Quasi-static deformation of a viscoelastic half-space by a displacement dislocation

The correspondence principle is used to get the Laplace transformed solution of the problem of the quasi-static deformation of a viscoelastic half-space by a shear displacement dislocation from the corresponding static elastic results. The transformed solution is inverted for the Voigt and the Maxwell viscoelastic models. It is shown that, for a vertical dip-slip fault, the surface displacements for the viscoelastic case are identical with the elastic displacements. In the case of a vertical strike-slip fault, detailed numerical results are obtained for both a point source and a finite rectangular source. It is found that the results for the viscoelastic models differ significantly from the corresponding elastic results.     

静态弹性介质中力及力偶产生位移的空间特征

弹性介质中力及力偶产生静态位移的空间特征是理解剪切位错源以及有限断层面在半无限弹性空间产生静态位错的基础。本文对这些理论作了简单回顾推导,将其产生的静态位移转换到球坐标系中,并绘出了三维情形下集中力、单力偶和双力偶在弹性介质中产生的位移场辐射花样。     

Theoretical amplitudes of body waves from a dislocation source in the earth III. P,S and surface reflections

Expressions are obtained for the ray-theoretical spectral amplitudes of body waves induced by a shear dislocation of arbitrary orientation and depth situated in a radially heterogeneous model of the earth. Account is taken of the azimuthal and colatitudinal radiation patterns of the source, the geometrical spreading, and the reflections and refractions at the free surface and at the mantle-core boundary.In this work spectral amplitudes are calculated for P, SH, SV, PP, PPP, PS, PSS, SP, SPP, SSH, SSSH, SSV, and SSSV. The results are presented in the form of tables for a source of strength U₀dS = 10¹⁵cm³, where U₀ is the amount of the dislocation and dS is the fault area. Given the slip and dip angles of the source, the amplitudes of these surface reflections and direct phases can be obtained from these tables for all azimuths, for most of the epicentral distances at which a particular phase is observable, and for all the fourteen focal depths included in the Jeffreys-Bullen tables. It is found that the depth of the source has a strong effect on the amplitudes of the body wave signals.     

1974年云南省昭通地震破裂机制

1974年5月11日,在云南省昭通地区发生了7.1级地震。震中区位于金沙江下游南岸的山地中。 本文中,作者分析了震区大地测量资料,根据破裂与应变的关系,确立这次地震震源破裂属于逆冲型。依据烈度衰减和余震分布特征建立了矩形滑动断层模式参数,并应用曼辛哈（Mansinha）和斯迈利（smylie）给出的倾斜、有限滑动断层位移场的精确解析表达式,求得平均倾向滑距。结果是:断层走向N6°W,倾向N84°E,倾角60°,断面长20公里,宽30公里;断面顶部距地表深度2.5公里;平均倾向滑距2.8米,地震矩5.4×10²⁶达因·厘米;应力降51巴;释放的应变能下限1.2×10²³尔格。 作者还扼要地讨论了P波节面解和这次地震发生的构造条件,并解释了一些宏观地震现象。     

Seismic ground motion in a layered half-space due to a Haskell-type source. I: Theory

In this paper, closed-form analytic expressions for the frequency-wave number domain Fourier amplitudes of the displacement field at the free surface of a layered, anelastic half-space are established. The displacement field is caused by a seismic source described by a shear dislocation propagating with constant velocity over a rectangular fault (Haskell's model). Three-dimensional plane wave propagation is considered in the layered half-space using a propagator-based formalism. The wave radiation from the source is decoupled into P-SV and SH motions and the two problems are treated separately. First, analytic expressions are calculated for the displacement field at the free surface due to unidirectional unit impulses. Then, these expressions are used to compute solutions for the displacement field due to effective point sources associated with a pure strike slip and a pure dip slip. Finally, these solutions are combined and integrated over the rectangular fault area to establish closed-form analytic expressions of the total displacement field at the free surface.     

基于线弹性位错模型反演1997年西藏玛尼Mw7.5级地震的干涉雷达同震形变场——Ⅱ滑动分布反演

1997年11月8日西藏M_w7.5级玛尼地震是干涉雷达技术应用于地震观测以来的一次重要事件.在第一部分中，我们应用广泛使用的Okada线弹性位错模型，假设断层的各个分段滑动量均匀，反演得到断层各个分段的几何参数和均匀滑动量.本部分的反演进一步去除滑动均匀假设，并利用更能反映断层真实状态的角形元位错模型（线弹性），在第一部分反演得到断层几何的基础上，反演断层面的静态位错分布.反演结果表明，线弹性滑动分布模型能够更好地解释观测数据，进一步提高反演的数据拟合程度.最终得到了断层面上的走滑和倾滑位错分布.首次得到的断层面滑动分布显示断层面滑动在浅部（0～12 km）比较集中，地震破裂长度约170 km，最大左旋走滑位移达4.8 m；反演结果还表明局部段落存在较大倾滑位移，量值达到1.9 m，这在断层模型中是不能忽略的，它可能是断层两侧形变不对称的原因之一；反演得到的标量地震矩为2.18×10²⁰ N·m，相当于矩震级M_w7.5，与Velasco等利用地震波形反演得到的结果一致.     

一种新的非均匀断层模型及其振幅谱的特征

本文提出了一种弯曲断层面的非均匀断裂模型。我们把弯曲断层面简化为锯齿形状,当每个锯齿上的滑动是均匀的,同时具有均匀的位错传播速度时,可以得到问题的封闭形式的精确解。对于不同的齿数、齿倾角和场方位角,计算了体波辐射的振幅谱。研究发现,弯曲断层会使谱曲线出现异常的峰值,异常峰值的位置与齿数有关,随齿数的增加向高频方向移动。齿倾角的变化会引起振幅谱曲线上异常峰附近谱包络线的变化。不同方位的观测点处的振幅谱形状各不相同。仔细地将观测谱与理论谱对比,有可能使人们了解断层面的非平面性质。     

计算分层介质中位错点源静态位移场的广义反射、透射系数矩阵和离散波数方法

本文将计算合成地震图的广义反射、透射系数矩阵和离散波数方法应用于静态问题,给出了分层介质中位错点源产生的静态位移场的计算方法。该方法保留了反射、透射矩阵方法的原有优点,通过将数值结果与解析解的对比表明,该方法具有较高的数值精度,可用于研究地震断层活动造成的地表形变。     

The estimation of shear-wave statics using in situ measurements in marine near-surface sediments

Shear‐wave statics in marine seismic exploration data are routinely too large to be estimated using conventional techniques. Near‐surface unconsolidated sediments are often characterized by low values of V_s and steep velocity gradients. Minor variations in sediment properties at these depths correspond to variations in the shear‐wave velocity and will produce significant static shifts. It is suggested that a significant proportion of the shear‐wave statics solution can be estimated by performing a separate high‐resolution survey to target near‐surface unconsolidated sediments. Love‐wave, shear‐wave refraction and geotechnical measurements were individually used to form high‐resolution near‐surface shear‐wave velocity models to estimate the shear‐wave statics for a designated survey line. Comparisons with predicted statics revealed that shear‐wave statics could not be estimated using a velocity model predicted by substituting geotechnical measurements into empirical relationships. Empirical relationships represent a vast simplification of the factors that control V_s and are therefore not sufficiently sensitive to estimate shear‐wave statics. Refraction measurements are potentially sensitive to short‐wavelength variations in sediment properties when combined with accurate navigational data. Statics estimated from Love‐wave data are less sensitive, and sometimes smoothed in appearance, since interpreted velocity values represent an average both laterally and vertically over the receiver array and the frequency–depth sensitivity range, respectively. For the survey site, statics estimated from near‐surface irregularities using shear‐wave refraction measurements represent almost half the total statics solution. More often, this proportion will be greater when bedrock relief is less.     

Mechanism and tectonic implications of the great Banda Sea earthquake of November 4, 1963

The Banda Sea earthquake of November 4, 1963 (h = 100 km, m_B = 7.8) is probably one of the largest intermediate-depth shocks to have occurred worldwide this century. The mechanism of this earthquake is studied in detail on the basis of P-wave first motion, surface wave and aftershock data. From the analysis of long-period multiple surface waves, a seismic moment of 3.1 × 10²⁸ dyn-cm is obtained, which is the largest reported so far for any intermediate or deep focus shock. This value, together with the estimated fault area of 90 × 70 km², gives an average dislocation of 7.0 m and a stress drop of 120 bar. This event represents an oblique thrust movement on a plane with dip direction N170°E, dip 48° and rake 52°. A geometrical consideration for the fault plane and the configuration of the inclined seismic zone beneath the Banda arc suggests, almost definitely, that the large-scale faulting took place within the subducted plate and offset it. Further repetition of such large-scale faulting might eventually break the subducted plate. The 1963 Banda Sea earthquake thus represents a seismological manifestation of the large-scale deformation of the subducted plate in the mantle.     

Effective relaxation time and viscosity of the earth inferred from the postseismic vertical deformations of the 1990 M S=7.0 Gonghe earthquake

The postseismic vertical deformation rates of the 1990 Gonghe M _S=7.0 earthquake appears to have decreased exponentially. Based on Okada’s coseismic surface displacement solution caused by a uniform fault slip in an elastic homogeneous half space, we derived its postseismic surface displacement by using a single-layer standard linear solid model, and further derived a simplified formula for determining the effective relaxation time and viscosity of the earth, which is independent of the dislocation parameters of the causative fault. From the postseismic vertical deformation of the 1990 Gonghe earthquake, we inferred that the effective relaxation time defined by τ=η/μ is 2.6 years, and the effective viscosity η is about 10¹⁸ Pa · s. This work was supported by Chinese Joint Seismological Science Foundation under the grants 92088 and 196098.     

Spatial distribution of near-fault ground motion

Introduction In order to explain severe damage of structures and ground surface near earthquake fault, many theoretical and numerical methods have been developed to study strong ground motion near the fault (Somerville, 1998) via the kinematic and dynamic source models. Moreover, a great number of valuable strong ground motion records, especially near the fault, have been acquired in recent years. These valuable records provide useful data for improving simulation approaches. Based on those r…     

On two-dimensional elastic dislocations in a multilayered half-space

The two-dimensional problem of a long displacement dislocation in a multilayered half-space is studied. Both plane strain and antiplane strain cases are considered. The Thomson-Haskell matrix method is used to obtain the static field caused by the dislocation. The source is represented in terms of the jumps at the source level in the depth-dependent factors in the Fourier integral representation of the displacements and stresses due to the source in an infinite medium. Explicit expressions for the surface displacements due to dip-slip and strike-slip faults of arbitrary dip are obtained. The formulation developed is quite convenient for numerical computation.     

根据地面形变的观测研究1966年邢台地震的震源过程

本文以完整的形式给出拉梅常数不相等情形的半无限弹性介质中任意倾角的矩形滑动断层引起的地震位移场解析表示式。以一些数值结果说明介质的泊松比、断层面的倾角、上界和下界对地面的地震位移场的影响。在比较1966年邢台地震的地形变资料和计算得到的各种走向、倾向、倾角、断层面长度、宽度、震源深度和错距的单个的矩形滑动断层引起的地面位移之后指出,简单的滑动断层错动模式不能同时很好地解释观测到的邢台地震的水平和垂直形变。为了解释观测结果,提出了一个复合的断层模式。这个复合断层模式由六个简单的矩形滑动断层构成。运用网格尝试法,得到了基本上符合观测到的水平和垂直位移场的震源参数。     

Coseismic Slip from the 6 October 2008, M w6.3 Damxung Earthquake, Tibetan Plateau, Constrained by InSAR Observations

Coseismic deformation fields of the 6 October 2008 M _w6.3 Damxung earthquake were obtained from interferometric synthetic aperture radar by using three descending and two ascending Envisat images. Significant coseismic surface deformation occurred within 20?km?×?20?km of the epicenter with a maximum displacement of ~0.3?m along the satellite line of sight. We model a linear elastic dislocation in a homogeneous half space and use a nonlinear constraint optimized algorithm to estimate the fault location, geometry and slip distribution. The results indicate a moment magnitude M _w6.3, and the earthquake is dominated by oblique normal and right-lateral slip with a maximum slip of 2.86?m at depth of 8?km. The rupture plane is about 15?km?×?14?km with strike S190°W and dip 55° to NW, located at a secondary fault of the Southeastern Piedmont of the Nyainqentanglha Mountains. Slip on normal faults in the Tibetan Plateau contributes to the rift evolution.     

Failure time variation derived from R–S relation: the role of the static stress perturbation

In general, earthquake cycle related to earthquake faulting could include four major processes which could be described by (1) fault locking, (2) self-acceleration or nucleation (possible foreshocks), (3) coseismic slip, and (4) post-stress relaxation and afterslip. A sudden static stress change/perturbation in the surrounding crust can advance/delay the fault instability or failure time and modify earthquake rates. Based on a simple one-dimensional spring-slider block model with the combination of rate-and-state-dependent friction relation, in this study, we have approximately derived the simple analytical solutions of clock advance/delay of fault failures caused by a sudden static Coulomb stress change applied in the different temporal evolution periods during an earthquake faulting. The results have been used in the physics-based explanation of delayed characteristic earthquake in Parkfield region, California, in which the next characteristic earthquake of M 6.0 after 1966 occurred in 2004 instead of around 1988 according to its characteristic return period of 22 years. At the same time, the analytical solutions also indicate that the time advance/delay in Coulomb stress change derived by the dislocation model has a certain limitation and fundamental flaw. Furthermore, we discussed the essential difference between rate- and state-variable constitutive (R–S) model and Coulomb stress model used commonly in current earthquake triggering study, and demonstrated that, in fact, the Coulomb stress model could be involved in the R–S model. The results, we have obtained in this study, could be used in the development of time-dependent fault interaction model and the probability calculation related to the time-dependent and renewal earthquake prediction model.     

Relative location and source mechanism of inland earthquakes in Northern Egypt

We have relocated 259 inland earthquakes in northern Egypt using the double-difference hypocenter technique. Among this dataset we are able to determine source mechanisms of 200 events using P-wave polarities and amplitude ratios as well. The studied earthquakes have been recorded by the Egyptian National Seismological Network from October 1997 to December 2006 with local magnitude (M_L) varies between 1.5 and 5.0. Three earthquake dislocations have been defined namely: Dahshour, southeast Beni-Suef, and Cairo-Suez district. Earthquake activities tend to occur in clusters along the first dislocation (Dahshour) however, relatively scattered along the second (southeast Beni-Suef) and the third (Cairo-Suez district) dislocations. At Dahshour dislocation three distinct clusters have been distinguished. Source mechanism solutions of Dahshour earthquakes displayed normal faulting with a strike-slip component to strike-slip faulting with a minor normal dip-slip component. Most of earthquake focal mechanism orientations are varying from NE-SW to NW-SE. The fault plane solutions of Beni-Suef earthquakes represented normal faulting with a strike-slip component. If the NNW-SSE striking plane has been chosen to be the actual fault plane, some solutions would indicated normal faulting with a sinistral strike-slip motion and other reflect normal faulting with a dextral strike-slip component. The fault plane solutions of Cairo-Suez district earthquakes are compatible with E-W to ENE-WSW striking normal fault with a dextral strike-slip motion.     

河北磁县西部山区最新地表破裂带的发现与1830年磁县7.5级地震的关系

本文介绍了磁县西部山区新近发现的最新地表破裂带。该地表破裂带近东西走向，长约７ｋｍ，由断层崖及地表沟槽组成。在地表粉末状灰岩破碎带中保存大量坚硬灰岩岩块，并见断层破碎带碎石盖在古腐植土之上。断层北盘下降，最新事件的最大垂直落差约７－１０ｍ，以正倾滑为主。个别地点断层显示左旋位移。该地表破裂带沿岔口活动断裂带分布，可认为是１８３０年磁县地震的地表破裂。     

断层附近地面地震动空间分布

运用震源位错模型, 分析矩形垂直断层及倾斜断层走向滑动和倾向滑动的近场地震动场，以地表地震动的傅立叶振幅谱比为参量考察断层附近地震动空间分布的特点. 结果表明, 断层附近的地震动强度主要受近旁子断层的控制，高强度的地震动分布在紧靠断层两侧有限的带状区域内，长周期分量受断层破裂传播方向性的影响. 走向滑动的方向性影响主要表现在垂直于断层走向的分量，倾向滑动则表现在平行于断层走向的分量，且深震在地面上引起的地震动强度分布比浅震要平缓，影响范围宽. 倾斜断层产生的地震动有明显的上盘效应，空间分布不对称，与观测结果相符. 最后给出了断层附近近场地震动强度分布拟合函数的表达式，并与美国的1997统一建筑规范规定的近场因子作了比较.      

Theoretical amplitudes of body waves from a dislocation source in the Earth II. Core phases

Expressions are obtained for the ray-theoretical spectral amplitudes of body waves induced by a shear dislocation of arbitrary orientation and depth situated in a radially heterogeneous model of the earth. Account is taken of the azimuthal and colatitudinal radiation patterns of the source, the geometrical spreading, and the reflections and refractions at the free surface and at the mantle-core boundary.In this work spectral amplitudes are calculated for PKP, PKS, SKP and SKS. The results are presented in the form of tables for a source of strength U₀dS = 10¹⁵ cm³, where U₀ is the amount of the dislocation and dS is the fault area. Given the slip and dip angles of the source, the amplitudes of the four core phases can be obtained from these tables for all azimuths, for most of the epicentral distances at which a particular phase is observable, and for all the fourteen focal depths included in the Jeffreys-Bullen tables. It is found that the depth of the source has a strong effect on the amplitudes of the body-wave signals.