各向异性介质qP波传播描述II:分离纯模式标量波

在各向异性地震波场中,qP波与qS波常常是耦合在一起的.多分量地震数据处理中一个关键环节就是波型分离(即模式解耦),以纵波成分为主的常规单分量地震数据的成像则需要合理描述标量qP波的传播算子.本文作者曾构建了在运动学上同弹性波动方程等价,动力学上突出标量qP波的伪纯模式波动方程.为了彻底消除qS波残余,本文根据波矢量与qP波偏振矢量之间的偏差,提出从伪纯模式波场提取纯模式标量qP波的方法.数值分析展示了投影偏差算子在波数域和空间域的特征.基于不同复杂程度理论模型的试验结果表明,联合"伪纯模式传播算子"与"投影偏差校正"可为各向异性介质分离模式波场传播过程提供一种简便的描述工具.     

Determining finite difference weights for the acoustic wave equation by a new dispersion‐relationship‐preserving method

Numerical simulation of the acoustic wave equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse‐time migration. With finite‐difference methods, the discretization of temporal and spatial derivatives in wave equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed wavenumber points within a wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the wave velocity. This new dispersion‐relationship‐preserving method relatively uniformly reduces the numerical dispersion over a large‐frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.     

A 27‐point scheme for a 3D frequency‐domain scalar wave equation based on an average‐derivative method

Based on an average‐derivative method and optimization techniques, a 27‐point scheme for a 3D frequency‐domain scalar wave equation is developed. Compared to the rotated‐coordinate approach, the average‐derivative optimal method is not only concise but also applies to equal and unequal directional sampling intervals. The resulting 27‐point scheme uses a 27‐point operator to approximate spatial derivatives and the mass acceleration term. The coefficients are determined by minimizing phase velocity dispersion errors and the resultant optimal coefficients depend on ratios of directional sampling intervals. Compared to the classical 7‐point scheme, the number of grid points per shortest wavelength is reduced from approximately 13 to approximately 4 by this 27‐point optimal scheme for equal directional sampling intervals and unequal directional sampling intervals as well. Two numerical examples are presented to demonstrate the theoretical analysis. The average‐derivative algorithm is also extended to a 3D frequency‐domain viscous scalar wave equation.     

基于改进粒子群算法的地震标量波方程反演

针对标准粒子群优化(PSO)算法存在易出现早熟而陷入局部最优以及进化后期收敛速度慢等缺陷,通过考虑粒子所处位置间相互作用,提出了一种改进的并行粒子群优化算法.由于引入粒子位置间的相互影响,减少了粒子搜索过程盲目性,因此能有效提高算法的收敛速度.数值试验表明,这种改进的粒子群算法适用于二维标量波方程的速度反演,且算法具有...     

Review on localized boundary integral equation:Discrete wavenumber method for 2D irregular layers

The pioneer study of simulating the wave field in media with irregular interface belongs to Aki and Larner.Since that many numerical methods on the subject have been developed,such as pure numerical techniques,ray method and boundary method.The boundary method based on boundary integral equation is a semi-analytical method which is suitable to modeling wave field induced by irregular border.According to the property of the applied Green's function the boundary methods can be sorted into space domain boundary method and wavenumber domain boundary method.For both of them it is necessary to solve a large equation,which means much computation is needed.Thus,it is difficult for the boundary methods to be applied in simulating wave field with high frequency or in large range.To develop a new method with less computation is meaningful.For this purpose,localized boundary integral equation,i.e.,discrete wavenumber method is proposed.It is rooted in the Bouchon-Campillo method,an important wavenumber domain boundary method.Firstly the force on interface is separated into two parts:one is on flat part and the other on irregular part of the interface.Then Fourier transform is applied to identify their relation,the unknown distributes only on irregular part.Consequently computation efficiency is dramatically improved.Importantly its accuracy is the same as that of Bouchon-Campillo.     

稀疏采样下陡角度构造的波动方程深度偏移成像

针对稀疏采样,特别是crossline方向稀疏采样的三维地震数据,提出了一个基于波动方程方法的陡角度构造深度偏移成像方法.文中针对一类混合域（空间和波数）的波动方程偏移方法展开研究.通过建立反假频的单程波算子和通过（形式上）填充空道重建理想采样的地震数据,有效地实现了陡倾角地层的准确成像.这一算法策略解决了波动方程偏移方法在实际应用中的一个关键问题,从而更好地发挥了波动方程偏移方法在复杂构造成像上的优势.二维理论数据（Marmousi模型）和三维实际地震资料成像结果表明本文方法是有效的.这一方法对现行的三维地震数据处理有重要的现实意义.     

轴对称各向异性介质波动方程深度偏移的对称非平稳相移方法

由所建立的三维qP波相速度表示式出发,导出并解析求解各向异性介质中的频散方程,得到三维各向异性介质中的相移算子,进而将以相移算子为基础的对称非平稳相移方法推广到各向异性介质,发展了一个三维各向异性介质的深度偏移方法. 文中使用的各向异性介质的速度模型与现行的各向异性构造的速度估计方法一致,将各向同性、弱各向异性及强各向异性统一在一个模型中. 所建立的各向异性介质对称非平稳相移波场延拓算子可以同时适应速度及各向异性参数横向变化;文中给出的算例虽然是针对二维VTI介质的,但所提出的算法同样适用于三维TI介质.     

Algorithms for solving the diffusive wave flood routing equation

Generally, the diffusive wave equation, obtained by neglecting the acceleration terms in the Saint-Venant equations, is used in flood routing in rivers. Methods based on the finite-difference discretization techniques are often used to calculate discharges at each time step. A modified form of the diffusive wave equation has been developed and new resolution algorithms proposed which are better adapted to flood routing along a complex river network. The two parameters of the equation, celerity and diffusivity, can then be taken as functions of the discharge. The resolution algorithm allows the use of any distribution of lateral inflow in space and time. The accuracy of the new algorithms were compared with a traditional algorithm by numerical experimentation. Special attention was given to the instability caused by the inflow signal which constitutes the upstream boundary condition. For the fully diffusive wave flood routing problem, all three algorithms tested gave good results. The results also indicate that the efficiency of the new algorithms could be significantly improved if the position of the x-axis is modified by rotation. The new algorithms were applied to flood routing simulation over the Gardon d'Anduze catchment (542 km²) in southern France.     

波动方程数值模拟的三种方法及对比

波动方程数值模拟方法是研究地震波场传播的一种重要手段,本文采用交错网格高阶有限差分方法分别对双程声波方程和双程弹性波方程进行了波场数值模拟,并且根据定位原理采用傅立叶有限差分算子进行了单程波方程数值模拟,在分析定位原理的基础上,对其计算过程稍作修改,将延拓到地面的波场直接由每个检波点接收,无需横向叠加过程,得到了单程声波方程共炮记录.基于不同波动方程的数值模拟结果表明,双程波方程结果包含直达波、多次波等干扰波,信噪比低;单程波数值模拟结果只包含了介质分界面的一次反射波,信噪比高,但对于大角度入射波误差较大,并且对于同一个地质模型而言,双程弹性波方程计算速度最慢,双程声波方程次之,单程声波方程计算速度最快.因此对于复杂地质模型,三种模拟方法可以取长补短,综合应用.     

双变参数标量纵波方程正演模拟方法

常见弹性波动理论的建立是基于介质均匀这一基本假设,实际介质的非均匀性非常普遍.为研究连续介质中波的传播特征,本文从弹性力学中建立弹性波动方程的三个基本方程出发,考虑连续介质弹性参数的空变特征,建立非均匀介质的弹性波动方程,利用Alkhalifah声学近似思想建立位移表征的纵波波动方程,利用本征值问题求解方法建立标量波频率-波数域传播算子,从而建立描述纵波传播的标量波方程,其中波函数为纵波位移的散度,不同于均匀介质标量波方程的波函数为位移势.随后推导含PML边界波动方程差分格式并建立不同模型数值模拟进行数值试算,与均匀假设标量波方程和变密度方程对比证明本方法的准确性和稳定性.     

井间地震波动方程正演数值模拟及其应用

井间地震正演模拟是在给定地层参数及边界条件的情况下求波动方程数值解的过程.本文详细推导了井间二维声波方程四阶差分方程;根据假设的包含楔形体和丘状体的理论地层模型,对其波场进行了模拟计算分析;据胜利油田垦71区块两口井的实际声波测井资料建立了精细速度模型,对其正演模拟的合成记录波场进行分析,并把合成记录反射波成像与实际的过井三维地震剖面进行了对比,验证了所设计观测系统的合理性.     

地震波传播的哈密顿表述及辛几何算法

地震波传播过程本质上是能量在传播过程中逐步损耗直至殆尽的过程，而在实际应用中，常在无能量损耗假设下，用弹性波动方程或标量波动方程描述它.在哈密顿(Hamilton)体系表述下，地震波传播过程即为一个无限维的哈密顿系统随时间的演化过程.若不计能量损耗，波场演化过程实质上为一个单参数连续的辛变换，因而对应的数值算法应为辛几何算法.本文首先从地震波标量方程出发，给出哈密顿体系下地震波传播的表述，即任意两个时刻的波场是通过辛变换联系起来的.随后，把波场在时间和相空间离散化后，给出了用于波场计算的一些辛格式，如显式辛格式、隐式辛格式和蛙跳辛格式.并进一步讨论了有限差分格式和辛格式的异同.然后，应用显式辛格式和同阶的有限差分方法给出了同一理论速度模型下的波场和Marmousi速度模型下的单炮记录.数值结果表明，辛算法是一类可行的波场模拟的数值算法.在时间步长较小时，有限差分方法是辛算法的一个很好近似.文中的理论和方法，为地震波传播理论及实际应用研究提供了新的途径.     

双平方根单程波动方程叠前τ偏移方法

本文将常规双平方根（DSR）单程波动方程从深度域变换到双程垂直走时（τ）域，由此推导出可从数学上实现“沉降观测”的单程波DSR传播算子. 其递归波场延拓算法包含波数域针对常速背景的相移处理和空间域针对横向速度扰动的相位校正，可以应对上覆地层速度横向变化对构造成像的影响. 结合零炮检距、零时间成像条件，提出了在τ域进行波场延拓与成像的DSR方程叠前偏移新方法. 为了克服其全三维偏移算法在实际应用中可能面临的困难，本文采用稳相近似，在crossline常炮检距偏移理论基础上推导了实用的共方位角叠前τ偏移方法. 数值试验表明，DSR方程叠前τ偏移在强横向非均匀介质中的成像精度与分辨率优于传统的时间域成像技术.     

An alternative Boussinesq equation considering the effect of hysteresis on coastal groundwater waves

This paper presents an alternative Boussinesq equation considering hysteresis effect via a third‐order derivative term. By introducing an improved moisture–pressure retention function, this equation describes, with reasonable precision, groundwater propagation in coastal aquifers subject to Dirichlet boundary condition of different oscillation frequencies. Test results confirmed that it is necessary to consider horizontal and vertical flows in unsaturated zone, because of their variable influences on hysteresis. Hysteresis in unsaturated zone can affect the water table wave number of groundwater wave motion, such as wave damping rate and phase lag. Oscillations with different periods exert different hysteresis effect on wave propagation. Truncation/shrinkage of unsaturated zones also affects the strength of hysteresis. These impacts can be reflected in the alternative Boussinesq equation by adjusting the parameter representing the variation rate of moisture associated with pressure change, as opposed to traditional computationally expensive hysteresis algorithms. The present Boussinesq equation is simple to use and can provide feasible basis for future coupling of groundwater and surface water models. Copyright © 2016 John Wiley & Sons, Ltd.     

带正则化校正的TTI介质qP波方程及其逆时偏移方法和应用

各向异性研究对地下介质精确成像有着重要的意义,在当前计算机硬件迅速发展及宽方位地震数据采集日益普遍的情况下,成像必须考虑介质的各向异性.逆时偏移是基于双程波动方程的较为精确的数值解的成像方法,所以相对于其他地震成像方法,它具有很大的优势,譬如不受反射界面的倾角限制、偏移速度结构合适时能够使回转波及多次波正确成像.在各向同性介质中,可使用标量波方程来模拟波场.而在各向异性介质中,P波和SV波是相互耦合的,即不存在单纯的标量波传播,通常利用能代表耦合波场中P波分量运动学特征的拟声波(qP波)进行偏移成像.本文中,我们推导出了TTI介质下qP波控制方程.该方程可采用显式有限差分格式进行求解.通过声学近似,若沿对称轴方向的剪切波速度为零,对于对称轴方向不变且ε≥δ的模型来说,可得到稳定的数值解.但对于TTI介质来说,由于沿对称轴方向各向异性参数是变化的,声学近似会引起波场传播及数值计算的不稳定.因此,我们提出了正则化有限横波的方法,很好地解决了这一问题.最后,给出了Foothill模型的测试结果及某探区实际资料试算结果,展示了采用这个方程进行复杂TTI模型正演和高质量逆时偏移成像结果,证实了该方法的正确性和实际资料应用中的有效性.     

3-D acoustic wave equation forward modeling with topography

In order to model the seismic wave field with surface topography, we present a method of transforming curved grids into rectangular grids in two different coordinate systems. Then the 3D wave equation in the transformed coordinate system is derived. The wave field is modeled using the finite-difference method in the transformed coordinate system. The model calculation shows that this method is able to model the seismic wave field with fluctuating surface topography and achieve good results. Finally, the energy curves of the direct and reflected waves are analyzed to show that surface topography has a great influence on the seismic wave＇s dynamic properties.     

复杂介质中平面波模拟的单程波方法

地震勘探中平面波分解技术在地震资料处理与反演领域均得以广泛应用,通过正演算法模拟平面波记录有助于理解和检验平面波分解的效果和精度.本文给出一种用以模拟复杂介质中平面波的数值算法,考虑了振幅随入射角度的变化.与前人研究的平面波模拟算法相比,该算法基于波动方程的单程波解法,不但适用于横向非均匀介质,在地层倾角水平条件下还能够准确模拟振幅随入射角关系.通过Marmousi模型的计算实例,证明了本文方法的可行性.     

基于GSLS模型TI介质衰减拟声波方程

随着计算机硬件技术的发展以及高分辨率勘探需求的增加,我们希望能够更准确地模拟地下介质,得到更丰富的地层信息.然而,传统的声学假设并不能描述实际地层所存在各向异性和黏滞性,使得成像分辨率较低.为了实现深部储层的高精度成像,本文同时考虑了介质的各向异性和黏滞性,从TI介质弹性波的基本理论出发,结合各向异性GSLS理论,并通过声学近似方法导出基于GSLS模型的各向异性衰减拟声波方程.数值模拟表明该方程既能准确地描述各向异性介质下的准P波运动学规律,又能体现地层的吸收衰减效应;模型逆时偏移结果表明,在实现成像过程中考虑各向异性和黏滞性的影响,能对高陡构造清晰成像,且剖面振幅相对均衡,分辨率较高.     

层状介质的声波波动方程反演

基于广义反射透射系数矩阵正演方法 ,讨论了层状介质的声波波动方程反问题 .推导出波数频率域中的雅可比矩阵的解析表达式 ,其计算在正演过程中求出 .采用最小二方法可得到层介质参数 .数值结果表明反演方法的正确有效性 .