Abstract：Several common-used wavefield extrapolating method up to now(such as splitstep Fourier method,Fourier finite-difference method,generalized screen method and finite-difference method in frequency space domain)can obtain a good imaging result in common shot gathers,but in order to take account of transmitting angle of different waves,quite a number of sidetraces need to be added when making migration for each shot,and shot points and receiver points need to be extrapolated downward separately,so there are considerable amount of computation.Aimed at above problems,the paper presented a wave equation pre-stack depth migration for common offset gathers based on double-square roots operator which can be used for 2-D and 3-D wave equation pre-stack depth imaging,the steps are:①the phase-shift formulae for wave field continuation can be obtained by stationary phase approach for intebration of wave field continuation on common-offset gathers in a condition of high-frequency hypothesis;②time-shift quantity of migration for wave field depth continuation in total uniform bed,time-shift quantity of migration in each bed and amplitude correction factor can be calculated by splitting velocity field into constant velocity background and variable velocity disturbance and then final wave field continuation value can be obtained.Pulse response test and theoretic model migration test show that the migration method has a higher computational efficiency and better imaging quality and suitable for imaging of complex geologic body.
