2D各向异性TTI介质中地震波场的射线法和波动方程数值模拟对比

尽管射线理论是基于波动方程高频假设下的一种近似理论,两者本应相互佐证共同发展完善,然而实际上确是平行独立的.鉴于此,本文提出了一种可以相互验证波场数值模拟或射线追踪数值模拟方法正确性和有效性的佐证方法.为了实现上述目的,我们首先将用于各向同性介质中多次波预测的分区多步不规则最短路径算法推广至各向异性TTI介质中,使其具备追踪各向异性TTI介质中多次波的能力.然后,通过伪谱法波场数值模拟和分区多步不规则最短路径算法预测得到的波场快照图、单炮地震记录剖面、以及合成理论地震图的分析对比,不但可以相互验证两种算法的正确性和有效性,同时对地震波在各向异性TTI介质中的传播规律和特点有了深刻的理解和认识.结果表明:本文提出的各向异性介质中多次波射线追踪算法是正确有效的.     

各向同性介质中射线理论与有限差分地震波场模拟方法比较研究

地震波场数值模拟不仅是研究复杂地区地震资料采集、处理和解释的有效辅助手段,而且是研究地球深部精细构造和地球深部探测的有效工具.射线理论和波动方程理论是地震波场数值模拟的理论基础.射线理论主要刻画地震波在介质中传播的走时场、地震射线等运动学属性;波动方程理论通过求解波动方程来描述地震波在介质中传播的弹性动力学响应(能量衰减、相位特征、偏振属性、以及全波形等).基于波动方程理论的波场数值模拟由于能够引入丰富的波场信息,使得人们对不同介质中地震波的传播过程有了较全面的了解.本文以二维层状均匀介质模型为例,通过射线追踪法和交错网格有限差分法模拟得到的波场快照图、单炮地震记录剖面、合成理论地震图的分析比较,不但对地震波在各向同性层状均匀介质中的传播规律和特点有了深刻的理解和认识,同时又可以相互验证两种不同方法的正确性和有效性.     

层状弹性介质全波射线追踪技术研究

射线追踪法是一种有效的地震波场数值模拟方法,在层析成像、叠前深度偏移及正演模拟等研究领域均占据重要地位.但相较于波动方程数值模拟方法,射线追踪法在获取较高运算速度的同时损失掉了地震波场的动力学信息,对于整个地震波场的地震波衰减以及转换波等问题都没有进行考虑.为了能够得到较为完整的合成地震记录并对地震资料做出更合理解释,本文在使用射线追踪法进行波场数值模拟的同时考虑了衰减信息,追踪转换波以弥补射线追踪法在动力学上的缺陷.在全波射线追踪过程中,通过追踪同类波和转换波,并计算该段射线的能量衰减,在保证高速计算的同时获得了较为完整的合成地震记录,取得较好的效果.     

基于分区多步快速行进法下3D起伏层状介质中多震相射线追踪

快速行进法(FMM)是一种求解程函方程数值解计算网格节点走时,然后向后处理进行射线追踪的方法.为了求取任意起伏界面下高精度多震相的地震走时与相应的射线路径,本文采用任意起伏地表条件下的的三维不等距上行差分公式结合分区多步计算技术实现了三维复杂层状起伏介质中多震相(透射、反射、转换波)地震走时的计算,利用上行有限差分公式逐次进行射线路径的追踪,并且通过与较为成熟的不规则最短路径法(ISPM)对比,验证了本算法的计算精度和有效性.数值模拟实例和对比结果表明该算法具有较高的计算精度,数值计算稳健,能灵活处理含任意三维起伏界面模型中多震相地震走时及相应射线路径的追踪问题.     

安新—宽城测深剖面的时域有限差分数值模拟

利用时域有限差分方法进行地震波模拟能够得到丰富的波场信息, 对研究复杂地质构造条件下的地震波波场十分有效。 该文在对时域有限差分方法进行概述的基础上, 以2002年4月施测的安新—宽城地震测深剖面资料为基础, 采用时域有限差分方法对该剖面进行二维全波数值模拟, 同时以理想匹配层作为模拟的吸收边界条件。 将模拟得到的合成地震图, 通过与野外实验得到的记录截面和射线追踪合成记录相比较和讨论, 验证了时域有限差分方法在模拟地震波传播过程的有效性。     

黏弹VTI介质井间地震高斯束波场正演数值模拟

为了研究黏弹VTI介质井间地震波的波场特征,理论分析地震波在黏弹VTI介质中传播特性的基础上,编程实现高斯射线束方法对黏弹VTI介质井间地震波场的正演模拟.为将黏弹VTI介质和完全弹性各向同性介质正演记录进行对比,将黏弹VTI介质的黏弹性参数和各向异性参数设定为零,得到完全弹性各向同性介质下的正演结果.两种介质正演结果对比显示的差异与地震波理论完全一致,证明了所研究的黏弹VTI介质井间地震高斯束正演数值模拟的正确性,为井间地震复杂介质地震波场研究提供了借鉴.     

地震波射线追踪方法研究综述

射线追踪法避免了对高阶偏微分波动方程的直接求解,是一种快速有效的地震波场数值模拟手段,在层析成像、叠前深度偏移及正演模拟等研究领域均占据重要地位.射线追踪方法众多,随着近些年的研究深入,许多不同于传统方法的新型算法得到了更为长足的发展.本文对其中已得到广泛应用的有限差分法、走时插值法、最短路径法以及波前构建法进行了分析,对算法的基本原理、优越性、运算精度与效率、存在的主要问题及改进方法等方面进行了讨论,分析了各算法的研究现状,并对射线追踪法的发展趋势进行了展望.     

VTI介质角度域转换波高斯束偏移成像方法研究

转换波偏移可以利用纵横波波场信息,得到高分辨率的成像结果,从而为油藏描述提供高质量的地震资料.目前的研究主要是利用纵波波场信息进行偏移成像,然而,传统的纵波方法在复杂探区成像时具有一定的局限性.为此,本文在各向异性介质声波射线追踪算法的基础上,推导出各向异性介质转换波射线追踪方程,发展了一种转换波射线追踪算法;并将研究的追踪算法应用到偏移成像中,提出了一种各向异性VTI介质角度域转换波高斯束偏移成像方法.通过各向异性VTI介质断块模型和复杂构造模型试算,说明了本文方法的正确性和有效性.模型试算的结果表明,在考虑地下各向异性时,本文研究的方法具有更好的成像效果,提取的角道集结果可以为偏移速度分析提供依据.     

地震波有限差分模拟综述

本文从有限差分法数值模拟技术的各个方面对地震波有限差分模拟的发展和现状进行了论述.波场的数值模拟技术是认识地震波传播规律，检验各种处理方法正确性的重要工具，地震波的数值模拟是地震波传播规律研究的必要手段，贯穿于地震资料的采集、处理、解释的整个过程中.有限差分法数值模拟技术相对于射线方法具有更高的精度，同时比有限元方法计算量小，因此在实际应用中占很重要的地位.     

三维多值走时地震波场重建及格林函数计算

针对三维复杂介质地震波传播数值计算中出现的多值走时情况,阐述了地震波场重建及格林函数计算中的困难,提出一种在相空间拉格朗日流形上的波场重建及格林函数计算方法．本文算法应用于三维叠前深度偏移处理流程时,可高效地获得均匀网格点上地震波多值走时及振幅的数值计算结果．文中还阐明两类数值计算过程判据,以在多值走时区域及计算的全区域中,控制射线追踪过程中的射线密度及格林函数计算精度．算例验证了本文方法的有效性．     

Seismic wavefield modelling in two-phase media including undulating topography with the modified Biot/squirt model by a curvilinear-grid finite difference method

In this paper, we deduced the corresponding first-order velocity–stress equation for curvilinear coordinates from the first-order velocity–stress equation based on the modified Biot/squirt model for a two-dimensional two-phase medium. The equations are then numerically solved by an optimized high-order non-staggered finite difference scheme, that is, the dispersion relation preserving/optimization MacCormack scheme. To implement undulating free-surface topography, we derive an analytical relationship between the derivatives of the particle velocity components and use the compact finite-difference scheme plus a traction-image method. In the undulating free surface and the undulating subsurface interface of two-phase medium, the complex reflected wave and transmitted wave can be clearly recognized in the numerical simulation results. The simulation results show that the curvilinear-grid finite-difference method, which uses a body-conforming grid to describe the undulating surface, can accurately reduce the numerical scattering effect of seismic wave propagation caused by the use of ladder-shaped grid to fit the surfaces when undulating topography is present in a two-phase isotropic medium.     

Seismic wavefront evolution of multiply reflected, transmitted, and converted phases in 2D/3D triangular cell model

Conventionally grid-cell-based schemes for simulating seismic wavefront propagation, such as the finite difference eikonal equation solver or the shortest-path method, usually adopt regular grids or cells in model parameterization to obtaining (but not exclusively) first arrivals only. However, later arrivals, which often result from the velocity interfaces or discontinuities, can be prevalent and significant (sometimes of large amplitude), making them potentially important additional information to use in practical applications. To better approximate the data acquisition geometry and the irregular interfaces, we exploit a triangular shortest-path method (TSPM; that is to use triangular cells in model parameterization) to simulate seismic wavefront evolution, comprising any kind of transmissions, reflections (or refractions), mode conversions, and combinations thereof, in 2D/3D heterogeneous media. A practical procedure, known as the multistage scheme, was incorporated with the TSPM to propagate seismic wavefronts from one interface (or subsurface in 3D) to the next. By treating each separate layer that the wavefront enters as an independent computational domain, one can simulate wavefront transmission and mode conversion by reinitializing it in the adjacent layer and wavefront reflection (and/or conversion) by reinitializing it in the incident layer. To further improve the computational accuracy, a second level of forward star scheme, previously defined in the grid model, is introduced into the triangular cell model. Several examples (including the Marmousi model) are used to demonstrate the viability and versatility of the multistage TSPM in heterogeneous media, even in the presence of high-velocity contrasts involving interfaces of relatively high curvature. With the introduction of the second level of forward star scheme, the total numbers of nodes are reduced sufficiently, and hereafter the computer memory is less required. Most important is that the computing accuracy with the second-level forward star scheme can be largely improved over those with the first level of forward star scheme applied in the multistage TSPM scheme.     

WAVEFRONT DIVERGENCE,MULTIPLES, AND CONVERTED WAVES IN SYNTHETIC SEISMOGRAMS*

Synthetic seismograms can be very useful in aiding understanding of wave propagation through models of real media, verification of geologic models derived from interpretation of field seismic data, and understanding the nature and complexity of wave phenomena. If meaningful results are to be obtained from synthetic seismograms, the method of their computation must, in general, include three-dimensional geometrical spreading of wavefronts associated with highly concentrated (i.e., point) sources. The method should also adequately represent the seismic response of solid-layered media by including enough primaries, multiples, and converted phases to accurately approximate the total wavefield. In addition to these features, it is also very helpful, although not always essential, if the method of seismogram computation provides for explicit identification of wave type and ray path for each arrival. Various seismograms, computed via asymptotic ray theory and an automatic ray generation scheme, are presented for a highly simplified North Sea velocity structure. This is done to illustrate the importance of the above features and to demonstrate the inadequacy of the plane-wave synthesis method of seismogram computation for point sources and the limitations of acoustic models of solid-layered media.     

椭球坐标系下多震相地震射线追踪

地震射线追踪方法技术在地震学领域有着较为广泛的应用,然而大多数算法建立在直角坐标系或球坐标系下,实际地球并非完美的球体,而是两极略扁的椭球体,因此,球坐标系下计算结果与真实情况存在一定误差.传统的做法一般是在球坐标系下进行计算,而后进行椭球校正.本文提出了一种直接在椭球体模型中采用分区多步最短路径算法进行多震相地震射线追踪的方法技术,实现了椭球坐标系下多震相地震波射线路径追踪和走时计算.与解析解的对比表明:该算法具有较高的计算精度,适用于任意形状的椭球体,且不需要进行额外的走时校正.数值模拟结果表明,计算所得P波和PcP反射波的走时与AK135走时表的误差小于0.1 s.当震中距较大时,使用球对称模型和椭球体模型计算所得的走时差异显著,说明采用椭球坐标系的必要性.     

裂缝诱导双相HTI介质地震波场错格伪谱法模拟与波场特征分析

裂缝诱导的双相具有水平对称轴的横向各向同性(HTI)介质模型是由一组平行排列的垂直裂缝嵌入到统计各向同性的流体饱和多孔隙岩石中而组成的,它综合考虑了裂缝型储层岩石的各向异性和孔隙性.高精度的地震波场数值模拟技术是研究该介质中地震波传播规律的主要方法.本文结合错格伪谱法和时间分裂法,求解描述该介质中地震波传播的一阶速度-应力方程.模拟了单层和双层模型中的地震波场,并对其进行了特征分析.研究结果表明:错格伪谱法能有效消除标准网格伪谱法波场模拟结果中出现的数值伪影现象,与时间分裂法结合能够获得稳定的、高精度的模拟结果;裂缝诱导双相HTI介质中的地震波场兼具裂缝各向异性介质和双相介质中传播的地震波的波场特征.     

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

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.     

射线法模拟分析井间地震观测的波场特征

按照井间地震的观测系统,用改进的突变点加插值射线追踪方法,追踪每炮每道的射线路径,计算几种主要类型的波沿射线路径的波至时间和射线振幅,制作井间地震多炮多道水平分量和垂直分量的合成记录.并将合成记录选排为井间共炮点道集、共接收点道集、共偏移距道集和共中心深度点道集,系统地分析了不同道集内几种主要类型的地震波的传播特征.对野外观测的实际井间地震记录进行了模拟,从复杂的井间地震记录中,识别出井间地震实际观测到的不同类型的波场,为随后的井间地震资料处理和应用提供了依据.     

地震信号的复地震道分析及应用

复地震道分析又称三瞬分析,该分析方法可将反映地震信号局部变化情况的地震波的瞬时振幅、瞬时相位和瞬时频率等信息分离开.本文应用Hilbert变换求解虚地震记录,用复地震道分析方法求取"三瞬"信息,并用该方法计算了理论合成地震记录的瞬时振幅、瞬时相位和瞬时频率,获得了较好的效果.同时,本文也利用该方法对某区块实际地震资料进行了处理,结果表明,复地震道分析方法获得的"三瞬"信息可反映地震信号的局部变化,有助于进行地震薄互层分析,并能提高数据的解释精度.     

地震勘探中相控阵震源的方向特性研究

电磁驱动式可控震源在城市浅层地震勘探中所面临的最突出的困难是微弱的反射信号常常淹没在很强的背景噪声之中.为了提高地震记录的信噪比,可以利用多台可控震源阵列实施相位控制形成定向地震波束以增强地震波的能量.本文讨论这种相控阵震源的波束形成机制.引入了地震波场的边际能量密度的概念,利用地震波场的时间切片技术,对模型空间各个方向上的能量强度进行了定量分析.用有限差分法对相控阵震源Chirp信号扫描的地震响应进行了数值模拟.当定向地震波束的汇聚带与观测排列的空间范围相一致时,相控阵震源合成地震记录的能量强度要显著高于单个可控震源情形的能量强度,波形振幅的均匀性要明显优于常规组合激发震源情形波形振幅的均匀性.     

VTI介质qP波方程高精度有限差分算子

波动方程有限差分法是一种使用广泛的地震波数值模拟方法.但是有限差分法本身固有存在着数值频散问题，会降低地震波场模拟的精度与分辨率.为了克服常规有限差分算子的数值频散，本文针对VTI介质地震波数值模拟问题，构造了频率-空间域qP波波动方程高精度有限差分优化算子，根据最优化理论中高斯-牛顿法确定了高精度有限差分算子的优化系数.利用常规差分算子和高精度优化差分算子对归一化相速度的频散关系精度进行了对比分析，并对均匀各向同性介质和均匀VTI介质中的qP波地震波场进行了有限差分数值模拟，通过频散关系精度分析和波场数值模拟结果表明：有限差分优化算子具有较高的波场数值模拟精度，有效压制了传统有限差分算子数值模拟中的数值频散现象，提高了有限差分算子精度，为VTI介质频率-空间域qP波正演模拟奠定了基础.