amplitude spectrum begins to spread after the main shock.It shows that the correlation decreases between the main shock and the aftershocks in mechanisms.(3)The results of focal mechanism groups show that the earthquake sequences are mainly strike slips.The stress distribution of the main pressure axis is nearly NS,which is the same as the structural stress field.(4)The magnitude and mechanism show that there is an agreement before the strong aftershock,which shows that the regional stress field is enhanced.

Variation of stress during the rupture process of the 1995 M_L=4.1 Shacheng, Hebei, China, earthquake sequence

According to the rupture dynamics of earthquakes, variations of the apparent stress and the difference between the static stress drop and the dynamic stress drop during the rupture of earthquakes are analyzed for the July 20, 1995 ML=4.1 Shacheng, Hebei, China, earthquake sequence. Results obtained show that the apparent stress for main-shock is about 5 MPa, and the average apparent stress for aftershocks 0.047 MPa. During the rupture of the main-shock, the dynamic stress drop is approximately 1.6 times greater than the static stress drop with the difference of nearly 2.7 MPa. The dynamic stress drop is less than the static stress drop for all aftershocks with the average difference of -0.75 MPa. Therefore, when the mainshock occurs the final stress on the focal fault is higher than the dynamic frictional stress, corresponding to that the fault is abruptly locked. When the aftershocks occur the final stress on the focal fault is lower than the dynamic frictional stress, corresponding to that the fault overshoots. It can be seen from the above results that there could be some differences in the physic processes between the mainshock and the aftershocks.

MOTION AND DEFORMATION OF VISCOUS DROP IN STOKES FLOW NEAR RIGID WALL

A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall, viscosity ratios, combined surface tension and buoyancy parameters and ambient flow parameters. Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes. When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances. When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes. In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow, buoyancy and the stronger wall action to the flow. The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis, which increases when the initial stand-off distance increases. When the initial stand-off distance increases the stress induced by drop motion decreases substantially. The surface tension effects resist the deformation and smooth the profile of the drop surfaces. The drop viscosity will reduce the deformation and migration of the drop.

Predicting numerically the large increases in extra pressure drop when boger fluids flow through

Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional vis-cosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Max- well (UCM) models to represent the behavior of so-called Boger fluids in axisymmetric contrac-tion flows, in (unsuccessful) attempts to predict the very large enhancements that were ob-served experimentally. In more recent studies, other constitutive models have been employed to interpret observed behavior and some pro-gress has been made, although finding a (re-spectable) model to describe observed contrac-tion-flow behavior, even qualitatively, has been frustratingly difficult. With this in mind, the present study discusses the ability of a well- known FENE type model (the so-called FENE- CR model) to describe observed behavior. For various reasons, an axisymmetric (4:1:4) con-traction/expansion geometry, with rounded corners, is singled out for special attention, and a new hybrid finite element/volume algo-rithm is utilized to conduct the modeling, which reflects an incremental pressure-correction time-stepping structure. New to this algo-rithmic formulation are techniques in time discretization, discrete treatment of pressure terms, and compatible stress/velocity-gradient representation. We shall argue that the current simulations for the FENE-CR model have re-sulted in a major improvement in the sort-for agreement between theory and experiment in this important bench-mark problem.

Effects of adjuvant Qishen Yiqi Drop Pill therapy on renal function changes and prognosis of patients with early diabetic nephropathy

Objective: To study the effects of adjuvant Qishen Yiqi Drop Pill therapy on renal function changes and prognosis of patients with early diabetic nephropathy. Methods: The patients with early diabetic nephropathy treated in our hospital between February 2015 and April 2017 were chosen and divided into two groups by random number table, observation group received Qishen Yiqi Drop Pill combined with conventional therapy and control group accepted conventional therapy. The renal function indexes, cytokine contents and oxygen free radical generation were compared before treatment and 3 months after treatment. Results:Urine UREA levels as well as serum β2 microglobulin (β2-MG), cystatin C (CysC), tumor necrosis factor-α (TNF-α), interleukin-6 (IL-6), stromal cell-derived factor-1 (SDF-1), interleukin-17 (IL-17), transforming growth factor-β1 (TGF-β1), malondialdehyde (MDA) and 8-iso-prostaglandin F2α (8-iso-PGF2α) contents of both groups were significantly lower while superoxide dismutase (SOD) and total antioxidant capacity (T-AOC) contents were significantly higher after treatment, and urine UREA level as well as serum β2-MG, CysC, TNF-α, IL-6, SDF-1, IL-17, TGF-β1, MDA and 8-iso-PGF2α contents of observation group after treatment was significantly lower than those of control group while SOD and T-AOC contents were significantly higher than those of control group. Conclusion: Adjuvant Qishen Yiqi Drop Pill therapy can improve the renal function and reduce the inflammatory response and oxidative stress response in early diabetic nephropathy.

The Effect of Drop-Landing Height on Tibia Bone Strain

Athletes and military recruits are often afflicted by stress fractures. Rigorous training programs consisting of increased repetitive mechanical loading may contribute to the high incidence of tibia stress fracture in the athletic and army populations. The purpose of this study was to assess the effect of incremented height on tibia bone strains and strain rates during landing. Seven healthy college males performed drop-landing tasks from 26 cm, 39 cm, and 52 cm, respectively. Tibia bone strains and strain rates were obtained through subject-specific multi-body dynamic computer simulations and finite element analyses. One-way repeated measures ANOVAs were conducted. Both 39 cm and 52 cm conditions resulted in larger tibia bone strains and strain rates than the 26 cm condition. The 52 cm condition also resulted in greater bone strains and strain rates than the 39 cm condition. A dose-response relationship exists between incremented landing height and bone strains and strain rates. Activities consisting of high impact landings are associated with increased risk of developing tibia stress fracture. When designing training programs involved high impact activities, athletes and military recruits should consider the effect of impact loading on tibia bone health and giving enough time for bones to adapt to new trainings.

考虑椭圆模型M_W≥5.5地震震源参数时域计算方法

为提高时效性,地震预警系统对震源的处理一般采用“点源”假定,不考虑震源尺度、破裂方向和震源区应力降,对震源参数简化处理使得预测地震动参数分布过于粗略,特别是对破坏性大震.本文应用日本地震(M_W≥5.5)强震动数据,考虑椭圆震源模型,提出了一种适用于中、大地震矩震级、拐角频率和应力降等震源参数时域计算方法,并分析了场地效应、地震动传播衰减、震源效应和滤波频带等因素对时域方法的影响.结果表明,该方法能利用P波信息快速获取震源能量释放过程,量化随破裂传播震源谱拐角频率、应力降和破裂面积的演化过程,为地震动预测提供更多重要的震源参数.

基于震源机制和地震定位研究2022年山西古交M_(L)4.1地震的发震构造

2022年2月20日山西太原古交市发生了M_(L)4.1地震,古交及周边县市震感强烈。此次地震的震中位于历史地震相对稀少、煤矿资源丰富的吕梁隆起区,其发震断裂尚不明确。为了更好地认识这次地震的发震构造,文中利用山西省测震台网的近震波形资料反演了地震的震源机制解,并获得最佳矩心深度。反演结果显示,古交地震是一次左旋走滑型地震事件,矩震级为M_(W)3.96,最佳双力偶解为:节面Ⅰ,走向90°、倾角86°、滑动角-19°;节面Ⅱ,走向182°、倾角70°、滑动角-175°;最佳矩心深度为3km,属于极浅源地震。地震序列重定位结果显示震中的优势展布方向近EW,与区域内断层基本为NE走向的分布格局差异显著。利用聚类分析方法得到古交地震的发震断层面中心解,结果显示断层的走向为91°,倾角为70°。另外,古交地震序列的应力降显著偏小,低于同区域背景地震至少1个数量级。结合实地调研的矿区生产情况和区域地质构造,认为古交地震序列的发震机制可能与震源区附近的煤田开采活动有关,开采活动致使局部应力改变,从而导致先存隐伏断层活化,进而触发此次地震。

乌什 M_(S)7.1地震序列及应力降特征研究

研究乌什M_(S)7.1地震序列时间和空间变化以及震源参数特征,结果表明地震余震主要分布在主震北东和南西两侧,展布与迈丹断裂的走向基本吻合。目前序列b值为0.67,h值为1.3,p值为1.28。震源机制解为逆冲型,应力降处于低值水平,序列衰减基本正常。此次地震为主震—余震型,最大余震为M_(S)5.8地震。

磐安地震序列的震源参数和谱振幅相关系数研究

基于浙江测震台网记录到的2017年2—9月磐安地区发生的地震序列资料,采用Brune震源模型理论和波谱分析方法,得到磐安震群序列的应力降、视应力等震源参数。利用台站的零频幅值,计算谱振幅相关系数。采用聚类分组,并结合Cut and Paste(CAP)反演方法得到ML4.0主地震事件的震源机制解,系统分析小地震的震源机制的一致性程度。结果显示:震源区应力降值在0.00~0.80 MPa之间,整体构造应力较低;谱振幅相关系数较低,在0.86~0.95之间,震源机制整体相似程度不高;应力积累没有形成一个优势方向,可能指示磐安序列为低摩擦应力的断层作用。研究结果表明:磐安地震序列为普通的小震序列,其震源机制类型与构造应力场基本一致;谱振幅相关分析法可为小震序列的震后快速判定提供重要依据。

震源应力降的国内外研究进展综述

应力降作为描述震源标度特性的基本参数,对于了解震源过程的物理性质至关重要,也是地震序列研究和地震危险性评估中必不可少的关键震源参数。为反映近年来国内外关于震源应力降研究的进展,整理了应力降的相关定义、计算方法,探讨了其与地震矩、构造块体、断层参数、震源深度和热流之间的相关性,并对其在构造地震序列研究、诱发地震研究、火山地震研究和地震动预测模型中的应用发展趋势进行梳理和综述。由于应力降的计算过程包含较多不确定性,特别是对于小地震而言,介质特性、数据限制、统计样本以及方法差异等都会对应力降值产生影响,建议在解释和应用的时候,采用多种方法交叉验证,并对不同构造区、不同类型的地震序列进行分别讨论。

循环荷载作用下木材顺纹受力特性与本构模型研究

木材循环受力特性与本构模型是木结构在地震、疲劳荷载作用下受力分析的关键。作者设计并加工了一种适用于顺纹循环加载的棱柱体狗骨状木试件与配套夹具,基于35个试件的单调受拉、单调受压等单调加载和循环受拉、循环受压、等幅拉-不等幅压、等幅拉压等循环加载试验,分析木材在不同加载条件下的变形特征、破坏模式、应力-应变全曲线性质与加卸载刚度变化行为,并结合木纤维损伤与断裂特征,进一步揭示木材单调/循环受力全过程变形机制。结果表明:木材顺纹拉应力呈前期稳定发展、后期随机跌落特征;顺纹受压在峰值荷载后产生屈曲和剪切两种典型局部化变形模式;循环加卸载骨架曲线与木材单调受拉/受压特征相似,卸载后的反向再加载刚度显著退化。在此基础上,建立能够综合描述木材单调与循环受力行为的统一本构模型,并由试验验证其正确性。研究结果可为木结构数值分析与力学评估提供依据。