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在交错网格有限差分算法中,模型网格剖分原则与正演计算效率密切相关.当模型存在小型非均质体或者低降速层等情况,为保证精度,满足稳定性条件,需缩小网格步长,导致局部过采样,计算效率低下.为保证模拟精度的同时保持高计算效率,通常采用变化的空间网格与时间步长相结合的高阶有限差分模拟方法对波场进行模拟.然而,时空双变算法存在着交错网格固有缺点,在模拟非均匀性较强的复杂介质波场传播时,需对介质参数进行平均或内插.同时,该算法在空间与时间上的变网格实现极为复杂.为压制变网格引起的虚假反射,提升模拟精度和计算效率,本文在时空双变网格算法的基础上,采用旋转差分角度的方式,提出了旋转时空双变交错网格算法.该方法既保留了旋转网格和双变网格的优势,又简化了时空双变算法流程,更利于推广和应用. 相似文献
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利用传统有限差分方法对基于Biot理论的双相介质波动方程进行数值求解时,由于慢纵波的存在,数值频散效应较为明显,影响模拟精度.相对于声学近似方程及普通弹性波方程,Biot双相介质波动方程在同等数值求解算法和精度要求条件下,其地震波场正演模拟需要更多的计算时间.本文针对Biot一阶速度-应力方程组发展了一种变阶数优化有限差分数值模拟方法,旨在同时提高其正演模拟的精度和效率.首先结合交错网格差分格式推导Biot方程的数值频散关系式.然后基于Remez迭代算法求取一阶空间偏导数的优化差分系数,并用于Biot方程的交错网格有限差分数值模拟.在此基础上把三类波的平均频散误差参数限制在给定的频散误差阈值和频率范围内,此时优化有限差分算子的长度就能自适应非均匀双相介质模型中的不同速度区间.数值频散曲线分析表明:基于Remez迭代算法的优化有限差分方法相较传统泰勒级数展开方法在大波数范围对频散误差的压制效果更明显;可变阶数的优化有限差分方法能取得与固定阶数优化有限差分方法相近的模拟精度.在均匀介质和河道模型的数值模拟实验中将本文变阶数优化有限差分算法与传统泰勒展开算法、最小二乘优化算法进行比较,进一步证明其在复杂地下介质中的有效性和适用性. 相似文献
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网格剖分程度直接影响着地震波正演数值模拟的计算精度及其计算量.以均匀介质模型为例,分析不同网格大小对波场模拟精度和计算量的影响,得出精细化网格剖分是实现高精度地震波正演模拟的有效方法,然而其计算量较大.以均匀倾斜介质模型为例,探讨倾斜地层网格剖分问题,数值实例分析不同震源频率对不同网格剖分方案引起的波场传播精度的影响,... 相似文献
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提出一种新的三维空间不规则网格有限差分方法,模拟具有地形构造的非均匀各向异性介质中弹性波传播过程. 该方法通过具有二阶时间精度和四阶空间精度的不规则交错网格差分算子来近似一阶弹性波动方程,与多重网格不同,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. 针对具有复杂物性参数和复杂几何特征的地层结构,使用精细不规则网格处理粗糙界面、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计算机内存和计算时间,而且具有令人满意的稳定性和精度. 相似文献
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在采用有限差分方法开展探地雷达复杂目标体精细结构模拟时,为了提高计算精度,常采用非均匀网格对目标区域划分小尺寸的网格,以压制离散网格频散现象和保证有限差分方法的稳定性.常规非均匀网格和自适应亚网格技术在网格剖分数量和粗细网格边界处理上难以达到计算效率和计算精度的均衡.本文根据隐形斗篷(invisible cloak)理论,将基于变换光学(Transformation optics)理论应用于有限差分探地雷达数值计算中.该理论的主要思想是基于目标参数变化而保持电磁场的传播不变性,在坐标变换后,Maxwell方程的形式可以维持不变,而使得相对介电常数与磁导率的表达式变得复杂.通过这种方式可以虚拟地扩大目标体所占的网格节点数,减少背景介质区域的网格数,不增加模型空间的网格总数.另外,这种网格划分方式不但提高了计算效率,同时也可以克服亚网格技术边界反射误差的影响.本文推导实现了基于变换光学的二维有限差分方法,通过典型探地雷达模型测试,对比分析了该方法与常规有限差分、变网格有限差分和自适应亚网格有限差分的优缺点.计算结果验证了基于变换光学的有限差分可用于探地雷达目标精细结构模拟,具有较高的计算精度和计算效率. 相似文献
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在地震波场数值模拟中, 交错网格有限差分技术得到了广泛的应用, 但是在弹性模量变化较大时, 通常会因插值而导致模拟误差增大. 旋转交错网格可以很好地克服这个缺点, 因而适合于各向异性介质正演模拟. 但是对于同样大小的网格单元, 旋转交错网格需要的步长比常规交错网格要大, 这会使梯度和散度算子的误差增大因而更易产生空间数值频散. 针对这些问题, 本文提出了旋转交错网格与紧致有限差分相结合的方法, 并基于模拟退火算法进行全局优化, 压制数值频散, 拓宽波数范围. 数值模拟结果表明, 此方法可以有效地压制数值频散, 且具有较高的模拟精度. 相似文献
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交错网格高阶差分方法是一种在保持效率的前提下提高弹性波模拟精度的有效方法.本文将可变空间网格与变化的时间步长技术引入到交错网格高阶差分弹性波模拟中,提出一种空间网格可任意奇数倍变化与时间步长任意变化的交错网格高阶差分弹性波模拟方法.一系列数值试验表明,该方法能够在保证模拟精度的同时,通过有效降低空间与时间维度上的过采样来显著提高弹性波模拟的效率.同时,该方法还能够精细刻画含孔缝洞介质以及横向变化剧烈介质的局部细微结构,减小弹性波模拟误差,提高介质细微结构处的弹性波传播模拟精度. 相似文献
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变网格正演模拟方法因其低存储、高效率等特点,在含低速带或小尺度异常体的地下介质的数值模拟中发挥了重大作用.变网格模拟算法的精度与模拟时采用的频率、细网格长度、网格比、介质速度等参数密切相关.当模拟参数选取不合理时,在粗、细网格的分界处会产生强能量虚假反射,严重降低波场模拟的精度及分辨率.因此,选择合理的参数以压制虚假反射的产生在变网格正演模拟中显得尤为重要.本文基于一维假设和平面波理论,结合变系数变网格算法,推导出在变网格声波方程正演模拟中由于网格变化所引起的虚假反射的反射率函数公式,该公式为反射率函数与频率、细网格步长、网格比、介质速度的函数.基于该函数表达式,本文通过理论分析和模型数值算例,系统分析了频率、细网格步长、网格比、介质速度等对于变网格数值模拟中虚假反射的影响.理论分析和数值模拟实验均表明:在声波方程变网格正演模拟中,到达临界位置(即虚假反射率函数为1)之前,频率越高、细网格步长越大、网格比越大、介质速度越低,虚假反射率越大,即虚假反射现象越明显;反之,虚假反射率越小,虚假反射越弱.本文推导出的反射率函数可为实际变网格数值模拟中的各参数选取提供理论指导. 相似文献
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传统的伪谱(PS)方法,采用傅里叶变换(FT)计算空间导数具有很高的精度,每个波长仅需要两个采样点,而时间导数采用有限差分(FD)近似因而精度较低.当采用大时间步长时,由于时空精度不平衡,PS法存在不稳定性问题.原始的k-space方法可以有效地克服这些问题但是却无法适用于非均匀介质.为了提高原始k-space方法模拟非均匀介质波动方程的精度,我们提出了一种新的k-space算子族.它是用非均匀介质的变速度代替原k-space算子中的常数补偿速度构造得到,引入低秩近似可以高效求解.我们将构造的新的k-space算子应用于耦合的二阶位移波动方程,而不是交错网格一阶速度应力波动方程,使模拟弹性波的计算存储量减少.我们从数学上证明了基于二阶波动方程的k-space方法与基于一阶波动方程的k-space方法是等价的.数值模拟实验表明,与传统的PS、交错网格PS和原始的k-space方法相比,我们的新方法可以在时间和空间步长较大的均匀和非均匀介质中,为弹性波的传播提供更精确的数值解.在保持稳定性和精度的同时,采用较大的时空采样间隔,可以大大降低数值模拟的计算成本. 相似文献
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高角度缝隙充填的碳酸盐岩储层可以等效为具有水平对称轴的横向各向同性介质.本文提出了适用于裂缝型碳酸盐岩的岩石物理模型构建流程,重点介绍了在碳酸盐岩各向同性背景中,综合利用微小裂隙模型和线性滑动模型添加缝隙系统,并分析了当缝隙充填不同流体时,各向异性参数随纵横波速比的变化特征.同时本文讨论了裂缝密度和缝隙充填流体对地震反射系数的影响,推导了不同类型流体充填时储层反射系数与裂缝密度的近似关系式,阐述了各向异性流体替换理论,最终实现饱含流体碳酸盐岩裂缝储层的纵横波速度和各向异性参数的估测.选取某碳酸盐岩工区A井对该方法进行试算,结果表明基于碳酸盐岩裂缝岩石物理模型估算的纵横波速度值与测井值吻合较好,而且估测所得的各向异性参数值也能够较好地反映出裂缝储层位置. 相似文献
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The acoustic wave velocity varies with fluid saturation and pore-fluid distribution. We use a P-wave source and the staggered grid finite-difference method, with second-order accuracy in time and eighth-order accuracy in space, to simulate the acoustic wave field in a fractured medium that is saturated with a two-phase pore fluid (gas & water). Further, we analyze the variation of acoustic wave velocity with saturation for different pore-fluid distribution modes. The numerical simulation method is simple and yields accurate results. 相似文献
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与其他偏移方法相比,逆时偏移基于精确的波动方程而不是对其近似,用时间外推来代替深度外推.因此,它具有良好的精度,不受地下构造倾角和介质横向速度变化的限制.激发时间成像条件的求取是叠前逆时偏移的难点之一,本文采用求解程函方程的方法得到地下各点的初至波走时,以此作为叠前逆时偏移的成像条件.基于任意矩形网格和局部平面波前近似的有限差分初至波走时计算方法精度较高并适用于强纵横向变速的复杂介质.试算结果表明,在复杂介质模型中利用叠前逆时深度偏移收到了很好的成像效果. 相似文献
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Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps. 相似文献
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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
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Peidong Shi Doug Angus Andy Nowacki Sanyi Yuan Yanyan Wang 《Surveys in Geophysics》2018,39(4):567-611
Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green’s function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data. 相似文献
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Introduction The calculation of seismic wave traveltimes is a basic and the most important step in tomo-graphy, seismic wave forward modeling and Kirchhoff prestack depth migration. Limitations withtraditional ray tracing fall into four categories. a) Analytical methods can only realize ray tracingfor simply varying velocity fields, so they have relative small applied-range; b) Shooting methodsof ray tracing can cause shadow zones. When the shadow zones exist the method will invalid; c)… 相似文献
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The Fourier spectral method and high-order differencing have both been shown to be very accurate in computing spatial derivatives of the acoustic wave equation, requiring only two and three gridpoints per shortest wavelength respectively. In some cases, however, there is a lack of flexibility as both methods use a uniform grid. If these methods are applied to structures with high vertical velocity contrasts, very often most of the model is oversampled. If a complicated interface has to be covered by a fine grid for exact representation, both methods become less attractive as the homogeneous regions are sampled more finely than necessary. In order avoid this limitation we present a differencing scheme in which the grid spacings can be extended or reduced by any integer factor at a given depth. This scheme adds more flexibility and efficiency to the acoustic modelling as the grid spacings can be changed according to the material properties and the model geometry. The time integration is carried out by the rapid expansion method. The spatial derivatives are computed using either the Fourier method or a high-order finite-difference operator in the x-direction and a modified high-order finite-difference operator in the z-direction. This combination leads to a very accurate and efficient modelling scheme. The only additional computation required is the interpolation of the pressure in a strip of the computational mesh where the grid spacing changes. 相似文献
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《Advances in water resources》1999,23(3):261-269
A study of the effects of grid discretization on the migration of DNAPL within a discrete-fracture network embedded in a porous rock matrix is presented. It is shown that an insufficiently fine discretization of the fracture elements can lead to an overprediction of the volume of DNAPL that continues to migrate vertically at the intersection of a vertical and horizontal fracture. Uniform discretization of elements at the scale of one centimetre (or less) accurately resolved the density and capillary pressure components of the head gradient in the DNAPL. An alternative, non-uniform method of discretization of elements within the discrete-fracture network is presented whereby only fracture elements immediately adjacent to fracture intersections are refined. To further limit the number of elements employed, the porous matrix elements adjacent to the fracture elements are not similarly refined. Results show this alternative method of discretization reduces the numerical error to an acceptable level, while allowing the simulation of field-scale DNAPL contamination problems. The results from two field-scale simulations of a DNAPL-contaminated carbonate bedrock site in Ontario, Canada are presented. These simulations compare different methods of grid discretization, and highlight the importance of grid refinement when simulating DNAPL migration problems in fractured porous media. 相似文献