平面波优化差分算子弹性波逆时偏移

An elastic-wave reverse-time migration method based on optimal finite-difference operators using a new plane wave solution

弹性波逆时偏移基于双程波动方程理论,不受倾角限制,对复杂模型具有较强的适应性,但高额的计算量和内存占用是其用于巨量地震资料处理的主要瓶颈。为此,推导了一种基于平面波优化的等效交错网格弹性波逆时偏移成像方法,通过优化差分系数降低正演波场的频散误差,达到使用低阶优化差分算子替代高阶传统差分算子、降低计算量的目的。在内存需求方面,采用二阶位移弹性波方程,避免了中间变量的出现,且引入了有效边界存储的策略,只利用边界附近区域的部分波场值控制逆时偏移的波场存储方式。模型测试表明:该方法6、10阶空间差分算子逆时偏移结果成像精度分别相当于10、18阶传统方法,有效节约了计算成本;相比于常规弹性波逆时偏移的波场存储方式,有效边界存储在增加部分计算量的前提下,能节约大量内存占用,且使用的差分算子长度越短,内存占用也越少。

Elastic-wave revere time migration based on the theory of two-way wave equation is not limited by the dip angle of formation,so it has a strong adaptability to complex models.However,high computing cost and a large memory limit its application for processing big seismic data.This paper deduces an elastic-wave reverse-time migration imaging method using equivalent staggered-grid finitedifference based on time-space domain optimization.To improve imaging accuracy,we reduce the dispersion error by optimizing difference operators,which means that a low-order difference operator can achieve the imaging accuracy of a high-order difference operator,so as to reduce the computing cost.To reduce memory usage,the second-order displacement equation is adopted to avoid intermediate variables.We also adopt an efficient boundary storage strategy,which uses the wavefield value near the boundary to control the reverse-time migration wavefield storage,which effectively reduces the memory use.Model tests show that the new method with a 6 th-order spatial difference has a similar imaging accuracy to the conventional staggered-grid scheme with the 10 th-order spatial difference,and the new method with a 10 th-order corresponds to the conventional method with a18 th-order difference.Compared with conventional elastic wavefield storage strategy,effective boundary storage strategy can save a lot of memory usage on the premise of increasing less computing cost,and this strategy is more beneficial to shorter difference operators.