Normal and shear stresses acting on arbitrarily oriented faults, earthquake energy, crustal GPE change, and the coefficient of friction

As usual, earthquake energy is defined as the total energy released from an earthquake, which is partitioned into radiated energy, friction energy, and rupture energy regardless of crustal gravitational potential energy (GPE) change. We analyze the energy and stress parameters in earthquake energy budget. For arbitrarily oriented faults, we deduce the formulas for calculating the normal and shear stresses acting on the fault under principal stresses. We show that shear stress is composed of horizontal and vertical shear stresses. Then, we provide the expressions for computing crustal GPE change and the coefficient of friction. The GPE change should be considered, except strike-slip faulting, when investigating earthquakes. Also, for various faulting types, we show that the ratio of differential stresses is related to the fault orientation and the relative magnitudes of stresses. Finally, “12 May, 2008, Wenchuan, Sichuan, China, M_W 7.9 Earthquake” is cited to analyze and calculate various energy/stress parameters and the coefficient of friction. Our result of GPE change coincides with the post-event field observations.     

地壳介质剪切波分裂研究的部分进展

剪切波穿过各向异性介质传播时会发生分裂现象,而在地壳中产生各向异性的主要因素是大量充满液体的定向排列的微裂隙。通过剪切波分裂参数可以研究地壳介质的特性、地壳应力状态及应力场的变化,并可用于地震预测。利用地壳介质各向异性特征研究断层性质也是一个新的动向。     

地壳深部稳定性——震源体破裂机制和摩擦滑动机制的综合研究

本文通过地壳应力测量结果和地震资料的综合分析,对深部应力状态与断层运动的关系作了讨论:进而应用库仑准则,推导了三维应力作用下完整岩体和已有的任意空间方向断层面的失稳条件及其滑动方式的解析表达式.通过建立描述岩体和已有断层稳定性的两个函数————破裂函数 Fm 和摩擦函数 Ff,给出了应用破裂机制和摩擦滑动机制综合分析地壳稳定性和失稳性态的方法:根据这种分析方法并结合华北平原区的水压致裂应力测量资料,以及孔隙压力、大地热流等观测结果,定量研究了本区地壳的稳定问题,计算并图示了地壳内破裂函数沿深度的分布,以及各种走向和倾向断层面上的摩擦函数和剪应力分布;计算中以 Byerlee 定律作为断层运动的约束条件,并考虑了地壳密度纵向非均匀性导致的垂直应力沿深度的非线性增长以及深部超静水压力的异常孔隙压力作用.结果表明,华北平原区地壳失稳性态主要表现为已有断层的滑动;伴有高剪应力降的断层运动的深度范围在8至2.0多公里之间:陡断层稳定性低于缓断层,其运动方式以走滑为主;本区 NNE-NE 走向的陡断层是一组易震断层,其震时错动为右旋走滑;孔隙压力的增长对地壳稳定性有显著的影响;华北平原区深部高异常孔隙压力是地震活动的一种重要背景.      

Seismic-frequency Laboratory Measurements of Shear Mode Viscoelasticity in Crustal Rocks II: Thermally Stressed Quartzite and Granite

—Forced torsional oscillation techniques have been used to explore the seismic-frequency shear mode viscoelasticity of specimens of two crustal rocks (Cape Sorell quartzite and Delegate aplite), cycled between room temperature and 700°C under conditions of moderate confining pressure. The anisotropy and intergranular inhomogeneity of thermal expansivity in these materials give rise to large deviatoric stresses, resulting in thermal cracking at temperatures above a pressure-dependent threshold temperature, associated with the onset of very pronounced temperature sensitivity of the shear modulus, in general accord with the predictions of fracture mechanics models. For Delegate aplite in particular, the shear modulus behaves reproducibly during multiple thermal cycles at different confining pressures, consistent with the notion that the thermal cracks are of low aspect ratio (minimum/maximum dimension), and are therefore readily closed by the prevailing confining pressure once the thermal stresses are removed. Marked frequency-dependent dissipation of shear strain energy is observed on heating each rock to temperatures ≥ 500°C, although the attenuation varies significantly with prior thermal history, probably as a result of progressive dehydration and relaxation of deviatoric stresses. Temperature and pressure dependent crack densities for Delegate aplite have been estimated by comparison of the observed shear moduli with those expected for a crack-free aggregate. In parallel with the forced oscillation tests, measurements have been made of the rate at which (argon) pore pressure equilibrium is re-established following a perturbation. Combination of these results, which provide a proxy for permeability, with the inferred crack densities indicates that the variation of permeability with crack density is well described by a percolation model with a threshold crack density of ～0.2.     

Propagation of slip along frictional surfaces

The propagation of slip along a pre-existing frictional plane is formulated for the faults containing interstitial fluid. When normal and shear stresses satisfy the effective frictional law, a frictional sliding occurs stably or unstably, depending on the inhomogeneities of the surface. For a slip to rapidly sweep the surface, the pore pressure of fluid must exceed the critical value that is related to the physical or geometrical irregularities of the surface. If this condition fails, stable sliding is expected, analogous to a seismic fault creep. This prediction makes the role of water in seismic faulting more clear.     

主应力轴持续旋转条件下饱和松砂的振动孔隙水压力特性

利用新研制的“土工静力-动力液压三轴-扭剪多功能剪切仪”,针对福建标准松砂,在三向非均等固结条件下,进行了能够模拟海洋波浪荷载作用下主应力轴连续旋转的循环耦合剪切试验。通过试验着重探讨了初始主应力方向、振动过程中主应力方向连续变化对不排水条件下砂土的振动孔隙水压力增长特性的影响。实验研究表明:在振动过程中主应力轴连续旋转的条件下,初始主应力方向对砂土的动孔压比与振次比之间关系具有显著的影响,随着初始大主应力与竖向之间夹角的增大,动孔压比的增长速度明显加快,具有较好的规律性;归一化孔压比与广义剪应变之间的关系基本上与初始主应力方向角和振动剪应力幅值无关。     

Preliminary analysis on the tectonic stress level in the source region of Tangshan earthquake

Introduction Analyzing tectonic stress field based on focal mechanism data is an important way to the study tectonic evolvement of lithosphere and associated dynamic process. Such studies growrapidly in China and abroad (Zoback, 1992; Plenefisch, Bonjer, 1997; XU, 1985; CUI, XIE, 1999). At present most of the studies focus on the inversion of focal mechanism data for the direction and relative magnitude of stress tensor, and few on absolute stress. Using focal mechanism and fault scratch,…     

Undrained cyclic triaxial behavior of saturated clays under variable confining pressure

A laboratory study on the undrained dynamic behavior of saturated clays in cyclic triaxial tests with a variable confining pressure (VCP tests) is presented. Tests were performed on remolded clayey samples using a dynamic triaxial device where the deviatoric stress and confining pressure can be varied simultaneously. Various cyclic stress paths have been applied on the specimens through varying the ratios or phase differences between the cyclic deviatoric stress and cyclic confining pressure. Specifically, the stress paths used in the present study were designed to simulate the coupling effects of simultaneously varying shear and normal stresses in clays due to earthquakes and other vibration sources. Test results obtained from this study show that the undrained response of saturated clays is strongly influenced by the variation of confining pressure, in terms of pore water pressure, development speed of cyclic strain and magnitude of cyclic strength. It is found that when strong P-waves are propagating in soil layers, VCP tests are more appropriate for the simulation of in situ stress fields than the conventional cyclic triaxial tests with a constant confining pressure (CCP tests).     

Seismic measurements of the internal properties of fault zones

The internal properties within and adjacent to fault zones are reviewed, principally on the basis of laboratory, borehole, and seismic refraction and reflection data. The deformation of rocks by faulting ranges from intragrain microcracking to severe alteration. Saturated microcracked and mildly fractured rocks do not exhibit a significant reduction in velocity, but, from borehole measurements, densely fractured rocks do show significantly reduced velocities, the amount of reduction generally proportional to the fracture density. Highly fractured rock and thick fault gouge along the creeping portion of the San Andreas fault are evidenced by a pronounced seismic low-velocity zone (LVZ), which is either very thin or absent along locked portions of the fault. Thus there is a correlation between fault slip behavior and seismic velocity structure within the fault zone; high pore pressure within the pronounced LVZ may be conductive to fault creep. Deep seismic reflection data indicate that crustal faults sometimes extend through the entire crust. Models of these data and geologic evidence are consistent with a composition of deep faults consisting of highly foliated, seismically anisotropic mylonites.     

复杂应力条件下饱和松砂单调与循环剪切特性的比较研究

本文利用大连理工大学新引进与开发的“土工静力-动力液压-三轴扭转多功能剪切仪”,针对福建标准砂,在不排水条件下同时进行了单调剪切试验与循环剪切试验,进而对其进行了对比分析。通过比较表明,应力-应变关系的应变软化和硬化特性与流滑变形和循环流动特性密切相关,当循环剪切应力水平高于单调剪切过程中应变软化阶段最小强度时将会发生流滑变形。无论在单调剪切中,还是在循环剪切中,稳定状态时的有效偏应力比随着大主应力方向与竖向之间夹角的增大而减小,在中主应力系数相同的条件下,循环剪切中呈现显著剪胀时的有效偏应力比和最终稳定状态时的有效偏应力比峰值分别与单调剪切中达到相变状态时的有效偏应力比和最终稳定有效偏应力比基本上一致。然而不排水条件下单调与循环剪切过程中孔隙水压力的增长特性却并不相同,循环剪切中的最大孔隙水压力随着初始主应力方向角的增大而减小,单调剪切中的最大孔隙水压力却随着主应力方向角的增大而增大。     

Can injection tests reveal the potential for fault movements?

The role of fluids in faulting mechanism and triggering earthquakes is widely accepted. The effective-stress law is the basis for the postulated theories. Using a generalized version of this law, applicable to both continuum and discontinuities, hydromechanical behaviour of a horizontal fracture in a hypothetical fluid-injection problem is investigated. In this problem the increasing intake flow rates, unpredictable by the traditional fluid-flow solutions, brings out another significant aspect of the role of the fluid pressure in rocks. By reducing the magnitude of the compressive effective stresses the fluid pressure causes elastic recovery in fractures. Simple rheologic models are used to demonstrate this fact. Such effects may lead to permeability increases in the rock mass, depending on the magnitude of the fluid pressure. Such variations in permeability, however, are governed by the path dependency of the fracture-deformation response. Therefore, a significant increase in permeability is an indication of comparability of the state of stress and the applied fluid pressure.This index may reveal the potential of hydroactivation of faults, as may arise in the regions of dam reservoirs, underground waste injections, and known faults, for certain ranges of working pressures relevant to each of the above-cited situations. Fluid-injection tests under constant working pressures are suggested as a means revealing the likelihood of movement on the faults.     

Triggered earthquakes and deep well activities

Earthquakes can be triggered by any significant perturbation of the hydrologic regime. In areas where potentially active faults are already close to failure, the increased pore pressure resulting from fluid injection, or, alternatively, the massive extraction of fluid or gas, can induce sufficient stress and/or strain changes that, with time, can lead to sudden catastrophic failure in a major earthquake. Injection-induced earthquakes typically result from the reduction in frictional strength along preexisting, nearby faults caused by the increased formation fluid pressure. Earthquakes associated with production appear to respond to more complex mechanisms of subsidence, crustal unloading, and poroelastic changes in response to applied strains induced by the massive withdrawal of subsurface material. As each of these different types of triggered events can occur up to several years after well activities have begun (or even several years after all well activities have stopped), this suggests that the actual triggering process may be a very complex combination of effects, particularly if both fluid extraction and injection have taken place locally. To date, more than thirty cases of earthquakes triggered by well activities can be documented throughout the United States and Canada. Based on these case histories, it is evident that, owing to preexisting stress conditions in the upper crust, certain areas tend to have higher probabilities of exhibiting such induced seismicity.     

紫坪铺水库区域地壳Qs成像及其与渗透关系研究

利用衰减结构层析成像方法尝试对紫坪铺水库区域地壳Q_s进行成像,获得该区浅层地壳静态及蓄水前、后的Q_s变化特征,结合实验研究成果、岩体岩性、断裂构造、水文地质条件探讨库水的渗透作用及其对地壳介质的影响,对研究区内地震活动类型及发震成因的介质物性变化进行了讨论.研究结果表明:紫坪铺水库区域地壳Q_s横向不均匀变化显著,库区周边近似存在低Q_s值环形区域,主要包括水库东北、东南、西南、西北及库区中段五个区域.其中,水库东北、库区中段、西南低Q_s区域与库水渗透关系密切,初步认为库水可能沿着通济场断裂中段和两端的岩石破碎带及节理、裂隙发育地区向地下渗透,使岩石孔隙中充满流体,内摩擦增大,地震波大大衰减,从而导致Q_s值大幅下降.同时,在西南区诱发了水库小震群,在东北区和东南区诱发了部分水库小震群.另外,紫坪铺水库区域东北、东南、西南三个小震群基本位于高Q_s值(低衰减)和低Q_s值(高衰减)过渡区域,可能由于低Q_s区地震波衰减大,不易积累能量,而高、低Q_s值的过渡区域,介质介于"软"、"硬"之间,有可能积累应变能,孕育地震.当高、低Q_s过渡区域岩石裂纹饱含水或部分含水后,水对裂纹边界起潮湿和润滑作用,降低了发震断层的抗剪强度,使滑动容易产生,从而诱发地震.     

Evolution of Stress Fields and Faulting in Seismic Zones

—Measurements indicate that stress magnitudes in the crust are normally limited by the frictional equilibrium on pre-existing, optimally oriented faults. Fault zones where these limitations are frequently reached are referred to as seismic zones. Fault zones in the crust concentrate stresses because their material properties are different from those of the host rock. Most fault zones are spatially relatively stable structures, however the associated seismicity in these zones is quite variable in space and time. Here we propose that this variability is attributable to stress-concentration zones that migrate and expand through the fault zone. We suggest that following a large earthquake and the associated stress relaxation, shear stresses of a magnitude sufficient to produce earthquakes occur only in those small parts of the seismic zone that, because of material properties and boundary conditions, encourage concentration of shear stress. During the earthquake cycle, the conditions for seismogenic fault slip migrate from these stress-concentration regions throughout the entire seismic zone. Thus, while the stress-concentration regions continue to produce small slips and small earthquakes throughout the seismic cycle, the conditions for slip and earthquakes are gradually reached in larger parts of, and eventually the whole, seismogenic layer of the seismic zone. Prior to the propagation of an earthquake fracture that gives rise to a large earthquake, the stress conditions in the zone along the whole potential rupture plane must be essentially similar. This follows because if they were not, then, on entering crustal parts where the state of stress was unfavourable to this type of faulting, the fault propagation would be arrested. The proposed necessary homogenisation of the stress field in a seismic zone as a precursor to large earthquakes implies that by monitoring the state of stress in a seismic zone, its large earthquakes may possibly be forecasted. We test the model on data from Iceland and demonstrate that it broadly explains the historical, as well as the current, patterns of seismogenic faulting in the South Iceland Seismic Zone.     

Moment Tensor Solutions and Triggering Environment for Earthquakes in Koyna-Warna Water Reservoirs Region,India

We consider nine earthquakes in the Koyna-Warna reservoir region on the western side of the Peninsular India. The deviatoric moment tensors of these earthquakes have been evaluated by minimizing the least-squares misfit between observed and synthetic seismograms. We use broadband seismograms of observatories at KARD and PUNE which are at distances of nearly 50 and 150 km, respectively, from the epicenters. Both surface wave inversion and the difference between the arrival times of SH and SV show the presence of an anisotropic crust. However, we have obtained an equivalent isotropic structure by improving the published crustal structures of this area through inversion of surface wave group velocity data. The deviatoric moment tensors of the earthquakes are decomposed into two components: double-couple and compensated linear vector dipoles (CLVD). The double-couple components of all the nine earthquakes show normal faulting with minor strike slip; the T axis is consistently subhorizontal with an average azimuth of 260.6° and the P axis is nearly vertical. The fault planes of six events give average strike direction and dip, respectively as 194.0° and 51.8° and are associated with the main fault of the area. The other three events lie in the southern part of this area and have strike direction between SSE and SE which is parallel to the tectonic features in this part. The CLVD component is generally within 20 percent of the total moment tensor. Recent studies show that anisotropy can produce source mechanism with CLVD up to 30 percent and can also cause high pore fluid pressure leading to fault instability more rapidly compared to conventional mechanism in an isotropic medium. It appears that the anisotropic crust, noted in the present work, is generating the CLVD component and also gives the proper environment to trigger earthquakes by reservoirs through pore fluid pressure.     

Comprehensive study on stability of deep crust and unstable behavior of earthquake source by both failure mechanism and frictional sliding mechanism

In this paper the relation between fault movement and stress state in deep crust is discussed, based on synthetic analysis of the crustal stresses measured over the world and the concerned data of focal mechanism. Using Coulomb criterion for shear failure and frictional slip, analytical expressions for estimating stabilities of intact rock and existing fault in the crust and for identifying the type of faulting (normal, strike-slip or thrust fault) are derived. By defining the Failure FunctionF _m and the Fraction FunctionF _f, which may describe steadiness of crustal rock and existing fault, respectively, a synthetic model is set up to consider both fracturing mechanism and the sliding mechanism. By this model, a method to study stability and unstable behavior of crustal rock and fault at different depths is given. According to the above model, quantitative study on the crustal stability in the North China plain is made in terms of the measured data of hydraulic fracturing stress, pore-fluid pressure, terrestrical heat flow in this region. The functionsF _m andF _f and the shear stresses on faults with different strike angle and dip angle at various depths in this region are calculated. In the calculation the constraint condition of fault movement obeys Byerlee’s Law, and the depth-dependent nonlinear change in the vertical stress due to inhomogeneity of crustal density and the high anomalous pore-fluid pressure in deep crust of this region are considered. The conclusions are: the unstable behavior of the crust in the North China plain is not failure of crustal rock but slip on existing fault; the depth range where stick-slip of fault may happen is about from 8 to 20 km or more; stability of steep fault is lower than that of gentle sloping fault; the shear stresses in the range where may occur stick-slip are nearly horizontal; the steep faults trending from NNE to NE in this region are liable to produce strong earthquakes, whose co-seismic faultings are, for the most part, right lateral slip; the change in pore-fluid pressure in depth remarkably affects the stability of the crust and the increase in pore-fluid pressure, therefore, would be an important factor exciting strong earthquake in this region. The above theoretical inferences are consistent with the data measured in this region. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologia Sinica,13, 450–461, 1991. This work is supported by Chinese Joint Seismological Science Foundation.     

地下水诱发的浅层前兆异常及其机理与有关的地震预报问题(1)

依照“源、场、外”相结合的地震科学研究思路,提出地下水诱发浅层前兆异常机理。认为降水等因素造成的地下水动态变化,可产生一种作用于地壳岩石的附加流体力;地震前,通过多种流体力作用,引起已经积累较高应力的地壳应力－－应变场调整变化,并使岩石强度改变,从而促进与诱发浅层地壳的构造变动;其结果是派生或伴生出地形变、地应力、水化学及地电阻率等多种浅层前兆异常。在降水、地下水的多种周期变化成分中,只有那些能与地壳应力－应变过程产生力学耦合的周期变化,才能调制与诱发出异常,这一部分变化可做为广义的地震前兆。孔隙压力、动水压力以及化学腐蚀等原理,是该异常机理的理论基础。列举出六方面的事实做为该机理直接的或间接的证据。     

Influence of background heterogeneity on traveltime shifts for compacting reservoirs

Compaction induced by pore‐pressure decrease inside a reservoir can be monitored by measuring traveltime shifts of reflection events on time‐lapse seismic data. Recently we introduced a perturbation‐based formalism to describe traveltime shifts caused by the 3D stress‐induced velocity field around a compacting reservoir. Application of this method to homogeneous background models showed that the offset variation of traveltime shifts is controlled primarily by the anisotropic velocity perturbations and can provide valuable information about the shear and deviatoric stresses. Here, we model and analyse traveltime shifts for compacting reservoirs whose elastic properties are different from those of the surrounding medium. For such models, the excess stress is influenced primarily by the contrast in the rigidity modulus μ across the reservoir boundaries. Synthetic examples demonstrate that a significant (25% or more) contrast in μ enhances the isotropic velocity perturbations outside the reservoir. Nevertheless, the influence of background heterogeneity is mostly confined to the reservoir and its immediate vicinity and the anisotropic velocity changes are still largely responsible for the offset dependence of traveltime shifts. If the reservoir is stiffer than the host rock, the background heterogeneity reduces anisotropic velocity perturbations inside the reservoir but increases them in the overburden. As a result, in this case, the magnitude of the offset variation of traveltime shifts is generally higher for reflections from interfaces above the reservoir. We also study compaction‐induced stress/strain and traveltime shifts for a stiff reservoir embedded in a softer layered model based on velocity profiles from the Valhall Field in the North Sea. Despite producing discontinuities in strain across medium interfaces, horizontal layering does not substantially alter the overall behaviour of traveltime shifts. The most pronounced offset variation of traveltime shifts is observed for overburden events recorded at common midpoints close to the reservoir edges. On the whole, prestack analysis of traveltime shifts should help better constrain compaction‐induced velocity perturbations in the presence of realistic background heterogeneity.     

1976年唐山7.8级地震成因探讨

根据唐山地区莫霍面隆升、大地构造、新构造运动特征,探讨1976年唐山7.8级地震发生的地质构造背景。唐山地震区位于辽翼台向斜北部,北邻燕山台褶带,地表发育规模不大的基岩断裂,为燕山期活动形成,新生代断裂活动性不强;地下发育深切地幔的深大断裂,与地表断裂位置相当。由震前地震前兆及震后异常现象,提出了地震发生的成因机制。唐山地震是由震前地幔拱起、岩浆上涌垂直力作用下,受NEE-SWW向区域应力场水平挤压,NNE-NE向唐山右旋剪切逆断裂活动,受阻于NW向蓟运河左旋剪切正断裂,地壳岩石间摩擦、破裂,两断裂在深部共轭交汇区应力闭锁、释放,最终导致该次地震的孕育、发生。     

应力对岩石中孔隙流体压力的影响和地下水位震前异常变化机理.

在不同的围压和初始孔隙压力作用下,对孔隙岩石试件进行了不排液的三轴压缩试验,观测了轴向应变和孔隙压力随差应力的变化.试验结果表明:在低差应力下,孔隙压力随差应力的增加而增加.在中等和高差应力下孔隙压力随差应力的增加而降低.在高差应力下,孔隙压力也会随差应力的大幅度降低而升高.基于上述试验,假定地下水位的震前异常变化是地壳岩石中差应力变化的反映.根据这种假定解释了唐山大震前震中及外围地区地下水位异常变化的特征.