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《地球物理学进展》2017,(5)
二维波动方程谱元法通常采用四边形网格,网格质量和属性建模方式对波场模拟精度和效率有较大影响.常规属性建模需要先建立几何模型再对其进行贴体网格剖分.但存在已知稠密属性控制点却难以建立复杂几何模型的问题.针对此问题,提出对模型进行矩形网格剖分并计算GLL点,利用属性控制点对所有GLL点进行插值以提高属性建模的效率.将属性建模方式归纳为单元属性建模方式和节点属性建模方式.在节点属性建模方式中分析了双线性插值、快速Gauss径向基函数插值法的计算效率,将两种插值算法集成于SPECFEM2D的属性建模程序中.实例表明两种属性建模方式对谱元法波场模拟都是有效的. 相似文献
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针对非均匀介质中热蠕变流动问题,给出了有限单元方法与网格－粒子方法联合求解新技术,即有限单元方法求解欧拉网格节点上的未知量,分布于单元内部作为物质成分标记的粒子反映变形过程.有限元法求解动量方程和连续性方程时引入了速度场和压力场等阶插值的压力场稳定的Petrov Galerkin方法,求解能量方程时采用了流线迎风Petrov Galerkin方法,网格－粒子算法中采用双线性插值与有限单元插值函数对应.有限单元计算与网格－粒子计算相对独立,两种方法计算的数据通过有限单元节点传递.同时,实现了三角形单元的算法和程序,解决了复杂结构条件下不规则网格计算的问题.通过经典方腔热对流问题验证了程序,给出了不规则形态块体沉降算例,并分析了数值解的稳定性. 相似文献
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针对走时线性插值法(LTI)的计算精度问题,利用非线性插值替代传统的线性插值。该方法利用边界上多个节点的走时,使得插值误差减小,从而提高整体边界网格离散点走时精度,同时保留LTI所具有快速、全局性的优点。数值模拟结果表明,非线性插值算法比LTI算法精度高,可以追踪包括直达波、折射波、透射波等多种射线路径,适合速度突变模型。 相似文献
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矩形网格有限差分法在地震波传播数值模拟方面具有计算速度快的显著优势,但该方法在处理复杂边界问题上存在着效率低的严重缺陷.本文针对分段光滑曲线边界定义了尖点处的一种正则导数,给出了矩形网格情形分段光滑曲线网格边界点法向导数的一种插值计算方法.采用矩形网格有限差分法对复杂边界地球介质模型进行地震波场数值模拟,并采用波场系列快照技术揭示地震波在起伏地表和复杂介质中的传播规律.模拟结果表明：法向导数插值计算方法为矩形网格有限差分法处理复杂边界提供了有效途径,采用波场系列快照技术可以清晰地展现地震波在反射界面的反射和透射规律、在尖点的绕射规律以及在自由表面的直达波和多次反射规律. 相似文献
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对于射线类偏移成像来说,求解射线追踪系统中所涉及的属性值不在网格节点上的插值计算问题是一个非常重要的环节,它影响到求解走时、路径和振幅信息的计算效率和精度,进而影响到整个偏移成像的质量和效率.本研究根据速度模型的空间梯度特点,考虑被插值点处速度的梯度在横向和纵向的分布特征,构建基于速度梯度空间变化的偏微分方程算法,将近几年发展起来的基于偏微分方程的定向插值算法引入到射线类偏移成像当中,实现射线追踪当中涉及的属性值不在网格节点上的插值计算.由于偏微分方程法本身固有的特性(局部特征不变性、解的唯一性和线性叠加性),因此,该算法可以实现不破坏原始速度模型空间梯度结构的非网格节点属性的插值计算.通过在常用的速度模型上的插值计算对比、不同速度模型上射线路径对比分析以及复杂介质模型上最后的偏移成像结果分析可以得出,应用基于速度梯度构建的偏微分方程插值算法在进行插值计算的过程当中可以实现不破坏原始速度模型空间速度梯度结构的属性计算,同时应用该算法可以最终提高射线类偏移成像的质量. 相似文献
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叠前逆时偏移等基于波场互相关原理的地球物理方法存在极大的计算与存储需求,因此采用合适的波场重构方法显得尤为重要.常规的随机边界法容易产生成像噪声,而有效边界法在三维情况仍难以实现,检查点技术具有内存要求小的特点,但存在较高的重算率,因此本文提出了插值原理的检查点技术波场重构方法.在满足Nyquist采样定理的前提下对相邻检查点间的波场进行规则抽样,将抽样波场作为插值节点,运用多项式插值算法重构任意时刻的波场,从而避免优化检查点技术反复递推造成的计算效率问题.数值实验表明：插值检查点重构算法能有效的恢复波场,其中三次样条插值重构精度最高,而牛顿法插值法计算代价较小适合于快速重构.经Sigsbee模型的叠前逆时偏移证明了插值算法的可行性,并且极大的提高了波场重构的计算效率.三维模型分析得出在增加少量存储的情况下插值重构法的重算率大幅度降低,存储量减少为有效边界法的7.1%,对于三维尺度的叠前逆时偏移有实际意义. 相似文献
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坐标变换法通过将物理空间的曲网格映射为计算空间的矩形网格,将起伏地表转化为水平地表,同时将物理空间的波动方程转化为计算空间的波动方程,在计算空间完成数值模拟,坐标变换的方法对处理起伏自由边界具有较好的适应性和应用效果。本文在传统坐标变换方法的基础上,根据计算区域速度差异采用不同的网格大小和采样时间步长,提出了一种基于时空双变网格的起伏地表坐标变换正演模拟方法。在编程实现算法的基础上,通过典型模型波场模拟试算结果分析可知:(1)变网格方法与常规方法波场模拟误差在0.5%左右;(2)变网格方法计算效率视不同的变网格区域面积及变网格大小可提高几倍量级,在本文模型和计算参数下提高约5倍。(3)在满足模拟精度及频散条件要求下,变网格方法较全局细网格算法能显著节约计算内存。为此,针对起伏地表数值模拟,本文方法具有较高的模拟计算精度和一定的适应性。 相似文献
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地震波初至走时的计算方法综述 总被引：3，自引：0，他引：3
在地震波场中,初至波到时信息由于初至震相可追踪、易识别性,在地震学领域占有重要的位置,广泛地应用于叠前偏移、叠前速度分析、地震走时层析成像及地震定位等.本文主要介绍了四类具有代表性的计算初至波走时的方法:(1)基于高频近似射线理论方法,如最短路径方法(SPM),及修正后的最短路径方法(MSPM);(2)基于程函方程的数值解方法,如有限差分方法(FD)、快速推进法(FMM)和快速扫描法(FSM);(3)基于惠更斯原理的波前构建法(WFC);(4)基于频率域波动方程数值解法(FWQ).最短路径方法计算精度较高,稳定性较好,但其需要采用更多的网格节点,因此计算效率低;程函方程数值解法无需计算射线路径,具有计算效率高、稳定性较好、易于实现等优势,但其计算精度较低,可以通过引入高阶差分格式得到提高;波前构建法计算精度高,稳定性好,但其需要在射线网格和规则网格之间做网格转换,因此计算效率较低;频率域波动方程方法能适应任意复杂介质,但其计算精度和计算效率较低. 相似文献
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The effect of mesh type on the accuracy and computational demands of a two-dimensional Godunov-type flood inundation model is critically examined. Cartesian grids, constrained and unconstrained triangular grids, constrained quadrilateral grids, and mixed meshes are considered, with and without local time stepping (LTS), to determine the approach that maximizes computational efficiency defined as accuracy relative to computational effort. A mixed-mesh numerical scheme is introduced so all grids are processed by the same solver. Analysis focuses on a wide range of dam-break type test cases, where Godunov-type flood models have proven very successful. Results show that different mesh types excel under different circumstances. Cartesian grids are 2–3 times more efficient with relatively simple terrain features such as rectilinear channels that call for a uniform grid resolution, while unstructured grids are about twice as efficient in complex domains with irregular terrain features that call for localized refinements. The superior efficiency of locally refined, unstructured grids in complex terrain is attributable to LTS; the locally refined unstructured grid becomes less efficient using global time stepping. These results point to mesh-type tradeoffs that should be considered in flood modeling applications. A mixed mesh model formulation with LTS is recommended as a general purpose solver because the mesh type can be adapted to maximize computational efficiency. 相似文献
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在许多地震反演和偏移成像方法中,都要涉及到射线路径和旅行时的计算.本文将波前面三角形网格剖分和三维波前重建法射线追踪技术结合使用,实现了射线路径和旅行时的准确快速计算.三维波前重建法射线追踪过程中可以保证稳定合理的射线密度,克服了常规射线追踪方法存在阴影区的问题.波前面三角形网格剖分在描述和拆分波前面时更加准确有效,而且不需太多的网格数目,从而提高了射线追踪的精度和效率.该方法在三维复杂构造成像方面有独特的优势,目前在实际的Kirchhoff 偏移中的已经有相关应用. 相似文献
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Seismic wavefront evolution of multiply reflected, transmitted, and converted phases in 2D/3D triangular cell model 总被引：1，自引：0，他引：1
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. 相似文献
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《Advances in water resources》2004,27(9):899-912
This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497–511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, “cage-shell” interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size—a coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid. 相似文献
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瞬变电磁三维时域有限差分（FDTD）正演的网格剖分受最小网格尺寸、时间步长、边界条件、目标尺寸、模型尺寸等的影响,结构化网格一直存在最小网格尺寸受限于异常目标尺寸的矛盾;尽管非均匀网格能够在保证模型尺寸的前提下尽可能的降低网格数量,但由于Yee网格结构的限制,非均匀网格不能无限制的扩大单一方向的尺寸,这是为了避免边界网格区域出现长宽比过大的畸形网格,影响计算精度甚至导致结果发散.在非均匀网格剖分的基础上,本文提出了瞬变电磁三维FDTD正演的多尺度网格方法,即首先使用较大尺寸的粗网格进行第一次剖分,然后在希望加密的区域进行二次剖分,使计算域中包含粗、细两套网格.尽管细网格包含在粗网格内部,但其具有Yee网格的全部属性,因而可以在网格中设置不同的电性参数模拟不同形状的目标.基于Maxwell方程组推导了细网格内电场和磁场的迭代公式,基于泰勒展开给出了设置粗、细网格后产生的内部边界条件,使电磁场的传播在粗、细网格和时间步进上得到统一.采用均匀半空间中包含三维低阻异常的经典模型和三维接触带复杂模型进行精度验证,发现多分辨网格方法计算结果满足精度要求.使用"L"型异常模型计算采用多分辨网格方法和不采用多分辨网格的传统FDTD方法对比计算效率,发现多分辨网格算法能够显著提高计算效率,并能够保证计算精度. 相似文献
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Traveltime computation by wavefront-orientated ray tracing 总被引：1，自引：0，他引：1
For multivalued traveltime computation on dense grids, we propose a wavefront‐orientated ray‐tracing (WRT) technique. At the source, we start with a few rays which are propagated stepwise through a smooth two‐dimensional (2D) velocity model. The ray field is examined at wavefronts and a new ray might be inserted between two adjacent rays if one of the following criteria is satisfied: (1) the distance between the two rays is larger than a predefined threshold; (2) the difference in wavefront curvature between the rays is larger than a predefined threshold; (3) the adjacent rays intersect. The last two criteria may lead to oversampling by rays in caustic regions. To avoid this oversampling, we do not insert a ray if the distance between adjacent rays is smaller than a predefined threshold. We insert the new ray by tracing it from the source. This approach leads to an improved accuracy compared with the insertion of a new ray by interpolation, which is the method usually applied in wavefront construction. The traveltimes computed along the rays are used for the estimation of traveltimes on a rectangular grid. This estimation is carried out within a region bounded by adjacent wavefronts and rays. As for the insertion criterion, we consider the wavefront curvature and extrapolate the traveltimes, up to the second order, from the intersection points between rays and wavefronts to a gridpoint. The extrapolated values are weighted with respect to the distances to wavefronts and rays. Because dynamic ray tracing is not applied, we approximate the wavefront curvature at a given point using the slowness vector at this point and an adjacent point on the same wavefront. The efficiency of the WRT technique is strongly dependent on the input parameters which control the wavefront and ray densities. On the basis of traveltimes computed in a smoothed Marmousi model, we analyse these dependences and suggest some rules for a correct choice of input parameters. With suitable input parameters, the WRT technique allows an accurate traveltime computation using a small number of rays and wavefronts. 相似文献
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加权近似解析离散化(WNAD) 方法是近年发展的一种在粗网格步长条件下能有效压制数值频散的数值模拟技术. 在地震勘探的实际应用中, 不是所有情况都适合使用空间大网格步长. 为适应波场模拟的实际需要, 本文给出了求解波动方程的非一致网格上的WNAD算法. 这种方法在低速区、介质复杂区域使用细网格, 在其他区域采用粗网格计算. 在网格过渡区域, 根据近似解析离散化方法的特点, 采用了新的插值公式, 使用较少的网格点得到较高的插值精度. 数值算例表明, 非一致网格上的WNAD方法能够有效压制数值频散, 显著减少计算内存需求量和计算时间, 进一步提高了地震波场的数值模拟效率. 相似文献
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The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ‘staircase fashion‘causing spurious diffractions. It is the aim of this work to eliminate these non-physical diffractions by using curved grids that generally follow the interfaces. A further advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled. One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so-called multiblock strategy). The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space. The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods. 相似文献
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When applying the conventional Fourier pseudospectral method (FSM) on a Cartesian grid that has a sufficient size to propagate a pulse, spurious diffractions from the staircase representation of the curved interfaces appear in the wavefield. It is demonstrated that these non-physical diffractions can be eliminated by using curved grids that conform to all the interfaces of the subsurface. Methods for solving the 2D acoustic wave equation using such curved grids have been published previously by the authors. Here the extensions to the full 2D elastic wave equations are presented. The curved grids are generated by using the so-called multiblock strategy which is a well-known concept in computational fluid dynamics. In principle the sub-surface is divided into a number of contiguous subdomains. A separate grid is generated for each subdomain patching the grid lines across domain boundaries to obtain a globally continuous grid. Using this approach, even configurations with pinch outs can be handled. The curved grid is taken to constitute a generalized curvilinear coordinate system. Thus, the elastic equations have to be written in a curvilinear frame before applying the numerical scheme. The method implies that twice the number of spatial derivatives have to be evaluated compared to the conventional FSM on a Cartesian grid. However, it is demonstrated that the extra terms are more than compensated for by the fewer grid points needed in the curved approach. 相似文献