共查询到20条相似文献，搜索用时 687 毫秒
1.
《应用地球物理》2017,(2)
地震波场数值模拟中不可避免地会出现边界反射,一般采用吸收边界条件以压制人工边界反射。目前常用的分裂式完全匹配层(PML)边界条件需要在边界处进行特殊处理,尤其是在三维情况下需要将变量分裂为三个分量,增加了数值模拟的计算时间和内存占用量。与分裂式PML吸收边界条件相比,混合吸收边界条件(HABC)具有易于实现、计算量小和吸收效果好等优点,可以提高三维波动方程数值模拟的计算效率。本文将基于一阶Higdon单程波方程的混合吸收边界条件从二维计算域发展到三维,提出了适用于三维弹性波数值模拟的混合吸收边界条件。均匀模型以及复杂模型的三维数值模拟结果表明,混合吸收边界条件与传统的完全匹配层边界条件相比,具有效率高、吸收效果好的优势。 相似文献
2.
《地震工程与工程振动》2016,(2)
在波动方程有限差分波场数值模拟中,为了使计算得到的边界波场值更接近于真实的边界波场值,需要使用边界条件以减少来自计算区域边界的人为反射能量。传统的分裂式完全匹配层(SPML)吸收边界条件不能有效吸收掠射波,后来发展的不分裂卷积完全匹配层(CPML)能够较好地处理这个问题,并且CPML在处理边界问题时无需对波场进行非物理分裂。本文针对Kelvin-Voigt模型的黏弹性介质,采用高阶交错网格有限差分方法进行数值模拟,同时利用CPML吸收边界条件进行边界处理。数值模拟结果表明:与弹性波相比,大角度入射产生的低频掠射波对黏弹性波的影响更大;CPML吸收边界条件对低频掠射波的吸收效果比传统的SPML吸收边界条件更好。 相似文献
3.
本文采用一种新的交错网格-Lebedev网格（LG）进行TTI介质的正演模拟研究,避免了Virieux标准交错网格（SSG）算法在处理TTI、单斜等各向异性介质时波场插值引入的数值误差,提高了模拟精度.在方法实现过程中,本文针对有限差分正演模拟面临的网格频散与边界反射两个关键性问题分别做了优化,并通过模型试算验证了它们的有效性与可行性：（1）结合最小二乘思想推导出新的频散改进差分系数（DIC）,该系数比Taylor系数更能有效地压制粗网格引起的数值频散,可以节约内存,提高计算效率;（2）将分裂的多轴完全匹配层（M-PML）吸收边界条件引入到LG算法中,解决了传统PML边界条件在某些各向异性介质中的不稳定现象并且具有较好的边界吸收效果. 相似文献
4.
以Carcione黏弹各向异性理论为基础,给出了适用于黏弹性具有任意倾斜对称轴横向各向同性介质(黏弹TTI介质)的二维三分量一阶速度-应力方程,采用旋转交错网格任意偶数阶精度有限差分格式求解该方程,并推导出了二维黏弹TTI介质完全匹配层(PML)吸收边界条件公式和相应的旋转交错网格任意偶数阶精度有限差分格式,实现了该类介质的地震波场数值模拟.数值模拟结果表明:该方法模拟精度高,边界吸收效果好,可以得到高精度的波场快照和合成记录;并且波场快照和合成记录能较好地反映地下介质的各向异性特征和黏弹性特征. 相似文献
5.
在地震波传播数值模拟的过程中,需要使用吸收边界条件从而达到衰减人为边界 反射的目的. 本文基于傍轴近似法提出了计算三维弹性波方程的吸收边界条件公式,表示了 各边界面、边棱和角点处波场所满足的单程波方程,并在三维弹性波数值模拟中进行了应用 . 理论模型及三维盐丘地质模型波场切片快照试算结果表明,该吸收边界条件可以有效地吸 收人为边界反射,适用于较大入射角情况,从而消除了边界有效波信息的干扰. 由于采用四 阶近似方程,在保证计算精度的前提下,该方法具有节省计算工作量和易于实现的特点. 相似文献
6.
《地球物理学进展》2016,(6)
在地震波传播数值模拟的过程中,需要使用吸收边界条件达到衰减人为边界反射的目的,其中完全匹配层(PML)吸收边界条件被认为是目前最理想的吸收边界条件.但在三维地震波传播数值模拟中直接应用常规的PML吸收边界条件存在编程实现复杂、计算资源需求高等不足之处.本文基于传统的NPML吸收边界条件,提出了一种改进的方法.该方法通过引入伸展函数和辅助变量,把PML介质中的三维弹性波动方程分解成正常计算项和衰减项,其中衰减项的计算只在PML区域内部进行,其值只与坐标轴的方向相关,可通过离散数值迭代求解.分析和试验结果表明,该方法避免了卷积运算,减少了辅助变量的个数,具有理论方程简洁、编程实现简单、计算资源需求少等优点,能更有效地解决三维地震波传播数值模拟中的吸收边界问题. 相似文献
7.
Liu和Sen（2010和2012）在地震波场数值模拟中提出一种混合吸收边界条件. 该方法具有计算量小、容易实现及吸收效果好等优点. 但现有的混合吸收边界条件是针对二阶位移-应力方程设计的,存在稳定性问题. 本文首先推导了两种速度-应力单程波方程：二阶Higdon单程波方程和一阶Higdon单程波方程. 进而提出基于一阶弹性波方程的混合吸收边界条件方法. 在内部区域和边界之间引入一个过渡区域,通过单程波与双程波方程平滑过渡来消除人工边界反射. 为了改善混合吸收边界条件的吸收效果和稳定性,我们采用了能同时吸收纵、横波反射的一阶单程波方程和与变量位置有关的加权系数. 为了验证混合吸收边界条件的有效性,将其与常规分裂完全匹配层（PML）方法进行了比较. 数值模拟结果表明,与PML边界条件相比,混合吸收边界条件在耗用更小计算时间和存储量的前提下,可以获得更好的吸收效果. 另外,本文提出的两种混合吸收边界条件中,混合一阶Higdon吸收边界条件具有更好的稳定性. 相似文献
8.
《地球物理学进展》2015,(1)
在应用有限差分法地震波场数值模拟过程中,模拟精度和计算效率是关键问题之一,特别是对于速度变化剧烈的含小尺度地质体的数值模拟尤为重要.为了既能精细刻画介质的局部结构,又能保证模拟的时效性,本文在传统交错网格有限差分算法的基础上,将变网格有限差分方法引入到交错网格高阶差分数值模拟中,对交错网格空间算法进行了改进,并避免了因插值因素影响模拟精度和计算效率.本文采用完全匹配层吸收边界条件实现对可变网格数值模拟的边界处理,根据完全匹配层吸收边界原理和参量的分裂思想,在不同的方向分别加相应的阻尼衰减因子,解决边界的反射问题.此外还分析了数值频散对于模拟结果的影响.文中分别设计了地堑和生物礁两个介质模型对可变交错网格算法的有效性和稳定性进行了验证.数值模拟结果表明,可变交错网格有限差分算法数值模拟能够对地下介质物性的空间变化进行准确刻画,进一步增强数值模拟对复杂介质的适应性,同时为地震数据的波场成像、纵横波联合解释等提供可靠依据. 相似文献
9.
本文采用一种新的交错网格-Lebedev网格(LG)进行TTI介质的正演模拟研究,避免了Virieux标准交错网格(SSG)算法在处理TTI、单斜等各向异性介质时波场插值引入的数值误差,提高了模拟精度.在方法实现过程中,本文针对有限差分正演模拟面临的网格频散与边界反射两个关键性问题分别做了优化,并通过模型试算验证了它们的有效性与可行性:(1)结合最小二乘思想推导出新的频散改进差分系数(DIC),该系数比Taylor系数更能有效地压制粗网格引起的数值频散,可以节约内存,提高计算效率;(2)将分裂的多轴完全匹配层(M-PML)吸收边界条件引入到LG算法中,解决了传统PML边界条件在某些各向异性介质中的不稳定现象并且具有较好的边界吸收效果. 相似文献
10.
双相介质地震波场数值模拟的迭积微分算子及其PML边界条件 总被引：1，自引：1，他引：0
将基于计算数学中Forsyte 广义正交多项式的迭积微分算子引入到地震波动方程的一阶速度--应力方程的空间微分运算中去,并采用时间错格有限差分算子替代传统的差分算子以匹配高精度的空间迭积微分算子,从而发展一种全新的地震波场正演模拟方法,来解决复杂非均匀介质模型中的波场传播问题.为了大幅衰减人工边界引起的反射,本文将完全匹配层(Perfectly Matched Layer,PML)吸收边界条件引入到所构建的方法中,以解决迭积微分算子法的边界问题.以二维波动方程为例,用迭积微分算子法实现了双相介质的地震波场正演模拟,模拟结果表明,双相介质模型较好地解释了含流体孔隙特性.同时也表明迭积微分算子法是一种非常实用、有效的数值模拟方法. 相似文献
11.
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
12.
在进行地震波模拟计算的过程中用有限的计算区域模拟地下无限空间,需要进行边界截断.为了在边界处不产生虚假反射影响模拟结果,需要引入吸收边界条件.本文采用的近似完全匹配层是一种新型非分裂完全匹配层,计算效率较高.同时相比于其他非分裂完全匹配层,其还具有不改变方程的形式、易于实现等优势.但是当入射波角度较大,边界吸收效果变弱,且残留在边界中的能量使近似完全匹配层变得极其不稳定.多轴复频移近似完全匹配层的提出就是为了改善对大角度入射波的吸收并且提高边界的稳定性.通过实验模拟和矩阵特征值灵敏度来研究多轴复频移近似完全匹配层的吸收效果及稳定性.结果表明该方法不仅能够吸收掠入波,而且对常规入射波的吸收也得到提升,同时拥有更好的稳定性. 相似文献
13.
介绍了完美匹配层(PML)人工边界可以吸收不同频率和任意角度入射波的原理以及PML人工边界的构造方法. 在此基础上,将PML人工边界应用于地震波动数值模拟的速度应力混合有限元格式中,探讨了PML应用的可行性,并通过数值试验研究了PML人工边界的反射率,比较了PML人工边界与多次透射公式(MTF)人工边界应用于体波和面波模拟中数值反射的差异,对两种边界的透射效果进行了分析. 结果表明, 尽管数值离散后PML人工边界不再保持完美匹配特性,但PML人工边界在近场波动数值模拟中可获得比MTF人工边界更为理想的吸收效果,在角点透射、大角度掠射情形下尤为明显;PML人工边界在混合有限元格式的数值算法中,未见失稳等不良反应,比MTF人工边界有更好的稳定性;在合理选择参数的情况下,PML人工边界的运算量可接受. 相似文献
14.
The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construc- tion process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investi- gated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in corner and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computa- tional efficiency of PML boundary is only a little lower than MTF boundary. 相似文献
15.
Mesh-free discretization, flexibly distributing nodes without computationally expensive meshing process, is able to deal with staircase problem, oversampling and undersampling problems and saves plenty of nodes through distributing nodes suitably with respect to irregular boundaries and model parameters. However, the time-domain mesh-free discretization usually exhibits poorer stability than that in regular grid discretization. In order to reach unconditional stability and easy implementation in parallel computing, we develop the frequency-domain finite-difference method in a mesh-free discretization, incorporated with two perfectly matched layer boundary conditions. Furthermore, to maintain the flexibility of mesh-free discretization, the nodes are still irregularly distributed in the absorbing zone, which complicates the situation of artificial boundary reflections. In this paper, we implement frequency-domain acoustic wave modelling in a mesh-free system. First, we present the perfectly matched layer boundary condition to suppress spurious reflections. Moreover, we develop the complex frequency shifted–perfectly matched layer boundary condition to improve the attenuation of grazing waves. In addition, we employ the radial-basis-function-generated finite difference method in the mesh-free discretization to calculate spatial derivatives. The numerical experiment on a rectangle homogeneous model shows the effectiveness of the perfectly matched layer boundary condition and the complex frequency shifted–perfectly matched layer boundary condition, and the latter one is better than the former one when absorbing large angle incident waves. The experiment on the Marmousi model suggests that the complex frequency shifted–perfectly matched layer boundary condition works well for complicated models. 相似文献
16.
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
17.
Application of the nearly perfectly matched layer for seismic wave propagation in 2D homogeneous isotropic media 总被引：1，自引：0，他引：1
Jingyi Chen 《Geophysical Prospecting》2011,59(4):662-672
Numerical modelling plays an important role in helping us understand the characteristics of seismic wave propagation. The presence of spurious reflections from the boundaries of the truncated computational domain is a prominent problem in finite difference computations. The nearly perfectly matched layer has been proven to be a very effective boundary condition to absorb outgoing waves in both electromagnetic and acoustic media. In this paper, the nearly perfectly matched layer technique is applied to elastic isotropic media to further test the method's absorbing ability. The staggered‐grid finite‐difference method (fourth‐order accuracy in space and second‐order accuracy in time) is used in the numerical simulation of seismic wave propagation in 2D Cartesian coordinates. In the numerical tests, numerical comparisons between the nearly perfectly matched layer and the convolutional perfectly matched layer, which is considered the best absorbing layer boundary condition, is also provided. Three numerical experiments demonstrate that the nearly perfectly matched layer has a similar performance to the convolutional perfectly matched layer and can be a valuable alternative to other absorbing layer boundary conditions. 相似文献
18.
探地雷达数值模拟中,时域有限差分法在时间和空间上一般采用二阶精度的中心差分近似(FDTD(2,2)),其形式简单,但数值色散误差较大,在复杂模型模拟时不能很好地反映模型的精细变化.高阶时域有限差分法能很好地改善数值色散带来的误差,提高模拟精度.本文基于三维高阶时域有限差分法的基本原理实现了探地雷达正演模拟,采用单轴各向异性完全匹配层(UPML)作为吸收边界条件,可以有效地吸收外向传播的电磁波,在大大地提高计算效率的同时,也能很好地改善边界的吸收效果.分析对比正演模拟结果,通过三维高阶时域有限差分正演能获得目标体准确电磁响应信息,并能很好的提高模拟精度. 相似文献
19.
数值频散和边界反射是频率域模拟时需要解决的两个重要问题.然而,受计算效率和分解阻抗矩阵时的内存占用量的制约,提高有限差分算子长度或增加有限差分网格数目均不是提高频率域模拟精度的最优解决方案.本文首先分析了数值频散产生的理论机制,在此基础上,推导了一种“波数补偿”的声波方程表达式来压制数值频散,并给出其物理意义,有效地改善了数值频散问题,提高了模拟精度;在边界问题上,本文采用多轴卷积完全匹配层(MCPML)边界条件代替传统的完全匹配层(PML)边界条件,快速吸收边界内的残余能量,压制边界反射.结合改进声波方程和MCPML边界条件,给出了一种高精度的频率域声波方程有限差分格式.数值模拟结果表明,在不增加计算量和内存占用量的前提下,本文研究的方法、正演精度高、波场模拟清晰、无干扰反射,是一种可靠高效的频率域模拟方法. 相似文献
20.
We derive a governing second-order acoustic wave equation in the time domain with a perfectly matched layer absorbing boundary condition for general inhomogeneous media. Besides, a new scheme to solve the perfectly matched layer equation for absorbing reflections from the model boundaries based on the rapid expansion method is proposed. The suggested scheme can be easily applied to a wide class of wave equations and numerical methods for seismic modelling. The absorbing boundary condition method is formulated based on the split perfectly matched layer method and we employ the rapid expansion method to solve the derived new perfectly matched layer equation. The use of the rapid expansion method allows us to extrapolate wavefields with a time step larger than the ones commonly used by traditional finite-difference schemes in a stable way and free of dispersion noise. Furthermore, in order to demonstrate the efficiency and applicability of the proposed perfectly matched layer scheme, numerical modelling examples are also presented. The numerical results obtained with the put forward perfectly matched layer scheme are compared with results from traditional attenuation absorbing boundary conditions and enlarged models as well. The analysis of the numerical results indicates that the proposed perfectly matched layer scheme is significantly effective and more efficient in absorbing spurious reflections from the model boundaries. 相似文献