Leaning

Echo delay is much like depth. We usually measure angles by their departure from the vertical ray, while in reality zero-offset data is rarely recorded. The best seismic data is usually far from vertical. In this chapter a pattern of thinking is developed that is oriented about a selected nonvertical ray. Rotation of coordinates does not solve the problem since after rotation, the plane on which measurements would be made would no longer be simply z=0. Rotation would also make a mess of the simple seismic velocity function v(z) by making it a strongly two-dimensional function v' ( x' , z' ). The view of offset presented in chapter may have seemed rather complete, but in fact it was not very general because square roots were expanded about the vertical ray. The Stolt stretch illustrated the advantage of leaving the hyperbola top and getting out on the flanks.

Linear moveout (LMO) is the way to reorient our thinking about nonvertical rays. While not widely incorporated in the modern production environment, this deeper view of offset is of special interest to researchers. It offers an understanding of multiple reflections, a subject untouched in chapter . It also offers a better understanding of velocity estimation.