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1.
During seismic wave propagation on a free surface, a strong material contrast boundary develops in response to interference by P- and S- waves to create a surfacewave phenomenon. To accurately determine the effects of this interface on surface-wave propagation, the boundary conditions must be accurately modeled. In this paper, we present a numerical approach based on the dynamic poroelasticity for a space–time-domain staggeredgrid finite-difference simulation in porous media that contain a free-surface boundary. We propose a generalized stess mirror formulation of the free-surface boundary for solids and fluids in porous media for the grid mesh on which lays the free-surface plane. Its analog is that used for elastic media, which is suitable for precise and stable Rayleigh-type surface-wave modeling. The results of our analysis of first kind of Rayleigh (R1) waves obtained by this model demonstrate that the discretization of the mesh in a similar way to that for elastic media can realize stable numerical solutions with acceptable precision. We present numerical examples demonstrating the efficiency and accuracy of our proposed method. 相似文献
2.
Frequency‐domain waveform modelling and inversion for coupled media using a symmetric impedance matrix 
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下载免费PDF全文 To simulate the seismic signals that are obtained in a marine environment, a coupled system of both acoustic and elastic wave equations is solved. The acoustic wave equation for the fluid region simulates the pressure field while minimizing the number of degrees of freedom of the impedance matrix, and the elastic wave equation for the solid region simulates several elastic events, such as shear waves and surface waves. Moreover, by combining this coupled approach with the waveform inversion technique, the elastic properties of the earth can be inverted using the pressure data obtained from the acoustic region. However, in contrast to the pure acoustic and elastic cases, the complex impedance matrix for the coupled media does not have a symmetric form because of the boundary (continuity) condition at the interface between the acoustic and elastic elements. In this study, we propose a manipulation scheme that makes the complex impedance matrix for acoustic–elastic coupled media to take a symmetric form. Using the proposed symmetric matrix, forward and backward wavefields are identical to those generated by the conventional approach; thus, we do not lose any accuracy in the waveform inversion results. However, to solve the modified symmetric matrix, LDLT factorization is used instead of LU factorization for a matrix of the same size; this method can mitigate issues related to severe memory insufficiency and long computation times, particularly for large‐scale problems. 相似文献
3.
Diffraction of seismic waves in an elastic, cracked halfplane using a boundary integral formulation 总被引：1，自引：0，他引：1
A. Rodríguez-Castellanos F. Luzn F.J. Snchez-Sesma 《Soil Dynamics and Earthquake Engineering》2005,25(11):827-837
The presence of subsurface cracks in a halfspace excited by elastic waves may give rise to scattered body and surface waves. For many engineering applications, such as non-destructive testing or oil exploration, the scattered field may yield valuable information to detect cracks and other scatterers. We use the Indirect Boundary Element Method (IBEM) to study the diffraction of P, SV waves with various incidence angles and Rayleigh surface waves. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. Our approach is usually called indirect BEM as the sources' strengths should be obtained as an intermediate step. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' Principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with previous results in the literature. Various crack configurations, including multiple cracks, are investigated. Results in frequency and time domains are displayed. Under certain conditions the amplitude spectra of those waves clearly show conspicuous resonance peaks. 相似文献
4.
根据弹性薄板理论和振动理论,运用边界元法(BEM)分析了薄板弯曲自由振动的频率特性,从薄板自由振动的微分方程式出发,采用动态基本解推导出其相应的边界积分方程式,计算中对边界积分方程进行缩减,应用频率扫描的方法研究薄板的动态特性,准确、有效地得到了其相应的固有频率、给出的数值算例证明了本文的方法简单、可行,且具有良好的解析计算精度。 相似文献
5.
Time-history responses on the surface by regularly distributed enormous embedded cavities:Incident SH-waves 下载免费PDF全文
下载免费PDF全文 The time-history responses of the surface were obtained for a linear elastic half-plane including regularly distributed enormous embedded circular cavities subjected to propagating obliquely incident plane SH-waves. An advanced numerical approach named half-plane time-domain boundary element method(BEM), which only located the meshes around the cavities, was used to create the model. By establishing the modified boundary integral equation(BIE)independently for each cavity and forming the matrices, the final coupled equation was solved step-by-step in the timedomain to obtain the boundary values. The responses were developed for a half-plane with 512 cavities. The amplification patterns were also obtained to illustrate the frequencydomain responses for some cases. According to the results,the presence of enormous cavities affects the scattering and diffraction of the waves arrived to the surface. The introduced method can be recommended for geotechnical/mechanical engineers to model structures in the fields of earthquake engineering and composite materials. 相似文献
6.
THE APPLICATION OF PML BOUNDARY CODITIONS IN THE SIMULATION OF SEISMIC WAVE BY THE HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCES AT THE TRANSVERSELY ISOTROPIC MEDIA 下载免费PDF全文
下载免费PDF全文 In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research. 相似文献
7.
单程波近似实际上是一种多次前向散射和单次后向散射近似.利用单程波近似来描述波传播可以极大地节省地震数值模拟的计算时间和内存,实现地震波长距离传播模拟和三维地震模拟快速计算.本文基于单程波近似和波动积分方程的分离变量逼近,从广义Lippmann-Schwinger波动积分方程推导出耦合反射/透射系数的单程波传播算子.该算子由两部分构成：分离变量Fourier单程波传播算子和薄板间的反射/透射系数表达.前者将常规的Fourier分裂步单程波传播算子(SSF)推广适应横向强速度变化介质和大角度传播波场.后者是利用垂直波数来表示反射/透射系数,自然耦合到波场传播的计算过程中,其为地质界面倾角的隐式表达,精确描述振幅随入射角的变化,能适应任意复杂的模型.通过两个数值算例和一个实际地质模型的计算,本文将该方法和边界元法进行了比较,结果表明：在算例给出的介质横向速度变化情况下,本文提出的方法在相位和振幅方面与全波数值方法基本吻合. 相似文献
8.
Numerical simulation in coupled elastic and poroelastic media is important in oil and gas exploration. However, the interface between elastic and poroelastic media is a challenge to handle. In order to deal with the coupled model, the first-order velocity–stress wave equations are used to unify the elastic and poroelastic wave equations. In addition, an arbitrary high-order discontinuous Galerkin method is used to simulate the wave propagation in coupled elastic–poroelastic media, which achieves same order accuracy in time and space domain simultaneously. The interfaces between the two media are explicitly tackled by the Godunov numerical flux. The proposed forms of numerical flux can be used efficiently and conveniently to simulate the wave propagation at the interfaces of the coupled model and handle the absorbing boundary conditions properly. Numerical results on coupled elastic–poroelastic media with straight and curved interfaces are compared with those from a software that is based on finite element method and the interfaces are handled by boundary conditions, demonstrating the feasibility of the proposed scheme in dealing with coupled elastic–poroelastic media. In addition, the proposed method is used to simulate a more complex coupled model. The numerical results show that the proposed method is feasible to simulate the wave propagation in such a media and is easy to implement. 相似文献
9.
Elastic wave propagation in an irregularly layered medium 总被引：1，自引：0，他引：1
Rossana Vai Jos Manuel Castillo-Covarrubias Francisco J. Snchez-Sesma Dimitri Komatitsch Jean-Pierre Vilotte 《Soil Dynamics and Earthquake Engineering》1999,18(1):385
The indirect boundary element method (IBEM) is used to simulate wave propagation in two-dimensional irregularly layered elastic media for internal line sources. The method is based on the integral representation for scattered elastic waves using single layer boundary sources. Fulfillment of the boundary conditions leads to a system of integral equations. Results are obtained in the frequency domain and seismograins are computed through Fourier synthesis. In order to test and validate the method we present various comparisons between our results and the time series obtained analytically for a buried line source in a half-space and by using the recently developed spectral element method (SEM). 相似文献
10.
基于双相各向异性介质模型,首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程,然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件. 最后,利用本文给出的有限元方法对双相PTL介质和双相各向同性介质中的弹性波传播进行了数值模拟. 结果表明:有限元方法和吸收边界条件有效、可行,在理想相界条件下,不论是从固体位移,还是从流体位移的波场快照都能看到明显的慢速拟P波;在黏滞相界情况下,能否观察到慢速拟P波,与含流体地层介质的耗散性质有关.对实际含流体介质,从流体位移分量的波场快照比从固体位移波场快照更容易观察到慢速拟P波. 相似文献
11.
TWO DIMENSIONAL FINITE ELEMENT-BOUNDARY ELEMENT COUPLING MODEL OF MAGNETOTELLURIC SOUNDING 下载免费PDF全文
下载免费PDF全文 This paper describes how to apply the boundary element method to solve 2-D magneto-telluric sounding problem and then couple the BEM with finite element method to deal with inhomogeneous geological structure and its relation to regional stress regime. The BEM is able to calculate precisely the derivative of field variables. Such a new approach can more flexibly than others set up the upper boundary condition of the air region. Two practical examples are given. One is the study of topographical effect on the MT fields using boundary element method. There is an inverse relationship between the change of apparent resistivity and the topographical variation. The other is a coupled model of a basin in Nei Monngol Autonomous Region. A lower resistivity zone must exist in the crust and should be thicker below the central portion of the basin. This seems to agree with the regional stress regime changed from extension in Mesozoic to compression in Cenozoic 相似文献
12.
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
13.
D. A. Angus 《Surveys in Geophysics》2014,35(2):359-393
The study of seismic body waves is an integral aspect in global, exploration and engineering scale seismology, where the forward modeling of waves is an essential component in seismic interpretation. Forward modeling represents the kernel of both migration and inversion algorithms as the Green’s function for wavefield propagation and is also an important diagnostic tool that provides insight into the physics of wave propagation and a means of testing hypotheses inferred from observational data. This paper introduces the one-way wave equation method for modeling seismic wave phenomena and specifically focuses on the so-called operator-root one-way wave equations. To provide some motivation for this approach, this review first summarizes the various approaches in deriving one-way approximations and subsequently discusses several alternative matrix narrow-angle and wide-angle formulations. To demonstrate the key strengths of the one-way approach, results from waveform simulation for global scale shear-wave splitting modeling, reservoir-scale frequency-dependent shear-wave splitting modeling and acoustic waveform modeling in random heterogeneous media are shown. These results highlight the main feature of the one-way wave equation approach in terms of its ability to model gradual vector (for the elastic case) and scalar (for the acoustic case) waveform evolution along the underlying wavefront. Although not strictly an exact solution, the one-way wave equation shows significant advantages (e.g., computational efficiency) for a range of transmitted wave three-dimensional global, exploration and engineering scale applications. 相似文献
14.
A study on the dynamic characteristics of rigid foundations with special geometries such as square or circular with concentric internal holes, is presented. The foundations are resting on a homogeneous, linear elastic halfspace and are subjected to external forces or seismic wave excitation. Both ‘relaxed’ and ‘non-relaxed’ boundary conditions at the interface between the foundation and the halfspace are considered, and several parametric studies are conducted to assess the influence of either type of boundary conditions upon each of the possible modes of vibration. Results for massive and massless foundations are presented in time and frequency domains for impulsive and harmonic excitations, respectively. A time domain boundary element method (BEM) developed by the authors for the solution of a class of 3-D soil-structure interaction (SSI) problems is used for all the analyses reported in this work. The accuracy and efficiency of the method and the BEM models developed in this work are assessed on the basis of comparison studies with published results. 相似文献
15.
非零偏VSP地震资料是一种多分量资料,处理非零偏VSP资料,弹性波叠前逆时深度偏移技术无疑是最适合的处理技术.本文从二维各向同性介质的弹性波波动方程出发,研究了对非零偏VSP资料进行叠前逆时深度偏移的偏移算法,讨论了逆时传播过程中的边值问题和数值频散问题及其相应的解决方案;采用求解程函方程计算得到地下各点的地震波初至时间作为成像时间,实现了非零偏VSP资料的叠前逆时深度偏移.最后进行了模型试算和非零偏VSP地震资料的试处理,结果表明该方法不受地层倾角限制,较适用于高陡构造地区或介质横向速度变化较大地区的非零偏VSP地震资料处理. 相似文献
16.
介质的弹性常数为三维四阶张量的分量,共有８１个,由于应力张量和应变张量的对称性及能量密度是应变的二次函数,一般各向异常性介质的独立弹性常数可减为２１个,如果介质具有较高的对称性,独立弹性常数的数目会更少。 对于地壳和上地幔,具有５个独立弹性常数的横向各向同性介质是一个非常好的近似,本研究中横向各向同性介质的对称轴方向可以是任意的（即对称轴可以不平等于铅直方向）,在此情况下,需要进行坐标变换,如果已知介质在某一坐标系（其坐标轴平行或垂直于介质的对称轴）中的弹性常数,我们能够容易地利用变换公式得到变换后新坐标系中的弹性常数。 本文提出了一种方案,利用伪谱法既能模拟横向各向同性介质中的平面波,也能模拟点源激发的波场。在勘探地球物理和地震学中,模拟横向各向同性介拮中传播的平面波及区域源产生的波是最重要的研究课题之一。然而在一般各向异性介质中,很难或不可能确定弹性波的相速度和偏振方向,但在横向各向同性介质中,则可以通过坐标变换来实现,这里我们所提出的方法可以用于横向各向同性介质中弹性波的模拟。 相似文献
17.
A boundary integral formulation is presented and applied to model the ground motion on alluvial valleys under incident P, S and Rayleigh waves. It is based on integral representations for the diffracted and the refracted elastic waves using single-layer boundary sources. This approach is called indirect BEM in the literature as the sources' strengths should be obtained as an intermediate step. Boundary conditions lead to a system of integral equations for boundary sources. A discretization scheme based on the numerical and analytical integration of exact Green's functions for displacements and tractions is used. Various examples are given for two-dimensional problems of diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half-space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response and suggest approximations of practical interest. For shallow alluvial valleys the response and its resonant frequencies are controlled by a coupling mechanism that involves both the simple one-dimensional shear beam model and the propagation of surface waves. 相似文献
18.
基于薄层法在研究层状介质中波的传播问题的高效性、边界单元法处理无限域问题的精确性,结合二者的优点提出三维层状地基薄层法基本解答,建立了基于三维层状半空间薄层法位移基本解答的半解析动力边界元法。该方法可有效的分析多层场地的动力问题,解决土-结构动力相互作用问题。同时分别对粘弹性上软下硬地基及上硬下软地基的三维空沟主动隔振进行了详细的分析。结果表明,两种情况下采用空沟屏障隔振均可以取得一定的隔振效果;同时,地基分层参数对空沟隔振体系的隔振效果影响显著。 相似文献
19.