An novel finite difference dispersion error elimination mechanism in the Lax–Wendroff high-order time discretization

IF 1.8 3区 地球科学 Q3 GEOCHEMISTRY & GEOPHYSICS Geophysical Prospecting Pub Date : 2024-09-26 DOI:10.1111/1365-2478.13611
Wenquan Liang, Yanfei Wang
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Abstract

Time domain finite difference methods have been widely used for wave-equation modelling in exploration geophysics over many decades. When using time domain finite difference methods, it is desirable to use a larger time step so as to save numerical simulation time. The Lax–Wendroff method is one of the well-known methods to allow larger time step without increasing the time grid dispersion. However, the Lax–Wendroff method suffers from more time consumption because there are more spatial derivatives required to be approximated by the finite difference operators. We propose a new finite difference scheme for the Lax–Wendroff method so as to reduce the numerical simulation time. Then we determine the finite difference operator coefficients and analyse the dispersion error of the proposed finite difference scheme for the Lax–Wendroff method. At last, we apply the proposed finite difference scheme for the Lax–Wendroff method to different velocity models. The numerical simulation results indicate that the proposed finite difference scheme for the Lax–Wendroff method can effectively suppress time grid dispersion and is more efficient compared to the traditional finite difference scheme for the Lax–Wendroff method.

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拉克斯-温德罗夫高阶时间离散化中的新型有限差分离散误差消除机制
几十年来,时域有限差分法被广泛用于勘探地球物理的波方程建模。在使用时域有限差分法时,最好使用较大的时间步长,以节省数值模拟时间。Lax-Wendroff 方法是一种著名的方法,可以在不增加时间网格离散度的情况下实现较大的时间步长。然而,Lax-Wendroff 方法耗时较多,因为有更多的空间导数需要用有限差分算子来近似。我们为 Lax-Wendroff 方法提出了一种新的有限差分方案,以减少数值模拟时间。然后,我们确定了有限差分算子系数,并分析了所提出的 Lax-Wendroff 方法有限差分方案的分散误差。最后,我们将所提出的 Lax-Wendroff 方法有限差分方案应用于不同的速度模型。数值模拟结果表明,与传统的 Lax-Wendroff 方法有限差分方案相比,所提出的 Lax-Wendroff 方法有限差分方案能有效抑制时间网格离散,效率更高。
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来源期刊
Geophysical Prospecting
Geophysical Prospecting 地学-地球化学与地球物理
CiteScore
4.90
自引率
11.50%
发文量
118
审稿时长
4.5 months
期刊介绍: Geophysical Prospecting publishes the best in primary research on the science of geophysics as it applies to the exploration, evaluation and extraction of earth resources. Drawing heavily on contributions from researchers in the oil and mineral exploration industries, the journal has a very practical slant. Although the journal provides a valuable forum for communication among workers in these fields, it is also ideally suited to researchers in academic geophysics.
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