基于变系数声波方程的地震深度偏移  

A Seismic Depth Migraton Method Based on Varied-coefficient Acoustic Equation

作　　者：曾祥芝[1,2] 杨文采[3] ZENG XIANGZHI;YANG WENCAI(China University of Geosciences of Wuhan,Wuhan 430074,China;Institute Of Geology,Chinese Acaderny Of Geological Sciences,Beijing 100037,China;School of Earth Science,Zhejiang University,Zhejiang 310058,China)

机构地区：[1]中国地质大学地球物理与空间信息学院,武汉430074 [2]中国地质科学院地质研究所,北京100037 [3]浙江大学地球科学学院,杭州310027

出　　处：《应用数学学报》2020年第6期923-938,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(41574111)资助项目。

摘　　要：理论分析表明,常系数声波方程与变系数声波方程之间有根本性的区别,变系数声波方程中波场的作用算子属于拟微分算子.地震学的理论应该建立在变系数声波方程的基础上,才更加准确.但是,变系数声波方程理论需要通过实际资料应用来检验.本文基于变系数声波方程上下行波分离与深度偏移方程降阶方法,导出二维和三维波速不均匀介质中的一种地震深度偏移方法.该方法在理论上应该有更高的精度,理论模型的实验证明了算法的正确性.利用塔里木盆地的实际资料的试验表明,基于变系数声波方程的深度偏移算法,不仅理论上是正确的,和一般声波方程的偏移算法相比,提供了更加清晰的细节,取得更加准确可靠的结果.实际资料试验证实了变系数波动方程的拟微分算子理论在地震勘探中具有重要的应用前景.Theoretical analysis shows that there is a fundamental difference between constant coefficient acoustic equation(CCAE)and variable coefficient acoustic equation(VCAE)The operator of wave field in VCAE belongs to pseudo differential operator.The theory of seismology should be based on the acoustic equation with VCAE,so it is more accurate.However,the theory of VCAE needs to be tested by the application of actual data.In this paper,based on the method of separating the up-and down-going waves of VCAE and reducing the order of depth migration equation,a seismic depth migration method in 2 D and3 D media with uneven wave velocity is derived.This method should have higher accuracy in theory,and the experiment of theoretical model proves the correctness of the algorithm.Based on the actual data of Tarim Basin,we have carried out a depth migration imaging experiment.The experimental results show that the depth migration algorithm based on the VCAE can provide clearer details and obtain more accurate and reliable results compared with the general acoustic equation migration algorithm.The actual data experiment proves that the pseudo differential operator theory of VCAE has an important application prospect in seismic exploration.

关 键 词：变系数波动方程 拟微分算子 地震勘探 地震偏移 计算实例 

分 类 号：P315.01[天文地球—地震学]