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1.
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.
相似文献2.
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. 相似文献
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Pieter S. Pauw Sjoerd E.A.T.M. van der Zee Anton Leijnse Gualbert H.P. Oude Essink 《Ground water》2016,54(4):521-531
This article deals with the quantification of saltwater upconing below horizontal wells in freshwater lenses using analytical solutions as a computationally fast alternative to numerical simulations. Comparisons between analytical calculations and numerical simulations are presented regarding three aspects: (1) cyclic pumping; (2) dispersion; and (3) finite horizontal wells in a finite domain (a freshwater lens). Various hydrogeological conditions and pumping regimes within a dry half year are considered. The results show that the influence of elastic and phreatic storage (which are not taken into account in the analytical solutions) on the upconing of the interface is minimal. Furthermore, the analytical calculations based on the interface approach compare well with numerical simulations as long as the dimensionless interface upconing is below 1/3, which is in line with previous studies on steady pumping. Superimposing an analytical solution for mixing by dispersion below the well over an analytical solution based on the interface approach is appropriate in case the vertical flow velocity around the interface is nearly constant but should not be used for estimating the salinity of the pumped groundwater. The analytical calculations of interface upconing below a finite horizontal well compare well with the numerical simulations in case the distance between the horizontal well and the initial interface does not vary significantly along the well and in case the natural fluctuation of the freshwater lens is small. In order to maintain a low level of salinity in the well during a dry half year, the dimensionless analytically calculated interface upconing should stay below 0.25. 相似文献
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A new numerical method is presented for propagating elastic waves in heterogeneous earth media, based on spectral approximations of the wavefield combined with domain decomposition techniques. The flexibility of finite element techniques in dealing with irregular geologic structures is preserved, together with the high accuracy of spectral methods. High computational efficiency can be achieved especially in 3D calculations, where the commonly used finite-difference approaches are limited both in the frequency range and in handling strongly irregular geometries. The treatment of the seismic source, introduced via a moment tensor distribution, is thoroughly discussed together with the aspects associated with its numerical implementation. The numerical results of the present method are successfully compared with analytical and numerical solutions, both in 2D and 3D. 相似文献
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基于前一篇文章中得到的关于三维层状孔隙介质中弹性波场的积分形式半解析解,本文通过离散波数法开展了数值模拟.将全空间均匀孔隙介质中单力点源和爆炸点源作用下弹性波场的解析解和我们的数值模拟结果进行对比,发现两者是完全一致的.而在一个两层半空间模型下的数值模拟,验证了固相位移Green函数的9组空间互易性情况.通过以上两种对比检验,验证了半解析解理论公式、数值模拟方法以及相应程序代码的正确性和可靠性.随后利用敏感度分析研究了不同的介质参数变化对爆炸点源在界面上会产生的反射波场的影响.通过垂直地震剖面模型的数值模拟,发现弹性波场能很好地反映孔隙介质物理性质的变化,同时也讨论了动力协调这一孔隙介质中的特殊现象.我们发展的基于半解析解的数值模拟方法可以为三维层状孔隙介质中弹性波传播特征的研究提供一种可供选择的有效工具和手段. 相似文献
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经典的微分等效介质(DEM)理论可用于确定多孔介质的弹性性质,但由于缺乏多重孔DEM方程,其估计的多重孔岩石的等效弹性模量依赖于包裹体(即不同孔隙纵横比的孔或缝)的添加顺序.本文首先从Kuster-Toksöz理论出发建立了Zimmermann和Norris两种形式的多重孔DEM方程.Norris形式的多重孔DEM方程预测的等效弹性模量总是位于Hashin-Shtrikman上下限内,而Zimmermann形式的多重孔DEM方程有时会越界.然后,通过使用干燥岩石模量比的解析近似式,对两个相互耦合的Norris形式DEM方程进行解耦得到干燥多重孔岩石的体积和剪切模量解析式.用全DEM方程的数值解对解析近似式的有效性进行了测试,解析公式的计算结果在整个孔隙度分布区间与数值解吻合良好.对实验室测量数据在假设岩石含有双重孔隙的情形下用双重孔DEM解析公式对岩石的弹性模量进行了预测,结果表明,解析式准确地预测了弹性模量随孔隙度的变化.双重孔(即软、硬孔)DEM解析模型可用来反演各孔隙类型的孔隙体积比,它可以通过实验室测量与理论预测之间的平方误差最小反演得到.砂岩样品的反演结果揭示,软孔的孔隙体积百分比与粘土含量没有明显的相关性. 相似文献
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A numerical procedure for a dynamic non-linear finite element analysis is proposed here to analyse three-dimensional reinforced concrete shear wall structures subjected to earthquake motions. A shear wall is modelled as a quasi-three dimensional structure which is composed of plane elements considering the in-plane stiffness of orthogonal flange panels. The proposed constitutive model is based on the non-linearity of reinforcement and concrete in which the tension stiffening in tension and the degradation of stiffness and strength in compression of concrete after cracking are considered. The acceleration-pulse method, which is a kind of explicit analytical procedure, is employed to solve the non-linear dynamic equations, where the dynamic equation can be solved without stiffness matrix and so the iterative procedure is not necessary for descending portion of stress–strain relationship caused by cracking and softening after compressive strength in concrete. The damping effect is considered by assuming equivalent viscous damping which can give good cyclic behaviours of inertia force vs. displacement relationships. This analytical method was applied to a test specimen of a reinforced concrete shear wall with a H-shaped section which was vibrated up to failure by using a large-scale shaking table with high -performance in Japan. The test was performed as one of the dynamic model tests for evaluation of seismic behaviour of nuclear reactor buildings. The calculations were performed sequentially from the elastic range to failure. The comparison with the test results shows that this approach has good accuracy. © 1997 by John Wiley & Sons Ltd 相似文献
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S. M. Molodenskii M. S. Molodenskii T. A. Begitova 《Izvestiya Physics of the Solid Earth》2016,52(5):660-673
In the first part of the paper, a new method was developed for solving the inverse problem of coseismic and postseismic deformations in the real (imperfectly elastic, radially and horizontally heterogeneous, self-gravitating) Earth with hydrostatic initial stresses from highly accurate modern satellite data. The method is based on the decomposition of the sought parameters in the orthogonalized basis. The method was suggested for estimating the ambiguity of the solution of the inverse problem for coseismic and postseismic deformations. For obtaining this estimate, the orthogonal complement is constructed to the n-dimensional space spanned by the system of functional derivatives of the residuals in the system of n observed and model data on the coseismic and postseismic displacements at a variety of sites on the ground surface with small variations in the models. Below, we present the results of the numerical modeling of the elastic displacements of the ground surface, which were based on calculating Green’s functions of the real Earth for the plane dislocation surface and different orientations of the displacement vector as described in part I of the paper. The calculations were conducted for the model of a horizontally homogeneous but radially heterogeneous selfgravitating Earth with hydrostatic initial stresses and the mantle rheology described by the Lomnitz logarithmic creep function according to (M. Molodenskii, 2014). We compare our results with the previous numerical calculations (Okado, 1985; 1992) for the simplest model of a perfectly elastic nongravitating homogeneous Earth. It is shown that with the source depths starting from the first hundreds of kilometers and with magnitudes of about 8.0 and higher, the discrepancies significantly exceed the errors of the observations and should therefore be taken into account. We present the examples of the numerical calculations of the creep function of the crust and upper mantle for the coseismic deformations. We also demonstrate the results of estimating the ambiguity of the models of postseismic deformations in the vicinity of the source of the Great Tohoku earthquake of March 11, 2011, which were obtained by the method of orthogonalization described in the first part of the paper. 相似文献
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A mathematical model of fresh groundwater flow from a semi-infinite confined aquifer into a sea (pool, trench, and the like) filled with salt water and having a freshwater layer above its horizon. To study this problem a mixed boundary-value problem of the theory of analytical functions is formulated and solved with the use of the Polubarinova-Kochina method. The obtained exact analytical relationships and numerical calculations are used to perform a detailed hydrodynamic analysis of the effect of the freshwater layer and other physical parameters of the model on the character and the extent of displacement. 相似文献
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模拟弹性波在孔隙介质中传播，需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射. 本文在前人工作基础上，首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法，并详细讨论了完全匹配层的构建及其有限差分算法实现. 首先，本文通过均匀孔隙模型的数值解与解析解的对比，验证所提出的数值方法的正确性；然后，本文考察了完全匹配层对不同入射角度入射波和自由表面上的瑞利波的吸收性能，将完全匹配层与廖氏和阻尼吸收边界进行了对比，研究了这三种吸收边界在不同吸收厚度情况下对弹性波吸收能力. 数值结果表明，在孔隙介质中，完全匹配层作为吸收边界能十分有效地吸收衰减外行波，无论对体波还是面波，是一种高效边界吸收算法. 相似文献
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Numerical investigation of alternative fracture stiffness measures and their respective scaling behaviours 
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下载免费PDF全文 We study the mechanical deformation of fractures under normal stress, via tangent and specific fracture stiffnesses, for different length scales using numerical simulations and analytical insights. First, we revisit an equivalent elastic layer model that leads to two expressions: the tangent stiffness is the sum of an “intrinsic” stiffness and the normal stress, and the specific stiffness is the tangent stiffness divided by the fracture aperture at current stress. Second, we simulate the deformation of rough fractures using a boundary element method where fracture surfaces represented by elastic asperities on an elastic half‐space follow a self‐affine distribution. A large number of statistically identical “parent” fractures are generated, from which sub‐fractures of smaller dimensions are extracted. The self‐affine distribution implies that the stress‐free fracture aperture increases with fracture length with a power law in agreement with the chosen Hurst exponent. All simulated fractures exhibit an increase in the specific stiffness with stress and an average decrease with increase in length consistent with field observations. The simulated specific and tangent stiffnesses are well described by the equivalent layer model provided the “intrinsic” stiffness slightly decreases with fracture length following a power law. By combining numerical simulations and the analytical model, the effect of scale and stress on fracture stiffness measures can be easily separated using the concept of “intrinsic” stiffness. We learn that the primary reason for the variability in specific stiffness with length comes from the fact that the typical aperture of the self‐affine fractures itself scales with the length of the fractures. 相似文献
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This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with
symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient
Chinese method called the max-min approach are presented to obtain an approximate solution. The major concern is to assess
the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by
examining their ability to establish an actual (numerical) solution. Therefore, the analytical results are compared with the
numerical results to illustrate the effectiveness and convenience of the proposed methods. 相似文献
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High-speed train seismology has come into being recently. This new kind of seismology uses a high-speed train as a repeatable moving seismic source. Therefore, Green's function for a moving source is needed to make theoretical studies of the high-speed train seismology. Green's function for three-dimensional elastic wave equation with a moving point source on the free surface is derived. It involves a line integral of the Green's function for a fixed point source with different positions and corresponding time delays. We give a rigorous mathematical proof of this Green's function. According to the principle of linear superposition, we have also obtained the Green's function for a group of moving sources which can be regarded as a model of a traveling high-speed train. Based on a temporal convolution, an analytical formula for other moving sources is also given. In terms of a moving Gaussian source, we deal with the issue of numerical calculations of the analytical formula. Applications to modelling of a traveling high-speed train are presented. We have considered both the land case and the bridge case for a traveling high-speed train. The theoretical seismograms show different waveform features for these two cases. 相似文献
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Zdeněk Martinec 《Pure and Applied Geophysics》2009,166(8-9):1167-1197
A semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous sphere induced by a surface toroidal force is derived. The model consists of a concentrically-nested elastic lithosphere, a viscoelastic mantle, and an eccentrically-nested viscoelastic core. Since numerical codes based on finite-element or spectral-finite-difference techniques for modelling viscoelastic relaxation in a spherical geometry in the presence of lateral viscosity variations are becoming more popular, reliable examples for testing and validating such codes are essential. The eccentrically-nested sphere solution has been tested by comparing it with two distinct results: The analytical solution for viscoelastic relaxation in concentrically-nested spheres and the time domain, spectral finite-element numerical solution for viscoelastic relaxation in eccentrically-nested spheres, with excellent agreement being obtained. 相似文献
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Dynamic effects of moving loads on road pavements: A review 总被引：3，自引：0，他引：3
This review paper deals with the dynamic response of road pavements to moving loads on their surface. The road pavement can be modeled as a beam, a plate, or the top layer of a layered soil medium. The foundation soil can be modeled as a system of elastic springs and dashpots or a homogeneous or layered half-space. The material behavior of the pavement can be elastic or viscoelastic, while that of the foundation layers elastic, viscoelastic, water-saturated poroelastic or even inelastic. The loads are concentrated or distributed of finite extent, may vary with time and move with constant or variable speed. The analysis is done by analytical, analytical/numerical and purely numerical methods, such as finite element and boundary element methods, under conditions of plane strain or full three-dimensionality. A number of representative examples is presented in order to illustrate the problem and the methods of analysis, demonstrate the dynamic effects of moving loads on the layered soil medium and indicate the implications of the results on road and airport pavement design. 相似文献
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We present an original implementation of the free-surface boundary condition in a mesh-free finite-difference method for simulating elastic wave propagation in the frequency domain. For elastic wave modelling in the frequency domain, the treatment of free surfaces is a key issue which requires special consideration. In the present study, the free-surface boundary condition is directly implemented at node positions located on the free-surface. Flexible nature of the mesh-free method for nodal distribution enables us to introduce topography into numerical models in an efficient manner. We investigate the accuracy of the proposed implementation by comparing numerical results with an analytical solution. The results show that the proposed method can calculate surface wave propagation even for an inclined free surface with substantial accuracy. Next, we calculate surface wave propagation in a model with a topographic surface using our method, and compare the numerical result with that using the finite-element method. The comparison shows the excellent agreement with each other. Finally, we apply our method to the SEG foothill model to investigate the effectiveness of the proposed method. Since the mesh-free method has high flexibility of nodal distribution, the proposed implementation would deal with models of topographic surface with sufficient accuracy and efficiency. 相似文献
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A comprehensive analytical solution is developed to examine the torsional vibration of an elastic foundation on a semi-infinite saturated elastic medium for the first time. First, the governing equations of saturated media are solved by use of Hankel transform techniques. Then, based on the assumption that the contact between the foundation and the half-space is perfectly bonded, this dynamic mixed boundary-value problem can lead to dual integral equations, which are further reduced to the standard Fredholm integral equations of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper. The numerical results indicate that the response of the elastic foundation strongly depends on the material and geometrical properties of both the saturated soil-foundation system and the load acting on the foundation. In most of the cases, the dynamic behavior of an elastic foundation on saturated media significantly differs from that of a rigid plate bearing on the elastic half-space. 相似文献