Velocity analysis by prestack depth migration: linear theory , by John T. Etgen

Imaging of seismic reflection data is accomplished by prestack depth migration of individual shot records followed by stacking the results at common surface locations. If the velocity model used fo rshot record migration does not correctly model the traveltimes of reflection events, the images of migrated shot profiles at a constant surface location (CSL) will be distorted from one another. This distortion can be used to estimate the error in the velocity model. The distortion among the images of the shot profiles can be removed with a residual moveout correction. In constant velocity medium the change in depth of images in a CSL gather due to a change in the velocity model can be found by applying a residual moveout correction in depth. The moveout is a function of the ratio of the imaging velocities, the original depth of the image, and the source and receiver locations. For perturbations to a general interval velocity model, the change in migrated depth of the migrated events in a CSL gather can be calculated through ray tracing. Applying Fermat's principle linearizes the relation between changes in the velocity model and changes in traveltime. Linearized geometrical relations describe how to map the change in traveltime to a change in migrated depth. Linear least squares theory can then be applied to find a change to the residual moveout curve that best fits the calculated changes in migrated depth observed in a CSL gather. The results is a linear operator that relates changes in interval velocity to changes in the parameters describing residual moveout using the intermediaries of traveltimes and migrated depth. the change of the stacking semblance of the images of migrated shot profiles due to a change of interval velocity can be computed without need to remigrate the data.


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