Traveltime formulas of near‐zero‐offset primary reflections for a curved 2D measurement surface

Abstract

Analytic moveout formulas for primary near‐zero‐offset reflections in various types of gathers (e.g., common midpoint, common shot, zero offset) play a significant role in the seismic reflection method. They are required in stacking methods like the common midpoint (CMP) or the common‐reflection‐surface (CRS) stack. They also play a very important role in Dix‐type traveltime inversions and are of prime interest for seismic imaging. They are particularly attractive if they can be given a physical interpretation, involving for instance the wavefront curvatures of specific waves. The new formulas presented here have such a form. They give particular attention to the influence that a smooth curved measurement surface has on the computation of the traveltime and the moveout in various gathers as well as on the normal‐moveout (NMO) velocity in the CMP gather. This influence should be accounted for in the CMP or CRS stack as well as in the Dix‐type inversion. In the computation of interval velocities and the recovery of the depth of reflectors, the new NMO velocity formula is therefore more suited than the root‐mean‐square or NMO velocity for a planar measurement surface. It can be extended to a rugged free surface (mountainous terrain), but this extension requires a different derivation and different considerations. The influence of the surface curvature on the NMO velocity can be estimated with the new formula given here.