求解一维波动方程反问题的消除多次波方法

1．引言一位早期的地球物理学家Noah曾经设想将船和电缆沉入海底采集数据，以避免由海面反射所形成的多次波混响，从而得到更为理想的地震勘探剖面，但是这一方法在实践中是很难实现的．1974年，Ril6y博士［6］从地震波的物理机制出发，提出了一种消除多次波的反卷积方法，可以通过资料处理来实现这个思想．在一继波动方程反问题的研究中，我们重新发现了这一方法［7］；称之为消除多次波方法．方法的基本思想是根据自由表面反射波响应与激发波响应之间的相似关系，通过变换来消除多次波混响，从而近似地得到所需的反射系数信息．与Riley…     

基于二维随机震源的地震波全波形反演研究

全波形反演利用全部的波场信息做反演求解,兼顾了地震波的运动学特征和动力学特征,是一种直接基于波动方程描述地震波在地下介质中的传播过程,能够获得地质结构和岩性资料的方法.但是作为一种非线性反演算法,如何提高全波形反演的计算速度和成像精度是目前优化反演的难点和重点.针对全波形反演的效率问题,采用分层和模块化的matlab工具箱,开展了基于随机震源的全波形反演数值计算,由于采用的方法可以给定计算节点上的多线程资源,易于编程,无需矩阵,有效的减少了外部krylov迭代的数量,并将提出的方法与常规全波形反演方法进行对比分析,证明了基于随机震源全波形反演更加高效.     

石油地震勘探波动方程速度反演方法评介

<正> 石油地震勘探中的速度反演问题是一个散射方程的混合初边值问题.它是波动方程散射问题的推广.由地表上点震源的激发给大地一个入射波,由于地层的不均匀性而产生反射波,整个波场是二者的迭加.根据反射波在地表的数据 (即边值条件,亦称附加条件)来确定地层中波传播的速度.由于地层的复杂性,目前主要以波动方程近似描述地震波的传播.入射波可以直接给出,也可以用一个常系数波动方程的定解问题来确定.反射波或全波也由一个波动方程的定解问题确定,方程中包含有需要反演的速度.     

横观各向同性电磁弹性介质中裂纹对SH波的散射

研究横观各向同性电磁弹性介质中裂纹和反平面剪切波之间的相互作用．根据电磁弹性介质的平衡运动微分方程、电位移和磁感应强度微分方程,得到SH波传播的控制场方程．引入线性变换,将控制场方程简化为Helmholtz方程和两个Laplace方程A·D2通过Fourier变换,并采用非电磁渗透型裂面边界条件,得到了柯西奇异积分方程组．利用Chebyshev多项式求解积分方程,得到应力场、电场和磁场以及动应力强度因子的表达,并给出了数值算例．     

矩形槽水中非传播孤波[英文]

本文主要研究在外部驱动下浅水槽内部的非传播孤波，用渐进方法中的多重尺度法较详细讨论和导出波动振幅所满足的非线性薛定谔方程及其非传播单孤波解。采用一些近似条件，又可以由非线性薛定谔方程得到两个独立的线性拉普拉斯方程。     

极坐标系下非分裂PML及时域有限元实现

在弹性波传播的数值模拟中,吸收边界被广泛应用于截取有限空间进行无限空间问题的分析.完全匹配层（perfect matched layer, PML）吸收边界较其他吸收边界条件具有更优越的吸收性能,已被成功应用于直角坐标系下的弹性波方程正演模拟.考虑极坐标系下二阶弹性波动方程,通过采用辅助函数的方法,提出了一种非分裂格式的完全匹配层吸收边界条件.并且基于Galerkin近似技术,给出了非对称以及轴对称条件下的时域有限元计算格式.通过数值算例分析了该极坐标系下分裂格式的完全匹配层吸收边界的有效性.     

饱和土中弹性波的传播速度

根据所建立的波动方程分析了饱和土中弹性波的弥散特性,并且用室内超声波和现场地震波试验结果进行验证.本文为由弹性波(尤其是P波)速度测得合理的饱和土物理力学参数提供了理论依据.     

地形构造中地震波传播的非对称交错网格模拟

提出了一种新的三维空间对称交错网格差分方法,模拟地形构造中弹性波传播过程．通过具有二阶时间精度和四阶空间精度的不规则网格差分算子用来近似一阶弹性波动方程,引入附加差分公式解决非均匀交错网格的不对称问题．该方法无需在精细网格和粗糙网格间进行插值,所有网格点上的计算在同一次空间迭代中完成．使用精细不规则网格处理海底粗糙界面、 断层和空间界面等复杂几何构造, 理论分析和数值算例表明, 该方法不但节省了大量内存和计算时间, 而且具有令人满意的稳定性和精度．在模拟地形构造中地震波传播时,该方法比常规方法效率更高．     

多孔介质瞬态分析中非分裂PML及时域有限元实现

在波场的数值模拟中,完全匹配层(perfectly matched layer,PML)已经被证明是一种十分有效的吸收技术,并得到了广泛的应用.为了解决具有无限域的多孔介质中2阶弹性波动方程数值模拟中的吸收边界问题,提出了一种非分裂格式的PML(non-splitting perfectly matched layer,NPML).首先,基于Biot多孔介质波动理论,建立了以固相和流相位移表示的2阶动力控制方程,其中考虑了固体颗粒和孔隙流体的可压缩性、惯性以及孔隙流体的粘性.其次,根据复伸展坐标变换的定义,通过Laplace变换获得了非分裂格式PML的频域表达式.然后,借助辅助函数将该方程变换到时间域内,得到了一种有效的非分裂PML.最后,基于Galerkin近似方法,给出了其时域有限元计算格式.通过数值算例分析了该非分裂格式的PML在饱和介质动力响应分析中的有效性.     

求解2—D波动方程系数反问题的迭代方法及收敛性

本文针对地震勘探中提出一类重要的２－Ｄ波动方程反演问题，通过定义一个新的非线性算子将２－Ｄ波动方程的反演问题归结为一个新的非线性算子方程，详细讨论了非线性算子的性质，给出了求解反问题的迭代方法，并证明了这种迭代方法的收敛性。     

流体饱和多孔隙介质波动方程小波有限差分法

研究流体饱和多孔隙介质中波动方程的数值模拟．针对求解二维弹性波方程问题,提出小波有限差分法．该方法综合了小波多分辨分析计算灵活、计算效率高特性和有限差分易于实现的优点．数值模拟的结果显示,此方法对于求解流体饱和多孔隙介质方程的数值模拟是有效稳定的．     

Method of solving equations of motion of viscoelastic media

A new method is proposed for solving dynamic problems for viscoelastic media based on the introduction of potential functions and transformation of equations of motion. The equations obtained for potential functions are used for constructing the general solution in the case of the effect of moving loads on viscoelastic media with plane-parallel interfaces. The problem of the propagation of Rayleigh surface waves is solved independently of the form of the kernels of the linear operators; a formula is obtained for determining the velocity of the Rayleigh surface wave with an arbitrary form of the viscoelastic operators. A method of experimental determination of the kernels determining the linear viscoelastic operators is proposed.V. V. Kuibyshev Moscow Civil Engineering Institute. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 429–435, May–June, 1973.     

求解二维浅水波方程的移动网格旋转通量法

为提高求解二维浅水波方程数值算法的分辨率,拟构造求解该方程的新算法:基于移动网格法,选用熵稳定数值通量函数,利用旋转不变性得到混合数值通量.该算法中,浅水波方程的数值求解和依据解的特性进行自适应疏密分布的网格计算过程交错进行.利用变分原理进行网格重构,新网格上的物理量采用二阶精度的守恒型插值公式计算,最终采用三阶强稳定Runge-Kutta法与满足热力学第二定律的熵稳定格式实现浅水波方程的数值求解.数值结果表明,新算法具有良好的间断捕捉能力,分辨率高.     

Symplectic and multi-symplectic wavelet collocation methods for two-dimensional Schrödinger equations

In this paper, we develop symplectic and multi-symplectic wavelet collocation methods to solve the two-dimensional nonlinear Schrödinger equation in wave propagation problems and the two-dimensional time-dependent linear Schrödinger equation in quantum physics. The Hamiltonian and the multi-symplectic formulations of each equation are considered. For both formulations, wavelet collocation method based on the autocorrelation function of Daubechies scaling functions is applied for spatial discretization and symplectic method is used for time integration. The conservation of energy and total norm is investigated. Combined with splitting scheme, splitting symplectic and multi-symplectic wavelet collocation methods are also constructed. Numerical experiments show the effectiveness of the proposed methods.     

旋波媒质中谱域电并矢Green函数的分解

介绍了一种推导无耗、互易和无界旋波媒质中谱域并矢Green函数表达式的新方法·　这种方法以Hemholtz定理以及并矢Diracδ函数的无散和无旋分解为基础,首先将电矢量的并矢Green函数方程分解成无散电矢量的并矢Green函数方程和无旋电矢量的并矢Green函数方程,然后经Fourier变换导出了旋波媒质中谱域电并矢Green函数的无散分解表达式和无旋分解表达式·　用这种方法推导旋波媒质中并矢Green函数就可以避免必须用波场的分解法和并矢Green函数的本征函数展开法·     

Chebyshev Wavelet collocation method for solving generalized Burgers–Huxley equation

In this paper, new and efficient numerical method, called as Chebyshev wavelet collocation method, is proposed for the solutions of generalized Burgers–Huxley equation. This method is based on the approximation by the truncated Chebyshev wavelet series. By using the Chebyshev collocation points, algebraic equation system has been obtained and solved. Approximate solutions of the generalized Burgers–Huxley equation are compared with exact solutions. These calculations demonstrate that the accuracy of the Chebyshev wavelet collocation solutions is quite high even in the case of a small number of grid points. Copyright © 2015 John Wiley & Sons, Ltd.     

Nonlinear modeling and analysis of electrically actuated viscoelastic microbeams based on the modified couple stress theory

A nonclassical nonlinear continuum model of electrically actuated viscoelastic microbeams is presented based on the modified couple stress theory to consider the microstructure effect in the framework of viscoelasticity. The nonlinear integral-differential governing equation and related boundary conditions of are derived based on the extended Hamilton's principle and Euler–Bernoulli hypothesis for viscoelastic microbeams with clamped-free, clamped-clamped, simply-supported boundary conditions. The proposed model accounts for system nonlinearities including the axial residual stress, geometric nonlinearity due to midplane stretching, electrical forcing with fringing effect. The behavior of the microbeam is simulated using generalized Maxwell viscoelastic model. A new generalized differential/integral quadrature method is developed to solve the resulting governing equation. The developed model is verified against elastic behavior and a favorable agreement is obtained. Efficiency of the developed model is demonstrated by analyzing the quasistatic pull-in phenomena of electrically actuated viscoelastic microbeams with different boundaries at various material length scale parameters and axial residual stresses in the framework of linear viscoelasticity.     

Pseudospectral time-domain method for pressure-release rough surface scattering using a surface transformation and image method

When numerically analyzing acoustic scattering at a pressure-release rough surface, the conventional pseudospectral time domain (PSTD) method using Fourier transform requires rigorous stability conditions in order to solve the spatial derivative in the wave equation on the irregular boundaries between the two media due to the Gibbs phenomenon and short wavelength in air. To eliminate such disadvantages, a new algorithm is proposed based on the Fourier PSTD method utilizing a surface boundary transformation and an image method. Irregular surface boundaries are flattened by transformation and then an image method is applied to the half-space domain. The efficiency and accuracy of the proposed PSTD method are better than the conventional Fourier PSTD method. Numerical results are presented for a sloped and a sinusoidal pressure-release surface.     

Energy estimates for two-dimensional space-Riesz fractional wave equation

Numerical Algorithms - The fractional wave equation governs the propagation of mechanical diffusive waves in viscoelastic media which exhibits a power-law creep, and consequently provided a...     

Stability for the damped wave equation with neutral delay

Of concern is a wave equation with a distributed neutral delay. We prove that, despite the destructive nature of delays in general, solutions may go back to the equilibrium state in an exponential manner as time goes to infinity. Reasonable conditions on the distributed neutral delay are established. This type of problems appear in the study of wave propagation in viscoelastic media and in acoustic wave propagation. It is not well studied so far.