Normal-moveout and velocity relations for flat and dipping beds and for long offsets

Accurate relations between XMO and velocity are needed in modern exploration seismology, especially in long-offset CDP work, where accurate NMO corrections must be made for stacking, and where several types of velocity averages may be computed with accuracy from NMO data. The velocity average associated with NMO is the time-rms velocity Unns. Even for long offsets the straight-ray computation using vrms is usually adequate, but a closer approximation for horizontal reflectors is obtained by reducing the NMO calculated from vrms or reducing the value of v2rms calculated from NMO by the factor [1-1.4(ΔT/T) (σ/vrms)2] where σ is the rms deviation of the velocity from its mean, T is zero-offset traveltime, and ΔT the NMO. The difference between time-average and time-rms velocities is often several percent.