Coda pattern and multipath propagation of Rayleigh waves at NORSAR

The coda of Rayleigh waves from fifteen earthquakes recorded at the Norwegian Seismic Array (NORSAR) have been analyzed in wavenumber space at periods of 40 and 20 sec. The power at 40 sec drops off faster vs. time, which reduces the probability of interference between events. On the other side, the capability of the array to resolve signals under various conditions is better at 20 sec. Since also the frequency distribution of signal power varies, one cannot determine any specific frequency as generally having the best signal/interference ratio. The detection problem is also complicated by considerable multipath propagation, which is most severe at 20 sec. Multipath arrivals with as much as 40–60° azimuthal deviation are frequently identified. Travel path solutions for different events are proposed, and usually the rays have been found to be refracted or reflected at continental boundaries. An atmospheric nuclear explosion from Lop Nor has been used to illustrate these various aspects of the problem of detecting one Rayleigh wave in the presence of another.     

Rayleigh waves in an inhomogeneous medium

Summary Dispersion in Rayleigh waves is discussed for semi-infinite media with = ₁(1 ± cos s z) and = ₁(1 ± cosh s z), being the rigidity of the medium. A few workers tried with the above Fourier type of model but failed to find the dispersive nature. Because they neglected s due to the complexity of the calculation they arrived at a non dispersive frequency equation. This difficulty is removed in this paper and a dispersive frequency equation is obtained which shows both direct and inverse dispersion. The second model leads to non-convergent solution forz but shows many interesting results which are also discussed.     

Amplitude curves ofP waves for the region of central Asia

Summary The amplitude-distance curves of P waves, valid for the region of Central Asia, were derived in the distance range between 13° and 36° using observations of a network of eight Caucasian seismic stations. The curves are characterized by an anomalous increase of amplitudes between 13° and 20° followed by a large decrease of amplitudes in the distance range between 20° and 35°. Both the increase and decrease of amplitudes are interrupted by several local maxima. A comparison of the present amplitude curves with those derived for the regions of South-Eastern Europe and Asia Minor enabled us to correlate the individual local maxima of amplitude curves and to investigate the variation of their position due to the lateral inhomogeneity of the upper mantle structure in Eurasia.A. Tskhakaya deceased in 1970.     

Structure and deformational character of strike-slip fault zones

Strike-slip fault zones observed either in the field or in model experiments generally consist of several subparallel faults which make these zones complicated in geometry and kinematics. The geometry of a strike-slip fault or shear zone is dependent on arrangement (pinnate or en echelon), on step (left step or right step), and on the rank )smaller faults within larger faults) of the subparallel fault. The relations and interactions of these three factors create a variety of dynamic circumstances and tectonic settings within the strike-slip fault zones. These include pull-aparts in the release area between subparallel faults, push-ups in the jogs where the subparallel faults overlap, and pivotal movements, or rotation, of single faults along the whole fault zone. Each kind of tectonic setting is in itself characteristic, each setting consists of many subtypes, which are controlled chiefly by the geometric parameters of the subparallel faults. One of the most important phenomena revealed in the field work is two different kinds of evolution of strike-slip fault zones: one is the evolution of a zone with a tensile component, which is related to the growth of rock bridges, and the other, of one with a compressional component, which develops by the destruction of rock bridges. In this paper we discuss, on the basis of recent research on four strike-slip fault zones in China, the essential characteristics of strike-slip faults and the possible causes of the observed structural phenomena. Attention is focussed on the deformation, development, and distribution of horizontal displacements within strike-slip fault zones.     

Rayleigh waves in a medium with an undulated surface

A numerical method is developed which can be used to determine the characteristics of Rayleigh wave propagation in a homogeneous medium where, at each surface point, the radius of curvature is large compared to the wavelength of Rayleigh waves. This method is deduced from experimental results on seismic modeling of some simple cases.In the general case we compute two effects of surface topography on the Rayleigh waves: a dispersion and attenuation of the waves due to the whole path and a local modulation of the displacement components depending on the local curvature. Therefore, both effects are not to be neglected in the case of precise measurement of the velocities and of the amplitudes from which the attenuation factor is carried out.     

A simplified analysis model for determining the seismic response of buried steel pipes at strike-slip fault crossings

The seismic response analysis of buried pipelines at fault crossings is a complex problem requiring nonlinear 3D soil-structure and large deformation analyses. Such analyses are computationally expensive and the results are hard to evaluate. Therefore, a simple numerical model is needed for engineering and design offices to determine the seismic demand of steel pipes at fault crossings. This paper presents a simplified numerical model for buried steel pipes crossing strike-slip faults and oriented perpendicular to the fault. Two pipes with different diameter to thickness (D/t) ratios and steel grades are used in the study. The proposed model permits plastic hinge formations in the pipe due to incrementally applied fault movements, allows determination of the critical length of the pipeline and measure strains developed on the tension and compression sides in the pipe. The model also considers the effect of bending as well as axial strains due to stretching.     

A coherency function model of ground motion at base rock corresponding to strike-slip fault

IntroductionEarthquakedamagesurveyandresearchresultshavedemonstratedthatspatialdistributiondifferenceofgroundmotionisoneoftheimportantreasonswhichcausedlongstructure(eglongspanbridge,undergroundpipe)destroy.Thathowtoprovideareasonableinputofgroundmotionfieldforaseismicdesignoflongstructureisaurgentprobleminearthquakeengineeringfield.Atpresent,themethodtostudyspatialvariationofgroundmotionsisadoptingstatisticanalysisbasedondensearrayrecordssuchasSMART-1array,etc,togetcoherencyfunctionofground…     

Analysis of quality factors for Rayleigh channel waves

To facilitate investigation of the effect of imperfect elastic dissipation on thepropagation of Rayleigh-type channel waves and use of their quality factors in investigationsof the properties of coal seams, a simple method for calculating the quality factor QR isproposed in this paper. Introduction of complex velocities into the dispersion function allowscalculation of the dispersion function of Rayleigh-type channel waves in coal seams. By thecontrol variable method, we analyzed changes in QR with changes in coal seam thickness andP- and S-wave Q-factors within the coal seam and adjacent rock layers. The numerical resultsshow that the trend of the QR curve is consistent with the group velocity curve. The minimumQR value occurs at the Airy phase frequency; the Airy phase frequency decreases as coal seamthickness increases. The value of QR increases with increasing Qs2 （quality factor for S wavein coal seam）. We can compensate for the absorption of Rayleigh-type channel waves usingthe computed QR curve. Inversion of the QR curve can also be used to predict the thicknessesand litholoeies of coal seams.     

Multiple scattering of seismic waves in fractured media: Velocity and effective attenuation of the coherent components ofP waves andS waves

We show that the multiple scattering by small fractures of seismic waves with wavelengths long compared to the fracture size and fracture spacing is indistinguishable from multiple-scattering effects produced by regular porosity, except for an orientation factor due to fracture alignment. The fractures reduce theP-wave andS-wave velocities and produce an effective attenuation of the coherent component of the seismic waves. The attenuation corresponds to 1000/Q of about unity for a Gaussian spectrum of fractures, and it varies with frequencyf asf ³. For a Kolmogorov spectrum of fractures of spectral index the attenuation is an order of magnitude or so larger and varies with frequency asf ^3-v The precise degree of attenuation depends upon the matrix properties, the fracture porosity, the degree of fracture anisotropy, the type of fluid filling the fractures, and the incidence angle of the wave.For fracture porosities less than about 15% theP-wave andS-wave velocities are decreased by the order of 5–10% with a lesser dependence on the type of fluid filling the fractures (gas, oil, or brine) and with a dependence on both the degree of anisotropy and the incident angle made by the wave. The tendency of fractures to occur perpendicularly to bedding suggests that the best way to measure seismically fractured rock behavior in situ is by using the travel-time delay and reflection amplitude. As both the offset and the azimuth of receivers vary from a shot, the travel-time delay and reflection amplitude should both show an elliptical pattern of behavior—the travel-time delay in response to the varying seismic speed, and the reflection amplitude in response to angular variations in the multiple scattering. Observations of attenuation at several frequencies should permit (a) determination of the spectrum of fractures (Gaussian versus Kolmogorovian) and (b) determination of the contribution of viscous damping to the effective attenuation.     

走滑断层和逆断层位错作用下地铁隧道损伤特征对比分析

隧道作为重要的轨道交通工程,近年来在地震中受到了不同程度的破坏,特别是跨断层的隧道,其抗震性能越来越受到人们的关注。为了能够更好地评价隧道的整体损伤情况及把握其损伤特征,以北京地铁7号线为研究对象,利用有限元软件ABAQUS建立模型,采用拟静力法,以隧道直径变化率作为损伤指标分析了隧道在走滑断层以及逆断层位错作用下的损伤特征,对比了两种断层位错作用下损伤状态与地震强度之间的关系、损伤范围和位置以及损伤程度。结果表明:跨断层隧道在断层错动作用下损伤只发生在断层带附近;当震级处于6.0～8.0级时,隧道衬砌损伤程度随震级的增大而增大;在覆土厚度相同的条件下,同震级时逆断层位错作用下隧道损伤程度要比走滑断层作用下大得多;走滑断层位错作用下隧道结构损伤主要发生在拱腰处,逆断层位错作用下主要发生在拱肩－拱脚以及拱顶－拱底处。     

A mechanical model for deformation and earthquakes on strike-slip faults

A two-dimensional model for stress accumulation and earthquake instability associated with strike-slip faults is considered. The model consists of an elastic lithosphere overlying a viscous asthenosphere, and a fault of finite width with an upper brittle zone having an elastoplastic response and a lower ductile zone having an elastoviscoplastic response. For the brittle, or seismic, zone the behavior of the fault material is assumed to be governed by a relation which involves strain hardening followed by a softening regime, with strength increasing with depth. For the fault material in the ductile, or aseismic, section, the viscous effect is included through use of a nonlinear creep law, and the strength is assumed to decrease with depth. Hence, because of the lesser strength and the viscous effect, continuous flow occurs at great depths, causing stress accumulation at the upper portion of the fault and leading to failure at the bottom of the brittle zone. The failure is initially due to localized strain softening but, with further flow, the material above the softened zone reaches its maximum strength and begins to soften. This process accelerates and may result in an unstable upward rupture propagation.Relations are developed for the history of deformation within the lithosphere, specifically for the velocity of particles within the fault and at the ground surface. The boundary-element method is used for a quantitative study, and numerical results are obtained and compared with the recorded surface deformation of the San Andreas fault. The effects of geometry and material properties on instability, on the history of the surface deformation, and on the earthquake recurrence time are studied. The results are presented in terms of variations of ground-surface shear strain and shear strain rate, and velocity of points within the fault at various times during the earthquake cycle.It is found that the location of rupture initiation, the possibility of a sudden rupture as opposed to stable creep, and also the ground deformation pattern and its history, all critically depend on the mechanical response of the material within the fault zone, especially that of the brittle section. Shorter earthquake recurrence times are obtained for shallower brittle zones and for a stiffer lithosphere. Lower viscosities of the aseismic zone and the absence of asthenospheric coupling tend to suppress instability and promote stable creep. The model results thus suggest that the overall viscosity of the ductile creeping zone must exceed a minimum value for a sudden upward propagating rupture to take place within the seismic section.     

Propagation of Rayleigh waves in a model of the cross-section of a mountain and its root

Summary This study deals with the theoretical investigation of a model of a mountain and its root. A Gaussian function with a set of constants is used to represent the surface of a mountain and a Gaussian with a different set of constants approximates the root i.e. the crust-mantle boundary underneath the mountain. The expressions for the amplitudes of the components of strain are obtained. Also the period equation as a function of distance (x) for the propagation of Rayleigh waves is derived here.     

基阶与高阶瑞利波联合反演研究

研究了六层层状介质模型瑞利波基阶和高模式波相速度对横波速度、深度的敏感性,结果表明：基阶波较高模式波对7 m以内浅部地层的横波速度更敏感,敏感性频带在10～25 Hz范围内,峰值频带集中在18 Hz左右;高模式波较基阶波对深部地层的横波速度更敏感,敏感性频带宽,峰值分散.基阶波对浅层的敏感性和高模式波穿透深度更深的特点为近地表岩土层二维横波速度结构的联合反演提供了前提条件.利用阻尼最小二乘SVD（Singular Value Decomposition）算法联合基阶与高模式波对理论模型和实例数据进行横波速度反演,反演结果表明联合反演增强了反演的稳定性,提高了反演的精度.     

On low period sub-oceanic Rayleigh waves and their attenuation

Summary In most cases it is found that Rayleigh waves in the period range I to 12 secs fail to cross appreciable oceanic paths. Several explanations have been given, but none seem very much satisfactory. Here an attempt has been made to show that the attenuation of the Rayleigh waves in the low period range is due to their passage through a non-uniform earth's crust, the non-uniformity arising due to the ocean. The ocean has been taken to be an indentation in a flat earth's crust, with horizontal bottom and slant sides. Approximate numerical calculations hint that the vertical component of displacement is attenuated more than the horizontal component.     

Landslide and tsunami hazard at Yate volcano,Chile as an example of edifice destruction on strike-slip fault zones

The edifice of Yate volcano, a dissected stratocone in the Andean Southern Volcanic Zone, has experienced multiple summit collapses throughout postglacial time restricted to sectors NE and SW of the summit. The largest such historic event occurred on 19th February 1965 when ～6.1–10?×?10⁶ m³ of rock and ice detached from 2,000-m elevation to the SW of the summit and transformed into a debris flow. In the upper part of the flow path, velocities are estimated to have reached 40 m s^?1. After travelling 7,500 m and descending 1,490 m, the flow entered an intermontane lake, Lago Cabrera. A wavemaker of estimated volume 9?±?3?×?10⁶ m³ generated a tsunami with an estimated amplitude of 25 m and a run-up of ～60 m at the west end of the lake where a settlement disappeared with the loss of 27 lives. The landslide followed 15 days of unusually heavy summer rain, which may have caused failure by increasing pore water pressure in rock mechanically weathered through glacial action. The preferential collapse directions at Yate result from the volcano’s construction on the dextral strike-slip Liquiñe-Ofqui fault zone. Movement on the fault during the lifetime of the volcano is thought to have generated internal instabilities in the observed failure orientations, at ～10° to the fault zone in the Riedel shear direction. This mechanically weakened rock may have led to preferentially orientated glacial valleys, generating a feedback mechanism with collapse followed by rapid glacial erosion, accelerating the rate of incision into the edifice through repeated landslides. Debris flows with magnitudes similar to the 1965 event are likely to recur at Yate, with repeat times of the order of 10² years. With a warming climate, increased glacial meltwater due to snowline retreat and increasing rain, at the expense of snow, may accelerate rates of edifice collapse, with implications for landslide hazard and risk at glaciated volcanoes, in particular those in strike-slip tectonic settings where orientated structural instabilities may exist.     

瑞雷波斜入射下层状半空间中沉积谷地周围的三维散射研究

针对层状半空间中沉积谷地对斜入射瑞雷波的三维散射问题, 采用直接刚度法计算自由场波场, 以层状半空间中移动斜线均布荷载动力格林影响函数求解三维散射波场, 建立了求解该问题的间接边界元方法. 通过与已有结果的比较, 验证了该方法的正确性, 并以均匀半空间以及弹性基岩上单一土层场地中沉积谷地为例进行了计算分析. 研究结果表明： 层状半空间与均匀半空间中沉积谷地对瑞雷波的散射存在显著差别; 层状半空间中瑞雷波的振动模态对沉积附近位移幅值有着重要影响; 土层刚度和厚度等参数也对沉积附近位移幅值大小及空间分布有着显著的影响.     

基于交叉梯度约束的地震初至纵波与瑞雷面波联合反演

本文提出了一种初至纵波（P波）与瑞雷面波的交叉梯度联合反演策略.通过对初至P波进行全波形反演可以获得近地表P波速度结构;通过对仅含瑞雷面波信息的地震数据转换到频率-波数域进行加窗振幅波形反演（Windowed-Amplitude Waveform Inversion,w-AWI）可获得近地表横波（S波）速度结构.在二者反演的目标函数中均加入P波速度和S波速度的交叉梯度作为正则化约束项,使得在反演过程中P波速度和S波速度相互制约,相互约束,从而实现对地震初至P波与瑞雷面波的联合反演.数值模拟结果表明交叉梯度联合反演可以提高S波速度反演分辨率,而P波速度反演结果并没有得到提高.实际资料的反演结果表明,交叉梯度联合反演能够获得更加可信的近地表速度结构.     

Coseismic and postseismic subsurface displacements and strains for a vertical strike-slip fault in a three-layer elastic medium

A three-layer elastic-gravitational fault displacement model using dislocation theory has been developed and used to examine the effect of layering of earth elastic moduli on surface and subsurface displacement fields for a vertical strike-slip fault. The model has been used to examine the effect of depth variation of elastic properties at coseismic and postseismic time scales. For pure strike-slip motion the effect of gravity on coseismic and postseismic horizontal deformation is negligible. For coseismic deformation the model predicts that (for constant Poisson's ratio) an increase in elastic moduli with depth attenuates the displacements within the upper layers with respect to displacement distribution for a uniform half-space, while an inclusion of a soft layer between the top layer and lower half-space amplifies upper layer displacements. The effect of variation in Poisson's ratio on surface and subsurface displacements has also been examined.The effect of postseismic stress relaxation on surface and subsurface displacements for a three-layer model has been calculated and compared with that of a uniformly relaxed half-space model. Layer 1 is assumed to correspond to the upper crust, layer 2 the lower crust and layer 3 the upper mantle. The effect of postseismic stress relaxation within a uniform half-space and within just the lower crust and upper mantle has been examined. Stress relaxation within the whole half-space decreases the amplitude and shortens the wavelength of displacements, while stress relaxation within the lower two layers increases the amplitude and broadens the wavelength of displacements. The difference between uniform and layered postseismic relaxation is particularly pronounced at the base of the crust.Coseismic and postseismic normal and volumetric strains for a vertical strike-slip fault have also been examined. For a uniformly relaxed half-space model, an increase in normal strains is shown with respect to the coseismic elastic solution, whereas the postseismic volumetric strain is effectively zero. For a three-layer model with stress relaxation in the lower layers only, the normal and volumetric strains within the top elastic layer resemble coseismic strains, while in the lower layers which suffer a rigidity decrease, the postseismic volumetric strain is effectively zero.