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OA

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 diffi-cult 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.Fi-nally,the calculated PSFs are applied to the conventional migration results via the data-driven,high-dimen-sional image-domain deconvolution,thereby realizing image-domain LSM.Ray-beam-based PSF calculation can effectively avoid the traveltime interpolation issues associated with central-ray methods,and its calculational ef-ficiency 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.