Abstract: Amplitude versus offset analysis is a fundamental tool for determining the physical properties of reservoirs but generally hampered by the blurred common image gathers (CIGs). The blurring can be optimally corrected using the blockwise least-squares prestack time migration (BLS-PSTM), where common-offset migrated sections are divided into a series of blocks related to the explicit offset-dependent Hessian matrix and the following inverse filtering is iteratively applied to invert the corresponding reflectivity. However, calculating the Hessian matrix is slow. We present a fast BLS-PSTM via accelerating Hessian calculation with dip-angle Fresnel zone (DFZ). DFZ is closely related to optimal migration aperture, which significantly attenuates migration swings and reduces the computational cost of PSTM. Specifically, our fast BLS-PSTM is implemented as a two-stage process. First, we limit the aperture for any imaging point with an approximated the projected Fresnel zone before calculating the Hessian matrix. Then, we determine whether a seismic trace contributes to the imaging point via DFZ during calculating the Hessian matrix. Numerical tests on synthetic and field data validate the distinct speedup with higher-quality CIGs compared to BLS-PSTM.