The CRE Method: An Alternative to CMP stacking

This paper presents new theoretical aspects concerning seismic stacking methods. We study in particular the homeomorphic imaging method called common-reflecting-element (CRE). For that, we consider a two-dimensional layered medium consisting of horizontal layers with constant velocities. The seismic data are a set of seismograms related to primary reflections that are sorted in a common-mid-point (CMP) gather. The CRE method is based on the reconstruction of a wavefront that has a circle as geometrical approximation and hypothetically originates at a reflection point. The formula used for the local time-correction (moveout) depends on the radius of curvature of the wavefront and the velocity of the first layer. Because this formula does not depend on a reference time, there is no problem with stretching effects. The consistency and accuracy of the CRE method are analysed considering situations where the wavefront does not exactly match a circle.