Combined Boundary of CPML and Feature Analysis within Frequency-Space Domain
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摘要: 在地震波场数值模拟过程中，边界反射是影响其模拟结果的一个重要因素。实际地下介质具有各向异性特征，传统的完全匹配层边界（PML）对于小入射角地震波具有良好效果，但该方法并不能有效地吸收低频波和大角度入射波。针对VTI介质边界反射的问题，本文提出在频率-空间域有限差分法数值模拟中采用卷积完全匹配层（CPML）和特征分析法的组合边界条件，并对该组合边界条件进行数值模拟实验和边界反射吸收效果分析，验证所提方法是一种可靠的人工吸收边界条件，能够有效地压制波场模拟过程中产生的边界反射。Abstract: In the process of numerical simulation, boundary reflection is an important factor which affect the numerical simulation results. The actual underground medium holds anisotropic characteristics. The traditional perfectly matched layer boundary (PML) shows good effect on small incident angle seismic waves, yet it can not effectively absorb low-frequency waves and large angle incident waves. To solve the problem of boundary reflection, in this paper, we propose a combined boundary condition using convolution perfectly matched layer (CPML) and eigenvalue analysis method to be applied in the numerical simulation of finite difference method in frequency space domain. The numerical simulation experiment and boundary reflection absorption effect analysis of the combined boundary condition verify that the proposed method is a reliable artificial absorption boundary condition, which can effectively suppress the boundary reflection generated in the process of wave field simulation.
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图 2 未加边界时的50 Hz单频波快照（a）和时间域150 ms波前快照（b）
Figure 2. 50 Hz single frequency snapshot (a) and 150 ms wavefront snapshot (b) without boundary attenuation in time domain
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图 3 施加特征分析法边界衰减后的50 Hz单频波快照（a）和150 ms时间域波前快照（b）
Figure 3. 50 Hz single frequency snapshot (a) and 150 ms wavefront snapshot (b) with the boundary attenuation of characteristic analysis method in time domain
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图 4 施加PML和特征分析组合边界后的50 Hz单频波快照（a）和150 ms时间域波前快照（b）
Figure 4. 50 Hz single frequency snapshot (a) and 150 ms wavefront snapshot (b) with the combination absorption boundary of PML and characteristic analysis method in time domain
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