Effects of Off-fault Damage on Earthquake Rupture Propagation: Experimental Studies

We review the results of a recent series of papers in which the interaction between a dynamic mode II fracture on a fault plane and off-fault damage has been studied using high-speed photography. In these experiments, fracture damage was created in photoelastic Homalite plates by thermal shock in liquid nitrogen and rupture velocities were measured by imaging fringes at the tips. In this paper we review these experiments and discuss how they might be scaled from lab to field using a recent theoretical model for dynamic rupture propagation. Three experimental configurations were investigated: An interface between two damaged Homalite plates, an interface between damaged and undamaged Homalite plates, and the interface between damaged Homalite and undamaged polycarbonate plates. In each case, the velocity was compared with that on a fault between the equivalent undamaged plates at the same load. Ruptures on the interface between two damaged Homalite plates travel at sub-Rayleigh velocities indicating that sliding on off-fault fractures dissipates energy, even though no new damage is created. Propagation on the interface between damaged and undamaged Homalite is asymmetric. Ruptures propagating in the direction for which the compressional lobe of their crack-tip stress field is in the damage (which we term the ‘C’ direction) are unaffected by the damage. In the opposite ‘T’ direction, the rupture velocity is significantly slower than the velocity in undamaged plates at the same load. Specifically, transitions to supershear observed using undamaged plates are not observed in the ‘T’ direction. Propagation on the interface between damaged Homalite and undamaged polycarbonate exhibits the same asymmetry, even though the elastically “favored” ‘+’ direction coincides with the ‘T’ direction in this case. The scaling properties of the interaction between the crack-tip field and pre-existing off-fault damage (i.e., no new damage is created) are explored using an analytic model for a nonsingular slip-weakening shear slip-pulse and verified using the velocity history of a slip pulse measured in the laboratory and a direct laboratory measurement of the interaction range using damage zones of various widths adjacent to the fault.     

灵武断裂晚第四纪活动特征及位移速率

灵武断裂是银川地堑南段的东侧构造边界,与灵武-吴忠地区的地震活动有密切的关系,以往研究程度较低.作者通过实际调查、探槽开挖、年代侧定、相关地貌年代测定、断错历史研究等方面的大量工作对该断层晚第四纪的活动性开展了比较系统的野外考察.本文以野外考察获得的资料为基础,论述了该断层晚第四纪的活动特征,估计了其垂直位移速率.     

A Damage Mechanics Model for Aftershocks

— All earthquakes are followed by an aftershock sequence. A universal feature of aftershock sequences is that they decay in time according to the modified Omori’s law, a power-law decay. In this paper we consider the applicability of damage mechanics to earthquake aftershocks. The damage variable introduced in damage mechanics quantifies the deviation of a brittle solid from linear elasticity. We draw an analogy between the metastable behavior of a stressed brittle solid and the metastable behavior of a superheated liquid. The nucleation of microcracks is analogous to the nucleation of bubbles in the superheated liquid. In this paper we obtain a solution for the evolution of damage after the instantaneous application of a constant strain to a rod. We show that the subsequent stress relaxation can reproduce the modified Omori’s law. It is argued that the aftershocks themselves cause random fluctuations similar to the thermal fluctuations associated with phase transitions.     

Fault Wear by Damage Evolution During Steady-State Slip

Slip along faults generates wear products such as gouge layers and cataclasite zones that range in thickness from sub-millimeter to tens of meters. The properties of these zones apparently control fault strength and slip stability. Here we present a new model of wear in a three-body configuration that utilizes the damage rheology approach and considers the process as a microfracturing or damage front propagating from the gouge zone into the solid rock. The derivations for steady-state conditions lead to a scaling relation for the damage front velocity considered as the wear-rate. The model predicts that the wear-rate is a function of the shear-stress and may vanish when the shear-stress drops below the microfracturing strength of the fault host rock. The simulated results successfully fit the measured friction and wear during shear experiments along faults made of carbonate and tonalite. The model is also valid for relatively large confining pressures, small damage-induced change of the bulk modulus and significant degradation of the shear modulus, which are assumed for seismogenic zones of earthquake faults. The presented formulation indicates that wear dynamics in brittle materials in general and in natural faults in particular can be understood by the concept of a “propagating damage front” and the evolution of a third-body layer.     

酒西盆地内部两条断裂晚第四纪滑动速率研究

通过卫星影像解译、差分GPS测量和地貌年代学样品采集,对位于酒西盆地内部的阴洼山断裂和新民堡断裂晚第四纪滑动速率进行了研究。阴洼山断裂发育于阴洼山东侧,总体走向315°,长约25 km;新民堡断裂整体走向300°,长约20 km,二者皆为全新世活动的逆断层。通过野外考察,选择典型断错地貌进行断层陡坎测量,结合所获相应地貌面的年代数据,得到阴洼山断裂和新民堡断裂晚第四纪垂直滑动速率分别为(0.08±0.02)mm/a和(0.11±0.02)mm/a。结合断裂倾角及前人研究资料,得到垂直祁连山方向酒西盆地内部断裂的地壳缩短速率约为1 mm/a,整个盆地地壳缩短速率约为2.4 mm/a。     

柯坪块体周缘主要断裂闭锁程度与滑动亏损速率的分布特征

利用西南天山山前柯坪块体周缘的多期中国大陆构造环境监测网络区域站及新疆维吾尔自治区地震局在该区域加密布设的多个GPS站点数据,基于负位错反演原理,采用Defnode软件反演,得到柯坪、皮羌和迈丹3条主要断裂的闭锁程度和滑动亏损速率分布特征.模拟结果与实测值总体一致,但略有细微差异,GPS点位密集处残差在1mm/a左右,...     

Structural Properties and Deformation Patterns of Evolving Strike-slip Faults: Numerical Simulations Incorporating Damage Rheology

We present results on evolving geometrical and material properties of large strike-slip fault zones and associated deformation fields, using 3-D numerical simulations in a rheologically-layered model with a seismogenic upper crust governed by a continuum brittle damage framework over a viscoelastic substrate. The damage healing parameters we employ are constrained using results of test models and geophysical observations of healing along active faults. The model simulations exhibit several results that are likely to have general applicability. The fault zones form initially as complex segmented structures and evolve overall with continuing deformation toward contiguous, simpler structures. Along relatively-straight mature segments, the models produce flower structures with depth consisting of a broad damage zone in the top few kilometers of the crust and highly localized damage at depth. The flower structures form during an early evolutionary stage of the fault system (before a total offset of about 0.05 to 0.1 km has accumulated), and persist as continued deformation localizes further along narrow slip zones. The tectonic strain at seismogenic depths is concentrated along the highly damaged cores of the main fault zones, although at shallow depths a small portion of the strain is accommodated over a broader region. This broader domain corresponds to shallow damage (or compliant) zones which have been identified in several seismic and geodetic studies of active faults. The models produce releasing stepovers between fault zone segments that are locations of ongoing interseismic deformation. Material within the fault stepovers remains damaged during the entire earthquake cycle (with significantly reduced rigidity and shear-wave velocity) to depths of 10 to 15 km. These persistent damage zones should be detectable by geophysical imaging studies and could have important implications for earthquake dynamics and seismic hazard.     

青藏高原东北缘主要断裂闭锁特征和滑动亏损研究

利用1999—2015年GPS水平速度场, 基于块体-位错模型, 反演了青藏高原东北缘4条主要断裂(海原断裂, 六盘山断裂, 陇县—宝鸡断裂, 西秦岭北缘断裂)的闭锁程度和滑动亏损速率的空间分布, 并分析了各断裂的地震危险性。 结果显示, 六盘山断裂南段、 陇县-宝鸡断裂北段、 西秦岭北缘断裂东段闭锁程度最强, 闭锁深度达到24 km左右; 西秦岭北缘断裂东段滑动亏损速率最大, 平均值达到3 mm/a; 六盘山断裂南段、 陇县—宝鸡断裂北段滑动亏损速率平均值达到1.9 mm/a, 稍弱于西秦岭北缘断裂东段; 海原断裂闭锁程度和滑动亏损速率相对较小, 闭锁程度和滑动亏损都仅分布在浅部。 我们认为现阶段海原断裂的地震危险性相对较小, 六盘山断裂南段、 陇县—宝鸡北段、 西秦岭北缘断裂东段地震危险性高于这些断裂的其他段落。 这些结果对于青藏高原东北缘地震危险性判定和地震灾害评估具有参考意义。     

Spatio-temporal Slip, and Stress Level on the Faults within the Western Foothills of Taiwan: Implications for Fault Frictional Properties

We use preseismic, coseismic, and postseismic GPS data of the 1999 Chi-Chi earthquake to infer spatio-temporal variation of fault slip and frictional behavior on the Chelungpu fault. The geodetic data shows that coseismic slip during the Chi-Chi earthquake occurred within a patch that was locked in the period preceding the earthquake, and that afterslip occurred dominantly downdip from the ruptured area. To first-order, the observed pattern and the temporal evolution of afterslip is consistent with models of the seismic cycle based on rate-and-state friction. Comparison with the distribution of temperature on the fault derived from thermo-kinematic modeling shows that aseismic slip becomes dominant where temperature is estimated to exceed 200° at depth. This inference is consistent with the temperature induced transition from velocity-weakening to velocity-strengthening friction that is observed in laboratory experiments on quartzo-feldspathic rocks. The time evolution of afterslip is consistent with afterslip being governed by velocity-strengthening frictional sliding. The dependency of friction, μ, on the sliding velocity, V, is estimated to be ${{\partial \mu }/{\partial \, {\rm ln}\, V}} = 8 \times 10^{ - 3}$ . We report an azimuthal difference of about 10–20° between preseismic and postseismic GPS velocities, which we interpret to reflect the very low shear stress on the creeping portion of the décollement beneath the Central Range, of the order of 1–3 MPa, implying a very low friction of about 0.01. This study highlights the importance of temperature and pore pressure in determining fault frictional sliding.     

正演推算1730年北京西郊地震的发震断层和滑动角

通过设定一定的标准,对1730年发生在北京西郊61/2级地震的破坏记录进行数字化,得到地震在地表造成的实际破坏的定量分布图像;使用有限差分方法,计算出两条可能的发震断层--NE向的清河隐伏断层和NW向的东北旺-小汤山断裂在滑动角为0°和90°时,在地表产生的加速度的分布.通过将峰值加速度分布图像与实际破坏程度定量分布图像进行拟合,推算出了两条可能发震断层在这次地震中的作用(权重)及滑动角,从而判断出此次地震的主要发震断层是东北旺-小汤山断裂.为增加结果的可信度,文中还讨论了不同的地表破坏程度数据化模型对拟合结果的影响.     

Can Damage Mechanics Explain Temporal Scaling Laws in Brittle Fracture and Seismicity?

Time delays associated with processes leading to a failure or stress relaxation in materials and earthquakes are studied in terms of continuum damage mechanics. Damage mechanics is a quasi-empirical approach that describes inelastic irreversible phenomena in the deformation of solids. When a rock sample is loaded, there is generally a time delay before the rock fails. This period is characterized by the occurrence and coalescence of microcracks which radiate acoustic signals of broad amplitudes. These acoustic emission events have been shown to exhibit power-law scaling as they increase in intensity prior to a rupture. In case of seismogenic processes in the Earth's brittle crust, all earthquakes are followed by an aftershock sequence. A universal feature of aftershocks is that their rate decays in time according to the modified Omori's law, a power-law decay. In this paper a model of continuum damage mechanics in which damage (microcracking) starts to develop when the applied stress exceeds a prescribed yield stress (a material parameter) is introduced to explain both laboratory experiments and systematic temporal variations in seismicity.     

渭河盆地断裂活动速率的粒子群算法反演

渭河盆地是我国典型的断陷盆地,是中国大陆地裂缝活动、地面沉降活动最剧烈的地区之一.本文利用2004-2007年间的GPS数据,采用粒子群算法与位错理论模型相结合,对渭河盆地主要断裂的三维滑动速率进行了反演计算分析.结果表明:(1)断裂活动性质与地质测量方法获得的结果基本一致:除韩城—华县断裂以张裂为主外,渭河盆地主要断裂均以正倾滑为主,并具有走滑特征,呈张裂的运动趋势;(2)从滑动速率来看,秦岭北侧大断裂速率最大,可达4.5 mm/a.固关—宝鸡断裂活动最小,活动速率仅为1 mm/a左右;(3)在趋势上与现有的地质资料基本一致,以EW向断裂活动最强,NE方向较强,而NW方向较弱,并且分布上呈现南强北弱的特征.     

Revisiting the Tidal Activation of Seismicity with a Damage Mechanics and Friction Point of View

— The Load Unload Response Ratio theory (LURR) puts forward the idea that the ratio of seismicity during times of increased tidal loading to times of decreased tidal loading takes on anomalously large values as the preparatory region of the earthquake approaches a critical state. We repeated the calculations of LURR for several earthquakes in California, for which results had been published, using estimates of the parameters which could be determined from the published work. We were unable to confirm any LURR ratio predictive significance. We test an alternative method of evaluating the influence of tidal stresses on earthquakes based on damage mechanics. As in rock mechanics experiments, it may be that anomalous activation of seismicity prior to large earthquakes occurs only during those time intervals when the applied stress exceeds values previously attained. We applied this approach to analyze the same data set used to test the LURR hypothesis, and it also failed to reveal any significant precursory indications. It may be that time-dependent failure processes such as self-driven nucleation occur on a time scale longer than the diurnal tide, thus destroying the expected synchronization.     

卡斯卡迪亚古陆俯冲带上的间歇式颤动和滑动: 静滑动的嘟囔声

我们在曾一度被认为很平静,具有独特非地震活动特征的地区,北卡斯卡迪亚古陆俯冲带下部界面上观测到一些重复发生的慢滑动事件。颤动式地震信号在时空上与过去6年里连续的地壳运动数据中识别出来的滑动事件相关。在滑动间隔期内,颤动活动小到几乎不存在。我们称这一相关的颤动和滑动现象为“间歇性颤动滑动(ETS)”,并认为ETS活动可用于卡斯卡迪亚古陆大型俯冲地震带应力聚集的实时监测。     

基于择优的块体模型解算南北地震带中南段主要断层滑动速率

In this paper, using the 1999 ~ 2007 GPS velocity field data, and by choosing the optimal block model, we obtained the deformation models applicable to the boundary zones of major blocks and the slip rates of block boundary faults on the mid-southern segment of the North-South Seismic Belt. The results show that： on the Longmenshan fault zone, the tensional and compressive slip rate is small on the Baoxing-Wenchuan segment, about 0. 5 ~ 1.8mm·a^-1, and the rate is relatively significant on the segment of the Wenchuan--Maoxian, as 1.8 ~3.8mm·a^-1; on the Xianshuihe fault belt, there is a certain difference in spatial distribution between the tensional slip rag.e and strike-slip rate： the tensional slip rate （ 8. lmm~a-1） is bigger than the sinistral strike-slip rate （ 4.8mm·a^-1） at the north of the Luhuo region; the tension and compression slip rate is basically the same as the strike-slip rate at Luhuo-Dawu; the Dawu-Kangding section presents a trend of decreased strike-slip rate and increased tensional slip rate; the Kangding-ghimian segment shows a strike-slip nature; the strike-slip rate is significantly greater than the tension/compression rate on the Xiaojiang fault zone; the slip rate on the Red River fault zone shows obvious spatial segmentation, the slip rate is smaller in its northwest part, but with a certain amount of tensional/compression component, 4. 7mm·a^-1 on the Jingdong segment. The segment east of Jingdong （ western Gejiu） is mainly of strike-slip, with a slip rate of 4. 5mm·a^-1.     

Slow Crack Propagation and Slip Correlations

— The propagation of an interfacial crack through a weak plane of a transparent Plexiglas block is studied experimentally. The toughness is controlled artificially by a sand blasting procedure, and fluctuates locally in space like uncorrelated random noise. The block is fractured in mode I at low speed (10^?7?10^?4 m/s). The crack front is observed optically with a microscope and a high resolution digital camera. During the propagation, the front is pinned by micro-regions of high toughness and becomes rough. Roughness of the crack front is analyzed in terms of self-affinity. The in-plane roughness exponent is shown to be 0.63±0.05. Experimental results are compared to a numerical model. The model reproduces the self-affine behavior of the crack front, i.e., long-range correlations of the roughness. Analogies between mode I and mode III are presented in order to discuss implications of the experimental results for creeping faults. Accordingly, correlations of the slip pattern are shown to exist over scales substantially larger than the asperity sizes.     

Maximum Link Distance between Strike-slip Faults: Observations and Constraints

—The maximum fault link distance (lateral separation) between two interacting strike-slip faults is studied in relation to fault length (combined length of the two interacting faults). Data collected for laboratory generated strike-slip faults indicate that fault linkage takes place when the lateral separation between two strike-slip faults is less than one tenth of the combined length of the two faults. Strike-slip faults developed in clay models require a smaller link distance than those developed in gouge materials. About 98% of the data collected for natural strike-slip faults and 93% of earthquake rupture data derived from Knuepfer (1989) follow the rule. These observations support a simple scaling relationship for strike-slip faults, i.e.,W≤ 0.1 L where Wis lateral link distance and L the combined fault length (An and Sammis, 1996a). Two possible explanations are discussed. Assuming a fault continues to be dominantly strike-slip after various fault coalescences, the fault link distance for both compressional coalescence (leading to restraining bend) and extensional coalescence (leading to releasing bend) can be constrained within 0.134 L. Assuming fault coalescence is caused by interaction between breakdown zones at fault tips, then the scaling relationship b = 0.1 l between the size of a breakdown zone, b,and the individual fault length, l (Scholz et al.,1993), leads to the scaling relationship W _max = 0.1 L where W _max is the maximum link distance.¶The above observed relationship between W _max and L may not hold if faults coalesce through preexisting faults, if a fault has a mixed mode other than strike-slip, or if a fault bend is caused by cross faulting rather than fault coalescence. Limited exposure of natural fault traces may also lead to errors in link distance measurements.     

东天山阜康断裂的变形方式与全新世滑动速率

利用实地调查资料对东天山阜康断裂的变形方式和全新世滑动速率进行分析与研究，结果表明：阜康断裂由4条低角度的南倾逆断层斜列组成，具有最新的构造活动性，端部断层活动较弱，全新世平均垂直滑动速率为0.13-0.33mm/a，中部断层活动强烈，全新世平均垂直滑动速率大于1.42mm/a；全新世断层活动方式总体上表现为稳定滑动，西段表现为多期间歇性活动，中、东段表现为持续性活动，更早时期存在直抵地表的快速错动。