波动方程快速三维深度偏移方法

THE FAST-SPEED METHODS FOR 3-D WAVE EQUATION DEPTH MIGRATION

研究了地下反射界面倾角不超过３０°，具有横向速度变化的三维构造的深度偏移问题．文中导出了３０°倾角深度偏移方程，提出了在时间－空间域中求解这种偏移方程的直接显式方法、因式分解方法及分裂－分解方法，并讨论了频率－空间域中的因式分解方法，后者适合于三维偏移的并行计算．对于三维深度偏移而言，以上方法具有差分精度高、计算工作量较少的优点．

In this paper the fast-speed migration methods of 3-D structure are studied. These methods are available for the cases that the propagation velocity in the media is laterally variable and the angle that the reflecting interfase makes with the horizontal is less than 30 degrees. We derived 30 degrees depth migration equation and proposed some numerical methods solving this class of migration equation. They are direct and explicit method, factorization method and splitting-factorization method. Furthermore, the factorization method for me frequency-space domain is discussed. The later is very available for parallel algorithm of 3-D migration. In comparison with some other methods, the methods presented in this paper possess higher difference accuracy and reductive computational efforts. The method is tested with impulse response. Both the numerical results and the theoretical analyses show the effectiveness of the methods.