起伏地表谱元逆时偏移方法

Reverse time migration for irregular topography based on spectral element method

谱元法综合了有限元法边界适应性强和谱方法精度高、收敛快的优点。研发了一种基于谱元法的起伏地表逆时偏移方法,采用切比雪夫谱元法并结合隐式Newmark时间积分法求取波场传播算子,推导出波动方程切比雪夫谱元逆时偏移算法(CSE-RTM),该算法在空间上具有谱精度,在时间上达到二阶精度。同时,为了充分利用计算机集群资源,提高该方法的并行效率,基于自由度凝聚和局部松弛的思想,推导了切比雪夫谱元逆时偏移方法的多级并行算法(HEP-CSE-RTM),该算法具有并行效率不随处理器数目增多而下降的优点。二维加拿大起伏地表逆掩断层模型及三维SEAM起伏地表复杂构造模型测试结果表明:该方法在起伏地表复杂构造区成像精度明显高于常规有限差分法逆时偏移,由于该方法本身具有谱方法的稀疏网格快速收敛特性,结合自由度凝聚的多级并行计算,运行效率大幅度提高,达到了与常规有限差分法逆时偏移相当的计算效率。

The spectral element method combines the advantages of strong boundary adaptability of the finite element method and high accuracy and fast convergence of the spectral method.For the high-precision seismic imaging of complex structures with irregular topography,a Chebyshev spectral-element reverse time migration method(CSE-RTM)was proposed.Using this method,the wave field propagation operator is obtained through the Chebyshev spectral element method coupled with the implicit Newmark time integral method.The method offers spectral accuracy in space and second-order accuracy in time.To improve the parallel efficiency,based on the concepts of cohesion degree and local relaxation,an integrated hierarchical equilibrium parallel Chebyshev spectral-element reverse time migration(HEP-CSE-RTM)algorithm was developed,which is a fine-grained central processing unit parallel computation method in two-level host-sub-processor mode.The advantage of this algorithm is that the parallel efficiency does not decrease as the number of processors increases.Model tests showed that in a complex structure with irregular topography,the imaging accuracy of the HEP-CSE-RTM algorithm was higher than that of the conventional finite-difference reverse time migration method(FD-RTM).Owing to the fast convergence of the spectral method on a sparse grid coupled with a parallel computational scheme,the calculation efficiency of the HEP-CSE-RTM is equivalent to that of the FD-RTM.