Runge-Kutta discontinuous Galerkin method for solving wave equations in 2D isotropic and anisotropic poroelastic media at low frequencies
Runge-Kutta discontinuous Galerkin method for solving wave equations in 2D isotropic and anisotropic poroelastic media at low frequencies
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DOI：
10.1190/geo2020-0707.1
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发表时间：
2021-05
期刊：
影响因子：
3.3
通讯作者：
Xijun He;Dinghui Yang;Yan-jie Zhou;Lei Yang;Xueyuan Huang
中科院分区：
文献类型：
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作者：
Xijun He;Dinghui Yang;Yan-jie Zhou;Lei Yang;Xueyuan Huang
本文提出了一种求解各向同性和各向异性孔隙弹性介质低频波动方程的龙格-库塔不连续伽辽金方法。首先，将二维Biot两相方程转化为具有耗散的一阶系统。然后，采用三阶龙格-库塔时间离散化的不连续伽辽金方法对系统进行离散化。研究了求解多孔方程的数值稳定性条件。我们在各向同性和各向异性孔隙弹性介质中进行了实例测试，验证了我们的方法。通过与细网格有限差分法的地震反应对比，验证了该方法的正确性。此外，数值结果表明，RKDG方法可以为粗网格上各向异性孔隙弹性介质提供清晰的快P波、慢P波和横波。两层多孔模型、水平界面的孔弹-弹性模型和正弦界面的各向同性-各向异性孔弹模型也证明了该方法可以处理复杂波的传播。因此，仿真结果表明，RKDG是求解Biot方程的一种准确、稳定的方法。
We have developed a Runge-Kutta discontinuous Galerkin (RKDG) method for solving wave equations in isotropic and anisotropic poroelastic media at low frequencies. First, the 2D Biot’s two-phase equations are transformed into a first-order system with dissipation. Then, the system is discretized by using the discontinuous Galerkin method with a third-order Runge-Kutta time discretization. The numerical stability conditions for solving porous equations are also investigated. We test several examples to validate our method in isotropic and anisotropic poroelastic media. Comparisons of seismic responses with the finite-difference method on fine grids show the correctness of this method. Moreover, the numerical results indicate that the RKDG method can provide clear fast P-, slow P-, and S-waves for anisotropic poroelastic media on coarse meshes. Also, a two-layer porous model, a poroelastic-elastic model with horizontal interface, and an isotropic-anisotropic poroelastic model with sinusoidal interface demonstrate that our method can deal with complex wave propagation. Therefore, the simulation results show that RKDG is an accurate and stable method for solving Biot’s equations.