On the disturbances in an inhomogenous medium due to transient forces and twists on the surface of a burried spherical source

Summary In this paper the displacements and stresses are obtained due to two types of forces: (i) transient normal forces, (ii) transient twists on the surface of a burried spherical source. The material is assumed to be inhomogeneous and spherically aeolotropic. Laplace transform technique has been used here.     

The transient disturbance produced in an elastic layer by a buried spherical source

Summary In this paper approximate expressions for the surface displacements due to a buried spherical source inside an isotropic elastic layer with one surface stress-free and the other (i) rigid, (ii) stress-free, have been obtained. Graphical representations for the surface displacements at a large distance have also been found.     

表面垂直位移和重力变化引起的大地水准面形变

在涉及表面垂直位移的地球物理正演和反演问题的研究中,表面真垂直位移等于表面视垂直位移和大地水准面高变化的和.本文从广义Bruns公式、广义stokes公式和广义Ve-ning-Meinesz公式出发,导出了用表面垂直位移和重力变化确定大地水准面形变的公式.讨论了表面垂直位移和重力变化对大地水准面高变化的影响.在此基础上,给出了表面荷载源、几种不同充填介质的膨胀源和位错源所引起的大地水准面高变化对视垂直位移影响的数值结果,分析了局部地球物理事件引起的大地水准面高变化的特点.最后给出了使用辽南地区的实际观测资料确定的局部大地水准面高变化以及对视垂直位移影响的计算结果.     

Magneto-elasticSH-type of motion

Summary TheSH-type of motion in an isotropic elastic halfspace with infinite electrical conductivity subjected to an uniform magnetic field and disturbed by a buried source is investigated. Expressions for the surface displacements for various type of sources are obtained by an application of Cagniard technique. Numerical calculation has been performed for the case of a diapole source moving parallel to the surface of the halfspace with an uniform velocity.     

SH waves from torsional sources in semi-infinite heterogeneous media

Summary The theory of Hankel transforms is used to obtain the displacement field forSH waves generated by time harmonic, buried, torsional sources in semi-infinite heterogenous media in which material properties are functions of the depth coordinate. An application to a heterogeneous medium with exponentially varying properties has been discussed. Surface displacements from a surface source have been evaluated at large distances from the source. The results have been compared with those for the homogeneous medium.     

Disturbances produced in a visco-elastic medium by transient torsional body forces

Summary The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above.     

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.     

SH-waves from a finite line source

Summary The displacements and shearing stresses in an infinite medium are obtained for a finite line source, taken as the limit of a prolate ellipsoid with the shearing stresses prescribed on its surface. The results have been extended to the case of a semi-infinite medium by the method of images.     

基于动摩擦应力下调滑移弱化机制，利用地表破裂同震位移约束2001年昆仑山口西MS8.1地震破裂传播速度

利用2001年昆仑山口西MS8.1地震现场观测所提供的地表破裂同震位移数据,使用简单滑移弱化破裂模型,估算了发震主断层上的破裂传播速度. 该模型中考虑了断层破裂时动摩擦过程中应力上调和下调机制对地震波辐射能量分配的影响. 对比Bouchon和Valleacute;e有关昆仑山口西地震主断层破裂传播速度超过剪切波速度,甚至达到P波速度的结果, 采用动摩擦应力下调时的滑移弱化模型 (分数应力降模型),结果表明,伴随较高的地震波辐射效率,主断层的平均破裂传播速度等于或小于瑞利波速度,这与许力生和陈运泰的体波反演结果,以及陈学忠震源应力场估算的结果是一致的. 最后,联系到由地表破裂现象所反映出的断层力学特征,如与视应力相关的分数应力降 (动摩擦应力下调), 基于滑移弱化模型, 讨论了可能的震源破裂机制.      

3D models of slow motions in the Earth’s crust and upper mantle in the source zones of seismically active regions and their comparison with highly accurate observational data: I. Main relationships

Constructing detailed models for postseismic and coseismic deformations of the Earth’s surface has become particularly important because of the recently established possibility to continuously monitor the tectonic stresses in the source zones based on the data on the time variations in the tidal tilt amplitudes. Below, a new method is suggested for solving the inverse problem about the coseismic and postseismic deformations in the real non-ideally elastic, radially and horizontally heterogeneous, self-gravitating Earth with a hydrostatic distribution of the initial stresses from the satellite data on the ground surface displacements. The solution of this problem is based on decomposing the parameters determining the geometry of the fault surface and the distribution of the dislocation vector on this surface and elastic modules in the source in the orthogonal bases. The suggested approach includes four steps: 1. Calculating (by the perturbation method) the variations in Green’s function for the radial and tangential ground surface displacements with small 3D variations in the mechanical parameters and geometry of the source area (i.e., calculating the functional derivatives of the three components of Green’s function on the surface from the distributions of the elastic moduli and creep function within the volume of the source area and Burgers’ vector on the surface of the dislocations); 2. Successive orthogonalization of the functional derivatives; 3. Passing from the decompositions of the residuals between the observed and modeled surface displacements in the system of nonorthogonalized functional derivatives to their decomposition in the system of orthogonalized derivatives; finding the corrections to the distributions of the sought parameters from the coefficients of their decompositions in the orthogonalized basis; and 4. Analyzing the ambiguity of the inverse problem solution by constructing the orthogonal complement to the obtained basis. The described approach has the following advantages over the method of steepest descent which was used in our previous works: 1. Application of the perturbation method significantly reduces the volume of the computations in the real problems of coseismic and postseismic deformations (by three to four orders of magnitude when the data from a few dozens of observation points are used); 2. In contrast to the method of steepest descent, the suggested method always provides stable results. This means that adding the new satellite data does not alter the previously calculated coefficients in the low-order harmonics of the distributions of the sought parameters in the orthogonalized basis; this only changes the coefficients of the increasingly higher harmonics which determine the smallscale details in the sought distributions. 3. In contrast to the method of steepest descent, the suggested method is not only capable of constructing stable partial solutions of the inverse problem but also estimating the ambiguity of these solutions. The ambiguity is represented in terms of the superposition of the known functions contained in the orthogonal complement and, hence, with the growth of the amount of the analyzed data it is determined by the linear combination of the increasingly higher harmonics. In the second part of the paper, we present the results of the model numerical computations of Green’s function for the elastic displacements of the ground surface, which correspond to the case of the arbitrary geometry of the dislocation surface and arbitrary orientation of the dislocation vector for the real model of the radially heterogeneous gravitating Earth with the hydrostatic distribution of the initial stresses. The numerical calculations of the creep function in the upper mantle for the coseismic deformations and the ambiguity of the models of postseismic deformations in the vicinity of the source of the Great Tohoku earthquake (Japan) of March 11, 2011 are illustrated by the examples.     

On the geodetic observations during 1965 to 1969 in the Koyna region, India

Limited reports of repeat triangulation and levelling surveys carried out in the Koyna region by Survey of India, before and after the 1967 Koyna earthquake, are available. We analyse these observations of horizontal and vertical displacements to investigate whether analysis of these observations can provide additional constraints on the source parameters of the 1967 Koyna earthquake. We calculate surface displacements due to coseismic slip on the subsurface rupture of the 1967 Koyna earthquake and also due to the Koyna reservoir water load. We find that the reported displacements are too large to be attributed to the coseismic displacements and/or to the displacements induced by the reservoir water load. We conclude that these observations contain large random and systematic errors.     

Constraints on rupture speed of the 2001 <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript> 8.1 West Kunlun Mountain Pass earthquake by co-seismic surface rupture slip displacements based on the slip-weakening mechanism with frictional undershoot involved

With co-seismic surface rupture slip displacements provided by the field observation for the 2001 M_S8.1 West Kunlun Mountain Pass earthquake, this paper estimates the rupture speed on the main faulting segment with a long straight fault trace on the surface based on a simple slip-weakening rupture model, in which the frictional overshoot or undershoot are involved in consideration of energy partition during the earthquake faulting. In contrast to the study of Bouchon and Vallée, in which the rupture propagation along the main fault could exceed the local shear-wave speed, perhaps reach the P-wave speed on a certain section of fault, our results show that, under a slip-weakening assumption combined with a frictional undershoot (partial stress drop model), average rupture speed should be equal to or less than the Rayleigh wave speed with a high seismic radiation efficiency, which is consistent with the result derived by waveform inversion and the result estimated from source stress field. Associated with the surface rupture mechanism, such as partial stress drop (frictional undershoot) associated with the apparent stress, an alternative rupture mechanism based on the slip-weakening model has also been discussed.     

Temporal variations in the tidal response of the medium in the vicinities of the sources of catastrophic earthquakes

The idea of predicting earthquakes by continuously monitoring temporal variations in the tidal response of the medium was suggested by Beaumont and Berger in 1974. However, it became possible to implement the idea only recently. This possibility has arisen due to the deployment of Global Seismic Network (GSN), which collects the data on tidal tilts and gravity in the epicenters of strong earthquakes before and after the strongest events. In this paper, we present the results of model analytical and numerical calculations of the elastic displacements of the Earth’s surface caused by the earthquakes and their preparatory processes. The analytical calculations are limited to the model of a uniform elastic halfspace; the numerical calculations, in addition to this model, also cover the models with radially heterogeneous distributions of elastic moduli in the crust and in the upper mantle, which are determined by the PREM model. We describe the results of modeling temporal variations in the tidal response of the medium in the vicinity of the source of a catastrophic earthquake. The model of seismic source is specified by the length and the orientations of the fault plane and by the value of the discontinuity in the tangential component of the displacement vector on the opposite sides of the fault. The model is based on the GPS data on the horizontal and vertical displacements of the Earth’s surface. We suggest the method for determining temporal changes in the tidal response of the medium in the seismically active regions. This method improves the sensitivity and time resolution of the standard techniques of sliding-window analysis by more than an order of magnitude. The comparative analysis of temporal variations in the tidal response of the medium in the zones of the magnitude 9 earthquake in Japan (March 9, 2011) illustrates the described approach.

     

Temporal variations in the tidal response of the medium in the vicinities of the sources of catastrophic earthquakes

The idea of predicting earthquakes by continuously monitoring temporal variations in the tidal response of the medium was suggested by Beaumont and Berger in 1974. However, it became possible to implement the idea only recently. This possibility has arisen due to the deployment of Global Seismic Network (GSN), which collects the data on tidal tilts and gravity in the epicenters of strong earthquakes before and after the strongest events. In this paper, we present the results of model analytical and numerical calculations of the elastic displacements of the Earth??s surface caused by the earthquakes and their preparatory processes. The analytical calculations are limited to the model of a uniform elastic halfspace; the numerical calculations, in addition to this model, also cover the models with radially heterogeneous distributions of elastic moduli in the crust and in the upper mantle, which are determined by the PREM model. We describe the results of modeling temporal variations in the tidal response of the medium in the vicinity of the source of a catastrophic earthquake. The model of seismic source is specified by the length and the orientations of the fault plane and by the value of the discontinuity in the tangential component of the displacement vector on the opposite sides of the fault. The model is based on the GPS data on the horizontal and vertical displacements of the Earth??s surface. We suggest the method for determining temporal changes in the tidal response of the medium in the seismically active regions. This method improves the sensitivity and time resolution of the standard techniques of sliding-window analysis by more than an order of magnitude. The comparative analysis of temporal variations in the tidal response of the medium in the zones of the magnitude 9 earthquake in Japan (March 9, 2011) illustrates the described approach.     

Constraints on rupture speed of the 2001 M S 8.1 West Kunlun Mountain Pass earthquake by co-seismic surface rupture slip displacements based on the slip-weakening mechanism with frictional undershoot involved

With co-seismic surface rupture slip displacements provided by the field observation for the 2001 MS8.1 West Kunlun Mountain Pass earthquake, this paper estimates the rupture speed on the main faulting segment with a long straight fault trace on the surface based on a simple slip-weakening rupture model, in which the frictional overshoot or undershoot are involved in consideration of energy partition during the earthquake faulting. In contrast to the study of Bouchon and Vallée, in which the rupture propagation along the main fault could exceed the local shear-wave speed, perhaps reach the P-wave speed on a certain section of fault, our results show that, under a slip-weakening assumption combined with a frictional undershoot (partial stress drop model), average rupture speed should be equal to or less than the Rayleigh wave speed with a high seismic radiation efficiency, which is consistent with the result derived by waveform inversion and the result estimated from source stress field. Associated with the surface rupture mechanism, such as partial stress drop (frictional undershoot) associated with the apparent stress, an alternative rupture mechanism based on the slip-weakening model has also been discussed.     

Parametric investigation of lateral spreading of gently sloping liquefied ground

This paper investigates the main parameters affecting the anticipated maximum surface displacements due to earthquake-induced lateral spreading of mildly sloping ground. The main tool used for this purpose is a numerical methodology employing a bounding surface plasticity model implemented in a finite difference code, which has been thoroughly validated against 16 published centrifuge lateral spreading experiments. This study shows that important problem parameters are the mean ground (surface) acceleration, the duration of strong shaking following the onset of liquefaction, the corrected SPT blowcount, the depth to the sliding plane, the inclination of the ground surface and the fines content of the liquefied soil layers. A new approximate multi-variable relation is proposed for the estimation of ground surface displacements due to lateral spreading in gently sloping ground, which includes the foregoing parameters. The form of the relation builds upon sliding block theory, but its final formulation is based on statistical analysis of the input data and the results from 120 parametric analyses performed with the validated numerical methodology. Comparison of the predictions of the proposed relation for ground surface displacement against pertinent field data (from 256 case histories) and centrifuge test measurements shows satisfactory accuracy. Furthermore, the variation of lateral displacements with depth is explored and distinct displacement patterns are proposed for uniform, 2-layer and 4-layer ground profiles.     

任意方向震源二维兰姆问题的一个精确解

均匀弹性半空间表面或内部震源产生的地震波场的解析解属于Lamb问题,采用Cagniard-deHoop方法,对与水平面呈任意夹角的表面线源,求解了其作用于弹性半空间时的拉普拉斯-傅里叶双积分变换解.以δ-脉冲函数为例,给出了任意方向作用力下波场的构成,并定量解出了P波、S波、首波和Rayleigh波等各波的位移表达式,分析了不同作用方向下各波位移的相对大小.建立数值模型并进行数值模拟,模拟结果验证了理论研究的正确性.研究成果为近地表地震波场的研究提供了理论依据.     

半空间异质隆起的出平面动力响应:地表运动

采用闭合解析解对水平地表圆形非匀质隆起出平面运动特征进行详细分析。结果表明：（1）隆起区域介质软硬程度对其出平面地表运动影响非常大，软质隆起表面的地表位移较匀质隆起情况有显著放大，地表运动波动效应明显增强，而硬质隆起则减弱地表运动；（2）软质隆起地表位移幅值最大反应和平均反应增大的程度一般来说至少不低于隆起区域波速降低的程度，很多情况是远大于波速降低的程度，但最大反应出现的位置和频段主要受入射波角度控制；（3）当波垂直传播时，地表位移放大出现在隆起顶部，频率随隆起区变软，明显向低频移动，可出现在很低频段内，且随隆起区变软放大更为显著；（4）当波掠入射时，地表最大位移出现在隆起后表面，地表运动仍然十分强烈，甚至比波垂直入射时隆起顶部反应还要大，但出现在较高频段内。     

Propagation of Rayleigh waves in a layer lying over a heterogeneous half space

Summary Propagation of Rayleigh waves in a layer lying over a heterogeneous incompressible half space has been studied. The dispersion equations have been derived and displacements due to an infinite line source have also been investigated.     

Modeling of changes in the tidal response of the environment to an impending earthquake

It has become possible to apply efficiently Beaumont and Berger’s idea (1974) about the possibility to predict earthquakes using continuous monitoring of temporal variations of the tidal response only in recent years, with the appearance of GPS data on the field of the Earth’s surface displacements in seismic regions, as well as with the appearance of the Global Seismographic Network (GSN) containing the tidal tiltmetric and gravimetric data in the vicinities of the epicenters of strong earthquakes in Peru (2001), Sumatra (2004), and Chile (2010) before and after the strongest seismic events. Below, we present the results of the modeling of temporal variations of the tidal response of the environment in the vicinities of the focus of catastrophic earthquakes. The model of the focus includes data on the expansion and orientation of the fault surface, as well as on the discontinuity of the tangential component of the displacement vector on the opposite shores. The model is constructed from the GPS data on horizontal and vertical displacements of the Earth’s surface.