Implications of stress-drop models of earthquakes for the inversion of stress drop from seismic observations

We discuss the inversion of stress drops from seismic observations on the basis of crack or stress-drop models of earthquake mechanism. Since a formal inverse problem cannot be posed at present we discuss implications of solutions to direct problems. We first discuss the static approximations used to obtain stress drop from seismic moment and source dimensions. We show that the geometrical effects are quite significant if only one source dimension has been retrieved from seismic observations. The effect of variable stress drop is discussed and we show that the inverted stress drop is not a simple average of the actual stress drops on the fault. We discuss the energy release during faulting and show that the apparent stress has a complicated relation to the stress drop on the fault. We also show that the static stress drops obtained by seismologists are a lower bound to the actual dynamic stress drops on the fault. This may in part explain disagreements with laboratory results. Finally, we discuss the inversion of source dimensions from the far-field radiation. We analyse two extreme, simple dynamical source models, a circular fault and a rectangular fault and show that geometry has a much more pronounced effect on radiation than is usually acknowledged.     

Apparent stress scaling for tectonic and induced seismicity: Model and observations

A macroscopic model of seismic sources provides a scaling relationship for the apparent stress, treated as a function of three independent parameters: seismic moment, rupture area size, and average slip acceleration. These parameters represent three different factors: kinematic, geometric and material. This relationship allows us to distinguish and explain the following statistical characteristics of the log apparent stress versus log seismic moment plot. The regional trends, represented by a series of 1/2 slope lines, are related to the averaged shape of slip velocity pulses, so they reflect kinematic characteristics of the rupture process. The global trend, represented by the 1/6 slope line, is expected to characterize sets of events of wide range of rupture area sizes and assumes dependence of rupture area size on total slip, so it is related to the rupture initiation, propagation and arrest conditions; therefore, it reflects earthquake rupture dynamics. Additional shiftings among the trend lines obtained for the smallest induced tremors, larger tectonic earthquakes, and slow tsunami earthquakes, reflect differences between the intact rock failure and the frictional slip failure, that is, between fracture energies of these different earthquake classes.     

张家口—渤海地震带中小地震应力降分布特征

采用河北测震台网资料,分析了张家口—渤海地震带2008—2018年1220条ML≥2.0地震的应力降.结果表明,应力降可能与应力有关,并且随震级的增加而出现不同尺度的变化,该区域应力降优势分布为0.70—3.00 MPa.     

A determination of source properties of large intraplate earthquakes in Alaska

Historically, large and potentially hazardous earthquakes have occurred within the interior of Alaska. However, most have not been adequately studied using modern methods of waveform modeling. The 22 July 1937, 16 October 1947, and 7 April 1958 earthquakes are three of the largest events known to have occurred within central Alaska (M _s =7.3,M _s =7.2 andM _s =7.3, respectively). We analyzed teleseismic body waves to gain information about the focal parameters of these events. In order to deconvolve the source time functions from teleseismic records, we first attempted to improve upon the published focal mechanisms for each event. Synthetic seismograms were computed for different source parameters, using the reflectivity method. A search was completed which compared the hand-digitized data with a suite of synthetic traces covering the complete parameter space of strike, dip, and slip direction. In this way, the focal mechanism showing the maximum correlation between the observed and calculated traces was found. Source time functions, i.e., the moment release as a function of time, were then deconvolved from teleseismic records for the three historical earthquakes, using the focal mechanisms which best fit the data. From these deconvolutions, we also recovered the depth of the events and their seismic moments. The earthquakes were all found to have a shallow foci, with depths of less than 10 km.The 1937 earthquake occurred within a northeast-southwest band of seismicity termed the Salcha seismic zone (SSZ). We confirm the previously published focal mechanism, indicating strike-slip faulting, with one focal plane parallel to the SSZ which was interpreted as the fault plane. Assuming a unilateral fault model and a reasonable rupture velocity of between 2 and 3 km/s, the 21 second rupture duration for this event indicates that all of the 65 km long SSZ may have ruptured during this event. The 1947 event, located to the south of the northwest-southeast trending Fairbanks seismic zone, was found to have a duration of about 11 seconds, thus indicating a rupture length of up to 30 km. The rupture duration of the 1958 earthquake, which occurred near the town of Huslia, approximately 400 km ENE of Fairbanks, was found to be about 9 seconds. This gives a rupture length consistent with the observed damage, an area of 16 km by 64 km.     

中国大陆现代构造应力场与强震活动

依据应力性状和力源特征,中国大陆现代构造应力场可划分为四级应力区.它们分别是2个一级应力区、4个二级应力区、5个三级应力区和26个四级应力区.通过分析中国大陆现代构造应力分区与强震活动之问的关系,初步获得以下结论:①构造应力作用强烈和复杂的地区是强震频发的地区;②应力区边界是强震集中发生的地带;③应力方向、应力结构类型...     

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

Introduction The study of tectonic stress field, a major branch of the Earth science, plays an important role in geodynamics. The world stress map plan started from 1980s and was leaded by Zoback. Lots of scientists from many countries participated this plan. The plan collected global tectonic stress measurements and research results and established global stress database. The world stress map was edited based on the global stress database. The world stress map reflected feature of global li…     

Earthquake strong motion simulated by stress drop models

Shallow strike slip earthquakes on vertical faults are modelled as two-dimensional antiplane strain ruptures in a uniformly prestressed homogeneous halfspace. Behind the rupture front, which is specified, the stress drops to a lower value. The elastodynamic boundary value problem is solved with a finite difference method. Several cases are studied, which include symmetric and one-directional rupture propagation, surface faulting, multiple events, variable rupture velocity, sticking and rebreaking of the fault plane. The time function of displacement, velocity and acceleration are interpreted as signals generated by events in the focus, namely starting, stopping and breaking through the surface of the rupture. The model explains peak velocity and peak acceleration in the near field of M5.5–6 earthquakes; which are typically about 0.2 m/s and 5 m/s² at 10 km epicentral distance, if the rupture velocity is close to the shear wave velocity. Sticking of the fault does not alter the accelerograms significantly, but it increases the seismic moment in simple events and decreases it in multiple events.Contribution No. 226, Geophysical Institute, University of Karlsruhe.     

由空间大地测量得到的太平洋板块现今构造运动与板内形变应变场

推导了板块的弹性运动方程.根据太平洋板块(PCFC)上空间大地测量的观测结果,建立了PCFC的弹性运动模型,该模型与板块实际运动状态的符合程度明显地优于刚体运动模型.研究表明：PCFC现今旋转的角速度比过去3Ma的平均值大0.037°/Ma;在PCFC内部存在明显的水平形变,在15°S以北和204.5°E以西地区存在一致的向西形变,北西与南西方向的形变速率分别为0.8～3.5 mm/a与1.0～3.4 mm/a;在板块的东南区存在一致的向东形变,北东与南东方向的形变速率分别为1.5～1.8 mm/a与2.8～9.1 mm/a.PCFC内部水平应变场的空间变化是有规律的,在PCFC的西北部,主压应变轴为NW-SE方向,主压应变率大于主张应变率;在PCFC的东南部,主压应变轴为NE-SW方向,主张应变率大于主压应变率;PCFC的东南边界是扩张边界,边界附近的主张应变率最大（平均为1.51×10-9/a）,主张应变轴基本上与洋中脊的扩张方向一致;PCFC的西北边界是俯冲边界,边界附近的主压应变率最大（平均为0.75×10-9/a）,主压应变轴基本上与太平洋板块的俯冲方向一致.     

Apparent stress scaling and statistical trends

Statistical relations between different earthquake parameters, such as M₀ (seismic moment), E_S (seismic energy), τ_a (apparent stress), A (rupture area), g (average slip acceleration), are investigated. For this purpose, a kinematic earthquake model representing averaged earthquake rupture process is formulated. The model implies a scaling relationship for τ_a as a function of three other parameters, related to kinematic (M₀), geometric (A) and material (g) source characteristics, which, according to the model, can change independently. This scaling relation is used to explain statistical trends that characterize different earthquake data sets (including micro-, small, moderate and large events) plotted in the log τ_a − log M₀ space, and to determine the area in this space, where typical earthquakes occur. The scaling relationship is interpreted in terms of the apparent stress minimum (i.e., the most uniform among the possible earthquake rupture patterns). It is concluded that, although the apparent stress increases on an average with increasing seismic moment, small and large earthquakes are essentially similar.     

新疆两次强震前后地震视应力变化

选取了喀什数字地震台记录的喀什及周边地区地震的宽频带波形资料,分析处理了2001～2005年Ms 3.5以上地震164次,通过数字地震波谱计算了标量地震矩和地震辐射能量,从而进行了视应力的计算.给出了巴楚-伽师Ms 6.8和乌什Ms 6.3强震前后视应力的时序变化情况,发现其视应力均表现出震前低应力阶段-主震前的逐渐上升-震后逐渐恢复的动态变化过程,即地震的孕震-发震-震后调整的阶段性变化特征.这一结果可为喀什及周边地区今后进行地震预测预报研究提供参考依据,对该区开展数字地震方面的研究也有所帮助.     

地震应力降研究进展

地震发生前后,地震断层面上会产生应力降。本文就应力降的定义、计算方法、影响因素、研究进展、存在问题及在地震研究中的应用等进行详细分析、整理,阐述地震应力降在国内外的研究进展,以期对地震活动的分析与研究提供参考。     

Effect of slip rate on stress drop

Recent observations made by Kanamori and Allen about earthquake recurrence time and average stress drop revealed a very interesting relation: earthquakes with longer recurrence times have higher average stress drops. They attributed the difference in stress drop to the difference in long-term average slip rate. To interpret their result in terms of the healing effect, we simulated earthquake recurrence with a one-dimensional mass-spring model, incorporating a recently developed rate-and-state dependent friction law for different loading rates and heterogeneous strength distributions. We first calculated the stress drop and recurrence time as functions of loading rate for a homogenous fault model. We found that the stress drop increases up to 30% when the loading rate decreases from 10 cm/yr to 0.01 mm/yr. Thus, the observed great variability of stress drop, from a few bars to a few hundred bars, which is obtained by replotting the data of Kanamori and Allen in the form of stress drop versus long-term slip rate, may not be attributable to the healing effect alone. Our numerical simulation shows that the variability may be due primarily to the spatial heterogeneity of strength on the fault. Our simulation also suggests that of the two empirical laws that were inferred from the same laboratory friction data, called the power law and the logarithmic law by Shimamoto and Logan, the former can explain the observed relation between stress drop and slip rate better than can the latter, at least for strike-slip fault. The logarithmic law is an earlier and simpler version of the rate-state-dependent friction law.     

State of tectonic stress in Shillong Plateau of northeast India

Tectonic stress regime in the Shillong plateau, northeast region of India, is examined by stress tensor inversion. Some 97 reliable fault plane solutions are used for stress inversion by the Michael and Gauss methods. Although an overall NNW-SSE compressional stress is observed in the area, the stress regime varies from western part to eastern part of the plateau. The eastern part of the plateau is dominated by NNE-SSW compression and the western part by NNW-SSE compression. The NNW-SSE compression in the western part may be due to the tectonic loading induced by the Himalayan orogeny in the north, and the NNE-SSW compression in the eastern part may be attributed to the influence of oblique convergence of the Indian plate beneath the Indo-Burma ranges. Further, Gravitational Potential Energy (GPE) derived stress also indicates a variation from west to east.     

利用静态、动态应力降比值判断东北地震震后趋势

统计分析2005年以来黑龙江及周边地区中强地震的频谱特征,分别计算各地震的应力降,利用静态与动态应力降比值,判断该区中强地震震后趋势。研究发现,2005年以来该区中强震Y值较大,在0.3—0.6,以孤立型地震为主。     

Scaling of stress drop and high-frequency fall-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 highfrequency fall-off constant is not an integer and varies with the size of the earthquake. In this article such a variation is explained in the perspective of the scaling of stress drop, which proposes a new approach to the study of the scaling of stress drop using seismic data with lower quality of completeness and high-frequency characteristics. The study on the source spectra of the aftershocks of the 1988 Lancang-Gengma, Yunnan, China earthquake shows that the high-frequency fall-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 the earthquake.     

糯扎渡水库地区地震活动和震源参数研究

本文利用糯扎渡水库台网和景洪水库台网记录的地震波形反演震源谱, 计算了2011年1月至2014年3月糯扎渡水库附近143个1.0级以上地震的震源参数。 分析研究发现: ① 糯扎渡水库蓄水后, 库区内地震活动明显增强, 尤其是在水位上升3~4个月后; ② 水库开始蓄水后, 库区内地震震源深度变浅, 一段时间以后则与库区外的差别减小; ③ 地震拐角频率随地震矩增大而减小, 且蓄水以后, 库区内地震拐角频率的对数与地震矩的对数线性关系更明显; ④ 应力降、 视应力与地震矩存在正相关关系, 且相同地震矩时库区内的应力降与视应力低于蓄水前和库区外的地震应力降与视应力值; ⑤ 蓄水对库区内地震的影响可延伸至库底10 km深度处, 且在3~6 km深度内影响最大、 库区内外地震频度与视应力均值差异最显著。     

黏滑实验的震级评估和应力降分析

本文通过三种结构模型的黏滑地震模拟实验,利用高频速度连续观测系统获得了地震失稳过程的速度特征,讨论了最大位移量的选取方法,估算了实验室黏滑型地震的矩震级,探讨了黏滑类型、应力降大小与震级的关系.结果表明,黏滑型地震的应力降过程可能包含一次到多次高频振荡,对应若干次黏滑子事件.高频振荡的摆动幅度很大,包含有多种频率成分,峰值速度0.003~0.008 m·s-1.初步估计黏滑型地震的震级范围为-4.4~-3级,断层构造面的差异对各种黏滑模型的地震震级分布有明显影响.总体来看应力降与地震震级没有明显相关性,决定地震震级的主要因素应当是震源尺度.     

Source mechanism of small-moderate earth- quakes and tectonic stress field in Yunnan Province

IntroductionYunnanProvinceislocatedinthesouthofNorth-SouthseismiczoneinChina.ItisoneofthehighseismicactiveregionsinChinesemainland.Morethanonehundredstrongearthquakeswithmagnitude6ormoreoccurredinthisregioninhistory.AsanimportantsoutheasternmarginofTibetanPlateau,YunnanregionisahotspotinstudyonthedynamicsofTibetanPlateau.Theactionsofcompressivestressinnorth-southorientationandgravitationalpotentialcausedlateralextrusionofmaterialintheplateauwiththeupliftingofTibetanPlateau.Severalblocksa…     

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

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甘肃景泰MS5.9地震前后小地震视应力计算讨论

分析处理甘肃数字化地震台网记录到的1999年11月至2000年6月的68个地震，给出了甘肃景泰2000年6月6日Ms5．9地震前后小地震的视应力变化情况，得到该区的视应力水平，并讨论了主震前后的视应力演化特征以及视应力与震级的关系。