Vertical image waves in elliptically anisotropic media

By reparameterization of the kinematic expressions for remigration in elliptically anisotropic media using a new ellipticity parameter, we derive a new image-wave equation in elliptically anisotropic media describing the position of the reflector as a function of the medium ellipticity. This image wave equation, which is a kind of medium-dependent one-way wave equation, can be used for automatically stretching a time-migrated image in depth until wells are tied or other given geologic criteria are met. In this way, it provides a useful means to use a priori depth information for finding an estimate of the vertical velocity, which cannot be detected from time processing only. Simple numerical examples confirm the validity of the image-wave equation even for nonconstant velocity.52110112