A THEORY OF NORMAL MOVEOUT

Three geophysical principles are shown to be sufficient to determine the most general, practical normal moveout (NMO) equation. The principles are reciprocity in a common midpoint (CMP) gather, finite slowness, and exact constant velocity limit. The resulting equation is the shifted hyperbola NMO equation that has three parameters. Comparisons at both near and far offsets between the shifted hyperbola NMO equation and the results for layered media assign geophysical meaning to the parameters. Two of the parameters, zero offset time and NMO velocity, are constants and control the very near offset behavior. The third parameter is dimensionless and controls the far offset behavior of the NMO curve, but it may be a function of offset so as to exactly fit any travel-time curve. The parameters may be found by a linear least-squares fit to data. The theory applies to all offsets for nonturning wave reflections in an isotropic earth for both P-waves and converted (P - SV) waves.