柯西波场及在角度域成像条件中的应用

角度域成像道集是叠前深度偏移的重要输出结果,它是偏移速度分析、各向异性分析和AVA分析等研究工作的基础.目前存在的角度域成像道集的生成方法受计算效率或角度分辨率的影响,仍然满足不了实际生产的要求.角度域成像道集的生成方法可以大致分为直接法和间接法两大类.在直接方法中,波矢量方向计算和局部平面波分解是两个最重要的内容,它们共同决定角度域成像条件的实现效率和角度域成像道集的质量.为了完善现有的角度域成像道集生成方法,本文提出一种新的波矢量计算方法和局部平面波分解方法.本文先用波动方程任意时刻的柯西条件构造一个只含原波场负频率成分的柯西波场,然后根据柯西波场在时间波数域的振幅谱计算波场的波矢量方向.该方法仅在需要计算波矢量方向的时刻合成柯西波场,不需要增加额外的数据读写操作,是一种高效的波矢量计算方法.本文还以柯西波场为基础提出一种高效的局部平面波分解方法,保证角度域成像条件的实现效率.结合柯西波场和局部平面波分解方法,本文最后给出一种新的角度域成像方法.文中最后的数值实验证明该方法得到的角度域成像道集具有理想的角度分辨率,可以反映地下构造的角度照明情况.

Cauchy wave field and its application in angle-domain imaging condition

Angle Domain Common-Imaging Gathers (ADCIGs) is an important output of pre-stack depth migration. It is the basis of migration velocity analysis, anisotropy analysis and AVA analysis. However, there are still a lot of problems that reduce the efficiency of the existing ADCIGs generating methods and hinder the application of ADCIGs.Methods used to generate ADCIGs are mainly divided into two types:direct and indirect methods. For the direct methods, wave vector computing method and local plane wave decomposing method are the most important for realizing angle domain imaging condition.They decide the efficiency of imaging condition and the quality of ADCIGs. In order to perfect the exiting methods, we propose a new wave vector computing method and an efficient local plane wave decomposing method in this paper. The new method proposed in this paper utilizes the Cauchy condition of wave equation at any given time to generate a complex-valued wave field called Cauchy Wave Filed (CWF), which contains the negative frequencies of original wave fields only. Since CWF contains negative frequencies only, the energy distribution of CWF in wave number domain reveals the propagating direction of original wave fields. The only added cost of new method is the generation of CWF when imaging condition is applied. Therefore, it avoids additional In Out cost and is an efficient method to computing the wave vector. In addition, an efficient local plane wave decomposing method is also proposed in this paper to reduce the computation cost of ADCIGs and make the new method applicable. With CWF and local plane wave, we give an efficient angle-domain imaging condition. The numerical examples given in this paper prove that the ADCIGs obtained by the new proposed method has an ideal angle resolution, and have the ability to reveal the angle illumination of subsurface.