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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.
Under the condition of complex surface, the finite difference seismic wavefield numerical simulation, due to the low velocity layer and the surface undulation, the model velocity distribution range becomes larger, the fine differential grid is generally used to suppress the dispersion and improve the analog resolution, but the fine mesh In order to solve this problem effectively, this paper presents a numerical simulation method for step-adaptive finite difference wave equation. (1) The new method is based on the velocity distribution in the model, The spatial step matching with the velocity is used to fine-tune the step size of the model space grid.For complex surface models with large velocity distribution, the new method not only can greatly reduce the number of mesh nodes in the model, Can improve the time sampling step of the wave field, reduce the number of time samples and improve the computational efficiency. (2) The second-order finite difference expressions of Laplace operators in non-synchronous long-boundary mesh nodes are deduced, which avoids interpolation at these nodes (3) In order to reduce the numerical dispersion caused by the finite difference, this paper adds to the conventional difference equation The dispersion correction term can effectively attenuate the high-wavenumber components and suppress the numerical dispersion.The numerical simulation of the wave field of the complex near-surface shows that the new adaptive step-length method proposed in this paper can effectively reduce the number of grid nodes and time The number of samplings greatly improves the computational efficiency, and the computational cost is increased more than the conventional coarse grid, but the result can reach the simulation result of the conventional fine grid.