用三维半解析边界元的子结构法分析凸起山包对地震波的散射

本文建立了一种三维半解析边界元子结构法。这种方法可在频域就三维轴对称凸起山包对地震波的散射进行分析。这种方法节省存储空间、计算工作量小。另外还叙述了拐角的处理方法。     

三维沉积盆地对地震动的放大效应间接边界元法模拟

基于一种高精度间接边界元法(IBEM), 实现了沉积盆地三维地震响应的频域、 时域精细求解, 并以半空间中椭球形沉积盆地对平面P波和SV波的散射为例, 着重探讨了入射角度、 入射波型、 入射频率、 盆地长宽比和深宽比对沉积盆地地震动放大效应的影响规律． 结果表明: 盆地形状对地震波的放大效应和空间分布状态具有显著影响, 且具体规律受控于入射波频段． ① 随着盆地深度增大, 盆地边缘面波发育更为充分, 在较宽频段内均会出现显著的地震动放大效应, 且深盆地的放大区域集中于盆地中部． ② 圆形盆地对地震波的汇聚效应最为显著, 而狭长盆地对地震波的汇聚作用相对较弱, 高频情况下可在盆地内部形成多个聚焦区域． ③ 不同波型入射下, 盆地对地震动放大效应的机制有所差异: P波入射下, 竖向位移放大主要是由于盆地边缘面波由四周向中部汇聚所致; SV波入射下, 边缘面波汇聚效应相对较弱, 而当盆地较深时, 底部透射体波和边缘面波易形成同相干涉从而显著放大地震动． 按盆地内外介质波速比为1/2, P波和SV波垂直入射下频域最大放大倍数分别为25和15, 时域放大倍数约为4.0和3.7(雷克子波)． ④ 低频波入射下, 位移从盆地中部向边缘逐渐减小, 且浅层沉积盆地对地表位移幅值的放大作用不明显． ⑤ P波和SV波的入射角度对盆地地震动放大幅值及空间分布特征也具有显著影响．      

近表面周期裂纹阵对SH波散射问题的边界元解

针对半空间中一近表面周期裂纹对SH波的散射问题,本文采用边界元法进行研究。利用周期性的条件,将问题归结为一个典型条带中含单个裂纹的问题,并推导出了以裂纹张开位移为未知函数的边界积分方程。为了解决高阶奇异的边界积分方程的数值计算问题,本文采用解析的方法进行降阶。计算了半空间表面的位移,与其他方法求解结果的比较证明了数值计算的可靠性。     

无破碎带断层场地对SH波的散射

在层状半空间精确动力刚度矩阵和斜线荷载动力格林函数的基础上建立间接边界元方法,在频域内求解无破碎带断层场地对入射平面SH波的散射。为方便求解,将总波场分解为自由波场和散射波场,自由波场由直接刚度法求得,断层两侧的散射波场通过在断层面上分别对两侧施加均布斜线荷载产生的动力响应来模拟,虚拟荷载的密度可通过引入断层表面的边界条件确定,最后叠加自由波场和散射波场求得总波场。以有落差断层和无落差断层模型为例进行数值计算,分析断层落差、断层倾角以及断层两侧介质的刚度比对散射效应的影响。研究表明,断层落差与波长相当时,断层对SH波的放大作用最大;地表位移幅值随着断层倾角的增大逐渐增大;若断层无落差且其两侧刚度不同时,一般刚度较小一侧地表位移幅值较大且振荡更为剧烈,波从刚度较小一侧入射时位移幅值放大尤为显著。     

圆弧形有水河谷场地对平面P波的散射

利用波函数展开法,在频域内给出了圆弧形充水河谷对平面P波散射问题的解析。并分析了入射波波长、入射角对充水河谷地形地面运动的影响。     

SH波地表散射的局域边界元模拟

本文提出了一种计算不规则起伏地形中SH波散射的有效方法——局域边界元法.本方法基于传统边界元法,为计算复杂地表散射问题提供了一种更加高效的解决方案.根据地震波满足的边界积分方程中牵引力格林函数的特性,我们将自由边界分解成水平部分和起伏部分.通过公式推导,可将水平部分的位移由起伏部分的位移通过格林函数线性叠加表示,因此只需对起伏部分的位移进行直接求解,从而极大地减少了待求解的未知数个数,显著提高了计算效率.通过与半圆形山谷SH波平面波入射的解析解比较,验证了方法的正确性.数值模型比较显示,局域边界元模拟结果与传统边界元数值解完全吻合,但是大幅提高了计算效率.因此,局域边界元法可以作为模拟不规则地形中地震波散射的有效工具.

     

含多个圆弧状沉积层河谷场地对平面SH波散射问题的解析解

利用波函数展开法给出了含多个圆弧状沉积层河谷(盆地)场地对平面SH波二维散射问题的一个解析解,并以具有三个沉积层的河谷为例,分析了河谷中沉积层层数与排列次序对SH波散射的影响。     

流体饱和半空间二维地形三分量弹性波散射间接边界元模拟

无限长局部地形地震波斜入射响应问题称为二维三分量问题,在计算量远小于三维的情况下,一定程度上反映了近地表场地的三维动力响应特征.基于天然土体的成层性及固液两相耦合特性,以层状多孔介质内部移动线荷载(孔隙水压)动力格林函数作为基本解,开展流体饱和半空间二维地形三分量弹性波散射的2.5维间接边界元模拟研究.总场响应由自由波...     

复杂地表边界元-体积元波动方程数值模拟

复杂近地表引起来自深部构造的地震反射信号振幅和相位的异常变化,是影响复杂近地表地区地震资料品质的主要原因.本文采用边界元-体积元方法,通过求解含复杂地表的波动积分方程,来模拟地震波在复杂近地表构造中的传播.其中,边界元法模拟地形起伏和表层地质结构对地震波传播的影响;体积元法模拟起伏地表下非均质低降速层的影响.与其他数值模拟方法比较,其主要优点为几何上精确描述不规则地表界面,实现精确模拟自由表面对地震波的边界散射;显式应用近地表地层界面的连续边界条件,实现半解析的数值模拟;分区处理近地表复杂结构,有效模拟复杂地表下非均匀介质对地震波场的体散射.数值试验结果表明了该方法的实用性和有效性.     

复杂介质地震波传播模拟中边界元法与有限差分法的比较研究

地震波场数值模拟是理论地球物理学和勘探地球物理学的重要研究手段.在众多数值模拟方法中边界元法和有限差分法是两种典型的地震波传播模拟计算方法.边界元法是一种半解析-半数值的边界型方法,它显式地利用边界连续条件,沿着地层边界进行离散,具有降维、高精度和自动满足远场辐射条件的优点;有限差分法是一种典型的基于微分的区域型方法,它隐式地使用边界连续条件,以空间网格形式进行离散和数值逼近,具有高效、实用和容易数值实现的优点.本文以一个半圆形均匀Valley模型和两个非均匀断裂/断层模型为例,从计算精度、计算效率、频散特性以及适用性等方面对这两种方法进行了比较研究.数值计算结果表明:边界元法可以精确地几何描述有内部断点、断面的复杂构造,能够精确地模拟内部不规则界面之间波的反射/传播;有限差分法不能以足够的精度描述几何断点和内部不规则边界.边界元法在高频时计算量大于有限差分法,有限差分法则需要更小的网格间距以压制数值频散.因此,在处理内部非均质和高频计算时,有限差分法更有效;在处理内部不规则边界、断点、大尺度等问题时,边界元法比有限差分法更有优势.     

3D seismic response of a 2D hill-valley staggered topography modeled by a 2.5D multi-domain IBEM

A two and a half dimensional(2.5 D) multidomain indirect boundary element method(IBEM) is developed to study the wave scattering of obliquely incident P-, SVand SH-waves by a hill-valley staggered topography in a multi-layered half-space. The IBEM algorithm includes using2.5 D full-space and half-space Green's functions to construct scattered fields in decomposed closed and opened half-space regions, respectively, and using the dynamic stiffness method to solve the free fields. All regions are finally integrated by introducing the compatibility conditions to obtain the total wave fields. The proposed 2.5 D IBEM has the flexibility in dealing with complex boundaries by directly applying the fictitious loads on the regions' boundaries, with a less storage requirement compared to the full 3 D models. Besides, by combining the specific advantages of the two kinds of Green's functions, the method is well suitable for handling coupled topographies with high accuracy. The method is validated by comparison with published results for a single valley as well as a single hill topography. The effects of height-to-width ratio of hill and layering on dynamic responses are further parametrically investigated by numerical implementations in frequency domain. Results show that the interaction between valley and hills can lead to a more significant amplification within the valley region, and dynamic responses are deeply influenced by the height-towidth of hill, simultaneously depending on incident angle and frequency. Besides, the site effects become more complex when the stratification feature is taken into account.     

地震波传播数值模拟

本文概述了地震数值模拟及其理论基础,阐述了地震数值模拟方法及特点．综述了地震数值模拟方法、三维建模和计算机硬件平台等方面的现状和进展．最后。给出了地震波数值模拟在地震勘探方法研究、地震观测系统优化设计、地震数据处理、地震资料解释、开发地震等方面的应用．     

圆弧状凹陷地形对平面SV波散射问题的宽频带解析解

利用波函数的Fourier-Bessel级数展开法,推导了具有不同深宽比的圆弧状凹陷地形对入射平面SV波二维散射问题的解析解。区别于现有其他解析解,利用柱函数的渐近性质,使得散射波的待定系数得以直接确定,避免了线性方程组的求解以及相应的高频波入射下的数值计算问题,从而拓展了解析解适用的频带范围。通过与已有解析解的比较论证了该解析解的正确性,并在一个较宽的频带范围内研究了圆弧状凹陷地形对入射平面SV波的散射效应。     

地震体波斜入射情形下台阶地形引起的波型转换

本文首次对地震体波斜入射情形下竖直、倾斜台阶地形引起的波型转换进行了数值模拟，结果表明：地震波的斜入射会使台阶上角点引起更强的转换面波；转换Rayleigh面波最大振幅可达弹性半空间表面自由场位移的1.1倍左右。     

2D surface topography boundary conditions in seismic wave modelling

New formulations of boundary conditions at an arbitrary two-dimensional (2D) free-surface topography are derived. The top of a curved grid represents the free-surface topography while the grid's interior represents the physical medium. The velocity–stress version of the viscoelastic wave equations is assumed to be valid in this grid. However, the rectangular grid version attained by grid transformation is used to model wave propagation in this work in order to achieve the numerical discretization. We show the detailed solution of the particle velocities at the free surface resulting from discretizing the boundary conditions by second-order finite-differences (FDs). The resulting system of equations is spatially unconditionally stable. The FD order is gradually increased with depth up to eighth order inside the medium. Staggered grids are used in both space and time, and the second-order leap-frog and Crank–Nicholson methods are used for time-stepping. We simulate point sources at the surface of a homogeneous medium with a plane free surface containing a hill and a trench. Applying parameters representing exploration surveys, we present examples with a randomly realized surface topography generated by a 1D von Kármán function of order 1. Viscoelastic simulations are presented using this surface with a homogeneous medium and with a layered, randomized medium realization, all generating significant scattering.     

The scattering of plane P_1 wave by a 3-D sedimentary basin in a fluid-saturated poroelastic half-space using IBEM

The indirect boundary element method(IBEM) is applied to investigate the scattering of elastic waves around a 3-D sedimentary basin filled with fluidsaturated poroelastic medium. Based on this method, the free field and scattered field can be solved according to the boundary conditions. And the numerical accuracy has been verified. The effects of parameters on elastic wave scattering are studied, such as boundary condition, incident frequency,incident angle and porosity of medium. Numerical results illustrate that the amplification effect of surface displacement near poroelastic sedimentary basin is notable. In addition, for the case of large porosity the drainage condition has a significant impact on the response amplitude. Due to the fluid exchange at the interface under the drained condition, the displacement amplitude can be much larger than that under the undrained condition in present study. The study can provide a theoretical basis for the anti-seismic design of engineering structures located in sedimentary basin.     

地震波动方程的局部间断有限元方法数值模拟

近年来,随着地震波数值模拟对计算精度和效率的要求越来越高,间断有限元方法开始受到越来越多的关注.本文中,针对具有吸收边界条件的二维地震声波波动方程,作者提出了一种基于局部间断有限元方法的数值模拟算法.该算法在空间上使用局部间断有限元方法进行离散,在时间上采用了显式蛙跳格式.在这种时空离散的组合方式下,每个时间步上,此算法在空间剖分的每个单元上的求解计算是相互独立的,因而具有极高的并行性.通过数值算例,我们将该算法与连续有限元方法进行了比较.结果表明,本算法不仅具有对起伏构造的良好适应性,而且在计算效率和计算精度等方面,都具有优越性.