基于射线束的海森矩阵高效计算方法及成像域最小二乘偏移

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中图分类号：P631 文献标识码：A DOI：10.13810/j.cnki.issn.1000-7210.20250164

Abstract：Least-squares migration （LSM） is an extension of classical migration methods within an inversion framework. Its core principle is to achieve high-resolution imaging of subsurface media by compensating for the effects of the Hessian matrix.However，the large size and sparse nature of the full Hessian matrix make it dificult to compute and characterize effectively，which constitutes an obstacle to the practical application of LSM. This paper first introduces an analytical representation of the Hessian matrix under the Born approximation. Given the sparsity of the Hessian matrix，an efficient approximation is performed using point spread functions （PSFs），and it is emphasized that traveltime calculation is key to constructing the Hessian matrix. Subsequently， a ray-beam-based traveltime calculation method is introduced to complete ray-beam-based PSF calculations.Finally，thecalculated PSFsare applied to the conventional migration results via the data-driven，high-dimensionalimage-domain deconvolution，thereby realizing image-domain LSM.Ray-beam-based PSF calculation can effectivelyavoid the traveltime interpolation issues associated withcentral-ray methods，and its calculational efficiency is significantly higher than that of PSF calculation methods based on forward modeling and migration. Numerical experiments and field data processing results validate the effectiveness of the proposed method.

Keywords： least-squares migration，traveltime calculation，point spread function （PSF），ray beam，image domain

0 引言

偏移成像是地震数据处理中定位地下构造、提高横向分辨率的有效手段[1-2]。（剩余11065字）