起伏地表条件下频率-空间域声波介质正演模拟

频率-空间域正演模拟是频率域及Laplace-Fourier域全波形反演的基础，起伏地表条件下波形反演算法的关键是正演算法中考虑起伏地表的影响。基于带PML吸收边界的声波波动方程，在已有最优9点有限差分正演算法的基础上构建了起伏地表条件下频率-空间域正演算法。通过应用变网格技术，进一步提高算法的计算效率、降低内存开销，使得大规模起伏地表模型的频率域正反演问题成为可能。理论分析及数值测试表明：通过对近地表区域进行局部网格加密，可有效地压制由于矩形网格离散引起的角点散射；结合变网格技术可较易获得5倍以上计算效率的提高及内存占用的降低，且随着模型尺度的增加及地表起伏高程差的减小，倍数将显著增加；在细网格与粗网格交界处产生的虚假反射振幅幅值控制在原始波场的2%以内，满足地震波场正反演的需求。

Acoustic Wave Modeling in Frequency-Spatial Domain with Surface Topography

Seismic wave modeling in frequency-space domain is the foundation of full waveform inversion in frequency and Laplace-Fourier domain. An accurate seismic wave modeling with surface topography is the kernel of full waveform inversion which can direct process data recorded on relief surface. Based on acoustic wave equation with PML absorption boundary condition, the free surface condition on relief surface is included into the optimized 9-points finite difference algorithm in frequency space domain. Then the variable grid method which refines the grid near the surface and remains the rest unchangeable is introduced to increase the computational efficiency and decrease the memory cost. The theoretical analysis and numerical test show that: 1) the diffraction caused by grid discretization of the relief surface can be suppressed by refining the grid; 2) through the variable grid method, computational efficiency can be improved for several times and the memory cost can also be decreased for several times easily; 3) the energy of artificial reflection caused by the boundary of fine and coarse grid is less than 2% of the energy of the original  wavefield which is acceptable for the seismic wavefield modeling and inversion.