Abstract: A method of constructing a 3D geologically plausible velocity model for efficient and accurate prestack imaging wherein embodiments of the invention provide: (1) a method of calibrating velocity functions, appropriately and effectively taking into account well (hard) and seismic (soft) data as well as geological features, and trend fitting (“iDEPTHing”) RMS velocities before curved-ray prestack time migration; (2) a method of calibrating and trend fitting (“iDEPTHing”) interval velocities before prestack depth migration, appropriately and effectively taking into account well (hard) and seismic (soft) data as well as geological features; and (3) a method of constructing a geologically plausible velocity model using the previous steps of velocity calibration and trend fitting RMS and interval velocities, for efficient sequential use in prestack time migration followed by prestack depth migration.