Root-mean-square (RMS) velocity. Consider an earth model consisting of a sequence of parallel horizontal layers of interval velocity in the -th layer. We label layers from 1 to , with the -th reflector being at the bottom of the -th layer. The two-way traveltime for seismic energy propagating perpendicularly through the -th layer is . The RMS velocity at the -th reflector, for travel perpendicular to the layers is
The average velocity for this path, at the -th reflector, is
The stacking velocity, the velocity determined from velocity analysis based on normal-moveout measurements, is often used to approximate RMS velocity; this is valid only in the limit as the offset approaches zero where interfaces are flat and horizontal, and layers are isotropic. The RMS velocity for the -th reflector is related to the NMO velocity at the N-th reflector via
where is the dip of the -th layer. The NMO and STACK velocities differ if the moveout deviates substantially from being hyperbolic, as would be seen with substantial anisotropy.