【摘要】 基于速度-应力形式的弹性波动方程，采用分部求和和同时逼近项技术建立的SBP-SAT方法，推导了横向各向同性(transversely isotropy, TI)介质的矩阵对称型(symmetric matrix form, SMF)弹性波动方程离散形式，并通过能量法进行了稳定性分析。将该方法应用于倾斜横向各向同性(tilted transverse isotropic,TTI)介质模型、垂直横向各向同性(transverse isotropy with a vertical axis of symmetry, VTI)介质和含裂缝及曲线域的复杂介质模型，对所得的速度幅值和单炮记录分析并总结规律；对不同时间步长、单元网格数的结果进行对比，得出计算效率并验证该方法在求解P-SV波传播问题上的正确性。数值模拟结果表明，该方法模拟精度高，适用性好，在地震数值模拟领域有很好的应用价值和前景。更多还原

【Abstract】 Based on the elastic wave equation in the form of velocity and stress, the discrete form of symmetric matrix form(SMF) elastic wave equation in transversely isotropy(TI) media was derived by the SBP-SAT method established by the techniques of the summation by parts and the simultaneous approximation terms. The stability of SMF elastic wave equation was analyzed by the energy method. An inclined tilted transverse isotropic(TTI) model, a layered VTI media model, and a complex media model with cracks and curve domains were all applied to the numerical model, and the obtained velocity amplitude and single shot records were analyzed and summarized. The computational efficiency was obtained and the and the correctness of the method in solving the P-SV wave propagation problem in TI media was verified, according to comparisons between the numerical results of various time steps and the number of cell grids. Numerical simulation results show that the method has high simulation accuracy and good applicability, and has good application value and prospects in the field of seismic numerical simulation.更多还原