A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluid–solid interface
A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluid–solid interface
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DOI：
10.1108/ec-12-2016-0438
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发表时间：
2018-03
影响因子：
1.6
通讯作者：
Jianping Huang;Wenyuan Liao;Zhenchun Li
中科院分区：
文献类型：
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作者：
Jianping Huang;Wenyuan Liao;Zhenchun Li
本文的目的是发展一种新的有限差分方法来求解地震波在流体-固体介质中的传播问题，流体和固体部分分别由声波和粘弹性波方程描述。设计/方法/途径本文介绍了一种地震波模拟方法的坐标变换方法。在新方法中，不规则的流固界面转化为水平界面。然后，提出了一种多块坐标转换方法，将各层划分为曲面网格，将各界面转换为水平界面。同时，根据每个区域内的形状和速度，在不同的区域中使用可变的网格大小。最后，在多块坐标变换法中采用了Lebedev标准交错耦合网格方法，以减少计算量。结果-不稳定的辅助坐标系所造成的标准交错网格方案解决了使用弯曲网格粘弹性波场分离策略。用这种新方法求解了几个数值算例。计算结果表明，该方法在求解具有不规则流固界面的区域上的地震波动方程时是稳定、高效和高精度的。独创性/价值首先，不规则的流体-固体界面转化为水平界面，通过使用坐标变换方法。由于界面法向角为90°时，正应力和剪应力均为零，因此压力和应力之间的转换易于实现，并适用于不同的不规则流固界面模型。此外，该方法还解决了梯形网格离散所引起的人工边界反射和不稳定问题。
Purpose The purpose of this paper is to develop a new finite difference method for solving the seismic wave propagation in fluid-solid media, which can be described by the acoustic and viscoelastic wave equations for the fluid and solid parts, respectively. Design/methodology/approach In this paper, the authors introduced a coordinate transformation method for seismic wave simulation method. In the new method, the irregular fluid–solid interface is transformed into a horizontal interface. Then, a multi-block coordinate transformation method is proposed to mesh every layer to curved grids and transforms every interface to horizontal interface. Meanwhile, a variable grid size is used in different regions according to the shape and the velocity within each region. Finally, a Lebedev-standard staggered coupled grid scheme for curved grids is applied in the multi-block coordinate transformation method to reduce the computational cost. Findings The instability in the auxiliary coordinate system caused by the standard staggered grid scheme is resolved using a curved grid viscoelastic wave field separation strategy. Several numerical examples are solved using this new method. It has been shown that the new method is stable, efficient and highly accurate in solving the seismic wave equation defined on domain with irregular fluid–solid interface. Originality/value First, the irregular fluid–solid interface is transformed into a horizontal interface by using the coordinate transformation method. The conversion between pressures and stresses is easy to implement and adaptive to different irregular fluid–solid interface models, because the normal stress and shear stress vanish when the normal angle is 90° in the interface. Moreover, in the new method, the strong false artificial boundary reflection and instability caused by ladder-shaped grid discretion are resolved as well.