f Velocity model updating using image gathers

For successful prestack depth migration an accurate veldoity model is needed. One method for model updating is based on image gather analysis. In an image gather all reflectors line up horizontally if the velocities are correct. This also holds for dipping reflectors, as all traces of an image gather belong to the same surface coordinate. The images of the reflector in an image galher curve upward, if the velocity used for the migration was too low, or downward, if the velocity was too high. This deviation can be used for model updating. Curves are fitted to the image gather, which depend on depth, offset and a parameter which relates the guessed to the true model. By calculating the coherency along the deviation curves one can estimate this parameter and hence calculate an update. In the recent past different authors found different equations for the deviation curve. AI-Yahya (1989) assumes straight ray paths and uses average slowness in his derivation of the deviation curve. Cox (1991) uses extrapolated wave fields and finds a formula for a one reflector model, which fits the curve better than Al-Yahya's. Cox and Wapenaar (1992) present an improved equation for the one reflector model following Maeland's (1991) parametric representation.