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为优化二维各向同性介质中弹性波频率域正演时阻抗矩阵的结构,减小正演所需内存,提高正演效率,在25点差分格式的基础上进行适当的简化,得到了二维弹性波频率域15点差分格式.利用该格式重新计算了弹性波方程中偏微分项和加速项的差分算子,减少了计算过程中的网格节点需求,构造了优化阻抗矩阵后的频率域正演矩阵方程;推导了纵波和横波相速度的频散公式,给出了不同泊松比条件下的频散曲线,得到了相速度误差控制范围±1%时每一横波波长内网格数需求.通过对比频散曲线和简单模型数值模拟时得到的波场快照、检波点处速度分量及单炮记录,验证了15点差分格式与25点差分格式相比,具有稍严格的网格间距需求、相当的计算精度、更少的计算时间和更小的阻抗矩阵带宽等特点.最后,利用复杂模型数值模拟对本方法的适应性进行了验证.
In order to optimize the structure of the impedance matrix when the elastic wave frequency domain forwards in two-dimensional isotropic medium, reduce the memory needed for forward modeling and improve the forward efficiency, based on the 25-point difference format, Dimensional elastic wave frequency domain 15-point difference format, the difference operator of partial differential term and acceleration term in elastic wave equation is recalculated using this scheme, which reduces the requirement of grid node in the calculation process and constructs the frequency after optimized impedance matrix Domain forward matrix equation. The dispersion formula of the phase velocities between the longitudinal and transverse waves is deduced. The dispersion curves of the phase velocities at different Poisson’s ratios are given. The grids within each transverse wavelength are obtained when the phase velocity error control range is ± 1% The numerical results show that the 15-point difference scheme has a slightly stricter grid compared with the 25-point difference scheme by comparing the snapshots of wavefields, velocity components at the detection points and single shot records obtained from the dispersion curves and the numerical simulations of simple models. Space requirement, considerable calculation accuracy, less computation time and smaller impedance matrix bandwidth.Finally, the adaptability of this method is verified by numerical simulation of complex models.