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

摘要

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 trav-eltime 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.