Normal moveout revisited: Inhomogeneous media and curved interfaces

Abstract

The equation of normal moveout, [Formula: see text], is valid for a reflection from the base of a single homogeneous and isotropic bed, but is only an approximation in the real world of multilayered, inhomogeneous media and curved interfaces. Using the theory of geometrical optics, we can find another second‐order equation which represents hyperbolas that are also symmetrical about the time axis. However, the centers of these hyperbolas do not coincide with the center of coordinates, but are shifted along the time axis. The equation describing this second type of hyperbola is [Formula: see text], where [Formula: see text] is the time of focusing depth and [Formula: see text], the velocity of the input medium. This equation is not only more accurate than the usual normal moveout, but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the [Formula: see text] analysis. This procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity section. [Formula: see text] analysis can also be used to build a stacked section without any manual picking of velocities. The same concepts can be extended to the section after stack, allowing recognition of the geometrical patterns of the reflectors.