基于第二类切比雪夫多项式直接展开的叠前深度偏移方法
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关键词： 频率—波数域，波场延拓，第二类切比雪夫展开，叠前深度偏移中图分类号：P61 文献标识码：A DOI：10. 1810/j. cnki. issn. 1000-7210. 2024028
Prestack depth migration method based on direct expansion of the second kind of Chebyshev polynomials
ZHANG Qi1，2，LI Zhenchun1，2，QU Yingming1，2，YANG Jing3，ZHANG Lei3tate Key Laboratory of Deep Oil and Gas，China University of Petroleum（East China），Qingdao，Shandong 266580，China；2. School of Geosciences，China University of Petroleum（East China），Qingdao，Shandong 266580，China；3. Data Processing Center，Geological Research Institute，BGP Inc. ，CNPC，Zhuozhou，Hebei ，China）
Abstract：The second kind of Chebyshev expansion has been widely used in numerical approximations since it has stricter constraints on the objective function compared to the first kind of Chebyshev expansion，resulting in smaller error accumulation. Starting from the frequency⁃domain acoustic wave equation，this paper introduces the second kind of Chebyshev expansion into the Fourier one ⁃way wave continuation operator to achieve wave⁃ field continuation. On this basis，with the use of the Born approximation theory and cross ⁃ correlation imaging conditions，prestack depth migration imaging is realized based on the direct expansion of the second kind of Che⁃ byshev polynomials. This method utilizes the accurate velocity at each location during depth propagation，re⁃ ducing errors compared to the conventional one⁃way wave continuation method which uses the mode of depth ⁃ layer background velocity combined with perturbation velocity. This achieves higher accuracy of the wavefield continuation operator under strong lateral velocity variations. The effectiveness of the method is verified through wavefield snapshot analysis and model imaging tests. It has significantly improved imaging accuracy compared to conventional prestack depth migration methods for one⁃way wave.
Keywords：frequency⁃wavenumber domain，wavefield continuation，second kind of Chebyshev expansion， prestack depth migration
张琦，李振春，曲英铭，等 . 基于第二类切比雪夫多项式直接展开的叠前深度偏移方法［J］. 石油地球物理勘探，2025，60（3）：710‑717.ZHANG Qi，LI Zhenchun，QU Yingming，et al. Prestack depth migration method based on direct expansion ofthe second kind of Chebyshev polynomials［J］. Oil Geophysical Prospecting，2025，60（3）：710‑717.
0 引言
地震偏移成像是在一定的数学物理模型（声介质，弹性介质等）基础上，应用相应的地球物理理论，将地面观测到的多次覆盖数据反传，消除地震波的传播效应，得到地下介质的模型图像。（剩余10038字）
