摘要
薄板近似与屏近似是为了实现De Wolf近似而提出的两种双域算法,广泛地应用于地震波数值模拟和偏移成像。算法实现过程中存在几个计算问题,如:F-K域空间假频问题、背景速度选取和薄板厚度划分问题、横向非均匀介质中的背景Green函数计算问题、如何处理横向非均匀性问题等。然而,针对上述计算问题的系统讨论还未见报道。针对这种现状,文中首先回顾了薄板近似法和屏近似法的具体实现。其次,对上述几个计算问题进行了系统的研究,具体为:①阐明了F-K域空间假频产生的原因,并利用纵、横向振幅衰减因子消除了空间假频现象;②对背景速度的选取进行了探究,尽可能保证薄板内整体速度扰动相对较小是背景速度选择的关键;③对比了不同薄板厚度下薄板近似法和屏近似法的正演记录和计算效率,并讨论了薄板划分的依据;④分析了背景Green函数不稳定性的原因,以及横向非均匀介质情况下的计算误差问题;⑤探讨了介质横向不均匀性对薄板近似和屏近似精度的影响,并提出了几种改善算子适应介质横向变化的方法。最后,利用三维简单层状模型和二维实际速度模型对讨论结果进行了测试。该研究结果可为薄板近似法和屏近似法在复杂介质的应用提供一定的理论基础。
The thin-slab approximation and the screen approximation are two dual-domain methods for implementing the De Wolf approximation,and are widely used in seismic wave numerical simulation and migration imaging.There are several computational problems in implementing the two algorithms,such as the space aliasing in the F-K domain,background velocity selection,thin slab thickness division,the calculation of background Green’s function in laterally heterogeneous media,and how to deal with lateral heterogeneity.However,there have been no reports on systematic discussions on the aforementioned computational problems.In response to this situation,this paper first reviews the specific realization of the thin slab approximation and the screen approximation method.Secondly,a systematic study is conducted on the aforementioned computational problems in five specific aspects.①The causes of spatial aliasing in the F-K domain are clarified,and the spatial aliasing problem is completely solved by use of vertical and horizontal amplitude attenuation factors.②The selection of background velocity is studied,and the key to selecting background velocity is to ensure that the overall velocity disturbance inside the thin slab is relatively small as much as possible.③Forward record and computational efficiency of the thin slab approximation method and the screen approximation method are com pared under different thickness conditions of the thin slab,and bases for the division of the thin slab are discussed.④The reasons for the instability of the background Green’s function are studied,as well as the computation error in the case of laterally heterogeneous media.⑤The influence of the lateral heterogeneity of the media on the accuracy of the thin-slab approximation and the screen approximation is discussed,and several methods are proposed to improve the algorithm operator’s adaptability to the lateral changes of the media.Finally,the discussion results are tested by use of a three-dimensional simple layered model and a two-
作者
孙华超
孙建国
SUN Huachao;SUN Jianguo(College of Geoexploration Science and Technology,Jilin University,Changchun,Jilin 130026)
出处
《石油地球物理勘探》
EI
CSCD
北大核心
2024年第5期989-1001,共13页
Oil Geophysical Prospecting
基金
国家自然科学基金项目“广义Kirchhoff型偏移成像理论与方法”(41974135)资助。
关键词
薄板近似
屏近似
空间假频
背景Green
函数
横向非均匀性
thin-slab approximation
screen approximation
spatial aliasing
background Green’s function
transverse inhomogeneity
