步长自适应的有限差分复杂地表波场数值模拟

发布时间：2018-03-03 04:16

本文选题：自适应网格　切入点：波动方程　出处：《地球物理学进展》2017年03期 　论文类型：期刊论文

【摘要】：复杂地表条件下的有限差分地震波场的数值模拟,由于受到低速层和地表起伏的限制,模型速度分布范围变大,一般使用精细的差分网格来抑制频散,提高模拟分辨率,但精细网格会显著增加计算成本.为了能有效地解决这一问题,本文提出一种步长自适应有限差分波动方程数值模拟方法.(1)新方法根据模型中的介质速度分布,对不同的速度区域采用与该速度匹配的空间步长,实现对模型空间网格的步长自适应精细划分.对于速度分布范围大的复杂地表模型,新方法不仅能够极大地减少模型的网格节点数,同时又能提高波场的时间采样步长,减少时间采样数,提高计算效率.(2)推导了不同步长边界网格节点Laplace算子的二阶有限差分表达式,避免了在这些结点进行插值计算产生的假扰动和数值不稳定问题.(3)为了降低有限差分产生的数值频散,本文在常规的差分方程中增加了一频散校正项,能有效地衰减了高波数成分,抑制了数值频散.对复杂近地表的波场数值模拟结果表明,本文提出的步长自适应新方法能够有效减少网格节点数和时间采样数,极大地提高计算效率,计算量比常规粗网格增加一些,但效果能够达到了常规精细网格的模拟结果.
[Abstract]:The numerical simulation of finite difference seismic wave field under complex surface condition is limited by the low velocity layer and surface fluctuation, and the velocity distribution range of the model becomes larger. The fine difference grid is generally used to suppress dispersion and improve the simulation resolution. In order to solve this problem effectively, a step size adaptive finite difference wave equation numerical simulation method, I. e., a new method based on the velocity distribution of the medium in the model, is presented in this paper. For different velocity regions, the space step size matched with the velocity is adopted to realize the adaptive fine partition of the model space mesh. For the complex surface model with large velocity distribution, The new method can not only greatly reduce the number of mesh nodes in the model, but also increase the time sampling step size of the wave field and reduce the number of time samples. The second order finite-difference expression of the Laplace operator of grid nodes with different step sizes is derived. In order to reduce the numerical dispersion generated by finite difference, a dispersion correction term is added to the ordinary difference equation. The numerical simulation results show that the proposed step size adaptive method can effectively reduce the number of mesh nodes and the number of time samples, and the numerical simulation results show that the proposed method can effectively reduce the number of mesh nodes and the number of time samples, and the numerical simulation results show that the proposed step size adaptive method can effectively reduce the number of mesh nodes and the number of time samples. The computational efficiency is greatly improved, and the computational complexity is a little more than that of the conventional coarse mesh, but the simulation results of the conventional fine mesh can be achieved.
【作者单位】：西安理工大学自动化与信息工程学院;
【基金】：国家自然科学基金资助重大项目课题(41390454)资助
【分类号】：P631.4

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