Least-squares migration is an advanced imaging technique capable of producing images with improved spatial resolution, balanced illumination, and reduced migration artifacts; however, the prohibitive computational cost poses a great challenge for its practical application. We have incorporated the beam methodology into the implementation of Kirchhoff time modeling/migration and developed a fast common-offset least-squares Kirchhoff beam time migration (LSKBTM). Different from conventional Kirchhoff time modeling/migration in which the seismic data are modeled/migrated trace by trace, the mapping operation in Kirchhoff beam time modeling/migration is performed in terms of beam components and is performed only at sparsely sampled beam centers. Therefore, the computational cost of LSKBTM is significantly reduced in comparison with that of least-squares Kirchhoff time migration (LSKTM). In addition, based on the second-order Taylor expansion of the diffraction traveltime, we introduce a quadratic correction term into the inverse/forward local slant stacking, effectively enhancing the computational accuracy of LSKBTM. We used 2D synthetic and 3D field data examples to verify the effectiveness of our method. Our results indicate that LSKBTM can produce images comparable with those of LSKTM, but at considerably reduced computational cost.

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