中文摘要：

研究交错网格Lowrank有限差分方法,分析该方法的精度和频散关系,并将其用于逆时偏移成像。交错网格Lowrank有限差分法通过在交错网格上匹配波场延拓算子的谱响应得到优化的差分系数。将交错网格Lowrank有限差分法用于构建地震波场,处理PML边界条件,给出用其实现逆时偏移的步骤,通过复杂模型试算验证方法的有效性。平面波理论频散分析表明,该方法能在较宽的波数范围内精确拟合频散关系,具有精度高、稳定性条件相对较宽等优点。数值结果表明,交错网格Lowrank有限差分逆时偏移能够对复杂构造进行准确成像,在保证成像精度的前提下节省计算量,具有较好的应用价值。

英文摘要：

Staggered grid Lowrank finite difference method was developed and the relationship between its accuracy and dispersion was analyzed. Staggered grid Lowrank finite difference designs Lowrank finite difference coefficients on a staggered grid to match the spectral response of the mix-domain propagation operator. The method was then applied in reverse time migration to build seismic wavefield as well as deal with PML boundary condition. The implementation steps in reverse time migration were also illustrated,and the method was verified with complex models. Dispersion analysis indicates that the method can match the dispersion relation for a wide range of wavenumbers with improved accuracy and stability. Numerical results show that the proposed method can be used to accurately image complex subsurface structures without increasing the computational cost.