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Theory of equivalent staggered-grid schemes: application to rotated and standard grids in anisotropic media

机译：等效交错网格方案的理论：应用于各向异性介质中的旋转网格和标准网格

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摘要

The previous finite-difference numerical schemes designed for direct application to second-order elastic wave equations in terms of displacement components are strongly dependent on Poisson's ratio. This fact makes theses schemes useless for modelling in offshore regions or even in onshore regions where there is a high Poisson's ratio material. As is well known, the use of staggered-grid formulations solves this drawback. The most common staggered-grid algorithms apply central-difference operators to the first-order velocity-stress wave equations. They have been one of the most successfully applied numerical algorithms for seismic modelling, although these schemes require more computational memory than those mentioned based on second-order wave equations. The goal of the present paper is to develop a general theory that enables one to formulate equivalent staggered-grid schemes for direct application to hyperbolic second-order wave equations. All the theory necessary to formulate these schemes is presented in detail, including issues regarding source application, providing a general method to construct staggered-grid formulations to a wide range of cases. Afterwards, the equivalent staggered-grid theory is applied to anisotropic elastic wave equations in terms of only velocity components (or similar displacements) for two important cases: general anisotropic media and vertical transverse isotropy media using, respectively, the rotated and the standard staggered-grid configurations. For sake of simplicity, we present the schemes in terms of velocities in the second- and fourth-order spatial approximations, with second-order approximation in time for 2D media. However, the theory developed is general and can be applied to any set of second-order equations (in terms of only displacement, velocity, or even stress components), using any staggered-grid configuration with any spatial approximation order in 2D or 3D cases. Some of these equivalent staggered-grid schemes require less computer memory than the corresponding standard staggered-grid formulation, although the programming is more evolved. As will be shown in theory and practice, with numerical examples, the equivalent staggered-grid schemes produce results equivalent to corresponding standard staggered-grid schemes with computational advantages. Finally, it is important to emphasize that the equivalent staggered-grid theory is general and can be applied to other modelling contexts, e.g., in electrodynamical and poroelastic wave propagation problems in a systematic and simple way.
机译：以前设计用于位移分量方面的直接应用于二阶弹性波方程的有限差分数值格式在很大程度上取决于泊松比。这一事实使得这些方案无法用于泊松比值很高的近海区域甚至陆上区域的建模。众所周知，交错网格配方的使用解决了这个缺点。最常见的交错网格算法将中心差分算子应用于一阶速度应力波方程。它们是地震建模最成功应用的数值算法之一，尽管这些方案比基于二阶波动方程的方案需要更多的计算内存。本文的目的是发展一种通用理论，使人们能够制定等效的交错网格方案以直接应用于双曲型二阶波动方程。详细介绍了制定这些方案所需的所有理论，包括有关源应用程序的问题，提供了在各种情况下构造交错网格公式的通用方法。此后，仅在两种重要情况下，仅将速度分量（或类似位移）用于等效弹性网格方程，将其应用于各向异性弹性波方程：一般各向异性介质和垂直横向各向同性介质分别使用旋转和标准交错介质。网格配置。为了简单起见，我们以二阶和四阶空间近似中的速度表示方案，其中二维介质在时间上近似为二阶。但是，开发的理论是通用的，可以在2D或3D情况下使用具有任何空间逼近顺序的任何交错网格配置，将其应用于任何二阶方程组（仅就位移，速度甚至应力分量而言） 。这些等效的交错网格方案中的某些方案比相应的标准交错网格公式所需的计算机内存更少，尽管编程更加完善。如理论和实践中所示，通过数值示例，等效交错网格方案产生的结果等同于具有计算优势的相应标准交错网格方案。最后，必须强调的是，等效交错网格理论是通用的，可以系统地，简单地应用于其他建模环境，例如电动力学和多孔弹性波传播问题。

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  • 来源
    《Geophysical Prospecting》 |2015年第5期|1097-1125|共29页
  • 作者

    Di Bartolo Leandro; Dors Cleberson; Mansur Webe J.;

  • 作者单位

    Coordenacao Geofis, Observ Nacl MCTI, BR-20921400 Rio De Janeiro, RJ, Brazil;

    Univ Fed Rio de Janeiro, Inst Alberto Luiz Coimbra Posgrad & Pesquisa Engn, Programa Engn Civil, BR-21945970 Rio De Janeiro, RJ, Brazil;

    Univ Fed Rio de Janeiro, Inst Alberto Luiz Coimbra Posgrad & Pesquisa Engn, Programa Engn Civil, BR-21945970 Rio De Janeiro, RJ, Brazil;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    FD modelling; Staggered grids; Anisotropy;

    机译：FD建模交错网格各向异性;

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